Merge "Make shutdown deadlock in ipc_comparison unlikely"
diff --git a/NO_BUILD_ROBORIO b/NO_BUILD_ROBORIO
index 5b9c693..36ae012 100644
--- a/NO_BUILD_ROBORIO
+++ b/NO_BUILD_ROBORIO
@@ -1,6 +1,7 @@
-@slycot_repo//...
-//frc971/control_loops/python/...
-//y2012/control_loops/python/...
+-//y2014_bot3/control_loops/python/...
-//y2014/control_loops/python/...
-//y2014_bot3/control_loops/python/...
-//y2015/control_loops/python/...
diff --git a/aos/common/type_traits.h b/aos/common/type_traits.h
index 4b5fa8c..53fae23 100644
--- a/aos/common/type_traits.h
+++ b/aos/common/type_traits.h
@@ -12,7 +12,7 @@
struct has_trivial_copy_assign : public std::integral_constant<bool,
// This changed between 4.4.5 and 4.6.3. Unless somebody discovers otherwise,
// 4.6 seems like a reasonable place to switch.
-#if ((__GNUC__ < 4) || (__GNUC_MINOR__ < 6)) && !defined(__clang__)
+#if ((__GNUC__ < 4) || (__GNUC__ == 4 && __GNUC_MINOR__ < 6)) && !defined(__clang__)
::std::has_trivial_assign<Tp>::value> {};
#else
::std::has_trivial_copy_assign<Tp>::value> {};
diff --git a/y2014/control_loops/python/extended_lqr.tex b/y2014/control_loops/python/extended_lqr.tex
new file mode 100644
index 0000000..52d0949
--- /dev/null
+++ b/y2014/control_loops/python/extended_lqr.tex
@@ -0,0 +1,766 @@
+\documentclass[a4paper,12pt]{article}
+\usepackage{amsmath}
+\begin{document}
+
+% From http://www.eecs.tufts.edu/~khan/Courses/Spring2013/EE194/Lecs/Lec9and10.pdf
+% and http://www.cs.unc.edu/~wens/WAFR2014-Sun.pdf
+% (which references http://maeresearch.ucsd.edu/skelton/publications/weiwei_ilqg_CDC43.pdf)
+% and http://arl.cs.utah.edu/pubs/ISRR2013.pdf
+
+\section{Backwards Pass}
+
+Let's start with some definitions for the standard LQR controller.
+$c_t(\boldsymbol{x}, \boldsymbol{u})$ is the cost for the iteration $t$ given that we are at $\boldsymbol{x}$ and are going to apply $\boldsymbol{u}$ for one cycle.
+$v_t(\boldsymbol{x})$ is the optimal cost-to-go for the starting point $\boldsymbol{x}$ at step $t$.
+$v_N(\boldsymbol{x})$ may be defined to be a different final cost from $v_t(\boldsymbol{x})$ if need be, where $N$ is the horizon.
+
+$$\begin{array}{rcl}
+c_t(\boldsymbol{x}, \boldsymbol{u}) &=&
+ \frac{1}{2}
+ \begin{bmatrix} \boldsymbol{x} \\ \boldsymbol{u} \end{bmatrix}^T
+ \begin{bmatrix} Q_t & P_t^T \\ P_t & R_t \end{bmatrix}
+ \begin{bmatrix} \boldsymbol{x} \\ \boldsymbol{u} \end{bmatrix} +
+ \begin{bmatrix} \boldsymbol{x} \\ \boldsymbol{u} \end{bmatrix}^T
+ \begin{bmatrix} \boldsymbol{q}_t \\ \boldsymbol{r}_t \end{bmatrix} +
+ q_t \\
+v_{t + 1}(\boldsymbol{x}) &=&
+ \frac{1}{2} \boldsymbol{x}^T S_{t + 1} \boldsymbol{x} + \boldsymbol{x}^T \boldsymbol{s}_{t + 1} + s_{t + 1} \\
+
+g_t(\boldsymbol{x}_t, \boldsymbol{u}_t) = \boldsymbol{x}_{t + 1}(\boldsymbol{u}_t) &=&
+ A_{t} \boldsymbol{x}_t + B_t \boldsymbol{u}_t + \boldsymbol{c}_{t} \\
+
+v_{t}(\boldsymbol{x}_t, \boldsymbol{u}_t) &=&
+ v_{t+1}(\boldsymbol{x}_{t+1}) +
+ c_t(\boldsymbol{x}_t, \boldsymbol{u}_t) \\\
+ &=&
+ v_{t+1}(g_t(\boldsymbol{x}_{t}, \boldsymbol{u}_t)) +
+ c_t(\boldsymbol{x}_t, \boldsymbol{u}_t)
+ \\
+\end{array}$$
+
+Now, let's calculate $v_t(\boldsymbol{x})$ given $v_{t+1}(\boldsymbol{x})$ and the step cost from $c_t(\boldsymbol{x})$.
+This tells us the cost of applying $\boldsymbol{u}$ starting from $\boldsymbol{x}$.
+We will then optimize over all $\boldsymbol{u}$ to find the optimal next state and cost for that state.
+This lets us then use dynamic programing methods to work out the optimal $\boldsymbol{x}$ and $\boldsymbol{u}$ at each timestep.
+
+We want to get a quadratic solution of the form
+$$v_{t}(\boldsymbol{x}) =
+ \frac{1}{2} \boldsymbol{x}^T S_{t} \boldsymbol{x} + \boldsymbol{x}^T \boldsymbol{s}_{t} + s_{t}$$ for each step.
+
+$$\begin{array}{rcl}
+v_{t}(\boldsymbol{x}, \boldsymbol{u}) &=&
+ \frac{1}{2} \left( A_{t}\boldsymbol{x} + B_{t}\boldsymbol{u} + \boldsymbol{c}_{t}\right)^T
+ S_{t + 1}
+ \left( A_{t}\boldsymbol{x} + B_{t}\boldsymbol{u} + \boldsymbol{c}_{t}\right) +
+ \left( A_{t}\boldsymbol{x} + B_{t}\boldsymbol{u} + \boldsymbol{c}_{t}\right)^T \boldsymbol{s}_{t + 1} +
+ s_{t + 1} + \\ &&
+ \frac{1}{2}
+ \begin{bmatrix} \boldsymbol{x} \\ \boldsymbol{u} \end{bmatrix}^T
+ \begin{bmatrix} Q_{t} & P_{t}^T \\ P_{t} & R_{t} \end{bmatrix}
+ \begin{bmatrix} \boldsymbol{x} \\ \boldsymbol{u} \end{bmatrix} +
+ \begin{bmatrix} \boldsymbol{x} \\ \boldsymbol{u} \end{bmatrix}^T
+ \begin{bmatrix} \boldsymbol{q}_{t} \\ \boldsymbol{r}_{t} \end{bmatrix} +
+ q_{t}
+\\
+&=&
+ \frac{1}{2} \left(
+ \boldsymbol{x}^T A_{t}^T S_{t + 1} A_{t} \boldsymbol{x} +
+ \boldsymbol{u}^T B_{t}^T S_{t + 1} A_{t} \boldsymbol{x} +
+ \boldsymbol{c}_t^T S_{t + 1} A_{t} \boldsymbol{x} + \right. \\ &&
+ \left. \boldsymbol{x}^T A_{t}^T S_{t + 1} B_{t} \boldsymbol{u} +
+ \boldsymbol{u}^T B_{t}^T S_{t + 1} B_{t} \boldsymbol{u} +
+ \boldsymbol{c}_t^T S_{t + 1} B_{t} \boldsymbol{u} + \right. \\ &&
+ \left. \boldsymbol{x}^T A_{t}^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{u}^T B_{t}^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t
+ \right) + \\ &&
+ \boldsymbol{x}^T A_{t}^T \boldsymbol{s}_{t + 1} +
+ \boldsymbol{u}^T B_{t}^T \boldsymbol{s}_{t + 1} +
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} +
+ s_{t + 1} + \\ &&
+ \frac{1}{2} \left(\boldsymbol{x}^T Q_t \boldsymbol{x} + \boldsymbol{u}^T P_t \boldsymbol{x} + \boldsymbol{x}^T P_t^T \boldsymbol{u} + \boldsymbol{u}^T R_t \boldsymbol{u} \right) + \boldsymbol{x}^T \boldsymbol{q}_t + \boldsymbol{u}^T \boldsymbol{r}_t + q_t
+\\
+&=&
+ \frac{1}{2} \left(
+ \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} A_{t} + Q_t \right) \boldsymbol{x} +
+ \boldsymbol{u}^T \left( B_{t}^T S_{t + 1} A_{t} + P_t \right) \boldsymbol{x} \right. + \\ &&
+ \left. \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} B_{t} + P_t^T \right) \boldsymbol{u} +
+ \boldsymbol{u}^T \left( B_{t}^T S_{t + 1} B_{t} + R_t \right) \boldsymbol{u} \right) + \\ &&
+ \boldsymbol{x}^T \left(A_{t}^T \boldsymbol{s}_{t + 1} +
+ \boldsymbol{q}_t \right)+
+
+ \boldsymbol{u}^T \left( B_{t}^T \boldsymbol{s}_{t + 1} +
+ \boldsymbol{r}_t \right) +
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1} +
+ q_t + \\ &&
+ \frac{1}{2} \left( \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{x}^T A_{t}^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{u}^T B_{t}^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{c}_t^T S_{t + 1} B_{t} \boldsymbol{u} +
+ \boldsymbol{c}_t^T S_{t + 1} A_{t} \boldsymbol{x} \right)
+\end{array}$$
+
+Now, let's find the optimal $\boldsymbol{u}$. Do this by evaluating $\frac{\partial}{\partial \boldsymbol{u}} v_t(\boldsymbol{x}, \boldsymbol{u}) = 0$.
+
+$$\begin{array}{rcl}
+\frac{\partial}{\partial \boldsymbol{u}} v_{t}(\boldsymbol{x}, \boldsymbol{u}) &=& \frac{1}{2} \left( 2 \boldsymbol{u}^T \left( B_{t}^T S_{t + 1} B_{t} + R_t \right) + 2 \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} B_{t} + P_t^T \right) + 2 \boldsymbol{c}_t^T S_{t + 1} B_{t} \right) + \\&&\boldsymbol{s}_{t + 1}^T B_{t} + \boldsymbol{r}_t^T \\
+
+\frac{\partial}{\partial \boldsymbol{u}} v_{t}(\boldsymbol{x}, \boldsymbol{u}) &=& \boldsymbol{u}^T \left( B_{t}^T S_{t + 1} B_{t} + R_t \right) + \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} B_{t} + P_t^T \right) + \boldsymbol{c}_t^T S_{t + 1} B_{t} + \boldsymbol{s}_{t + 1}^T B_{t} + \boldsymbol{r}_t^T \\
+0 &=& \boldsymbol{u}^T \left( B_{t}^T S_{t + 1} B_{t} + R_t \right) + \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} B_{t} + P_t^T \right) + \boldsymbol{c}_t^T S_{t + 1} B_{t} + \boldsymbol{s}_{t + 1}^T B_{t} + \boldsymbol{r}_t^T
+\end{array}$$
+$$\begin{array}{rcl}
+\boldsymbol{u}^T \left( B_{t}^T S_{t + 1} B_{t} + R_t \right) &=& - \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} B_{t} + P_t^T \right) - \boldsymbol{c}_t^T S_{t + 1} B_{t} - \boldsymbol{s}_{t + 1}^T B_{t} - \boldsymbol{r}_t^T \\
+\left( B_{t}^T S_{t + 1} B_{t} + R_t \right) \boldsymbol{u} &=& - \left( B_{t}^T S_{t + 1} A_{t} + P_t \right) \boldsymbol{x} - B_t^T S_{t + 1} \boldsymbol{c}_t - B_{t}^T \boldsymbol{s}_{t + 1}- \boldsymbol{r}_t \\
+\boldsymbol{u} &=& - \left( B_{t}^T S_{t + 1} B_{t} + R_t \right) ^{-1} \left( \left( B_{t}^T S_{t + 1} A_{t} + P_t \right) \boldsymbol{x} + B_t^T S_{t + 1} \boldsymbol{c}_t + B_{t}^T \boldsymbol{s}_{t + 1} + \boldsymbol{r}_t \right)
+\end{array}$$
+
+This gives us the optimal $\boldsymbol{u}$. There are some substitutions defined here from the 2013 paper which make it easier to read.
+Note: the 2014 paper uses different letters for these same quantities\dots
+\\
+$$\begin{array}{rcl}
+C_t &=& B^T_t S_{t + 1} A_t + P_t \\
+E_t &=& B_{t}^T S_{t + 1} B_{t} + R_t \\
+L_t &=& - E_t ^{-1} C_t \\
+
+\boldsymbol{e}_t &=& B_t^T S_{t + 1} \boldsymbol{c}_t + B_{t}^T \boldsymbol{s}_{t + 1} + \boldsymbol{r}_t \\
+\boldsymbol{l}_t &=& - E^{-1}_t \boldsymbol{e}_t \\
+
+D_t &=& A_t^T S_{t + 1} A_t + Q_t \\
+\boldsymbol{d}_t &=& A_t^T S_{t + 1} \boldsymbol{c}_t + A_{t}^T \boldsymbol{s}_{t + 1} + \boldsymbol{q}_t
+\\
+\boldsymbol{u} &=& L_t \boldsymbol{x} + \boldsymbol{l}_t
+\end{array}$$
+
+With these, we can simplify $\boldsymbol{u}$ a bit and make it look like the 2014 paper has it.
+
+$$\begin{array}{rcl}
+ \boldsymbol{u} &=& -E_t^{-1} \left( C_t \boldsymbol{x} + \boldsymbol{e}_t \right) \\
+ \boldsymbol{u} &=& -E_t^{-1} C_t \boldsymbol{x} - E_t^{-1} \boldsymbol{e}_t
+\end{array}$$
+
+For reference, here are some equivalences between the symbols used in the 2013
+paper (the ones we use) and the 2014 paper.
+TODO(Brian): Figure out where the ones in the 2014 paper are defined instead of
+guessing by pattern-matching.
+\\ \begin{tabular}{ | r | l | }
+ \hline
+ 2013 paper (ours) & 2014 paper \\
+ \hline
+ $C_t$ & $E_t$ \\
+ $D_t$ & $C_t$ \\
+ $\boldsymbol{d}_t$ & $\boldsymbol{c}_t$ \\
+ $E_t$ & $D_t$ \\
+ $\boldsymbol{e}_t$ & $\boldsymbol{d}_t$ \\
+ \hline
+\end{tabular} \\
+
+Now, let's solve for the new cost function.
+
+$$\begin{array}{rcl}
+v_{t}(\boldsymbol{x}, \boldsymbol{u}) &=&
+ \frac{1}{2} \left(
+ \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} A_{t} + Q_t \right) \boldsymbol{x} +
+ \boldsymbol{u}^T \left( B_{t}^T S_{t + 1} A_{t} + P_t \right) \boldsymbol{x} \right. + \\ &&
+ \left. \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} B_{t} + P_t^T \right) \boldsymbol{u} +
+ \boldsymbol{u}^T \left( B_{t}^T S_{t + 1} B_{t} + R_t \right) \boldsymbol{u} \right) + \\ &&
+ \boldsymbol{x}^T \left(A_{t}^T \boldsymbol{s}_{t + 1} +
+ \boldsymbol{q}_t \right)+
+
+ \boldsymbol{u}^T \left( B_{t}^T \boldsymbol{s}_{t + 1} +
+ \boldsymbol{r}_t \right) +
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1} +
+ q_t + \\ &&
+ \frac{1}{2} \left( \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{x}^T A_{t}^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{u}^T B_{t}^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{c}_t^T S_{t + 1} B_{t} \boldsymbol{u} +
+ \boldsymbol{c}_t^T S_{t + 1} A_{t} \boldsymbol{x} \right)
+\\
+&=&
+ \frac{1}{2} \left(
+ \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} A_{t} + Q_t \right) \boldsymbol{x} +
+ \boldsymbol{u}^T \left( B_{t}^T S_{t + 1} A_{t} + P_t \right) \boldsymbol{x} \right. + \\ &&
+ \left. \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} B_{t} + P_t^T \right) \boldsymbol{u} +
+ \boldsymbol{u}^T \left( B_{t}^T S_{t + 1} B_{t} + R_t \right) \boldsymbol{u} \right) + \\ &&
+
+ \boldsymbol{x}^T \left(A_{t}^T \boldsymbol{s}_{t + 1} + \boldsymbol{q}_t +
+ \frac{1}{2} A_{t}^T S_{t + 1} \boldsymbol{c}_t \right) + \\ &&
+
+ \boldsymbol{u}^T \left( B_{t}^T \boldsymbol{s}_{t + 1} + \boldsymbol{r}_t +
+ \frac{1}{2} B_{t}^T S_{t + 1} \boldsymbol{c}_t \right) + \\ &&
+
+ \frac{1}{2} \boldsymbol{c}_t^T S_{t + 1} \left( A_t \boldsymbol{x} +
+ B_t \boldsymbol{u} + \boldsymbol{c}_t \right) + \\ &&
+
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1} + q_t
+\\
+&=&
+ \frac{1}{2} \left(
+ \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} A_{t} + Q_t \right) \boldsymbol{x} +
+ \boldsymbol{u}^T \left( B_{t}^T S_{t + 1} A_{t} + P_t \right) \boldsymbol{x} \right. + \\ &&
+ \left. \boldsymbol{x}^T \left( A_{t}^T S_{t + 1} B_{t} + P_t^T \right) \boldsymbol{u} +
+ \boldsymbol{u}^T \left( B_{t}^T S_{t + 1} B_{t} + R_t \right) \boldsymbol{u} \right) + \\ &&
+
+ \boldsymbol{x}^T \left(A_{t}^T \boldsymbol{s}_{t + 1} + \boldsymbol{q}_t +
+ A_{t}^T S_{t + 1} \boldsymbol{c}_t \right) + \\ &&
+
+ \boldsymbol{u}^T \left( B_{t}^T \boldsymbol{s}_{t + 1} + \boldsymbol{r}_t +
+ B_{t}^T S_{t + 1} \boldsymbol{c}_t \right) + \\ &&
+
+ \frac{1}{2} \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1} + q_t
+\\
+&=&
+ \frac{1}{2} \left(
+ \boldsymbol{x}^T D_t \boldsymbol{x} +
+ \boldsymbol{u}^T C_t \boldsymbol{x} +
+ \boldsymbol{x}^T C_t^T \boldsymbol{u} +
+ \boldsymbol{u}^T E_t \boldsymbol{u} \right) + \\ &&
+
+ \boldsymbol{x}^T \boldsymbol{d}_t +
+ \boldsymbol{u}^T \boldsymbol{e}_t + \\ &&
+
+ \frac{1}{2} \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1} + q_t
+\\
+&=&
+ \frac{1}{2} \left(
+ \boldsymbol{x}^T D_t \boldsymbol{x} +
+ \left( L_t \boldsymbol{x} + \boldsymbol{l}_t \right)^T C_t \boldsymbol{x} \right. + \\ &&
+ \left. \boldsymbol{x}^T C_t^T \left( L_t \boldsymbol{x} + \boldsymbol{l}_t \right) +
+ \left( L_t \boldsymbol{x} + \boldsymbol{l}_t \right)^T E_t \left( L_t \boldsymbol{x} + \boldsymbol{l}_t \right) \right) + \\ &&
+
+ \boldsymbol{x}^T \boldsymbol{d}_t +
+ \left( L_t \boldsymbol{x} + \boldsymbol{l}_t \right)^T \boldsymbol{e}_t + \\&&
+
+ \frac{1}{2} \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1} + q_t
+\\
+&=&
+ \frac{1}{2} \left(
+ \boldsymbol{x}^T D_t \boldsymbol{x} + \right.
+ \boldsymbol{x}^T L_t^T C_t \boldsymbol{x} + \boldsymbol{l}_t^T C_t \boldsymbol{x} + \\ &&
+
+ \left. \boldsymbol{x}^T C_t^T L_t \boldsymbol{x} + \boldsymbol{x}^T C_t^T \boldsymbol{l}_t +
+
+ \boldsymbol{x}^T L_t^T E_t L_t \boldsymbol{x} +
+ \boldsymbol{l}_t^T E_t L_t \boldsymbol{x} +
+ \boldsymbol{x}^T L_t^T E_t \boldsymbol{l}_t +
+ \boldsymbol{l}_t^T E_t \boldsymbol{l}_t \right) + \\&&
+
+ \boldsymbol{x}^T \boldsymbol{d}_t +
+ \boldsymbol{x}^T L_t^T \boldsymbol{e}_t + \boldsymbol{l}^T_t \boldsymbol{e}_t + \\&&
+
+ \frac{1}{2} \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1} + q_t
+\\
+&=&
+ \frac{1}{2}
+ \boldsymbol{x}^T \left(
+ D_t +
+ L_t^T C_t +
+ C_t^T L_t +
+ L_t^T E_t L_t
+ \right) \boldsymbol{x} + \\ &&
+
+ \boldsymbol{x}^T \left(
+ \frac{1}{2} \left( C_t^T \boldsymbol{l}_t +
+ L_t^T E_t \boldsymbol{l}_t \right) +
+ \boldsymbol{d}_t +
+ L_t^T \boldsymbol{e}_t \right) +
+ \frac{1}{2} \left( \boldsymbol{l}_t^T E_t L_t + \boldsymbol{l}_t^T C_t \right) \boldsymbol{x} + \\ &&
+
+ \frac{1}{2} \boldsymbol{l}_t^T E_t \boldsymbol{l}_t +
+ \boldsymbol{l}^T_t \boldsymbol{e}_t +
+
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1} + q_t +
+ \frac{1}{2} \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t
+\\
+&=&
+ \frac{1}{2}
+ \boldsymbol{x}^T \left(
+ D_t +
+ L_t^T C_t +
+ C_t^T L_t +
+ L_t^T E_t L_t
+ \right) \boldsymbol{x} + \\ &&
+
+ \boldsymbol{x}^T \left(
+ C_t^T \boldsymbol{l}_t +
+ L_t^T E_t \boldsymbol{l}_t +
+ \boldsymbol{d}_t +
+ L_t^T \boldsymbol{e}_t \right) + \\ &&
+
+ \frac{1}{2} \boldsymbol{l}_t^T E_t \boldsymbol{l}_t +
+ \boldsymbol{l}^T_t \boldsymbol{e}_t +
+
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1} + q_t +
+ \frac{1}{2} \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t
+\end{array}$$
+
+Ok, let's now pull out the 3 variables of interest and do further simplification.
+
+$$\begin{array}{rcl}
+v_{t}(\boldsymbol{x}) &=&
+ \frac{1}{2} \boldsymbol{x}^T S_{t} \boldsymbol{x} + \boldsymbol{x}^T \boldsymbol{s}_{t} + s_{t} \\
+S_t &=&
+ D_t +
+ L_t^T C_t +
+ C_t^T L_t +
+ L_t^T E_t L_t \\
+ &=&
+ D_t -
+ C_t^T E_t^{-1} C_t -
+ C_t^T E_t^{-1} C_t +
+ C_t^T E_t^{-1} C_t \\
+ &=& D_t - C_t^T E_t^{-1} C_t
+\\
+\boldsymbol{s}_t &=&
+ \left( C_t^T + L_t^T E_t \right) \boldsymbol{l}_t +
+ \boldsymbol{d}_t +
+ L_t^T \boldsymbol{e}_t \\
+
+ &=&
+ \left( C_t^T - C_t^T E_t^{-1} E_t \right) \boldsymbol{l}_t +
+ \boldsymbol{d}_t -
+ C_t^T E_t^{-1} \boldsymbol{e}_t \\
+ &=& \boldsymbol{d}_t - C_t^T E_t^{-1} \boldsymbol{e}_t
+\\
+s_t &=&
+ \frac{1}{2} \boldsymbol{l}_t^T E_t \boldsymbol{l}_t +
+ \boldsymbol{l}^T_t \boldsymbol{e}_t +
+
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1} + q_t +
+ \frac{1}{2} \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t
+\\
+&=&
+\frac{1}{2} \boldsymbol{e}_t^T E_t^{-1} E_t E_t^{-1} \boldsymbol{e}_t -
+ \boldsymbol{e}_t^T E_t^{-1} \boldsymbol{e}_t +
+
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1} + q_t +
+
+ \frac{1}{2} \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t
+\\
+&=&
+q_t - \frac{1}{2} \boldsymbol{e}_t^T E_t^{-1} \boldsymbol{e}_t +
+
+ \frac{1}{2} \boldsymbol{c}_t^T S_{t + 1} \boldsymbol{c}_t +
+ \boldsymbol{c}_t^T \boldsymbol{s}_{t + 1} + s_{t + 1}
+\end{array}$$
+
+For better or worse, everything but the constant term matches both the 2013
+paper (which has no constant term) and the 2014 paper.
+The constant term does not match the 2014 paper, but we're pretty sure it's
+correct (extended\_lqr\_derivation.py verifies what we have).
+The 2014 paper has this for the constant term instead:
+$$\begin{array}{rcl}
+s_t &=&
+ q_t - \frac{1}{2} \boldsymbol{e}_t^T E_t^{-1} \boldsymbol{e}_t
+\end{array}$$
+
+\section{Forwards Pass}
+
+Let's define the forwards pass to build the cost-to-come function.
+We must use the same cycle cost, $c_t(\boldsymbol{x}, \boldsymbol{u})$, as the backwards pass.
+The initial cost $v_0(\boldsymbol{x})$ needs to evaluate to $0$ at $\boldsymbol{x}_0$ since
+there is no cost needed to get from $\boldsymbol{x}_0$ to $\boldsymbol{x}_0$.
+
+$$\begin{array}{rcl}
+\bar v_{t}(\boldsymbol{x}) &=&
+ \frac{1}{2} \boldsymbol{x}^T \bar S_{t} \boldsymbol{x} + \boldsymbol{x}^T \boldsymbol{\bar s}_{t} + \bar s_{t} \\
+
+\bar g_t(\boldsymbol{x}_{t + 1}, \boldsymbol{u}) = \boldsymbol{x}_{t}(\boldsymbol{u}) &=&
+ \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t} \\
+
+\bar c_{t + 1}(\boldsymbol{x}_{t+1}, \boldsymbol{u}) &=& c_t(\bar g_{t}(\boldsymbol{x}_{t + 1}, \boldsymbol{u}), \boldsymbol{u}) \\
+
+\bar v_{t + 1}(\boldsymbol{x}_{t+1}, \boldsymbol{u}) &=&
+ \bar v_{t}(\boldsymbol{x}_{t}) +
+ \bar c_t(\boldsymbol{x}_{t + 1}, \boldsymbol{u}_t)
+ \\
+&=&
+ \bar v_{t}(\bar g_t(\boldsymbol{x}_{t + 1}, \boldsymbol{u})) +
+ c_t(\bar g_{t}(\boldsymbol{x}_{t + 1}, \boldsymbol{u}), \boldsymbol{u}) \\
+ \\
+\end{array}$$
+
+It is important to note that the optimal $\boldsymbol{u}$ used to get from $\boldsymbol{x}_t$ to $\boldsymbol{x}_{t+1}$
+when evaluating $g_t(\boldsymbol{x}, \boldsymbol{u})$ is the same optimal $\boldsymbol{u}$
+used to get from $\boldsymbol{x}_{t+1}$ to $\boldsymbol{x}_t$ when evaluating $\bar g_{t}(\boldsymbol{x}_{t + 1}, \boldsymbol{u})$.
+Conveniently, this means that the $\boldsymbol{u}_t$, $L_t$, and $\boldsymbol{l}_t$ calculated in both the forwards and backwards passes is the same.
+
+Like before, we want to get a quadratic solution of the form
+$$\bar v_{t + 1}(\boldsymbol{x}_{t+1}) =
+ \frac{1}{2} \boldsymbol{x}_{t+1}^T \bar S_{t + 1} \boldsymbol{x}_{t+1} + \boldsymbol{x}_{t+1}^T \boldsymbol{\bar s}_{t + 1} + \bar s_{t + 1}$$ for each step.
+
+$$\begin{array}{rcl}
+\bar v_{t + 1}(\boldsymbol{x}_{t+1}, \boldsymbol{u}) &=&
+ \frac{1}{2} \left(\bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right)^T
+ \bar S_{t}
+ \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) + \\ &&
+ \left(\bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) ^T \boldsymbol{\bar s}_{t} + \bar s_{t} + \\&&
+ \frac{1}{2}
+ \begin{bmatrix} \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) \\ \boldsymbol{u} \end{bmatrix}^T
+ \begin{bmatrix} Q_t & P_t^T \\ P_t & R_t \end{bmatrix}
+ \begin{bmatrix} \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) \\ \boldsymbol{u} \end{bmatrix} + \\&&
+ \begin{bmatrix} \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) \\ \boldsymbol{u} \end{bmatrix}^T
+ \begin{bmatrix} \boldsymbol{q}_t \\ \boldsymbol{r}_t \end{bmatrix} +
+ q_t \\
+
+ &=&
+ \frac{1}{2} \left(\bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right)^T
+ \bar S_{t}
+ \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) + \\ &&
+ \left(\bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) ^T \boldsymbol{\bar s}_{t} + \bar s_{t} + \\&&
+
+ \frac{1}{2} \left(
+ \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right)^T Q_t \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) + \right. \\&&
+ \boldsymbol{u}^T P_t \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) + \\&&
+ \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right)^T P_t^T \boldsymbol{u} + \\&&
+ \left. \boldsymbol{u}^T R_t \boldsymbol{u} \right) + \\&&
+
+ \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right)^T \boldsymbol{q}_t + \boldsymbol{u}^T \boldsymbol{r}_t + q_t \\
+
+ &=&
+ \frac{1}{2} \left(\bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right)^T
+ \left( \bar S_{t} + Q_t \right)
+ \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) + \\ &&
+ \left(\bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) ^T \boldsymbol{\bar s}_{t} + \bar s_{t} + \\&&
+
+ \frac{1}{2} \left(
+ \boldsymbol{u}^T P_t \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right) \right. + \\&&
+ \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right)^T P_t^T \boldsymbol{u} + \\&&
+ \left. \boldsymbol{u}^T R_t \boldsymbol{u} \right) + \\&&
+
+ \left( \bar A_{t} \boldsymbol{x}_{t + 1} + \bar B_t \boldsymbol{u} + \boldsymbol{\bar c}_{t}\right)^T \boldsymbol{q}_t + \boldsymbol{u}^T \boldsymbol{r}_t + q_t \\
+
+ &=& \frac{1}{2} \left(
+ \boldsymbol{x}_{t + 1}^T \bar A_t^T \left( \bar S_t + Q_t \right) \bar A_t \boldsymbol{x}_{t + 1} +
+ \boldsymbol{x}_{t + 1}^T \bar A_t^T \left( \bar S_t + Q_t \right) \bar B_t \boldsymbol{u} +
+ \boldsymbol{x}_{t + 1}^T \bar A_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t + \right. \\&&
+ \boldsymbol{u}^T \bar B_t^T \left( \bar S_t + Q_t \right) \bar A_t \boldsymbol{x}_{t + 1} +
+ \boldsymbol{u}^T \bar B_t^T \left( \bar S_t + Q_t \right) \bar B_t \boldsymbol{u} +
+ \boldsymbol{u}^T \bar B_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t + \\&&
+ \left. \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \bar A_t \boldsymbol{x}_{t + 1} +
+ \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \bar B_t \boldsymbol{u} +
+ \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t \right) + \\&&
+
+ \boldsymbol{x}_{t + 1}^T \bar A_t^T \boldsymbol{\bar s}_t +
+ \boldsymbol{u}^T \bar B_t^T \boldsymbol{\bar s}_t +
+ \boldsymbol{\bar c}_t^T \boldsymbol{\bar s}_t +
+
+ \bar s_t + \\ &&
+
+ \frac{1}{2} \left( \boldsymbol{u}^T P_t \bar A_{t} \boldsymbol{x}_{t + 1} +
+ \boldsymbol{u}^T P_t \bar B_{t} \boldsymbol{u} +
+ \boldsymbol{u}^T P_t \boldsymbol{\bar c}_{t} \right) + \\&&
+ \frac{1}{2} \left( \boldsymbol{x}_{t+1}^T \bar A^T_t P_t^T \boldsymbol{u} +
+ \boldsymbol{u}^T \bar B^T_{t} P_t^T \boldsymbol{u} +
+ \boldsymbol{\bar c}_t^T P^T_t \boldsymbol{u} \right) + \\&&
+
+ \frac{1}{2} \boldsymbol{u}^T R_t \boldsymbol{u} + \\&&
+
+ \boldsymbol{x}^T_{t + 1} \bar A^T_t \boldsymbol{q}_t +
+ \boldsymbol{u}^T \bar B^T_t \boldsymbol{q}_t +
+ \boldsymbol{\bar c}_t^T \boldsymbol{q}_t +
+
+ \boldsymbol{u}^T \boldsymbol{r}_t + q_t
+\end{array}$$
+
+Now, let's find the optimal $\boldsymbol{u}$.
+Do this by evaluating
+$\frac{\partial}{\partial \boldsymbol{u}} \bar v_t(\boldsymbol{x}, \boldsymbol{u}) = 0$.
+
+$$\begin{array}{rcl}
+\frac{\partial}{\partial \boldsymbol{u}} \bar v_{t + 1}(\boldsymbol{x}_{t+1}, \boldsymbol{u})
+ &=& \frac{1}{2} \left(
+ \boldsymbol{x}_{t + 1}^T \bar A_t^T \left( \bar S_t + Q_t \right) \bar B_t +
+
+ \left(\bar B_t^T \left( \bar S_t + Q_t \right) \bar A_t \boldsymbol{x}_{t + 1}\right)^T + \right. \\&&
+
+ 2 \boldsymbol{u}^T \bar B_t^T \left( \bar S_t + Q_t \right) \bar B_t +
+ \left( \bar B_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t \right)^T + \\&&
+ \left. \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \bar B_t \right) + \\&&
+ \boldsymbol{\bar s}_t ^T \bar B_t + \\&&
+
+ \frac{1}{2} \left( P_t \bar A_{t} \boldsymbol{x}_{t + 1}\right) ^T +
+ \frac{1}{2} \boldsymbol{x}_{t+1}^T \bar A^T_t P_t^T + \\&&
+
+ \frac{1}{2} \boldsymbol{u}^T \left( P_t \bar B_{t} + \bar B_t^T P_t^T \right) +
+ \frac{1}{2} \boldsymbol{u}^T \left( \bar B^T_{t} P_t^T + P_t \bar B_t \right) + \\&&
+ \frac{1}{2} \left( P_t \boldsymbol{\bar c}_{t} \right)^T +
+ \frac{1}{2} \boldsymbol{\bar c}^T_{t} P_t^T +
+
+ \boldsymbol{u}^T R_t + \\&&
+
+ \left(\bar B^T_t \boldsymbol{q}_t\right)^T +
+
+ \boldsymbol{r}_t^T \\
+
+ &=&
+ \boldsymbol{x}_{t + 1}^T \bar A_t^T \left( \bar S_t + Q_t \right) \bar B_t +
+ \boldsymbol{u}^T \bar B_t^T \left( \bar S_t + Q_t \right) \bar B_t +
+
+ \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \bar B_t + \\&&
+
+ \boldsymbol{\bar s}_t ^T \bar B_t + \\&&
+
+ \boldsymbol{x}_{t+1}^T \bar A^T_t P_t^T + \\&&
+
+ \boldsymbol{u}^T \left( \bar B^T_{t} P_t^T + P_t \bar B_t \right) + \\&&
+ \boldsymbol{\bar c}^T_{t} P_t^T +
+
+ \boldsymbol{u}^T R_t + \\&&
+
+ \boldsymbol{q}_t^T \bar B_t +
+ \boldsymbol{r}_t^T \\
+0 &=&
+ \boldsymbol{x}_{t + 1}^T \left( \bar A_t^T \left( \bar S_t + Q_t \right) \bar B_t + \bar A^T_t P_t^T \right) + \\&&
+
+ \boldsymbol{u}^T \left(
+ \bar B_t^T \left( \bar S_t + Q_t \right) \bar B_t +
+ \bar B^T_{t} P_t^T + P_t \bar B_t + R_t
+ \right) + \\&&
+
+ \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \bar B_t +
+ \boldsymbol{\bar s}_t^T \bar B_t +
+ \boldsymbol{\bar c}^T_{t} P_t^T +
+ \boldsymbol{q}_t^T \bar B_t +
+ \boldsymbol{r}_t^T \\
+\end{array}$$
+
+$$\begin{array}{rcl}
+ \boldsymbol{u}^T \left(
+ \bar B_t^T \left( \bar S_t + Q_t \right) \bar B_t +
+ \bar B^T_{t} P_t^T + P_t \bar B_t + R_t
+ \right)
+ &=&
+ - \boldsymbol{x}_{t + 1}^T \left( \bar A_t^T \left( \bar S_t + Q_t \right) \bar B_t + \bar A^T_t P_t^T \right) - \\&&
+
+
+ \left( \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \bar B_t +
+ \boldsymbol{\bar s}_t^T \bar B_t +
+ \boldsymbol{\bar c}^T_{t} P_t^T +
+ \boldsymbol{q}_t^T \bar B_t +
+ \boldsymbol{r}_t^T \right) \\
+
+\left(
+ \bar B_t^T \left( \bar S_t + Q_t \right) \bar B_t +
+ \bar B^T_{t} P_t^T + P_t \bar B_t + R_t
+\right) \boldsymbol{u}
+ &=&
+ - \left( \bar B_t^T \left( \bar S_t + Q_t \right) \bar A_t + P_t \bar A_t \right) \boldsymbol{x}_{t + 1} - \\&&
+
+ \left( \bar B_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t +
+ \bar B_t^T \boldsymbol{\bar s}_t +
+ P_t \boldsymbol{\bar c}_{t} +
+ \bar B_t^T \boldsymbol{q}_t +
+ \boldsymbol{r}_t \right) \\
+\end{array}$$
+
+Some substitutions to use for simplifying:
+
+$$\begin{array}{rcl}
+\bar C_t &=& \bar B_t^T \left( \bar S_t + Q_t \right) \bar A_t + P_t \bar A_t \\
+\bar E_t &=&
+ \bar B_t^T \left( \bar S_t + Q_t \right) \bar B_t +
+ \bar B^T_{t} P_t^T + P_t \bar B_t + R_t \\
+\bar L_t &=& - \bar E_t^{-1} \bar C_t \\
+
+\boldsymbol{\bar e}_t &=&
+ \bar B_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t +
+ \bar B_t^T \boldsymbol{\bar s}_t +
+ P_t \boldsymbol{\bar c}_{t} +
+ \bar B_t^T \boldsymbol{q}_t +
+ \boldsymbol{r}_t \\
+\boldsymbol{\bar l}_t &=& - \bar E_t^{-1} \boldsymbol{\bar e}_t \\
+
+\bar D_t &=& \bar A_t^T \left( \bar S_t + Q_t \right) \bar A_t \\
+\boldsymbol{\bar d}_t &=&
+ \bar A_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t +
+ \bar A_t^T \left( \boldsymbol{\bar s}_t + \boldsymbol{q}_t \right) \\
+
+\boldsymbol{u} &=& - \bar E_t^{-1} \bar C_t \boldsymbol{x}_{t + 1} - \bar E_t^{-1} \boldsymbol{\bar e}_t \\
+\boldsymbol{u} &=& \bar L_t \boldsymbol{x}_{t + 1} + \boldsymbol{\bar l}_t \\
+
+\bar E_t \boldsymbol{u} &=& -\bar C_t \boldsymbol{x}_{t + 1} - \boldsymbol{\bar e}_t
+\end{array}$$
+
+Now, let's solve for the new cost function.
+
+$$\begin{array}{rcl}
+\bar v_{t + 1}(\boldsymbol{x}_{t+1}, \boldsymbol{u})
+ &=& \frac{1}{2} \left(
+ \boldsymbol{x}_{t + 1}^T \bar A_t^T \left( \bar S_t + Q_t \right) \bar A_t \boldsymbol{x}_{t + 1} +
+ \boldsymbol{x}_{t + 1}^T \bar A_t^T \left( \bar S_t + Q_t \right) \bar B_t \boldsymbol{u} +
+ \boldsymbol{x}_{t + 1}^T \bar A_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t + \right. \\&&
+ \boldsymbol{u}^T \bar B_t^T \left( \bar S_t + Q_t \right) \bar A_t \boldsymbol{x}_{t + 1} +
+ \boldsymbol{u}^T \bar B_t^T \left( \bar S_t + Q_t \right) \bar B_t \boldsymbol{u} +
+ \boldsymbol{u}^T \bar B_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t + \\&&
+ \left. \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \bar A_t \boldsymbol{x}_{t + 1} +
+ \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \bar B_t \boldsymbol{u} +
+ \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t \right) + \\&&
+
+ \boldsymbol{x}_{t + 1}^T \bar A_t^T \boldsymbol{\bar s}_t +
+ \boldsymbol{u}^T \bar B_t^T \boldsymbol{\bar s}_t +
+ \boldsymbol{\bar c}_t^T \boldsymbol{\bar s}_t +
+
+ \bar s_t + \\ &&
+
+ \frac{1}{2} \left( \boldsymbol{u}^T P_t \bar A_{t} \boldsymbol{x}_{t + 1} +
+ \boldsymbol{u}^T P_t \bar B_{t} \boldsymbol{u} +
+ \boldsymbol{u}^T P_t \boldsymbol{\bar c}_{t} \right) + \\&&
+ \frac{1}{2} \left( \boldsymbol{x}_{t+1}^T \bar A^T_t P_t^T \boldsymbol{u} +
+ \boldsymbol{u}^T \bar B^T_{t} P_t^T \boldsymbol{u} +
+ \boldsymbol{\bar c}_t^T P^T_t \boldsymbol{u} \right) + \\&&
+
+ \frac{1}{2} \boldsymbol{u}^T R_t \boldsymbol{u} + \\&&
+
+ \boldsymbol{x}^T_{t + 1} \bar A^T_t \boldsymbol{q}_t +
+ \boldsymbol{u}^T \bar B^T_t \boldsymbol{q}_t +
+ \boldsymbol{\bar c}_t^T \boldsymbol{q}_t +
+
+ \boldsymbol{u}^T \boldsymbol{r}_t + q_t \\
+
+\bar v_{t + 1}(\boldsymbol{x}_{t+1}, \boldsymbol{u})
+ &=& \frac{1}{2} \left(
+ \boldsymbol{x}_{t + 1}^T \bar D_t \boldsymbol{x}_{t + 1} +
+ \boldsymbol{x}_{t + 1}^T \bar C_t^T \boldsymbol{u} +
+ \boldsymbol{u}^T \bar C_t \boldsymbol{x}_{t + 1} +
+ \boldsymbol{u}^T \bar E_t \boldsymbol{u} \right) + \\&&
+
+ \boldsymbol{x}_{t + 1}^T \boldsymbol{\bar d}_t +
+
+ \boldsymbol{u}^T \boldsymbol{\bar e}_t + \\&&
+
+ \frac{1}{2} \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t +
+ \boldsymbol{\bar c}_t^T \boldsymbol{\bar s}_t + \boldsymbol{\bar c}_t^T \boldsymbol{q}_t + \bar s_t + q_t \\
+
+\bar v_{t + 1}(\boldsymbol{x}_{t+1})
+ &=& \frac{1}{2} \left(
+ \boldsymbol{x}_{t + 1}^T \bar D_t \boldsymbol{x}_{t + 1} + \right. \\ &&
+ \boldsymbol{x}_{t + 1}^T \bar C_t^T \left( -\bar E_t^{-1} \bar C_t \boldsymbol{x}_{t + 1} - \bar E_t^{-1} \boldsymbol{\bar e}_t \right) + \\&&
+ \left( -\bar E_t^{-1} \bar C_t \boldsymbol{x}_{t + 1} - \bar E_t^{-1} \boldsymbol{\bar e}_t \right)^T \bar C_t \boldsymbol{x}_{t + 1} + \\&&
+ \left. \left( -\bar E_t^{-1} \bar C_t \boldsymbol{x}_{t + 1} - \bar E_t^{-1} \boldsymbol{\bar e}_t \right)^T \bar E_t \left( -\bar E_t^{-1} \bar C_t \boldsymbol{x}_{t + 1} - \bar E_t^{-1} \boldsymbol{\bar e}_t \right) \right) + \\&&
+
+ \boldsymbol{x}_{t + 1}^T \boldsymbol{\bar d}_t +
+
+ \left( -\bar E_t^{-1} \bar C_t \boldsymbol{x}_{t + 1} - \bar E_t^{-1} \boldsymbol{\bar e}_t \right)^T \boldsymbol{\bar e}_t + \\&&
+
+ \frac{1}{2} \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t +
+ \boldsymbol{\bar c}_t^T \boldsymbol{\bar s}_t + \boldsymbol{\bar c}_t^T \boldsymbol{q}_t + \bar s_t + q_t \\
+
+\bar v_{t + 1}(\boldsymbol{x}_{t+1})
+ &=& \frac{1}{2}
+ \boldsymbol{x}_{t + 1}^T \left(\bar D_t - \bar C_t^T \bar E_t^{-1} \bar C_t \right) \boldsymbol{x}_{t + 1} + \\ &&
+
+ \boldsymbol{x}_{t + 1}^T \left(\boldsymbol{\bar d}_t
+ - \bar C_t^T \bar E_t^{-1} \boldsymbol{\bar e}_t \right)\\&&
+
+ - \frac{1}{2} \boldsymbol{\bar e}_t^T \bar E_t^{-1} \boldsymbol{\bar e}_t +
+ \frac{1}{2} \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t +
+ \boldsymbol{\bar c}_t^T \boldsymbol{\bar s}_t + \boldsymbol{\bar c}_t^T \boldsymbol{q}_t + \bar s_t + q_t \\
+\end{array}$$
+
+Ok, let's now pull out the 3 variables of interest and do further simplification.
+
+$$\begin{array}{rcl}
+\bar v_{t + 1}(\boldsymbol{x}_{t+1}) &=& \frac{1}{2} \boldsymbol{x}_{t + 1}^T \bar S_{t + 1} \boldsymbol{x}_{t + 1} + \boldsymbol{x}_{t + 1}^T \boldsymbol{\bar s}_{t + 1} + \bar s_{t+1} \\
+ \bar S_{t + 1} &=& \bar D_t - \bar C_t^T \bar E_t^{-1} \bar C_t \\
+ \boldsymbol{\bar s}_{t + 1} &=&
+ \left(\boldsymbol{\bar d}_t - \bar C_t^T \bar E_t^{-1} \boldsymbol{\bar e}_t \right)\\
+
+\bar s_{t+1} &=&
+ - \frac{1}{2} \boldsymbol{\bar e}_t^T \bar E_t^{-1} \boldsymbol{\bar e}_t +
+ \frac{1}{2} \boldsymbol{\bar c}_t^T \left( \bar S_t + Q_t \right) \boldsymbol{\bar c}_t +
+ \boldsymbol{\bar c}_t^T \boldsymbol{\bar s}_t + \boldsymbol{\bar c}_t^T \boldsymbol{q}_t + \bar s_t + q_t \\
+\end{array}$$
+
+\newpage
+\section{Detailed work for a few transformations}
+
+$$\begin{array}{l}
+\begin{bmatrix} \boldsymbol{x} \\ \boldsymbol{u} \end{bmatrix}^T
+\begin{bmatrix} Q_{t} & P_{t}^T \\ P_{t} & R_{t} \end{bmatrix}
+\begin{bmatrix} \boldsymbol{x} \\ \boldsymbol{u} \end{bmatrix} \\
+
+\begin{bmatrix} \boldsymbol{x}_1 & \boldsymbol{x}_2 & \boldsymbol{u}_1 & \boldsymbol{u}_2 \end{bmatrix}
+\left[\begin{array}{cc|cc}
+ Q_{t11} & Q_{t12} & P_{t11} & P_{t21} \\
+ Q_{t21} & Q_{t22} & P_{t12} & P_{t22} \\
+ \hline
+ P_{t11} & P_{t12} & R_{t11} & R_{t12} \\
+ P_{t21} & P_{t22} & R_{t21} & R_{t22} \\
+\end{array}\right]
+\begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \\ \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix}
+\\
+\begin{bmatrix}
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \\ \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} Q_{t11} \\ Q_{t21} \\ P_{t11} \\ P_{t21} \end{bmatrix} &
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \\ \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} Q_{t12} \\ Q_{t22} \\ P_{t12} \\ P_{t22} \end{bmatrix} &
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \\ \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} P_{t11} \\ P_{t12} \\ R_{t11} \\ R_{t21} \end{bmatrix} &
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \\ \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} P_{t21} \\ P_{t22} \\ R_{t12} \\ R_{t22} \end{bmatrix} &
+\end{bmatrix}
+\begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \\ \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix}
+\\
+\begin{bmatrix}
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} Q_{t11} \\ Q_{t21} \end{bmatrix}
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} Q_{t12} \\ Q_{t22} \end{bmatrix}
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} P_{t11} \\ P_{t12} \end{bmatrix}
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} P_{t21} \\ P_{t22} \end{bmatrix}
+\end{bmatrix}
+\begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \\ \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} + \\ \quad
+\begin{bmatrix}
+ \begin{bmatrix} \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} P_{t11} \\ P_{t21} \end{bmatrix} &
+ \begin{bmatrix} \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} P_{t12} \\ P_{t22} \end{bmatrix} &
+ \begin{bmatrix} \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} R_{t11} \\ R_{t21} \end{bmatrix} &
+ \begin{bmatrix} \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} R_{t12} \\ R_{t22} \end{bmatrix} &
+\end{bmatrix}
+\begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \\ \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix}
+\\
+\begin{bmatrix} \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} Q_{t11} \\ Q_{t21} \end{bmatrix} &
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} Q_{t12} \\ Q_{t22} \end{bmatrix}\end{bmatrix}
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \end{bmatrix} +
+\begin{bmatrix} \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} P_{t11} \\ P_{t12} \end{bmatrix} &
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} P_{t21} \\ P_{t22} \end{bmatrix}\end{bmatrix}
+ \begin{bmatrix} \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} + \\ \quad
+\begin{bmatrix} \begin{bmatrix} \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} P_{t11} \\ P_{t21} \end{bmatrix} &
+ \begin{bmatrix} \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} P_{t12} \\ P_{t22} \end{bmatrix}\end{bmatrix}
+ \begin{bmatrix} \boldsymbol{x}_1 \\ \boldsymbol{x}_2 \end{bmatrix} +
+\begin{bmatrix} \begin{bmatrix} \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} R_{t11} \\ R_{t21} \end{bmatrix} &
+ \begin{bmatrix} \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix} \cdot
+ \begin{bmatrix} R_{t12} \\ R_{t22} \end{bmatrix}\end{bmatrix}
+ \begin{bmatrix} \boldsymbol{u}_1 \\ \boldsymbol{u}_2 \end{bmatrix}
+\\
+\boldsymbol{x}^T Q_t \boldsymbol{x} + \boldsymbol{u}^T P_t \boldsymbol{x} + \boldsymbol{x}^T P_t^T \boldsymbol{u} + \boldsymbol{u}^T R_t \boldsymbol{u}
+\end{array}$$
+\\ \\
+$$\begin{array}{l}
+\begin{bmatrix} \boldsymbol{x} \\ \boldsymbol{u} \end{bmatrix}^T
+\begin{bmatrix} \boldsymbol{q}_{t} \\ \boldsymbol{r}_{t} \end{bmatrix}
+\\
+\begin{bmatrix} \boldsymbol{x}_1 & \boldsymbol{x}_2 & \boldsymbol{u}_1 & \boldsymbol{u}_2 \end{bmatrix}
+\begin{bmatrix} \boldsymbol{q}_{t1} \\ \boldsymbol{q}_{t2} \\ \boldsymbol{r}_{t1} \\ \boldsymbol{r}_{t1} \end{bmatrix}
+\\
+\boldsymbol{x}^T \boldsymbol{q}_t + \boldsymbol{u}^T \boldsymbol{r}_t
+\end{array}$$
+
+\end{document}
diff --git a/y2014/control_loops/python/extended_lqr_derivation.py b/y2014/control_loops/python/extended_lqr_derivation.py
new file mode 100755
index 0000000..248c6fc
--- /dev/null
+++ b/y2014/control_loops/python/extended_lqr_derivation.py
@@ -0,0 +1,410 @@
+#!/usr/bin/python2
+
+# This file checks our math in extended_lqr.tex.
+
+from __future__ import print_function
+from __future__ import division
+
+import sys
+import random
+
+import sympy
+
+'''
+* `x_t1` means `x_{t + 1}`. Using `'x_t + 1'` as the symbol name makes the non-
+ latex output really confusing, so not doing that.
+* `xb` means `\\boldsymbol{x}`. Written as `'xbold'` in the symbol name because
+ that's what sympy.latex recognizes.
+* `xb_tb` means `\\boldsymbol{\\bar x}_t. Written as `'xboldbar'` in the symbol
+ name so sympy.latex recognizes it.
+'''
+
+# sympy.latex
+
+# n in the 2013 paper
+number_of_states = sympy.Symbol('states', integer=True)
+# m in the 2013 paper
+number_of_inputs = sympy.Symbol('inputs', integer=True)
+number_of_outputs = sympy.Symbol('outputs', integer=True)
+
+DIMENSIONS = set([number_of_states, number_of_inputs, number_of_outputs])
+
+A_t = sympy.MatrixSymbol('A_t', number_of_states, number_of_states)
+B_t = sympy.MatrixSymbol('B_t', number_of_states, number_of_inputs)
+cb_t = sympy.MatrixSymbol('cbold_t', number_of_states, 1)
+A_tb = sympy.MatrixSymbol('Abar_t', number_of_states, number_of_states)
+B_tb = sympy.MatrixSymbol('Bbar_t', number_of_states, number_of_inputs)
+cb_tb = sympy.MatrixSymbol('cboldbar_t', number_of_states, 1)
+
+Q_t = sympy.MatrixSymbol('Q_t', number_of_states, number_of_states)
+P_t = sympy.MatrixSymbol('P_t', number_of_inputs, number_of_states)
+R_t = sympy.MatrixSymbol('R_t', number_of_inputs, number_of_inputs)
+qb_t = sympy.MatrixSymbol('qbold_t', number_of_states, 1)
+rb_t = sympy.MatrixSymbol('rbold_t', number_of_inputs, 1)
+q_t = sympy.MatrixSymbol('q_t', 1, 1)
+
+S_t1 = sympy.MatrixSymbol('S_t1', number_of_states, number_of_states)
+sb_t1 = sympy.MatrixSymbol('sbold_t1', number_of_states, 1)
+s_t1 = sympy.MatrixSymbol('s_t1', 1, 1)
+S_tb = sympy.MatrixSymbol('Sbar_t', number_of_states, number_of_states)
+sb_tb = sympy.MatrixSymbol('sboldbar_t', number_of_states, 1)
+s_tb = sympy.MatrixSymbol('sbar_t', 1, 1)
+
+xb_t = sympy.MatrixSymbol('xbold_t', number_of_states, 1)
+ub_t = sympy.MatrixSymbol('ubold_t', number_of_inputs, 1)
+xb_t1 = sympy.MatrixSymbol('xbold_t1', number_of_states, 1)
+ub_t1 = sympy.MatrixSymbol('ubold_t1', number_of_inputs, 1)
+
+half = sympy.Integer(1) / sympy.Integer(2)
+xb = sympy.MatrixSymbol('xbold', number_of_states, 1)
+ub = sympy.MatrixSymbol('ubold', number_of_inputs, 1)
+
+CONSTANTS = set([
+ A_t, B_t, cb_t,
+ S_t1, sb_t1, s_t1,
+ A_tb, B_tb, cb_tb,
+ S_tb, sb_tb, s_tb,
+ P_t, Q_t, R_t, qb_t, rb_t, q_t,
+ ])
+
+SYMMETRIC_CONSTANTS = set([
+ S_t1, S_tb,
+ Q_t, R_t,
+ ])
+
+def verify_equivalent(a, b, inverses={}):
+ def get_matrices(m):
+ matrices = m.atoms(sympy.MatrixSymbol)
+ new_matrices = set()
+ for matrix in matrices:
+ if matrix in inverses:
+ new_matrices.update(inverses[matrix].atoms(sympy.MatrixSymbol))
+ matrices.update(new_matrices)
+ a_matrices, b_matrices = get_matrices(a), get_matrices(b)
+ if a_matrices != b_matrices:
+ raise RuntimeError('matrices different: %s vs %s' % (a_matrices,
+ b_matrices))
+ a_symbols, b_symbols = a.atoms(sympy.Symbol), b.atoms(sympy.Symbol)
+ if a_symbols != b_symbols:
+ raise RuntimeError('symbols different: %s vs %s' % (a_symbols, b_symbols))
+ if not a_symbols < DIMENSIONS:
+ raise RuntimeError('not sure what to do with %s' % (a_symbols - DIMENSIONS))
+
+ if a.shape != b.shape:
+ raise RuntimeError('Different shapes: %s and %s' % (a.shape, b.shape))
+
+ for _ in range(10):
+ subs_symbols = {s: random.randint(1, 5) for s in a_symbols}
+ for _ in range(10):
+ diff = a - b
+ subs_matrices = {}
+ def get_replacement(*args):
+ try:
+ m = sympy.MatrixSymbol(*args)
+ if m not in subs_matrices:
+ if m in inverses:
+ i = inverses[m].replace(sympy.MatrixSymbol, get_replacement, simultaneous=False)
+ i_evaled = sympy.ImmutableMatrix(i.rows, i.cols,
+ lambda x,y: i[x, y].evalf())
+ subs_matrices[m] = i_evaled.I
+ else:
+ rows = m.rows.subs(subs_symbols)
+ cols = m.cols.subs(subs_symbols)
+ new_m = sympy.ImmutableMatrix(rows, cols,
+ lambda i,j: random.uniform(-5, 5))
+ if m in SYMMETRIC_CONSTANTS:
+ if rows != cols:
+ raise RuntimeError('Non-square symmetric matrix %s' % m)
+ def calculate_cell(i, j):
+ if i > j:
+ return new_m[i, j]
+ else:
+ return new_m[j, i]
+ new_m = sympy.ImmutableMatrix(rows, cols, calculate_cell)
+ subs_matrices[m] = new_m
+ return subs_matrices[m]
+ except AttributeError as e:
+ # Stupid sympy silently eats AttributeErrors and treats them as
+ # "no replacement"...
+ raise RuntimeError(e)
+ # subs fails when it tries doing matrix multiplies between fixed-size ones
+ # and the rest of the equation which still has the symbolic-sized ones.
+ # subs(simultaneous=True) wants to put dummies in for everything first,
+ # and Dummy().transpose() is broken.
+ # replace() has the same issue as subs with simultaneous being True.
+ # lambdify() has no idea what to do with the transposes if you replace all
+ # the matrices with ones of random sizes full of dummies.
+ diff = diff.replace(sympy.MatrixSymbol, get_replacement,
+ simultaneous=False)
+ for row in range(diff.rows):
+ for col in range(diff.cols):
+ result = diff[row, col].evalf()
+ if abs(result) > 1e-7:
+ raise RuntimeError('difference at (%s, %s) is %s' % (row, col,
+ result))
+
+def verify_arguments(f, *args):
+ matrix_atoms = f.atoms(sympy.MatrixSymbol) - CONSTANTS
+ if matrix_atoms != set(args):
+ print('Arguments expected to be %s, but are %s, in:\n%s' % (
+ sorted(args), sorted(list(matrix_atoms)), f), file=sys.stderr)
+ raise RuntimeError
+
+def make_c_t():
+ x_and_u = sympy.BlockMatrix(((xb,), (ub,)))
+ c_t = (half * x_and_u.transpose() *
+ sympy.BlockMatrix(((Q_t, P_t.T), (P_t, R_t))) * x_and_u +
+ x_and_u.transpose() * sympy.BlockMatrix(((qb_t,), (rb_t,))) +
+ q_t)
+ verify_arguments(c_t, xb, ub)
+ return c_t
+
+def check_backwards_cost():
+ g_t = A_t * xb_t + B_t * ub_t + cb_t
+ verify_arguments(g_t, xb_t, ub_t)
+ v_t1 = half * xb.transpose() * S_t1 * xb + xb.transpose() * sb_t1 + s_t1
+ verify_arguments(v_t1, xb)
+ v_t = (v_t1.subs(xb, g_t) + make_c_t()).subs({xb_t: xb, ub_t: ub})
+ verify_arguments(v_t, xb, ub)
+
+ v_t_for_cost = (
+ half * (
+ xb.transpose() * (A_t.transpose() * S_t1 * A_t + Q_t) * xb +
+ ub.transpose() * (B_t.transpose() * S_t1 * A_t + P_t) * xb +
+ xb.transpose() * (A_t.transpose() * S_t1 * B_t + P_t.T) * ub +
+ ub.transpose() * (B_t.transpose() * S_t1 * B_t + R_t) * ub) +
+ xb.transpose() * (A_t.transpose() * sb_t1 + qb_t) +
+ ub.transpose() * (B_t.transpose() * sb_t1 + rb_t) +
+ cb_t.transpose() * sb_t1 +
+ s_t1 + q_t +
+ half * (cb_t.transpose() * S_t1 * cb_t +
+ xb.transpose() * A_t.transpose() * S_t1 * cb_t +
+ ub.transpose() * B_t.transpose() * S_t1 * cb_t +
+ cb_t.transpose() * S_t1 * B_t * ub +
+ cb_t.transpose() * S_t1 * A_t * xb))
+ verify_equivalent(v_t, v_t_for_cost)
+
+ v_t_now = (
+ half * (xb.T * (A_t.T * S_t1 * A_t + Q_t) * xb +
+ ub.T * (B_t.T * S_t1 * A_t + P_t) * xb +
+ xb.T * (A_t.T * S_t1 * B_t + P_t.T) * ub +
+ ub.T * (B_t.T * S_t1 * B_t + R_t) * ub) +
+ xb.T * (A_t.T * sb_t1 + qb_t) +
+ ub.T * (B_t.T * sb_t1 + rb_t) +
+ cb_t.T * sb_t1 + s_t1 + q_t +
+ half * (cb_t.T * S_t1 * cb_t +
+ xb.T * A_t.T * S_t1 * cb_t +
+ ub.T * B_t.T * S_t1 * cb_t +
+ cb_t.T * S_t1 * B_t * ub +
+ cb_t.T * S_t1 * A_t * xb))
+
+ v_t_now = (
+ half * (xb.T * (A_t.T * S_t1 * A_t + Q_t) * xb +
+ ub.T * (B_t.T * S_t1 * A_t + P_t) * xb +
+ xb.T * (A_t.T * S_t1 * B_t + P_t.T) * ub +
+ ub.T * (B_t.T * S_t1 * B_t + R_t) * ub) +
+ xb.T * (A_t.T * sb_t1 + qb_t + half * A_t.T * S_t1 * cb_t) +
+ ub.T * (B_t.T * sb_t1 + rb_t + half * B_t.T * S_t1 * cb_t) +
+ half * cb_t.T * S_t1 * (A_t * xb + B_t * ub + cb_t) +
+ cb_t.T * sb_t1 + s_t1 + q_t)
+
+ v_t_now = (
+ half * (xb.T * (A_t.T * S_t1 * A_t + Q_t) * xb +
+ ub.T * (B_t.T * S_t1 * A_t + P_t) * xb +
+ xb.T * (A_t.T * S_t1 * B_t + P_t.T) * ub +
+ ub.T * (B_t.T * S_t1 * B_t + R_t) * ub) +
+ xb.T * (A_t.T * sb_t1 + qb_t + A_t.T * S_t1 * cb_t) +
+ ub.T * (B_t.T * sb_t1 + rb_t + B_t.T * S_t1 * cb_t) +
+ half * cb_t.T * S_t1 * cb_t +
+ cb_t.T * sb_t1 + s_t1 + q_t)
+
+ C_t = B_t.T * S_t1 * A_t + P_t
+ E_t = B_t.T * S_t1 * B_t + R_t
+ E_t_I = sympy.MatrixSymbol('E_t^-1', E_t.cols, E_t.rows)
+ L_t = -E_t_I * C_t
+ eb_t = B_t.T * S_t1 * cb_t + B_t.T * sb_t1 + rb_t
+ lb_t = -E_t_I * eb_t
+ D_t = A_t.T * S_t1 * A_t + Q_t
+ db_t = A_t.T * S_t1 * cb_t + A_t.T * sb_t1 + qb_t
+
+ v_t_now = (
+ half * (xb.T * D_t * xb + ub.T * C_t * xb +
+ xb.T * C_t.T * ub + ub.T * E_t * ub) +
+ xb.T * db_t + ub.T * eb_t +
+ half * cb_t.T * S_t1 * cb_t +
+ cb_t.T * sb_t1 + s_t1 + q_t)
+
+ v_t_final = (
+ half * xb.T * (D_t + L_t.T * C_t + C_t.T * L_t + L_t.T * E_t * L_t) * xb +
+ xb.T * (C_t.T * lb_t + L_t.T * E_t * lb_t + db_t + L_t.T * eb_t) +
+ half * lb_t.T * E_t * lb_t +
+ lb_t.T * eb_t +
+ cb_t.T * sb_t1 + s_t1 + q_t + half * cb_t.T * S_t1 * cb_t
+ )
+ verify_arguments(v_t_final, xb, E_t_I)
+ verify_equivalent(v_t.subs(ub, L_t * xb + lb_t), v_t_final, {E_t_I: E_t})
+
+ def v_t_from_s(this_S_t, this_sb_t, this_s_t):
+ return half * xb.T * this_S_t * xb + xb.T * this_sb_t + this_s_t
+
+ S_t_new_first = D_t + L_t.T * C_t + C_t.T * L_t + L_t.T * E_t * L_t
+ sb_t_new_first = db_t - C_t.T * E_t_I * eb_t
+ s_t_new_first = (half * lb_t.T * E_t * lb_t +
+ lb_t.T * eb_t +
+ cb_t.T * sb_t1 +
+ s_t1 + q_t +
+ half * cb_t.T * S_t1 * cb_t)
+ verify_equivalent(v_t_from_s(S_t_new_first, sb_t_new_first, s_t_new_first),
+ v_t_final, {E_t_I: E_t})
+
+ S_t_new_end = D_t - C_t.T * E_t_I * C_t
+ sb_t_new_end = db_t - C_t.T * E_t_I * eb_t
+ s_t_new_end = (q_t - half * eb_t.T * E_t_I * eb_t +
+ half * cb_t.T * S_t1 * cb_t + cb_t.T * sb_t1 + s_t1)
+ verify_equivalent(v_t_from_s(S_t_new_end, sb_t_new_end, s_t_new_end),
+ v_t_final, {E_t_I: E_t})
+
+def check_forwards_cost():
+ v_tb = half * xb.T * S_tb * xb + xb.T * sb_tb + s_tb
+ verify_arguments(v_tb, xb)
+ g_tb = A_tb * xb_t1 + B_tb * ub + cb_tb
+ verify_arguments(g_tb, xb_t1, ub)
+ c_t1b = make_c_t().subs(xb, g_tb)
+ verify_arguments(c_t1b, xb_t1, ub)
+ v_t1b = v_tb.subs(xb, g_tb) + c_t1b
+ verify_arguments(v_t1b, xb_t1, ub)
+
+ v_t1b_now = (
+ half * g_tb.T * S_tb * g_tb +
+ g_tb.T * sb_tb + s_tb +
+ half * (g_tb.T * Q_t * g_tb +
+ ub.T * P_t * g_tb +
+ g_tb.T * P_t.T * ub +
+ ub.T * R_t * ub) +
+ g_tb.T * qb_t + ub.T * rb_t + q_t)
+
+ v_t1b_for_cost = (
+ half * (xb_t1.T * A_tb.T * (S_tb + Q_t) * A_tb * xb_t1 +
+ xb_t1.T * A_tb.T * (S_tb + Q_t) * B_tb * ub +
+ xb_t1.T * A_tb.T * (S_tb + Q_t) * cb_tb +
+ ub.T * B_tb.T * (S_tb + Q_t) * A_tb * xb_t1 +
+ ub.T * B_tb.T * (S_tb + Q_t) * B_tb * ub +
+ ub.T * B_tb.T * (S_tb + Q_t) * cb_tb +
+ cb_tb.T * (S_tb + Q_t) * A_tb * xb_t1 +
+ cb_tb.T * (S_tb + Q_t) * B_tb * ub +
+ cb_tb.T * (S_tb + Q_t) * cb_tb) +
+ xb_t1.T * A_tb.T * sb_tb +
+ ub.T * B_tb.T * sb_tb +
+ cb_tb.T * sb_tb +
+ s_tb +
+ half * (ub.T * P_t * A_tb * xb_t1 +
+ ub.T * P_t * B_tb * ub +
+ ub.T * P_t * cb_tb) +
+ half * (xb_t1.T * A_tb.T * P_t.T * ub +
+ ub.T * B_tb.T * P_t.T * ub +
+ cb_tb.T * P_t.T * ub) +
+ half * ub.T * R_t * ub +
+ xb_t1.T * A_tb.T * qb_t + ub.T * B_tb.T * qb_t + cb_tb.T * qb_t +
+ ub.T * rb_t + q_t)
+ verify_equivalent(v_t1b, v_t1b_for_cost)
+
+ S_and_Q = S_tb + Q_t
+
+ v_t1b_now = (
+ half * (xb_t1.T * A_tb.T * S_and_Q * A_tb * xb_t1 +
+ xb_t1.T * A_tb.T * S_and_Q * B_tb * ub +
+ xb_t1.T * A_tb.T * S_and_Q * cb_tb +
+ ub.T * B_tb.T * S_and_Q * A_tb * xb_t1 +
+ ub.T * B_tb.T * S_and_Q * B_tb * ub +
+ ub.T * B_tb.T * S_and_Q * cb_tb +
+ cb_tb.T * S_and_Q * A_tb * xb_t1 +
+ cb_tb.T * S_and_Q * B_tb * ub +
+ cb_tb.T * S_and_Q * cb_tb) +
+ xb_t1.T * A_tb.T * sb_tb +
+ ub.T * B_tb.T * sb_tb +
+ cb_tb.T * sb_tb +
+ s_tb +
+ half * (ub.T * P_t * A_tb * xb_t1 +
+ ub.T * P_t * B_tb * ub +
+ ub.T * P_t * cb_tb) +
+ half * (xb_t1.T * A_tb.T * P_t.T * ub +
+ ub.T * B_tb.T * P_t.T * ub +
+ cb_tb.T * P_t.T * ub) +
+ half * ub.T * R_t * ub +
+ xb_t1.T * A_tb.T * qb_t +
+ ub.T * B_tb.T * qb_t +
+ cb_tb.T * qb_t +
+ ub.T * rb_t +
+ q_t)
+
+ C_tb = B_tb.T * S_and_Q * A_tb + P_t * A_tb
+ E_tb = B_tb.T * S_and_Q * B_tb + B_tb.T * P_t.T + P_t * B_tb + R_t
+ E_tb_I = sympy.MatrixSymbol('Ebar_t^-1', E_tb.cols, E_tb.rows)
+ L_tb = -E_tb_I * C_tb
+ eb_tb = B_tb.T * S_and_Q * cb_tb + B_tb.T * sb_tb + P_t * cb_tb + B_tb.T * qb_t + rb_t
+ lb_tb = -E_tb_I * eb_tb
+ D_tb = A_tb.T * S_and_Q * A_tb
+ db_tb = A_tb.T * S_and_Q * cb_tb + A_tb.T * (sb_tb + qb_t)
+
+ v_t1b_now = (
+ half * (xb_t1.T * D_tb * xb_t1 +
+ xb_t1.T * C_tb.T * ub +
+ ub.T * C_tb * xb_t1 +
+ ub.T * E_tb * ub) +
+ xb_t1.T * db_tb +
+ ub.T * eb_tb +
+ half * cb_tb.T * S_and_Q * cb_tb +
+ cb_tb.T * sb_tb +
+ cb_tb.T * qb_t +
+ s_tb + q_t)
+
+ v_t1b_final = (
+ half * xb_t1.T * (D_tb - C_tb.T * E_tb_I * C_tb) * xb_t1 +
+ xb_t1.T * (db_tb - C_tb.T * E_tb_I * eb_tb) +
+ -half * eb_tb.T * E_tb_I * eb_tb +
+ half * cb_tb.T * S_and_Q * cb_tb +
+ cb_tb.T * sb_tb +
+ cb_tb.T * qb_t +
+ s_tb + q_t)
+ verify_arguments(v_t1b_final, xb_t1, E_tb_I)
+ verify_equivalent(v_t1b.subs(ub, -E_tb_I * C_tb * xb_t1 - E_tb_I * eb_tb),
+ v_t1b_final, {E_tb_I: E_tb})
+
+def check_forwards_u():
+ S_and_Q = S_tb + Q_t
+
+ diff_start = (
+ half * (xb_t1.T * A_tb.T * S_and_Q * B_tb +
+ (B_tb.T * S_and_Q * A_tb * xb_t1).T +
+ 2 * ub.T * B_tb.T * S_and_Q * B_tb +
+ (B_tb.T * S_and_Q * cb_tb).T +
+ cb_tb.T * S_and_Q * B_tb) +
+ sb_tb.T * B_tb +
+ half * (P_t * A_tb * xb_t1).T +
+ half * xb_t1.T * A_tb.T * P_t.T +
+ half * ub.T * (P_t * B_tb + B_tb.T * P_t.T) +
+ half * ub.T * (B_tb.T * P_t.T + P_t * B_tb) +
+ half * (P_t * cb_tb).T +
+ half * cb_tb.T * P_t.T +
+ ub.T * R_t +
+ (B_tb.T * qb_t).T + rb_t.T)
+ verify_arguments(diff_start, xb_t1, ub)
+
+ diff_end = (
+ xb_t1.T * (A_tb.T * S_and_Q * B_tb + A_tb.T * P_t.T) +
+ ub.T * (B_tb.T * S_and_Q * B_tb + B_tb.T * P_t.T + P_t * B_tb + R_t) +
+ cb_tb.T * S_and_Q * B_tb +
+ sb_tb.T * B_tb +
+ cb_tb.T * P_t.T +
+ qb_t.T * B_tb +
+ rb_t.T)
+ verify_equivalent(diff_start, diff_end)
+
+def main():
+ sympy.init_printing(use_unicode=True)
+ check_backwards_cost()
+ check_forwards_cost()
+ check_forwards_u()
+
+if __name__ == '__main__':
+ main()
diff --git a/y2014_bot3/BUILD b/y2014_bot3/BUILD
index 3ec0bb5..1c07423 100644
--- a/y2014_bot3/BUILD
+++ b/y2014_bot3/BUILD
@@ -16,21 +16,22 @@
'//frc971/queues:gyro',
'//y2014_bot3/autonomous:auto_queue',
'//y2014_bot3/control_loops/rollers:rollers_queue',
- '//y2014_bot3/control_loops/drivetrain:drivetrain_queue',
+ '//frc971/control_loops/drivetrain:drivetrain_queue',
],
)
aos_downloader(
- name = 'download',
+ name = 'download_stripped',
start_srcs = [
- '//aos:prime_start_binaries',
- '//y2014_bot3/control_loops/drivetrain:drivetrain',
- '//y2014_bot3/control_loops/rollers:rollers',
- '//y2014_bot3/autonomous:auto',
- ':joystick_reader',
- '//y2014_bot3/wpilib:wpilib_interface',
+ ':joystick_reader.stripped',
+ '//aos:prime_start_binaries_stripped',
+ '//y2014_bot3/autonomous:auto.stripped',
+ '//y2014_bot3/control_loops/drivetrain:drivetrain.stripped',
+ '//y2014_bot3/control_loops/rollers:rollers.stripped',
+ '//y2014_bot3/wpilib:wpilib_interface.stripped',
+
],
srcs = [
- '//aos:prime_binaries',
+ '//aos:prime_binaries_stripped',
],
)
diff --git a/y2014_bot3/autonomous/BUILD b/y2014_bot3/autonomous/BUILD
index f90ce74..bfd7f34 100644
--- a/y2014_bot3/autonomous/BUILD
+++ b/y2014_bot3/autonomous/BUILD
@@ -20,8 +20,7 @@
deps = [
':auto_queue',
'//aos/common/controls:control_loop',
- '//y2014_bot3/control_loops/drivetrain:drivetrain_queue',
- '//y2014_bot3/control_loops/drivetrain:drivetrain_lib',
+ '//frc971/control_loops/drivetrain:drivetrain_queue',
'//y2014_bot3/control_loops/rollers:rollers_queue',
'//aos/common:time',
'//aos/common/util:phased_loop',
diff --git a/y2014_bot3/autonomous/auto.cc b/y2014_bot3/autonomous/auto.cc
index 3724cbe..80f2b09 100644
--- a/y2014_bot3/autonomous/auto.cc
+++ b/y2014_bot3/autonomous/auto.cc
@@ -8,13 +8,12 @@
#include "aos/common/logging/logging.h"
#include "aos/common/logging/queue_logging.h"
+#include "frc971/control_loops/drivetrain/drivetrain.q.h"
#include "y2014_bot3/autonomous/auto.q.h"
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.q.h"
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.h"
#include "y2014_bot3/control_loops/rollers/rollers.q.h"
using ::aos::time::Time;
-using ::y2014_bot3::control_loops::drivetrain_queue;
+using ::frc971::control_loops::drivetrain_queue;
using ::y2014_bot3::control_loops::rollers_queue;
namespace y2014_bot3 {
@@ -35,7 +34,7 @@
void ResetDrivetrain() {
LOG(INFO, "resetting the drivetrain\n");
- control_loops::drivetrain_queue.goal.MakeWithBuilder()
+ ::frc971::control_loops::drivetrain_queue.goal.MakeWithBuilder()
.control_loop_driving(false)
.steering(0.0)
.throttle(0.0)
@@ -47,11 +46,11 @@
}
void InitializeEncoders() {
- control_loops::drivetrain_queue.status.FetchAnother();
+ ::frc971::control_loops::drivetrain_queue.status.FetchAnother();
left_initial_position =
- control_loops::drivetrain_queue.status->estimated_left_position;
+ ::frc971::control_loops::drivetrain_queue.status->estimated_left_position;
right_initial_position =
- control_loops::drivetrain_queue.status->estimated_right_position;
+ ::frc971::control_loops::drivetrain_queue.status->estimated_right_position;
}
void HandleAuto() {
@@ -63,7 +62,7 @@
InitializeEncoders();
LOG(INFO, "Driving\n");
- control_loops::drivetrain_queue.goal.MakeWithBuilder()
+ ::frc971::control_loops::drivetrain_queue.goal.MakeWithBuilder()
.control_loop_driving(false)
.highgear(false)
.quickturn(false)
@@ -76,7 +75,7 @@
.Send();
time::SleepFor(time::Time::InSeconds(2.0));
- control_loops::drivetrain_queue.goal.MakeWithBuilder()
+ ::frc971::control_loops::drivetrain_queue.goal.MakeWithBuilder()
.control_loop_driving(false)
.highgear(false)
.quickturn(false)
diff --git a/y2014_bot3/control_loops/drivetrain/BUILD b/y2014_bot3/control_loops/drivetrain/BUILD
index 32afd4b..6bd7e33 100644
--- a/y2014_bot3/control_loops/drivetrain/BUILD
+++ b/y2014_bot3/control_loops/drivetrain/BUILD
@@ -2,45 +2,6 @@
load('/aos/build/queues', 'queue_library')
-cc_binary(
- name = 'replay_drivetrain',
- srcs = [
- 'replay_drivetrain.cc',
- ],
- deps = [
- ':drivetrain_queue',
- '//aos/common/controls:replay_control_loop',
- '//aos/linux_code:init',
- ],
-)
-
-queue_library(
- name = 'drivetrain_queue',
- srcs = [
- 'drivetrain.q',
- ],
- deps = [
- '//aos/common/controls:control_loop_queues',
- ],
-)
-
-cc_library(
- name = 'polydrivetrain_plants',
- srcs = [
- 'polydrivetrain_dog_motor_plant.cc',
- 'drivetrain_dog_motor_plant.cc',
- 'polydrivetrain_cim_plant.cc',
- ],
- hdrs = [
- 'polydrivetrain_dog_motor_plant.h',
- 'drivetrain_dog_motor_plant.h',
- 'polydrivetrain_cim_plant.h',
- ],
- deps = [
- '//frc971/control_loops:state_feedback_loop',
- ],
-)
-
genrule(
name = 'genrule_drivetrain',
visibility = ['//visibility:private'],
@@ -51,47 +12,55 @@
outs = [
'drivetrain_dog_motor_plant.h',
'drivetrain_dog_motor_plant.cc',
+ 'kalman_drivetrain_motor_plant.h',
+ 'kalman_drivetrain_motor_plant.cc',
+ ],
+)
+
+genrule(
+ name = 'genrule_polydrivetrain',
+ visibility = ['//visibility:private'],
+ cmd = '$(location //y2014_bot3/control_loops/python:polydrivetrain) $(OUTS)',
+ tools = [
+ '//y2014_bot3/control_loops/python:polydrivetrain',
+ ],
+ outs = [
+ 'polydrivetrain_dog_motor_plant.h',
+ 'polydrivetrain_dog_motor_plant.cc',
+ 'polydrivetrain_cim_plant.h',
+ 'polydrivetrain_cim_plant.cc',
],
)
cc_library(
- name = 'drivetrain_lib',
- hdrs = [
- 'drivetrain.h',
- ],
+ name = 'polydrivetrain_plants',
srcs = [
- 'drivetrain.cc',
+ 'polydrivetrain_dog_motor_plant.cc',
+ 'drivetrain_dog_motor_plant.cc',
+ 'kalman_drivetrain_motor_plant.cc',
+ ],
+ hdrs = [
+ 'polydrivetrain_dog_motor_plant.h',
+ 'drivetrain_dog_motor_plant.h',
+ 'kalman_drivetrain_motor_plant.h',
],
deps = [
- ':polydrivetrain_plants',
- ':drivetrain_queue',
- '//aos/common/controls:control_loop',
- '//aos/common/controls:polytope',
'//frc971/control_loops:state_feedback_loop',
- '//frc971/control_loops:coerce_goal',
- '//frc971/queues:gyro',
- '//aos/common/logging:queue_logging',
- '//aos/common/logging:matrix_logging',
- '//aos/common:math',
- '//aos/common/util:log_interval',
- '//frc971:shifter_hall_effect',
],
)
-cc_test(
- name = 'drivetrain_lib_test',
+cc_library(
+ name = 'drivetrain_base',
srcs = [
- 'drivetrain_lib_test.cc',
+ 'drivetrain_base.cc',
+ ],
+ hdrs = [
+ 'drivetrain_base.h',
],
deps = [
- '//aos/testing:googletest',
- ':drivetrain_queue',
- ':drivetrain_lib',
- '//aos/common/controls:control_loop_test',
- '//frc971/control_loops:state_feedback_loop',
- '//frc971/queues:gyro',
- '//aos/common:queues',
- '//aos/common/network:team_number',
+ ':polydrivetrain_plants',
+ '//frc971/control_loops/drivetrain:drivetrain_config',
+ '//frc971:shifter_hall_effect',
],
)
@@ -101,8 +70,8 @@
'drivetrain_main.cc',
],
deps = [
- ':drivetrain_lib',
- ':drivetrain_queue',
+ ':drivetrain_base',
'//aos/linux_code:init',
+ '//frc971/control_loops/drivetrain:drivetrain_lib',
],
)
diff --git a/y2014_bot3/control_loops/drivetrain/drivetrain.cc b/y2014_bot3/control_loops/drivetrain/drivetrain.cc
deleted file mode 100644
index 125dd24..0000000
--- a/y2014_bot3/control_loops/drivetrain/drivetrain.cc
+++ /dev/null
@@ -1,571 +0,0 @@
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.h"
-
-#include <stdio.h>
-#include <sched.h>
-#include <cmath>
-#include <memory>
-#include "Eigen/Dense"
-
-#include "aos/common/logging/logging.h"
-#include "aos/common/controls/polytope.h"
-#include "aos/common/commonmath.h"
-#include "aos/common/logging/queue_logging.h"
-#include "aos/common/logging/matrix_logging.h"
-
-#include "frc971/control_loops/state_feedback_loop.h"
-#include "frc971/control_loops/coerce_goal.h"
-#include "y2014_bot3/control_loops/drivetrain/polydrivetrain_cim_plant.h"
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.q.h"
-#include "frc971/queues/gyro.q.h"
-#include "frc971/shifter_hall_effect.h"
-#include "y2014_bot3/control_loops/drivetrain/drivetrain_dog_motor_plant.h"
-#include "y2014_bot3/control_loops/drivetrain/polydrivetrain_dog_motor_plant.h"
-
-using ::frc971::sensors::gyro_reading;
-
-namespace y2014_bot3 {
-namespace control_loops {
-
-class DrivetrainMotorsSS {
- public:
- class LimitedDrivetrainLoop : public StateFeedbackLoop<4, 2, 2> {
- public:
- LimitedDrivetrainLoop(StateFeedbackLoop<4, 2, 2> &&loop)
- : StateFeedbackLoop<4, 2, 2>(::std::move(loop)),
- U_Poly_((Eigen::Matrix<double, 4, 2>() << 1, 0, -1, 0, 0, 1, 0, -1)
- .finished(),
- (Eigen::Matrix<double, 4, 1>() << 12.0, 12.0, 12.0, 12.0)
- .finished()) {
- ::aos::controls::HPolytope<0>::Init();
- T << 1, -1, 1, 1;
- T_inverse = T.inverse();
- }
-
- bool output_was_capped() const { return output_was_capped_; }
-
- private:
- virtual void CapU() {
- const Eigen::Matrix<double, 4, 1> error = R() - X_hat();
-
- if (::std::abs(U(0, 0)) > 12.0 || ::std::abs(U(1, 0)) > 12.0) {
- mutable_U() =
- U() * 12.0 / ::std::max(::std::abs(U(0, 0)), ::std::abs(U(1, 0)));
- LOG_MATRIX(DEBUG, "U is now", U());
- // TODO(Austin): Figure out why the polytope stuff wasn't working and
- // remove this hack.
- output_was_capped_ = true;
- return;
-
- LOG_MATRIX(DEBUG, "U at start", U());
- LOG_MATRIX(DEBUG, "R at start", R());
- LOG_MATRIX(DEBUG, "Xhat at start", X_hat());
-
- Eigen::Matrix<double, 2, 2> position_K;
- position_K << K(0, 0), K(0, 2), K(1, 0), K(1, 2);
- Eigen::Matrix<double, 2, 2> velocity_K;
- velocity_K << K(0, 1), K(0, 3), K(1, 1), K(1, 3);
-
- Eigen::Matrix<double, 2, 1> position_error;
- position_error << error(0, 0), error(2, 0);
- const auto drive_error = T_inverse * position_error;
- Eigen::Matrix<double, 2, 1> velocity_error;
- velocity_error << error(1, 0), error(3, 0);
- LOG_MATRIX(DEBUG, "error", error);
-
- const auto &poly = U_Poly_;
- const Eigen::Matrix<double, 4, 2> pos_poly_H =
- poly.H() * position_K * T;
- const Eigen::Matrix<double, 4, 1> pos_poly_k =
- poly.k() - poly.H() * velocity_K * velocity_error;
- const ::aos::controls::HPolytope<2> pos_poly(pos_poly_H, pos_poly_k);
-
- Eigen::Matrix<double, 2, 1> adjusted_pos_error;
- {
- const auto &P = drive_error;
-
- Eigen::Matrix<double, 1, 2> L45;
- L45 << ::aos::sign(P(1, 0)), -::aos::sign(P(0, 0));
- const double w45 = 0;
-
- Eigen::Matrix<double, 1, 2> LH;
- if (::std::abs(P(0, 0)) > ::std::abs(P(1, 0))) {
- LH << 0, 1;
- } else {
- LH << 1, 0;
- }
- const double wh = LH.dot(P);
-
- Eigen::Matrix<double, 2, 2> standard;
- standard << L45, LH;
- Eigen::Matrix<double, 2, 1> W;
- W << w45, wh;
- const Eigen::Matrix<double, 2, 1> intersection =
- standard.inverse() * W;
-
- bool is_inside_h;
- const auto adjusted_pos_error_h = frc971::control_loops::DoCoerceGoal(
- pos_poly, LH, wh, drive_error, &is_inside_h);
- const auto adjusted_pos_error_45 =
- frc971::control_loops::DoCoerceGoal(pos_poly, L45, w45,
- intersection, nullptr);
- if (pos_poly.IsInside(intersection)) {
- adjusted_pos_error = adjusted_pos_error_h;
- } else {
- if (is_inside_h) {
- if (adjusted_pos_error_h.norm() > adjusted_pos_error_45.norm()) {
- adjusted_pos_error = adjusted_pos_error_h;
- } else {
- adjusted_pos_error = adjusted_pos_error_45;
- }
- } else {
- adjusted_pos_error = adjusted_pos_error_45;
- }
- }
- }
-
- LOG_MATRIX(DEBUG, "adjusted_pos_error", adjusted_pos_error);
- mutable_U() =
- velocity_K * velocity_error + position_K * T * adjusted_pos_error;
- LOG_MATRIX(DEBUG, "U is now", U());
- } else {
- output_was_capped_ = false;
- }
- }
-
- const ::aos::controls::HPolytope<2> U_Poly_;
- Eigen::Matrix<double, 2, 2> T, T_inverse;
- bool output_was_capped_ = false;
- };
-
- DrivetrainMotorsSS()
- : loop_(new LimitedDrivetrainLoop(
- ::y2014_bot3::control_loops::drivetrain::MakeDrivetrainLoop())),
- filtered_offset_(0.0),
- gyro_(0.0),
- left_goal_(0.0),
- right_goal_(0.0),
- raw_left_(0.0),
- raw_right_(0.0) {
- // Low gear on both.
- loop_->set_controller_index(0);
- }
-
- void SetGoal(double left, double left_velocity, double right,
- double right_velocity) {
- left_goal_ = left;
- right_goal_ = right;
- loop_->mutable_R() << left, left_velocity, right, right_velocity;
- }
- void SetRawPosition(double left, double right) {
- raw_right_ = right;
- raw_left_ = left;
- Eigen::Matrix<double, 2, 1> Y;
- Y << left + filtered_offset_, right - filtered_offset_;
- loop_->Correct(Y);
- }
- void SetPosition(double left, double right, double gyro) {
- // Decay the offset quickly because this gyro is great.
- const double offset = (right - left - gyro * kDrivetrainTurnWidth) / 2.0;
- filtered_offset_ = 0.25 * offset + 0.75 * filtered_offset_;
- gyro_ = gyro;
- SetRawPosition(left, right);
- }
-
- void SetExternalMotors(double left_voltage, double right_voltage) {
- loop_->mutable_U() << left_voltage, right_voltage;
- }
-
- void Update(bool stop_motors, bool enable_control_loop) {
- if (enable_control_loop) {
- loop_->Update(stop_motors);
- } else {
- if (stop_motors) {
- loop_->mutable_U().setZero();
- loop_->mutable_U_uncapped().setZero();
- }
- loop_->UpdateObserver(loop_->U());
- }
- ::Eigen::Matrix<double, 4, 1> E = loop_->R() - loop_->X_hat();
- LOG_MATRIX(DEBUG, "E", E);
- }
-
- double GetEstimatedRobotSpeed() const {
- // lets just call the average of left and right velocities close enough
- return (loop_->X_hat(1, 0) + loop_->X_hat(3, 0)) / 2;
- }
-
- double GetEstimatedLeftEncoder() const { return loop_->X_hat(0, 0); }
-
- double GetEstimatedRightEncoder() const { return loop_->X_hat(2, 0); }
-
- bool OutputWasCapped() const { return loop_->output_was_capped(); }
-
- void SendMotors(DrivetrainQueue::Output *output) const {
- if (output) {
- output->left_voltage = loop_->U(0, 0);
- output->right_voltage = loop_->U(1, 0);
- output->left_high = false;
- output->right_high = false;
- }
- }
-
- const LimitedDrivetrainLoop &loop() const { return *loop_; }
-
- private:
- ::std::unique_ptr<LimitedDrivetrainLoop> loop_;
-
- double filtered_offset_;
- double gyro_;
- double left_goal_;
- double right_goal_;
- double raw_left_;
- double raw_right_;
-};
-
-class PolyDrivetrain {
- public:
- enum Gear { HIGH, LOW };
- // Stall Torque in N m
- static constexpr double kStallTorque = 2.42;
- // Stall Current in Amps
- static constexpr double kStallCurrent = 133.0;
- // Free Speed in RPM. Used number from last year.
- static constexpr double kFreeSpeed = 4650.0;
- // Free Current in Amps
- static constexpr double kFreeCurrent = 2.7;
- // Moment of inertia of the drivetrain in kg m^2
- // Just borrowed from last year.
- static constexpr double J = 10;
- // Mass of the robot, in kg.
- static constexpr double m = 68;
- // Radius of the robot, in meters (from last year).
- static constexpr double rb = 0.66675 / 2.0;
- static constexpr double kWheelRadius = 0.04445;
- // Resistance of the motor, divided by the number of motors.
- static constexpr double kR =
- (12.0 / kStallCurrent / 4 + 0.03) / (0.93 * 0.93);
- // Motor velocity constant
- static constexpr double Kv =
- ((kFreeSpeed / 60.0 * 2.0 * M_PI) / (12.0 - kR * kFreeCurrent));
- // Torque constant
- static constexpr double Kt = kStallTorque / kStallCurrent;
-
- PolyDrivetrain()
- : U_Poly_((Eigen::Matrix<double, 4, 2>() << /*[[*/ 1, 0 /*]*/,
- /*[*/ -1, 0 /*]*/,
- /*[*/ 0, 1 /*]*/,
- /*[*/ 0, -1 /*]]*/).finished(),
- (Eigen::Matrix<double, 4, 1>() << /*[[*/ 12 /*]*/,
- /*[*/ 12 /*]*/,
- /*[*/ 12 /*]*/,
- /*[*/ 12 /*]]*/).finished()),
- loop_(new StateFeedbackLoop<2, 2, 2>(
- ::y2014_bot3::control_loops::MakeVelocityDrivetrainLoop())),
- ttrust_(1.1),
- wheel_(0.0),
- throttle_(0.0),
- quickturn_(false),
- stale_count_(0),
- position_time_delta_(0.01),
- left_gear_(LOW),
- right_gear_(LOW),
- counter_(0) {
- last_position_.Zero();
- position_.Zero();
- }
-
- static double MotorSpeed(bool high_gear, double velocity) {
- if (high_gear) {
- return velocity / kDrivetrainHighGearRatio / kWheelRadius;
- } else {
- return velocity / kDrivetrainLowGearRatio / kWheelRadius;
- }
- }
-
- void SetGoal(double wheel, double throttle, bool quickturn, bool highgear) {
- const double kWheelNonLinearity = 0.5;
- // Apply a sin function that's scaled to make it feel better.
- const double angular_range = M_PI_2 * kWheelNonLinearity;
-
- quickturn_ = quickturn;
- wheel_ = sin(angular_range * wheel) / sin(angular_range);
- wheel_ = sin(angular_range * wheel_) / sin(angular_range);
- if (!quickturn_) {
- wheel_ *= 1.5;
- }
-
- static const double kThrottleDeadband = 0.05;
- if (::std::abs(throttle) < kThrottleDeadband) {
- throttle_ = 0;
- } else {
- throttle_ = copysign((::std::abs(throttle) - kThrottleDeadband) /
- (1.0 - kThrottleDeadband),
- throttle);
- }
-
- Gear requested_gear = highgear ? HIGH : LOW;
- left_gear_ = right_gear_ = requested_gear;
- }
-
- void SetPosition(const DrivetrainQueue::Position *position) {
- if (position == NULL) {
- ++stale_count_;
- } else {
- last_position_ = position_;
- position_ = *position;
- position_time_delta_ = (stale_count_ + 1) * 0.01;
- stale_count_ = 0;
- }
- }
-
- double FilterVelocity(double throttle) {
- const Eigen::Matrix<double, 2, 2> FF =
- loop_->B().inverse() *
- (Eigen::Matrix<double, 2, 2>::Identity() - loop_->A());
-
- constexpr int kHighGearController = 3;
- const Eigen::Matrix<double, 2, 2> FF_high =
- loop_->controller(kHighGearController).plant.B().inverse() *
- (Eigen::Matrix<double, 2, 2>::Identity() -
- loop_->controller(kHighGearController).plant.A());
-
- ::Eigen::Matrix<double, 1, 2> FF_sum = FF.colwise().sum();
- int min_FF_sum_index;
- const double min_FF_sum = FF_sum.minCoeff(&min_FF_sum_index);
- const double min_K_sum = loop_->K().col(min_FF_sum_index).sum();
- const double high_min_FF_sum = FF_high.col(0).sum();
-
- const double adjusted_ff_voltage = ::aos::Clip(
- throttle * 12.0 * min_FF_sum / high_min_FF_sum, -12.0, 12.0);
- return (adjusted_ff_voltage +
- ttrust_ * min_K_sum * (loop_->X_hat(0, 0) + loop_->X_hat(1, 0)) /
- 2.0) /
- (ttrust_ * min_K_sum + min_FF_sum);
- }
-
- double MaxVelocity() {
- const Eigen::Matrix<double, 2, 2> FF =
- loop_->B().inverse() *
- (Eigen::Matrix<double, 2, 2>::Identity() - loop_->A());
-
- constexpr int kHighGearController = 3;
- const Eigen::Matrix<double, 2, 2> FF_high =
- loop_->controller(kHighGearController).plant.B().inverse() *
- (Eigen::Matrix<double, 2, 2>::Identity() -
- loop_->controller(kHighGearController).plant.A());
-
- ::Eigen::Matrix<double, 1, 2> FF_sum = FF.colwise().sum();
- int min_FF_sum_index;
- const double min_FF_sum = FF_sum.minCoeff(&min_FF_sum_index);
- // const double min_K_sum = loop_->K().col(min_FF_sum_index).sum();
- const double high_min_FF_sum = FF_high.col(0).sum();
-
- const double adjusted_ff_voltage =
- ::aos::Clip(12.0 * min_FF_sum / high_min_FF_sum, -12.0, 12.0);
- return adjusted_ff_voltage / min_FF_sum;
- }
-
- void Update() {
- // TODO(austin): Observer for the current velocity instead of difference
- // calculations.
- ++counter_;
-
- const double current_left_velocity =
- (position_.left_encoder - last_position_.left_encoder) /
- position_time_delta_;
- const double current_right_velocity =
- (position_.right_encoder - last_position_.right_encoder) /
- position_time_delta_;
- const double left_motor_speed = MotorSpeed(left_gear_ == HIGH,
- current_left_velocity);
- const double right_motor_speed = MotorSpeed(right_gear_ == HIGH,
- current_right_velocity);
-
- {
- CIMLogging logging;
-
- // Reset the CIM model to the current conditions to be ready for when we
- // shift.
- logging.left_in_gear = true;
- logging.left_motor_speed = left_motor_speed;
- logging.left_velocity = current_left_velocity;
-
- logging.right_in_gear = true;
- logging.right_motor_speed = right_motor_speed;
- logging.right_velocity = current_right_velocity;
-
- LOG_STRUCT(DEBUG, "currently", logging);
- }
-
- {
- // FF * X = U (steady state)
- const Eigen::Matrix<double, 2, 2> FF =
- loop_->B().inverse() *
- (Eigen::Matrix<double, 2, 2>::Identity() - loop_->A());
-
- // Invert the plant to figure out how the velocity filter would have to
- // work
- // out in order to filter out the forwards negative inertia.
- // This math assumes that the left and right power and velocity are
- // equals,
- // and that the plant is the same on the left and right.
- const double fvel = FilterVelocity(throttle_);
-
- const double sign_svel = wheel_ * ((fvel > 0.0) ? 1.0 : -1.0);
- double steering_velocity;
- if (quickturn_) {
- steering_velocity = wheel_ * MaxVelocity();
- } else {
- steering_velocity = ::std::abs(fvel) * wheel_;
- }
- const double left_velocity = fvel - steering_velocity;
- const double right_velocity = fvel + steering_velocity;
- LOG(DEBUG, "l=%f r=%f\n", left_velocity, right_velocity);
-
- // Integrate velocity to get the position.
- // This position is used to get integral control.
- loop_->mutable_R() << left_velocity, right_velocity;
-
- if (!quickturn_) {
- // K * R = w
- Eigen::Matrix<double, 1, 2> equality_k;
- equality_k << 1 + sign_svel, -(1 - sign_svel);
- const double equality_w = 0.0;
-
- // Construct a constraint on R by manipulating the constraint on U
- ::aos::controls::HPolytope<2> R_poly = ::aos::controls::HPolytope<2>(
- U_Poly_.H() * (loop_->K() + FF),
- U_Poly_.k() + U_Poly_.H() * loop_->K() * loop_->X_hat());
-
- // Limit R back inside the box.
- loop_->mutable_R() = frc971::control_loops::CoerceGoal(
- R_poly, equality_k, equality_w, loop_->R());
- }
-
- const Eigen::Matrix<double, 2, 1> FF_volts = FF * loop_->R();
- const Eigen::Matrix<double, 2, 1> U_ideal =
- loop_->K() * (loop_->R() - loop_->X_hat()) + FF_volts;
-
- for (int i = 0; i < 2; i++) {
- loop_->mutable_U()[i] = ::aos::Clip(U_ideal[i], -12, 12);
- }
-
- // TODO(austin): Model this better.
- // TODO(austin): Feedback?
- loop_->mutable_X_hat() =
- loop_->A() * loop_->X_hat() + loop_->B() * loop_->U();
- }
- }
-
- void SendMotors(DrivetrainQueue::Output *output) {
- if (output != NULL) {
- output->left_voltage = loop_->U(0, 0);
- output->right_voltage = loop_->U(1, 0);
- output->left_high = left_gear_ == HIGH;
- output->right_high = right_gear_ == HIGH;
- }
- }
-
- private:
- const ::aos::controls::HPolytope<2> U_Poly_;
-
- ::std::unique_ptr<StateFeedbackLoop<2, 2, 2>> loop_;
-
- const double ttrust_;
- double wheel_;
- double throttle_;
- bool quickturn_;
- int stale_count_;
- double position_time_delta_;
- Gear left_gear_;
- Gear right_gear_;
- DrivetrainQueue::Position last_position_;
- DrivetrainQueue::Position position_;
- int counter_;
-};
-
-constexpr double PolyDrivetrain::kStallTorque;
-constexpr double PolyDrivetrain::kStallCurrent;
-constexpr double PolyDrivetrain::kFreeSpeed;
-constexpr double PolyDrivetrain::kFreeCurrent;
-constexpr double PolyDrivetrain::J;
-constexpr double PolyDrivetrain::m;
-constexpr double PolyDrivetrain::rb;
-constexpr double PolyDrivetrain::kWheelRadius;
-constexpr double PolyDrivetrain::kR;
-constexpr double PolyDrivetrain::Kv;
-constexpr double PolyDrivetrain::Kt;
-
-void DrivetrainLoop::RunIteration(const DrivetrainQueue::Goal *goal,
- const DrivetrainQueue::Position *position,
- DrivetrainQueue::Output *output,
- DrivetrainQueue::Status *status) {
- // TODO(aschuh): These should be members of the class.
- static DrivetrainMotorsSS dt_closedloop;
- static PolyDrivetrain dt_openloop;
-
- bool bad_pos = false;
- if (position == nullptr) {
- LOG_INTERVAL(no_position_);
- bad_pos = true;
- }
- no_position_.Print();
-
- bool control_loop_driving = false;
- if (goal) {
- double wheel = goal->steering;
- double throttle = goal->throttle;
- bool quickturn = goal->quickturn;
- bool highgear = goal->highgear;
-
- control_loop_driving = goal->control_loop_driving;
- double left_goal = goal->left_goal;
- double right_goal = goal->right_goal;
-
- dt_closedloop.SetGoal(left_goal, goal->left_velocity_goal, right_goal,
- goal->right_velocity_goal);
- dt_openloop.SetGoal(wheel, throttle, quickturn, highgear);
- }
-
- if (!bad_pos) {
- const double left_encoder = position->left_encoder;
- const double right_encoder = position->right_encoder;
- if (gyro_reading.FetchLatest()) {
- LOG_STRUCT(DEBUG, "using", *gyro_reading.get());
- dt_closedloop.SetPosition(left_encoder, right_encoder,
- gyro_reading->angle);
- } else {
- dt_closedloop.SetRawPosition(left_encoder, right_encoder);
- }
- }
- dt_openloop.SetPosition(position);
- dt_openloop.Update();
-
- if (control_loop_driving) {
- dt_closedloop.Update(output == NULL, true);
- dt_closedloop.SendMotors(output);
- } else {
- dt_openloop.SendMotors(output);
- if (output) {
- dt_closedloop.SetExternalMotors(output->left_voltage,
- output->right_voltage);
- }
- dt_closedloop.Update(output == NULL, false);
- }
-
- // set the output status of the control loop state
- if (status) {
- status->robot_speed = dt_closedloop.GetEstimatedRobotSpeed();
- status->estimated_left_position = dt_closedloop.GetEstimatedLeftEncoder();
- status->estimated_right_position = dt_closedloop.GetEstimatedRightEncoder();
-
- status->estimated_left_velocity = dt_closedloop.loop().X_hat(1, 0);
- status->estimated_right_velocity = dt_closedloop.loop().X_hat(3, 0);
- status->output_was_capped = dt_closedloop.OutputWasCapped();
- status->uncapped_left_voltage = dt_closedloop.loop().U_uncapped(0, 0);
- status->uncapped_right_voltage = dt_closedloop.loop().U_uncapped(1, 0);
- }
-}
-
-} // namespace control_loops
-} // namespace y2014_bot3
diff --git a/y2014_bot3/control_loops/drivetrain/drivetrain.h b/y2014_bot3/control_loops/drivetrain/drivetrain.h
deleted file mode 100644
index dfb7269..0000000
--- a/y2014_bot3/control_loops/drivetrain/drivetrain.h
+++ /dev/null
@@ -1,58 +0,0 @@
-#ifndef Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_H_
-#define Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_H_
-
-#include "Eigen/Dense"
-
-#include "aos/common/controls/polytope.h"
-#include "aos/common/controls/control_loop.h"
-#include "aos/common/controls/polytope.h"
-#include "aos/common/util/log_interval.h"
-
-#include "frc971/shifter_hall_effect.h"
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.q.h"
-
-namespace y2014_bot3 {
-namespace control_loops {
-
-// Constants
-// TODO(comran): Get actual constants.
-constexpr double kDrivetrainTurnWidth = 0.63;
-constexpr double kDrivetrainEncoderRatio = 18.0 / 44.0;
-constexpr double kDrivetrainHighGearRatio =
- kDrivetrainEncoderRatio * 18.0 / 60.0;
-constexpr double kDrivetrainLowGearRatio = kDrivetrainHighGearRatio;
-const ::frc971::constants::ShifterHallEffect kDrivetrainRightShifter{
- 555, 657, 660, 560, 0.2, 0.7};
-const ::frc971::constants::ShifterHallEffect kDrivetrainLeftShifter{
- 555, 660, 644, 552, 0.2, 0.7};
-// End constants
-
-class DrivetrainLoop
- : public aos::controls::ControlLoop<control_loops::DrivetrainQueue> {
- public:
- // Constructs a control loop which can take a Drivetrain or defaults to the
- // drivetrain at y2014_bot3::control_loops::drivetrain
- explicit DrivetrainLoop(control_loops::DrivetrainQueue *my_drivetrain =
- &control_loops::drivetrain_queue)
- : aos::controls::ControlLoop<control_loops::DrivetrainQueue>(
- my_drivetrain) {
- ::aos::controls::HPolytope<0>::Init();
- }
-
- protected:
- // Executes one cycle of the control loop.
- virtual void RunIteration(
- const control_loops::DrivetrainQueue::Goal *goal,
- const control_loops::DrivetrainQueue::Position *position,
- control_loops::DrivetrainQueue::Output *output,
- control_loops::DrivetrainQueue::Status *status);
-
- typedef ::aos::util::SimpleLogInterval SimpleLogInterval;
- SimpleLogInterval no_position_ = SimpleLogInterval(
- ::aos::time::Time::InSeconds(0.25), WARNING, "no position");
-};
-
-} // namespace control_loops
-} // namespace y2014_bot3
-
-#endif // Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_H_
diff --git a/y2014_bot3/control_loops/drivetrain/drivetrain.q b/y2014_bot3/control_loops/drivetrain/drivetrain.q
deleted file mode 100644
index 1b97f81..0000000
--- a/y2014_bot3/control_loops/drivetrain/drivetrain.q
+++ /dev/null
@@ -1,104 +0,0 @@
-package y2014_bot3.control_loops;
-
-import "aos/common/controls/control_loops.q";
-
-// For logging information about the state of the shifters.
-struct CIMLogging {
- // Whether the code thinks the left side is currently in gear.
- bool left_in_gear;
- // Whether the code thinks the right side is currently in gear.
- bool right_in_gear;
- // The velocity in rad/s (positive forward) the code thinks the left motor
- // is currently spinning at.
- double left_motor_speed;
- // The velocity in rad/s (positive forward) the code thinks the right motor
- // is currently spinning at.
- double right_motor_speed;
- // The velocity estimate for the left side of the robot in m/s (positive
- // forward) used for shifting.
- double left_velocity;
- // The velocity estimate for the right side of the robot in m/s (positive
- // forward) used for shifting.
- double right_velocity;
-};
-
-queue_group DrivetrainQueue {
- implements aos.control_loops.ControlLoop;
-
- message Goal {
- // Position of the steering wheel (positive = turning left when going
- // forwards).
- double steering;
- // Position of the throttle (positive forwards).
- double throttle;
- // True to shift into high, false to shift into low.
- bool highgear;
- // True to activate quickturn.
- bool quickturn;
- // True to have the closed-loop controller take over.
- bool control_loop_driving;
- // Position goal for the left side in meters when the closed-loop controller
- // is active.
- double left_goal;
- // Velocity goal for the left side in m/s when the closed-loop controller
- // is active.
- double left_velocity_goal;
- // Position goal for the right side in meters when the closed-loop
- // controller is active.
- double right_goal;
- // Velocity goal for the right side in m/s when the closed-loop controller
- // is active.
- double right_velocity_goal;
- };
-
- message Position {
- // Relative position of the left side in meters.
- double left_encoder;
- // Relative position of the right side in meters.
- double right_encoder;
- // The speed in m/s of the left side from the most recent encoder pulse,
- // or 0 if there was no edge within the last 5ms.
- double left_speed;
- // The speed in m/s of the right side from the most recent encoder pulse,
- // or 0 if there was no edge within the last 5ms.
- double right_speed;
- };
-
- message Output {
- // Voltage to send to the left motor(s).
- double left_voltage;
- // Voltage to send to the right motor(s).
- double right_voltage;
- // True to set the left shifter piston for high gear.
- bool left_high;
- // True to set the right shifter piston for high gear.
- bool right_high;
- };
-
- message Status {
- // Estimated speed of the center of the robot in m/s (positive forwards).
- double robot_speed;
- // Estimated relative position of the left side in meters.
- double estimated_left_position;
- // Estimated relative position of the right side in meters.
- double estimated_right_position;
- // Estimated velocity of the left side in m/s.
- double estimated_left_velocity;
- // Estimated velocity of the right side in m/s.
- double estimated_right_velocity;
-
- // The voltage we wanted to send to the left side last cycle.
- double uncapped_left_voltage;
- // The voltage we wanted to send to the right side last cycle.
- double uncapped_right_voltage;
- // True if the output voltage was capped last cycle.
- bool output_was_capped;
- };
-
- queue Goal goal;
- queue Position position;
- queue Output output;
- queue Status status;
-};
-
-queue_group DrivetrainQueue drivetrain_queue;
diff --git a/y2014_bot3/control_loops/drivetrain/drivetrain_base.cc b/y2014_bot3/control_loops/drivetrain/drivetrain_base.cc
new file mode 100644
index 0000000..bca3f24
--- /dev/null
+++ b/y2014_bot3/control_loops/drivetrain/drivetrain_base.cc
@@ -0,0 +1,47 @@
+#include "y2014_bot3/control_loops/drivetrain/drivetrain_base.h"
+
+#include "frc971/control_loops/drivetrain/drivetrain_config.h"
+
+#include "frc971/control_loops/state_feedback_loop.h"
+#include "y2014_bot3/control_loops/drivetrain/drivetrain_dog_motor_plant.h"
+#include "y2014_bot3/control_loops/drivetrain/polydrivetrain_dog_motor_plant.h"
+#include "y2014_bot3/control_loops/drivetrain/kalman_drivetrain_motor_plant.h"
+
+using ::frc971::control_loops::drivetrain::DrivetrainConfig;
+
+namespace y2014_bot3 {
+namespace control_loops {
+namespace drivetrain {
+
+using ::frc971::constants::ShifterHallEffect;
+
+const ShifterHallEffect kThreeStateDriveShifter{0.0, 0.0, 0.0, 0.0, 0.25, 0.75};
+
+const DrivetrainConfig &GetDrivetrainConfig() {
+ static DrivetrainConfig kDrivetrainConfig{
+ ::frc971::control_loops::drivetrain::ShifterType::SIMPLE_SHIFTER,
+ ::frc971::control_loops::drivetrain::LoopType::OPEN_LOOP,
+
+ ::y2014_bot3::control_loops::drivetrain::MakeDrivetrainLoop,
+ ::y2014_bot3::control_loops::drivetrain::MakeVelocityDrivetrainLoop,
+ ::y2014_bot3::control_loops::drivetrain::MakeKFDrivetrainLoop,
+
+ drivetrain::kDt,
+ drivetrain::kRobotRadius,
+ drivetrain::kWheelRadius,
+ drivetrain::kV,
+
+ drivetrain::kHighGearRatio,
+ drivetrain::kLowGearRatio,
+
+ // No shifter sensors, so we could put anything for the things below.
+ kThreeStateDriveShifter,
+ kThreeStateDriveShifter,
+ false};
+
+ return kDrivetrainConfig;
+};
+
+} // namespace drivetrain
+} // namespace control_loops
+} // namespace y2014_bot3
diff --git a/y2014_bot3/control_loops/drivetrain/drivetrain_base.h b/y2014_bot3/control_loops/drivetrain/drivetrain_base.h
new file mode 100644
index 0000000..d2e54f9
--- /dev/null
+++ b/y2014_bot3/control_loops/drivetrain/drivetrain_base.h
@@ -0,0 +1,20 @@
+#ifndef Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_DRIVETRAIN_BASE_H_
+#define Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_DRIVETRAIN_BASE_H_
+
+#include "frc971/control_loops/drivetrain/drivetrain_config.h"
+
+namespace y2014_bot3 {
+namespace control_loops {
+namespace drivetrain {
+
+const double kDrivetrainEncoderRatio =
+ (17.0 / 50.0) /*output reduction*/ * (24.0 / 64.0) /*encoder gears*/;
+
+const ::frc971::control_loops::drivetrain::DrivetrainConfig &
+GetDrivetrainConfig();
+
+} // namespace drivetrain
+} // namespace control_loops
+} // namespace y2014_bot3
+
+#endif // Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_DRIVETRAIN_BASE_H_
diff --git a/y2014_bot3/control_loops/drivetrain/drivetrain_constants.h b/y2014_bot3/control_loops/drivetrain/drivetrain_constants.h
deleted file mode 100644
index 28848b0..0000000
--- a/y2014_bot3/control_loops/drivetrain/drivetrain_constants.h
+++ /dev/null
@@ -1,26 +0,0 @@
-#ifndef BOT3_CONTROL_LOOPS_DRIVETRAIN_CONSTANTS_H_
-#define BOT3_CONTROL_LOOPS_DRIVETRAIN_CONSTANTS_H_
-
-#include "bot3/shifter_hall_effect.h"
-
-namespace bot3 {
-namespace control_loops {
-
-constexpr constants::ShifterHallEffect kBot3LeftDriveShifter =
- {426, 171, 0.6, 0.47};
-constexpr constants::ShifterHallEffect kBot3RightDriveShifter =
- {424, 172, 0.62, 0.55};
-
-constexpr double kBot3TurnWidth = 0.5;
-constexpr double kBot3DrivetrainDoneDistance = 0.02;
-
-constexpr double kBot3LowGearRatio = 14.0 / 60.0 * 17.0 / 50.0;
-constexpr double kBot3HighGearRatio = 30.0 / 44.0 * 17.0 / 50.0;
-
-// If this is true, we don't use the analog hall effects for shifting.
-constexpr bool kBot3SimpleShifting = true;
-
-} // control_loops
-} // bot3
-
-#endif
diff --git a/y2014_bot3/control_loops/drivetrain/drivetrain_lib_test.cc b/y2014_bot3/control_loops/drivetrain/drivetrain_lib_test.cc
deleted file mode 100644
index 3953951..0000000
--- a/y2014_bot3/control_loops/drivetrain/drivetrain_lib_test.cc
+++ /dev/null
@@ -1,295 +0,0 @@
-#include <unistd.h>
-
-#include <memory>
-
-#include "gtest/gtest.h"
-#include "aos/common/network/team_number.h"
-#include "aos/common/controls/polytope.h"
-#include "aos/common/controls/control_loop_test.h"
-
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.q.h"
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.h"
-#include "frc971/control_loops/state_feedback_loop.h"
-#include "frc971/control_loops/coerce_goal.h"
-#include "y2014_bot3/control_loops/drivetrain/drivetrain_dog_motor_plant.h"
-#include "frc971/queues/gyro.q.h"
-
-namespace y2014_bot3 {
-namespace control_loops {
-namespace testing {
-
-class Environment : public ::testing::Environment {
- public:
- virtual ~Environment() {}
- // how to set up the environment.
- virtual void SetUp() {
- aos::controls::HPolytope<0>::Init();
- }
-};
-::testing::Environment* const holder_env =
- ::testing::AddGlobalTestEnvironment(new Environment);
-
-class TeamNumberEnvironment : public ::testing::Environment {
- public:
- // Override this to define how to set up the environment.
- virtual void SetUp() { aos::network::OverrideTeamNumber(971); }
-};
-
-::testing::Environment* const team_number_env =
- ::testing::AddGlobalTestEnvironment(new TeamNumberEnvironment);
-
-// Class which simulates the drivetrain and sends out queue messages containing
-// the position.
-class DrivetrainSimulation {
- public:
- // Constructs a motor simulation.
- // TODO(aschuh) Do we want to test the clutch one too?
- DrivetrainSimulation()
- : drivetrain_plant_(
- new StateFeedbackPlant<4, 2, 2>(drivetrain::MakeDrivetrainPlant())),
- my_drivetrain_queue_(".y2014_bot3.control_loops.drivetrain",
- 0x8a8dde77, ".y2014_bot3.control_loops.drivetrain.goal",
- ".y2014_bot3.control_loops.drivetrain.position",
- ".y2014_bot3.control_loops.drivetrain.output",
- ".y2014_bot3.control_loops.drivetrain.status") {
- Reinitialize();
- }
-
- // Resets the plant.
- void Reinitialize() {
- drivetrain_plant_->mutable_X(0, 0) = 0.0;
- drivetrain_plant_->mutable_X(1, 0) = 0.0;
- drivetrain_plant_->mutable_Y() =
- drivetrain_plant_->C() * drivetrain_plant_->X();
- last_left_position_ = drivetrain_plant_->Y(0, 0);
- last_right_position_ = drivetrain_plant_->Y(1, 0);
- }
-
- // Returns the position of the drivetrain.
- double GetLeftPosition() const { return drivetrain_plant_->Y(0, 0); }
- double GetRightPosition() const { return drivetrain_plant_->Y(1, 0); }
-
- // Sends out the position queue messages.
- void SendPositionMessage() {
- const double left_encoder = GetLeftPosition();
- const double right_encoder = GetRightPosition();
-
- ::aos::ScopedMessagePtr<control_loops::DrivetrainQueue::Position> position =
- my_drivetrain_queue_.position.MakeMessage();
- position->left_encoder = left_encoder;
- position->right_encoder = right_encoder;
- position.Send();
- }
-
- // Simulates the drivetrain moving for one timestep.
- void Simulate() {
- last_left_position_ = drivetrain_plant_->Y(0, 0);
- last_right_position_ = drivetrain_plant_->Y(1, 0);
- EXPECT_TRUE(my_drivetrain_queue_.output.FetchLatest());
- drivetrain_plant_->mutable_U() << my_drivetrain_queue_.output->left_voltage,
- my_drivetrain_queue_.output->right_voltage;
- drivetrain_plant_->Update();
- }
-
- ::std::unique_ptr<StateFeedbackPlant<4, 2, 2>> drivetrain_plant_;
- private:
- DrivetrainQueue my_drivetrain_queue_;
- double last_left_position_;
- double last_right_position_;
-};
-
-class DrivetrainTest : public ::aos::testing::ControlLoopTest {
- protected:
- // Create a new instance of the test queue so that it invalidates the queue
- // that it points to. Otherwise, we will have a pointer to shared memory that
- // is no longer valid.
- DrivetrainQueue my_drivetrain_queue_;
-
- // Create a loop and simulation plant.
- DrivetrainLoop drivetrain_motor_;
- DrivetrainSimulation drivetrain_motor_plant_;
-
- DrivetrainTest() : my_drivetrain_queue_(".y2014_bot3.control_loops.drivetrain",
- 0x8a8dde77,
- ".y2014_bot3.control_loops.drivetrain.goal",
- ".y2014_bot3.control_loops.drivetrain.position",
- ".y2014_bot3.control_loops.drivetrain.output",
- ".y2014_bot3.control_loops.drivetrain.status"),
- drivetrain_motor_(&my_drivetrain_queue_),
- drivetrain_motor_plant_() {
- ::frc971::sensors::gyro_reading.Clear();
- }
-
- void VerifyNearGoal() {
- my_drivetrain_queue_.goal.FetchLatest();
- my_drivetrain_queue_.position.FetchLatest();
- EXPECT_NEAR(my_drivetrain_queue_.goal->left_goal,
- drivetrain_motor_plant_.GetLeftPosition(),
- 1e-2);
- EXPECT_NEAR(my_drivetrain_queue_.goal->right_goal,
- drivetrain_motor_plant_.GetRightPosition(),
- 1e-2);
- }
-
- virtual ~DrivetrainTest() {
- ::frc971::sensors::gyro_reading.Clear();
- }
-};
-
-// Tests that the drivetrain converges on a goal.
-TEST_F(DrivetrainTest, ConvergesCorrectly) {
- my_drivetrain_queue_.goal.MakeWithBuilder().control_loop_driving(true)
- .left_goal(-1.0)
- .right_goal(1.0).Send();
- for (int i = 0; i < 200; ++i) {
- drivetrain_motor_plant_.SendPositionMessage();
- drivetrain_motor_.Iterate();
- drivetrain_motor_plant_.Simulate();
- SimulateTimestep(true);
- }
- VerifyNearGoal();
-}
-
-// Tests that it survives disabling.
-TEST_F(DrivetrainTest, SurvivesDisabling) {
- my_drivetrain_queue_.goal.MakeWithBuilder().control_loop_driving(true)
- .left_goal(-1.0)
- .right_goal(1.0).Send();
- for (int i = 0; i < 500; ++i) {
- drivetrain_motor_plant_.SendPositionMessage();
- drivetrain_motor_.Iterate();
- drivetrain_motor_plant_.Simulate();
- if (i > 20 && i < 200) {
- SimulateTimestep(false);
- } else {
- SimulateTimestep(true);
- }
- }
- VerifyNearGoal();
-}
-
-// Tests that never having a goal doesn't break.
-TEST_F(DrivetrainTest, NoGoalStart) {
- for (int i = 0; i < 20; ++i) {
- drivetrain_motor_plant_.SendPositionMessage();
- drivetrain_motor_.Iterate();
- drivetrain_motor_plant_.Simulate();
- }
-}
-
-// Tests that never having a goal, but having driver's station messages, doesn't
-// break.
-TEST_F(DrivetrainTest, NoGoalWithRobotState) {
- for (int i = 0; i < 20; ++i) {
- drivetrain_motor_plant_.SendPositionMessage();
- drivetrain_motor_.Iterate();
- drivetrain_motor_plant_.Simulate();
- SimulateTimestep(true);
- }
-}
-
-::aos::controls::HPolytope<2> MakeBox(double x1_min, double x1_max,
- double x2_min, double x2_max) {
- Eigen::Matrix<double, 4, 2> box_H;
- box_H << /*[[*/ 1.0, 0.0 /*]*/,
- /*[*/-1.0, 0.0 /*]*/,
- /*[*/ 0.0, 1.0 /*]*/,
- /*[*/ 0.0,-1.0 /*]]*/;
- Eigen::Matrix<double, 4, 1> box_k;
- box_k << /*[[*/ x1_max /*]*/,
- /*[*/-x1_min /*]*/,
- /*[*/ x2_max /*]*/,
- /*[*/-x2_min /*]]*/;
- ::aos::controls::HPolytope<2> t_poly(box_H, box_k);
- return t_poly;
-}
-
-class CoerceGoalTest : public ::testing::Test {
- public:
- EIGEN_MAKE_ALIGNED_OPERATOR_NEW
-};
-
-// WHOOOHH!
-TEST_F(CoerceGoalTest, Inside) {
- ::aos::controls::HPolytope<2> box = MakeBox(1, 2, 1, 2);
-
- Eigen::Matrix<double, 1, 2> K;
- K << /*[[*/ 1, -1 /*]]*/;
-
- Eigen::Matrix<double, 2, 1> R;
- R << /*[[*/ 1.5, 1.5 /*]]*/;
-
- Eigen::Matrix<double, 2, 1> output =
- ::frc971::control_loops::CoerceGoal(box, K, 0, R);
-
- EXPECT_EQ(R(0, 0), output(0, 0));
- EXPECT_EQ(R(1, 0), output(1, 0));
-}
-
-TEST_F(CoerceGoalTest, Outside_Inside_Intersect) {
- ::aos::controls::HPolytope<2> box = MakeBox(1, 2, 1, 2);
-
- Eigen::Matrix<double, 1, 2> K;
- K << 1, -1;
-
- Eigen::Matrix<double, 2, 1> R;
- R << 5, 5;
-
- Eigen::Matrix<double, 2, 1> output =
- ::frc971::control_loops::CoerceGoal(box, K, 0, R);
-
- EXPECT_EQ(2.0, output(0, 0));
- EXPECT_EQ(2.0, output(1, 0));
-}
-
-TEST_F(CoerceGoalTest, Outside_Inside_no_Intersect) {
- ::aos::controls::HPolytope<2> box = MakeBox(3, 4, 1, 2);
-
- Eigen::Matrix<double, 1, 2> K;
- K << 1, -1;
-
- Eigen::Matrix<double, 2, 1> R;
- R << 5, 5;
-
- Eigen::Matrix<double, 2, 1> output =
- ::frc971::control_loops::CoerceGoal(box, K, 0, R);
-
- EXPECT_EQ(3.0, output(0, 0));
- EXPECT_EQ(2.0, output(1, 0));
-}
-
-TEST_F(CoerceGoalTest, Middle_Of_Edge) {
- ::aos::controls::HPolytope<2> box = MakeBox(0, 4, 1, 2);
-
- Eigen::Matrix<double, 1, 2> K;
- K << -1, 1;
-
- Eigen::Matrix<double, 2, 1> R;
- R << 5, 5;
-
- Eigen::Matrix<double, 2, 1> output =
- ::frc971::control_loops::CoerceGoal(box, K, 0, R);
-
- EXPECT_EQ(2.0, output(0, 0));
- EXPECT_EQ(2.0, output(1, 0));
-}
-
-TEST_F(CoerceGoalTest, PerpendicularLine) {
- ::aos::controls::HPolytope<2> box = MakeBox(1, 2, 1, 2);
-
- Eigen::Matrix<double, 1, 2> K;
- K << 1, 1;
-
- Eigen::Matrix<double, 2, 1> R;
- R << 5, 5;
-
- Eigen::Matrix<double, 2, 1> output =
- ::frc971::control_loops::CoerceGoal(box, K, 0, R);
-
- EXPECT_EQ(1.0, output(0, 0));
- EXPECT_EQ(1.0, output(1, 0));
-}
-
-} // namespace testing
-} // namespace control_loops
-} // namespace y2014_bot3
diff --git a/y2014_bot3/control_loops/drivetrain/drivetrain_main.cc b/y2014_bot3/control_loops/drivetrain/drivetrain_main.cc
index 588bc89..a0f0a83 100644
--- a/y2014_bot3/control_loops/drivetrain/drivetrain_main.cc
+++ b/y2014_bot3/control_loops/drivetrain/drivetrain_main.cc
@@ -1,10 +1,14 @@
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.h"
-
#include "aos/linux_code/init.h"
+#include "frc971/control_loops/drivetrain/drivetrain.h"
+#include "y2014_bot3/control_loops/drivetrain/drivetrain_base.h"
+
+using ::frc971::control_loops::drivetrain::DrivetrainLoop;
+
int main() {
::aos::Init();
- y2014_bot3::control_loops::DrivetrainLoop drivetrain;
+ DrivetrainLoop drivetrain(
+ ::y2014_bot3::control_loops::drivetrain::GetDrivetrainConfig());
drivetrain.Run();
::aos::Cleanup();
return 0;
diff --git a/y2014_bot3/control_loops/drivetrain/polydrivetrain_cim_plant.cc b/y2014_bot3/control_loops/drivetrain/polydrivetrain_cim_plant.cc
deleted file mode 100644
index 75bae13..0000000
--- a/y2014_bot3/control_loops/drivetrain/polydrivetrain_cim_plant.cc
+++ /dev/null
@@ -1,49 +0,0 @@
-#include "y2014_bot3/control_loops/drivetrain/polydrivetrain_cim_plant.h"
-
-#include <vector>
-
-#include "frc971/control_loops/state_feedback_loop.h"
-
-namespace y2014_bot3 {
-namespace control_loops {
-
-StateFeedbackPlantCoefficients<1, 1, 1> MakeCIMPlantCoefficients() {
- Eigen::Matrix<double, 1, 1> A;
- A << 0.783924473544;
- Eigen::Matrix<double, 1, 1> B;
- B << 8.94979586973;
- Eigen::Matrix<double, 1, 1> C;
- C << 1;
- Eigen::Matrix<double, 1, 1> D;
- D << 0;
- Eigen::Matrix<double, 1, 1> U_max;
- U_max << 12.0;
- Eigen::Matrix<double, 1, 1> U_min;
- U_min << -12.0;
- return StateFeedbackPlantCoefficients<1, 1, 1>(A, B, C, D, U_max, U_min);
-}
-
-StateFeedbackController<1, 1, 1> MakeCIMController() {
- Eigen::Matrix<double, 1, 1> L;
- L << 0.773924473544;
- Eigen::Matrix<double, 1, 1> K;
- K << 0.086473980503;
- Eigen::Matrix<double, 1, 1> A_inv;
- A_inv << 1.2756330919;
- return StateFeedbackController<1, 1, 1>(L, K, A_inv, MakeCIMPlantCoefficients());
-}
-
-StateFeedbackPlant<1, 1, 1> MakeCIMPlant() {
- ::std::vector< ::std::unique_ptr<StateFeedbackPlantCoefficients<1, 1, 1>>> plants(1);
- plants[0] = ::std::unique_ptr<StateFeedbackPlantCoefficients<1, 1, 1>>(new StateFeedbackPlantCoefficients<1, 1, 1>(MakeCIMPlantCoefficients()));
- return StateFeedbackPlant<1, 1, 1>(&plants);
-}
-
-StateFeedbackLoop<1, 1, 1> MakeCIMLoop() {
- ::std::vector< ::std::unique_ptr<StateFeedbackController<1, 1, 1>>> controllers(1);
- controllers[0] = ::std::unique_ptr<StateFeedbackController<1, 1, 1>>(new StateFeedbackController<1, 1, 1>(MakeCIMController()));
- return StateFeedbackLoop<1, 1, 1>(&controllers);
-}
-
-} // namespace control_loops
-} // namespace y2014_bot3
diff --git a/y2014_bot3/control_loops/drivetrain/polydrivetrain_cim_plant.h b/y2014_bot3/control_loops/drivetrain/polydrivetrain_cim_plant.h
deleted file mode 100644
index 0def071..0000000
--- a/y2014_bot3/control_loops/drivetrain/polydrivetrain_cim_plant.h
+++ /dev/null
@@ -1,20 +0,0 @@
-#ifndef Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_POLYDRIVETRAIN_CIM_PLANT_H_
-#define Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_POLYDRIVETRAIN_CIM_PLANT_H_
-
-#include "frc971/control_loops/state_feedback_loop.h"
-
-namespace y2014_bot3 {
-namespace control_loops {
-
-StateFeedbackPlantCoefficients<1, 1, 1> MakeCIMPlantCoefficients();
-
-StateFeedbackController<1, 1, 1> MakeCIMController();
-
-StateFeedbackPlant<1, 1, 1> MakeCIMPlant();
-
-StateFeedbackLoop<1, 1, 1> MakeCIMLoop();
-
-} // namespace control_loops
-} // namespace y2014_bot3
-
-#endif // Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_POLYDRIVETRAIN_CIM_PLANT_H_
diff --git a/y2014_bot3/control_loops/drivetrain/polydrivetrain_dog_motor_plant.cc b/y2014_bot3/control_loops/drivetrain/polydrivetrain_dog_motor_plant.cc
deleted file mode 100644
index 8fc4049..0000000
--- a/y2014_bot3/control_loops/drivetrain/polydrivetrain_dog_motor_plant.cc
+++ /dev/null
@@ -1,133 +0,0 @@
-#include "y2014_bot3/control_loops/drivetrain/polydrivetrain_dog_motor_plant.h"
-
-#include <vector>
-
-#include "frc971/control_loops/state_feedback_loop.h"
-
-namespace y2014_bot3 {
-namespace control_loops {
-
-StateFeedbackPlantCoefficients<2, 2, 2> MakeVelocityDrivetrainLowLowPlantCoefficients() {
- Eigen::Matrix<double, 2, 2> A;
- A << 0.953388055571, 0.0100729449137, 0.0100729449137, 0.953388055571;
- Eigen::Matrix<double, 2, 2> B;
- B << 0.0119133285199, -0.00257449680311, -0.00257449680311, 0.0119133285199;
- Eigen::Matrix<double, 2, 2> C;
- C << 1.0, 0.0, 0.0, 1.0;
- Eigen::Matrix<double, 2, 2> D;
- D << 0.0, 0.0, 0.0, 0.0;
- Eigen::Matrix<double, 2, 1> U_max;
- U_max << 12.0, 12.0;
- Eigen::Matrix<double, 2, 1> U_min;
- U_min << -12.0, -12.0;
- return StateFeedbackPlantCoefficients<2, 2, 2>(A, B, C, D, U_max, U_min);
-}
-
-StateFeedbackPlantCoefficients<2, 2, 2> MakeVelocityDrivetrainLowHighPlantCoefficients() {
- Eigen::Matrix<double, 2, 2> A;
- A << 0.953388055571, 0.0100729449137, 0.0100729449137, 0.953388055571;
- Eigen::Matrix<double, 2, 2> B;
- B << 0.0119133285199, -0.00257449680311, -0.00257449680311, 0.0119133285199;
- Eigen::Matrix<double, 2, 2> C;
- C << 1.0, 0.0, 0.0, 1.0;
- Eigen::Matrix<double, 2, 2> D;
- D << 0.0, 0.0, 0.0, 0.0;
- Eigen::Matrix<double, 2, 1> U_max;
- U_max << 12.0, 12.0;
- Eigen::Matrix<double, 2, 1> U_min;
- U_min << -12.0, -12.0;
- return StateFeedbackPlantCoefficients<2, 2, 2>(A, B, C, D, U_max, U_min);
-}
-
-StateFeedbackPlantCoefficients<2, 2, 2> MakeVelocityDrivetrainHighLowPlantCoefficients() {
- Eigen::Matrix<double, 2, 2> A;
- A << 0.953388055571, 0.0100729449137, 0.0100729449137, 0.953388055571;
- Eigen::Matrix<double, 2, 2> B;
- B << 0.0119133285199, -0.00257449680311, -0.00257449680311, 0.0119133285199;
- Eigen::Matrix<double, 2, 2> C;
- C << 1.0, 0.0, 0.0, 1.0;
- Eigen::Matrix<double, 2, 2> D;
- D << 0.0, 0.0, 0.0, 0.0;
- Eigen::Matrix<double, 2, 1> U_max;
- U_max << 12.0, 12.0;
- Eigen::Matrix<double, 2, 1> U_min;
- U_min << -12.0, -12.0;
- return StateFeedbackPlantCoefficients<2, 2, 2>(A, B, C, D, U_max, U_min);
-}
-
-StateFeedbackPlantCoefficients<2, 2, 2> MakeVelocityDrivetrainHighHighPlantCoefficients() {
- Eigen::Matrix<double, 2, 2> A;
- A << 0.953388055571, 0.0100729449137, 0.0100729449137, 0.953388055571;
- Eigen::Matrix<double, 2, 2> B;
- B << 0.0119133285199, -0.00257449680311, -0.00257449680311, 0.0119133285199;
- Eigen::Matrix<double, 2, 2> C;
- C << 1.0, 0.0, 0.0, 1.0;
- Eigen::Matrix<double, 2, 2> D;
- D << 0.0, 0.0, 0.0, 0.0;
- Eigen::Matrix<double, 2, 1> U_max;
- U_max << 12.0, 12.0;
- Eigen::Matrix<double, 2, 1> U_min;
- U_min << -12.0, -12.0;
- return StateFeedbackPlantCoefficients<2, 2, 2>(A, B, C, D, U_max, U_min);
-}
-
-StateFeedbackController<2, 2, 2> MakeVelocityDrivetrainLowLowController() {
- Eigen::Matrix<double, 2, 2> L;
- L << 0.933388055571, 0.0100729449137, 0.0100729449137, 0.933388055571;
- Eigen::Matrix<double, 2, 2> K;
- K << 31.3080614945, 7.61126069778, 7.61126069778, 31.3080614945;
- Eigen::Matrix<double, 2, 2> A_inv;
- A_inv << 1.04900794038, -0.0110832091253, -0.0110832091253, 1.04900794038;
- return StateFeedbackController<2, 2, 2>(L, K, A_inv, MakeVelocityDrivetrainLowLowPlantCoefficients());
-}
-
-StateFeedbackController<2, 2, 2> MakeVelocityDrivetrainLowHighController() {
- Eigen::Matrix<double, 2, 2> L;
- L << 0.933388055571, 0.0100729449137, 0.0100729449137, 0.933388055571;
- Eigen::Matrix<double, 2, 2> K;
- K << 31.3080614945, 7.61126069778, 7.61126069778, 31.3080614945;
- Eigen::Matrix<double, 2, 2> A_inv;
- A_inv << 1.04900794038, -0.0110832091253, -0.0110832091253, 1.04900794038;
- return StateFeedbackController<2, 2, 2>(L, K, A_inv, MakeVelocityDrivetrainLowHighPlantCoefficients());
-}
-
-StateFeedbackController<2, 2, 2> MakeVelocityDrivetrainHighLowController() {
- Eigen::Matrix<double, 2, 2> L;
- L << 0.933388055571, 0.0100729449137, 0.0100729449137, 0.933388055571;
- Eigen::Matrix<double, 2, 2> K;
- K << 31.3080614945, 7.61126069778, 7.61126069778, 31.3080614945;
- Eigen::Matrix<double, 2, 2> A_inv;
- A_inv << 1.04900794038, -0.0110832091253, -0.0110832091253, 1.04900794038;
- return StateFeedbackController<2, 2, 2>(L, K, A_inv, MakeVelocityDrivetrainHighLowPlantCoefficients());
-}
-
-StateFeedbackController<2, 2, 2> MakeVelocityDrivetrainHighHighController() {
- Eigen::Matrix<double, 2, 2> L;
- L << 0.933388055571, 0.0100729449137, 0.0100729449137, 0.933388055571;
- Eigen::Matrix<double, 2, 2> K;
- K << 31.3080614945, 7.61126069778, 7.61126069778, 31.3080614945;
- Eigen::Matrix<double, 2, 2> A_inv;
- A_inv << 1.04900794038, -0.0110832091253, -0.0110832091253, 1.04900794038;
- return StateFeedbackController<2, 2, 2>(L, K, A_inv, MakeVelocityDrivetrainHighHighPlantCoefficients());
-}
-
-StateFeedbackPlant<2, 2, 2> MakeVelocityDrivetrainPlant() {
- ::std::vector< ::std::unique_ptr<StateFeedbackPlantCoefficients<2, 2, 2>>> plants(4);
- plants[0] = ::std::unique_ptr<StateFeedbackPlantCoefficients<2, 2, 2>>(new StateFeedbackPlantCoefficients<2, 2, 2>(MakeVelocityDrivetrainLowLowPlantCoefficients()));
- plants[1] = ::std::unique_ptr<StateFeedbackPlantCoefficients<2, 2, 2>>(new StateFeedbackPlantCoefficients<2, 2, 2>(MakeVelocityDrivetrainLowHighPlantCoefficients()));
- plants[2] = ::std::unique_ptr<StateFeedbackPlantCoefficients<2, 2, 2>>(new StateFeedbackPlantCoefficients<2, 2, 2>(MakeVelocityDrivetrainHighLowPlantCoefficients()));
- plants[3] = ::std::unique_ptr<StateFeedbackPlantCoefficients<2, 2, 2>>(new StateFeedbackPlantCoefficients<2, 2, 2>(MakeVelocityDrivetrainHighHighPlantCoefficients()));
- return StateFeedbackPlant<2, 2, 2>(&plants);
-}
-
-StateFeedbackLoop<2, 2, 2> MakeVelocityDrivetrainLoop() {
- ::std::vector< ::std::unique_ptr<StateFeedbackController<2, 2, 2>>> controllers(4);
- controllers[0] = ::std::unique_ptr<StateFeedbackController<2, 2, 2>>(new StateFeedbackController<2, 2, 2>(MakeVelocityDrivetrainLowLowController()));
- controllers[1] = ::std::unique_ptr<StateFeedbackController<2, 2, 2>>(new StateFeedbackController<2, 2, 2>(MakeVelocityDrivetrainLowHighController()));
- controllers[2] = ::std::unique_ptr<StateFeedbackController<2, 2, 2>>(new StateFeedbackController<2, 2, 2>(MakeVelocityDrivetrainHighLowController()));
- controllers[3] = ::std::unique_ptr<StateFeedbackController<2, 2, 2>>(new StateFeedbackController<2, 2, 2>(MakeVelocityDrivetrainHighHighController()));
- return StateFeedbackLoop<2, 2, 2>(&controllers);
-}
-
-} // namespace control_loops
-} // namespace y2014_bot3
diff --git a/y2014_bot3/control_loops/drivetrain/polydrivetrain_dog_motor_plant.h b/y2014_bot3/control_loops/drivetrain/polydrivetrain_dog_motor_plant.h
deleted file mode 100644
index 4442d35..0000000
--- a/y2014_bot3/control_loops/drivetrain/polydrivetrain_dog_motor_plant.h
+++ /dev/null
@@ -1,32 +0,0 @@
-#ifndef Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_POLYDRIVETRAIN_DOG_MOTOR_PLANT_H_
-#define Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_POLYDRIVETRAIN_DOG_MOTOR_PLANT_H_
-
-#include "frc971/control_loops/state_feedback_loop.h"
-
-namespace y2014_bot3 {
-namespace control_loops {
-
-StateFeedbackPlantCoefficients<2, 2, 2> MakeVelocityDrivetrainLowLowPlantCoefficients();
-
-StateFeedbackController<2, 2, 2> MakeVelocityDrivetrainLowLowController();
-
-StateFeedbackPlantCoefficients<2, 2, 2> MakeVelocityDrivetrainLowHighPlantCoefficients();
-
-StateFeedbackController<2, 2, 2> MakeVelocityDrivetrainLowHighController();
-
-StateFeedbackPlantCoefficients<2, 2, 2> MakeVelocityDrivetrainHighLowPlantCoefficients();
-
-StateFeedbackController<2, 2, 2> MakeVelocityDrivetrainHighLowController();
-
-StateFeedbackPlantCoefficients<2, 2, 2> MakeVelocityDrivetrainHighHighPlantCoefficients();
-
-StateFeedbackController<2, 2, 2> MakeVelocityDrivetrainHighHighController();
-
-StateFeedbackPlant<2, 2, 2> MakeVelocityDrivetrainPlant();
-
-StateFeedbackLoop<2, 2, 2> MakeVelocityDrivetrainLoop();
-
-} // namespace control_loops
-} // namespace y2014_bot3
-
-#endif // Y2014_BOT3_CONTROL_LOOPS_DRIVETRAIN_POLYDRIVETRAIN_DOG_MOTOR_PLANT_H_
diff --git a/y2014_bot3/control_loops/drivetrain/replay_drivetrain.cc b/y2014_bot3/control_loops/drivetrain/replay_drivetrain.cc
deleted file mode 100644
index 4f83c9e..0000000
--- a/y2014_bot3/control_loops/drivetrain/replay_drivetrain.cc
+++ /dev/null
@@ -1,24 +0,0 @@
-#include "aos/common/controls/replay_control_loop.h"
-#include "aos/linux_code/init.h"
-
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.q.h"
-
-// Reads one or more log files and sends out all the queue messages (in the
-// correct order and at the correct time) to feed a "live" drivetrain process.
-
-int main(int argc, char **argv) {
- if (argc <= 1) {
- fprintf(stderr, "Need at least one file to replay!\n");
- return EXIT_FAILURE;
- }
-
- ::aos::InitNRT();
-
- ::aos::controls::ControlLoopReplayer<::y2014_bot3::control_loops::DrivetrainQueue>
- replayer(&::y2014_bot3::control_loops::drivetrain_queue, "drivetrain");
- for (int i = 1; i < argc; ++i) {
- replayer.ProcessFile(argv[i]);
- }
-
- ::aos::Cleanup();
-}
diff --git a/y2014_bot3/control_loops/python/BUILD b/y2014_bot3/control_loops/python/BUILD
index bb8dc29..756b60e 100644
--- a/y2014_bot3/control_loops/python/BUILD
+++ b/y2014_bot3/control_loops/python/BUILD
@@ -6,7 +6,21 @@
'drivetrain.py',
],
deps = [
+ '//external:python-gflags',
'//external:python-glog',
'//frc971/control_loops/python:controls',
]
)
+
+py_binary(
+ name = 'polydrivetrain',
+ srcs = [
+ 'polydrivetrain.py',
+ 'drivetrain.py',
+ ],
+ deps = [
+ '//external:python-gflags',
+ '//external:python-glog',
+ '//frc971/control_loops/python:controls',
+ ],
+)
diff --git a/y2014_bot3/control_loops/python/drivetrain.py b/y2014_bot3/control_loops/python/drivetrain.py
index 4231887..b0555a0 100755
--- a/y2014_bot3/control_loops/python/drivetrain.py
+++ b/y2014_bot3/control_loops/python/drivetrain.py
@@ -4,10 +4,16 @@
from frc971.control_loops.python import controls
import numpy
import sys
+import argparse
from matplotlib import pylab
+import gflags
import glog
+FLAGS = gflags.FLAGS
+
+gflags.DEFINE_bool('plot', False, 'If true, plot the loop response.')
+
class CIM(control_loop.ControlLoop):
def __init__(self):
super(CIM, self).__init__("CIM")
@@ -22,10 +28,10 @@
# Moment of inertia of the CIM in kg m^2
self.J = 0.0001
# Resistance of the motor, divided by 2 to account for the 2 motors
- self.R = 12.0 / self.stall_current
+ self.resistance = 12.0 / self.stall_current
# Motor velocity constant
self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) /
- (12.0 - self.R * self.free_current))
+ (12.0 - self.resistance * self.free_current))
# Torque constant
self.Kt = self.stall_torque / self.stall_current
# Control loop time step
@@ -33,9 +39,9 @@
# State feedback matrices
self.A_continuous = numpy.matrix(
- [[-self.Kt / self.Kv / (self.J * self.R)]])
+ [[-self.Kt / self.Kv / (self.J * self.resistance)]])
self.B_continuous = numpy.matrix(
- [[self.Kt / (self.J * self.R)]])
+ [[self.Kt / (self.J * self.resistance)]])
self.C = numpy.matrix([[1]])
self.D = numpy.matrix([[0]])
@@ -54,36 +60,34 @@
class Drivetrain(control_loop.ControlLoop):
def __init__(self, name="Drivetrain", left_low=True, right_low=True):
super(Drivetrain, self).__init__(name)
+ # Number of motors per side
+ self.num_motors = 2
# Stall Torque in N m
- self.stall_torque = 2.42
+ self.stall_torque = 2.42 * self.num_motors * 0.60
# Stall Current in Amps
- self.stall_current = 133.0
+ self.stall_current = 133.0 * self.num_motors
# Free Speed in RPM. Used number from last year.
- self.free_speed = 4650.0
+ self.free_speed = 5500.0
# Free Current in Amps
- self.free_current = 2.7
+ self.free_current = 4.7 * self.num_motors
# Moment of inertia of the drivetrain in kg m^2
- # Just borrowed from last year.
- self.J = 10
+ self.J = 1.8
# Mass of the robot, in kg.
- self.m = 68
- # Radius of the robot, in meters (from last year).
- self.rb = 0.9603 / 2.0
+ self.m = 37
+ # Radius of the robot, in meters (requires tuning by hand)
+ self.rb = 0.601 / 2.0
# Radius of the wheels, in meters.
self.r = 0.0508
# Resistance of the motor, divided by the number of motors.
- self.R = 12.0 / self.stall_current / 2
+ self.resistance = 12.0 / self.stall_current
# Motor velocity constant
self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) /
- (12.0 - self.R * self.free_current))
+ (12.0 - self.resistance * self.free_current))
# Torque constant
self.Kt = self.stall_torque / self.stall_current
# Gear ratios
- self.G_const = 18.0 / 44.0 * 18.0 / 60.0
-
- self.G_low = self.G_const
- self.G_high = self.G_const
-
+ self.G_low = 28.0 / 60.0 * 19.0 / 50.0
+ self.G_high = 28.0 / 48.0 * 19.0 / 50.0
if left_low:
self.Gl = self.G_low
else:
@@ -101,10 +105,10 @@
self.msp = 1.0 / self.m + self.rb * self.rb / self.J
self.msn = 1.0 / self.m - self.rb * self.rb / self.J
# The calculations which we will need for A and B.
- self.tcl = -self.Kt / self.Kv / (self.Gl * self.Gl * self.R * self.r * self.r)
- self.tcr = -self.Kt / self.Kv / (self.Gr * self.Gr * self.R * self.r * self.r)
- self.mpl = self.Kt / (self.Gl * self.R * self.r)
- self.mpr = self.Kt / (self.Gr * self.R * self.r)
+ self.tcl = -self.Kt / self.Kv / (self.Gl * self.Gl * self.resistance * self.r * self.r)
+ self.tcr = -self.Kt / self.Kv / (self.Gr * self.Gr * self.resistance * self.r * self.r)
+ self.mpl = self.Kt / (self.Gl * self.resistance * self.r)
+ self.mpr = self.Kt / (self.Gr * self.resistance * self.r)
# State feedback matrices
# X will be of the format
@@ -124,17 +128,16 @@
self.D = numpy.matrix([[0, 0],
[0, 0]])
- #glog.debug('THE NUMBER I WANT %s', str(numpy.linalg.inv(self.A_continuous) * -self.B_continuous * numpy.matrix([[12.0], [12.0]])))
self.A, self.B = self.ContinuousToDiscrete(
self.A_continuous, self.B_continuous, self.dt)
- # Poles from last year.
- self.hp = 0.65
- self.lp = 0.83
- self.PlaceControllerPoles([self.hp, self.lp, self.hp, self.lp])
- glog.info('K %s', str(self.K))
- q_pos = 0.07
- q_vel = 1.0
+ if left_low or right_low:
+ q_pos = 0.12
+ q_vel = 1.0
+ else:
+ q_pos = 0.14
+ q_vel = 0.95
+
self.Q = numpy.matrix([[(1.0 / (q_pos ** 2.0)), 0.0, 0.0, 0.0],
[0.0, (1.0 / (q_vel ** 2.0)), 0.0, 0.0],
[0.0, 0.0, (1.0 / (q_pos ** 2.0)), 0.0],
@@ -143,10 +146,10 @@
self.R = numpy.matrix([[(1.0 / (12.0 ** 2.0)), 0.0],
[0.0, (1.0 / (12.0 ** 2.0))]])
self.K = controls.dlqr(self.A, self.B, self.Q, self.R)
- glog.info('A %s', str(self.A))
- glog.info('B %s', str(self.B))
- glog.info('K %s', str(self.K))
- glog.info('Poles are %s', str(numpy.linalg.eig(self.A - self.B * self.K)[0]))
+
+ glog.debug('DT q_pos %f q_vel %s %s', q_pos, q_vel, name)
+ glog.debug(str(numpy.linalg.eig(self.A - self.B * self.K)[0]))
+ glog.debug('K %s', repr(self.K))
self.hlp = 0.3
self.llp = 0.4
@@ -154,11 +157,102 @@
self.U_max = numpy.matrix([[12.0], [12.0]])
self.U_min = numpy.matrix([[-12.0], [-12.0]])
+
self.InitializeState()
+
+class KFDrivetrain(Drivetrain):
+ def __init__(self, name="KFDrivetrain", left_low=True, right_low=True):
+ super(KFDrivetrain, self).__init__(name, left_low, right_low)
+
+ self.unaugmented_A_continuous = self.A_continuous
+ self.unaugmented_B_continuous = self.B_continuous
+
+ # The states are
+ # The practical voltage applied to the wheels is
+ # V_left = U_left + left_voltage_error
+ #
+ # [left position, left velocity, right position, right velocity,
+ # left voltage error, right voltage error, angular_error]
+ #
+ # The left and right positions are filtered encoder positions and are not
+ # adjusted for heading error.
+ # The turn velocity as computed by the left and right velocities is
+ # adjusted by the gyro velocity.
+ # The angular_error is the angular velocity error between the wheel speed
+ # and the gyro speed.
+ self.A_continuous = numpy.matrix(numpy.zeros((7, 7)))
+ self.B_continuous = numpy.matrix(numpy.zeros((7, 2)))
+ self.A_continuous[0:4,0:4] = self.unaugmented_A_continuous
+ self.A_continuous[0:4,4:6] = self.unaugmented_B_continuous
+ self.B_continuous[0:4,0:2] = self.unaugmented_B_continuous
+ self.A_continuous[0,6] = 1
+ self.A_continuous[2,6] = -1
+
+ self.A, self.B = self.ContinuousToDiscrete(
+ self.A_continuous, self.B_continuous, self.dt)
+
+ self.C = numpy.matrix([[1, 0, 0, 0, 0, 0, 0],
+ [0, 0, 1, 0, 0, 0, 0],
+ [0, -0.5 / self.rb, 0, 0.5 / self.rb, 0, 0, 0]])
+
+ self.D = numpy.matrix([[0, 0],
+ [0, 0],
+ [0, 0]])
+
+ q_pos = 0.05
+ q_vel = 1.00
+ q_voltage = 10.0
+ q_encoder_uncertainty = 2.00
+
+ self.Q = numpy.matrix([[(q_pos ** 2.0), 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
+ [0.0, (q_vel ** 2.0), 0.0, 0.0, 0.0, 0.0, 0.0],
+ [0.0, 0.0, (q_pos ** 2.0), 0.0, 0.0, 0.0, 0.0],
+ [0.0, 0.0, 0.0, (q_vel ** 2.0), 0.0, 0.0, 0.0],
+ [0.0, 0.0, 0.0, 0.0, (q_voltage ** 2.0), 0.0, 0.0],
+ [0.0, 0.0, 0.0, 0.0, 0.0, (q_voltage ** 2.0), 0.0],
+ [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, (q_encoder_uncertainty ** 2.0)]])
+
+ r_pos = 0.0001
+ r_gyro = 0.000001
+ self.R = numpy.matrix([[(r_pos ** 2.0), 0.0, 0.0],
+ [0.0, (r_pos ** 2.0), 0.0],
+ [0.0, 0.0, (r_gyro ** 2.0)]])
+
+ # Solving for kf gains.
+ self.KalmanGain, self.Q_steady = controls.kalman(
+ A=self.A, B=self.B, C=self.C, Q=self.Q, R=self.R)
+
+ self.L = self.A * self.KalmanGain
+
+ unaug_K = self.K
+
+ # Implement a nice closed loop controller for use by the closed loop
+ # controller.
+ self.K = numpy.matrix(numpy.zeros((self.B.shape[1], self.A.shape[0])))
+ self.K[0:2, 0:4] = unaug_K
+ self.K[0, 4] = 1.0
+ self.K[1, 5] = 1.0
+
+ self.Qff = numpy.matrix(numpy.zeros((4, 4)))
+ qff_pos = 0.005
+ qff_vel = 1.00
+ self.Qff[0, 0] = 1.0 / qff_pos ** 2.0
+ self.Qff[1, 1] = 1.0 / qff_vel ** 2.0
+ self.Qff[2, 2] = 1.0 / qff_pos ** 2.0
+ self.Qff[3, 3] = 1.0 / qff_vel ** 2.0
+ self.Kff = numpy.matrix(numpy.zeros((2, 7)))
+ self.Kff[0:2, 0:4] = controls.TwoStateFeedForwards(self.B[0:4,:], self.Qff)
+
+ self.InitializeState()
+
+
def main(argv):
+ argv = FLAGS(argv)
+ glog.init()
+
# Simulate the response of the system to a step input.
- drivetrain = Drivetrain()
+ drivetrain = Drivetrain(left_low=False, right_low=False)
simulated_left = []
simulated_right = []
for _ in xrange(100):
@@ -166,26 +260,37 @@
simulated_left.append(drivetrain.X[0, 0])
simulated_right.append(drivetrain.X[2, 0])
- #pylab.plot(range(100), simulated_left)
- #pylab.plot(range(100), simulated_right)
- #pylab.show()
+ if FLAGS.plot:
+ pylab.plot(range(100), simulated_left)
+ pylab.plot(range(100), simulated_right)
+ pylab.suptitle('Acceleration Test')
+ pylab.show()
# Simulate forwards motion.
- drivetrain = Drivetrain()
+ drivetrain = Drivetrain(left_low=False, right_low=False)
close_loop_left = []
close_loop_right = []
+ left_power = []
+ right_power = []
R = numpy.matrix([[1.0], [0.0], [1.0], [0.0]])
- for _ in xrange(100):
+ for _ in xrange(300):
U = numpy.clip(drivetrain.K * (R - drivetrain.X_hat),
drivetrain.U_min, drivetrain.U_max)
drivetrain.UpdateObserver(U)
drivetrain.Update(U)
close_loop_left.append(drivetrain.X[0, 0])
close_loop_right.append(drivetrain.X[2, 0])
+ left_power.append(U[0, 0])
+ right_power.append(U[1, 0])
- #pylab.plot(range(100), close_loop_left)
- #pylab.plot(range(100), close_loop_right)
- #pylab.show()
+ if FLAGS.plot:
+ pylab.plot(range(300), close_loop_left, label='left position')
+ pylab.plot(range(300), close_loop_right, label='right position')
+ pylab.plot(range(300), left_power, label='left power')
+ pylab.plot(range(300), right_power, label='right power')
+ pylab.suptitle('Linear Move')
+ pylab.legend()
+ pylab.show()
# Try turning in place
drivetrain = Drivetrain()
@@ -200,9 +305,11 @@
close_loop_left.append(drivetrain.X[0, 0])
close_loop_right.append(drivetrain.X[2, 0])
- #pylab.plot(range(100), close_loop_left)
- #pylab.plot(range(100), close_loop_right)
- #pylab.show()
+ if FLAGS.plot:
+ pylab.plot(range(100), close_loop_left)
+ pylab.plot(range(100), close_loop_right)
+ pylab.suptitle('Angular Move')
+ pylab.show()
# Try turning just one side.
drivetrain = Drivetrain()
@@ -217,25 +324,75 @@
close_loop_left.append(drivetrain.X[0, 0])
close_loop_right.append(drivetrain.X[2, 0])
- #pylab.plot(range(100), close_loop_left)
- #pylab.plot(range(100), close_loop_right)
- #pylab.show()
+ if FLAGS.plot:
+ pylab.plot(range(100), close_loop_left)
+ pylab.plot(range(100), close_loop_right)
+ pylab.suptitle('Pivot')
+ pylab.show()
# Write the generated constants out to a file.
- glog.info('Output one')
- drivetrain_low_low = Drivetrain(name="DrivetrainLowLow", left_low=True, right_low=True)
- drivetrain_low_high = Drivetrain(name="DrivetrainLowHigh", left_low=True, right_low=False)
- drivetrain_high_low = Drivetrain(name="DrivetrainHighLow", left_low=False, right_low=True)
- drivetrain_high_high = Drivetrain(name="DrivetrainHighHigh", left_low=False, right_low=False)
+ drivetrain_low_low = Drivetrain(
+ name="DrivetrainLowLow", left_low=True, right_low=True)
+ drivetrain_low_high = Drivetrain(
+ name="DrivetrainLowHigh", left_low=True, right_low=False)
+ drivetrain_high_low = Drivetrain(
+ name="DrivetrainHighLow", left_low=False, right_low=True)
+ drivetrain_high_high = Drivetrain(
+ name="DrivetrainHighHigh", left_low=False, right_low=False)
- if len(argv) != 3:
- glog.fatal('Expected .h file name and .cc file name')
+ kf_drivetrain_low_low = KFDrivetrain(
+ name="KFDrivetrainLowLow", left_low=True, right_low=True)
+ kf_drivetrain_low_high = KFDrivetrain(
+ name="KFDrivetrainLowHigh", left_low=True, right_low=False)
+ kf_drivetrain_high_low = KFDrivetrain(
+ name="KFDrivetrainHighLow", left_low=False, right_low=True)
+ kf_drivetrain_high_high = KFDrivetrain(
+ name="KFDrivetrainHighHigh", left_low=False, right_low=False)
+
+ if len(argv) != 5:
+ print "Expected .h file name and .cc file name"
else:
+ namespaces = ['y2014_bot3', 'control_loops', 'drivetrain']
dog_loop_writer = control_loop.ControlLoopWriter(
"Drivetrain", [drivetrain_low_low, drivetrain_low_high,
drivetrain_high_low, drivetrain_high_high],
- namespaces=['y2014_bot3', 'control_loops', 'drivetrain'])
+ namespaces = namespaces)
+ dog_loop_writer.AddConstant(control_loop.Constant("kDt", "%f",
+ drivetrain_low_low.dt))
+ dog_loop_writer.AddConstant(control_loop.Constant("kStallTorque", "%f",
+ drivetrain_low_low.stall_torque))
+ dog_loop_writer.AddConstant(control_loop.Constant("kStallCurrent", "%f",
+ drivetrain_low_low.stall_current))
+ dog_loop_writer.AddConstant(control_loop.Constant("kFreeSpeedRPM", "%f",
+ drivetrain_low_low.free_speed))
+ dog_loop_writer.AddConstant(control_loop.Constant("kFreeCurrent", "%f",
+ drivetrain_low_low.free_current))
+ dog_loop_writer.AddConstant(control_loop.Constant("kJ", "%f",
+ drivetrain_low_low.J))
+ dog_loop_writer.AddConstant(control_loop.Constant("kMass", "%f",
+ drivetrain_low_low.m))
+ dog_loop_writer.AddConstant(control_loop.Constant("kRobotRadius", "%f",
+ drivetrain_low_low.rb))
+ dog_loop_writer.AddConstant(control_loop.Constant("kWheelRadius", "%f",
+ drivetrain_low_low.r))
+ dog_loop_writer.AddConstant(control_loop.Constant("kR", "%f",
+ drivetrain_low_low.resistance))
+ dog_loop_writer.AddConstant(control_loop.Constant("kV", "%f",
+ drivetrain_low_low.Kv))
+ dog_loop_writer.AddConstant(control_loop.Constant("kT", "%f",
+ drivetrain_low_low.Kt))
+ dog_loop_writer.AddConstant(control_loop.Constant("kLowGearRatio", "%f",
+ drivetrain_low_low.G_low))
+ dog_loop_writer.AddConstant(control_loop.Constant("kHighGearRatio", "%f",
+ drivetrain_high_high.G_high))
+
dog_loop_writer.Write(argv[1], argv[2])
+ kf_loop_writer = control_loop.ControlLoopWriter(
+ "KFDrivetrain", [kf_drivetrain_low_low, kf_drivetrain_low_high,
+ kf_drivetrain_high_low, kf_drivetrain_high_high],
+ namespaces = namespaces)
+ kf_loop_writer.Write(argv[3], argv[4])
+
if __name__ == '__main__':
sys.exit(main(sys.argv))
diff --git a/y2014_bot3/control_loops/python/polydrivetrain.py b/y2014_bot3/control_loops/python/polydrivetrain.py
index 2ffbed6..e047c11 100755
--- a/y2014_bot3/control_loops/python/polydrivetrain.py
+++ b/y2014_bot3/control_loops/python/polydrivetrain.py
@@ -2,14 +2,23 @@
import numpy
import sys
-import polytope
-import drivetrain
-import control_loop
-import controls
+from frc971.control_loops.python import polytope
+from y2014_bot3.control_loops.python import drivetrain
+from frc971.control_loops.python import control_loop
+from frc971.control_loops.python import controls
from matplotlib import pylab
+import gflags
+import glog
+
__author__ = 'Austin Schuh (austin.linux@gmail.com)'
+FLAGS = gflags.FLAGS
+
+try:
+ gflags.DEFINE_bool('plot', False, 'If true, plot the loop response.')
+except gflags.DuplicateFlagError:
+ pass
def CoerceGoal(region, K, w, R):
"""Intersects a line with a region, and finds the closest point to R.
@@ -110,8 +119,8 @@
self.B_continuous = numpy.matrix(
[[self._drivetrain.B_continuous[1, 0], self._drivetrain.B_continuous[1, 1]],
[self._drivetrain.B_continuous[3, 0], self._drivetrain.B_continuous[3, 1]]])
- self.C = numpy.matrix(numpy.eye(2));
- self.D = numpy.matrix(numpy.zeros((2, 2)));
+ self.C = numpy.matrix(numpy.eye(2))
+ self.D = numpy.matrix(numpy.zeros((2, 2)))
self.A, self.B = self.ContinuousToDiscrete(self.A_continuous,
self.B_continuous, self.dt)
@@ -119,12 +128,12 @@
# FF * X = U (steady state)
self.FF = self.B.I * (numpy.eye(2) - self.A)
- self.PlaceControllerPoles([0.6, 0.6])
+ self.PlaceControllerPoles([0.67, 0.67])
self.PlaceObserverPoles([0.02, 0.02])
self.G_high = self._drivetrain.G_high
self.G_low = self._drivetrain.G_low
- self.R = self._drivetrain.R
+ self.resistance = self._drivetrain.resistance
self.r = self._drivetrain.r
self.Kv = self._drivetrain.Kv
self.Kt = self._drivetrain.Kt
@@ -174,10 +183,14 @@
[[0.0],
[0.0]])
+ self.U_ideal = numpy.matrix(
+ [[0.0],
+ [0.0]])
+
# ttrust is the comprimise between having full throttle negative inertia,
# and having no throttle negative inertia. A value of 0 is full throttle
# inertia. A value of 1 is no throttle negative inertia.
- self.ttrust = 1.1
+ self.ttrust = 1.0
self.left_gear = VelocityDrivetrain.LOW
self.right_gear = VelocityDrivetrain.LOW
@@ -229,9 +242,9 @@
self.CurrentDrivetrain().r)
#print gear_name, "Motor Energy Difference.", 0.5 * 0.000140032647 * (low_omega * low_omega - high_omega * high_omega), "joules"
high_torque = ((12.0 - high_omega / self.CurrentDrivetrain().Kv) *
- self.CurrentDrivetrain().Kt / self.CurrentDrivetrain().R)
+ self.CurrentDrivetrain().Kt / self.CurrentDrivetrain().resistance)
low_torque = ((12.0 - low_omega / self.CurrentDrivetrain().Kv) *
- self.CurrentDrivetrain().Kt / self.CurrentDrivetrain().R)
+ self.CurrentDrivetrain().Kt / self.CurrentDrivetrain().resistance)
high_power = high_torque * high_omega
low_power = low_torque * low_omega
#if should_print:
@@ -250,16 +263,16 @@
#goal_gear_is_high = True
if not self.IsInGear(current_gear):
- print gear_name, 'Not in gear.'
+ glog.debug('%s Not in gear.', gear_name)
return current_gear
else:
is_high = current_gear is VelocityDrivetrain.HIGH
if is_high != goal_gear_is_high:
if goal_gear_is_high:
- print gear_name, 'Shifting up.'
+ glog.debug('%s Shifting up.', gear_name)
return VelocityDrivetrain.SHIFTING_UP
else:
- print gear_name, 'Shifting down.'
+ glog.debug('%s Shifting down.', gear_name)
return VelocityDrivetrain.SHIFTING_DOWN
else:
return current_gear
@@ -303,7 +316,7 @@
# wheel.
self.left_gear = self.right_gear = True
- if False:
+ if True:
self.left_gear = self.ComputeGear(self.X[0, 0], should_print=True,
current_gear=self.left_gear,
gear_name="left")
@@ -316,8 +329,7 @@
if self.IsInGear(self.right_gear):
self.right_cim.X[0, 0] = self.MotorRPM(self.right_shifter_position, self.X[0, 0])
- steering *= 2.3
- if True or self.IsInGear(self.left_gear) and self.IsInGear(self.right_gear):
+ if self.IsInGear(self.left_gear) and self.IsInGear(self.right_gear):
# Filter the throttle to provide a nicer response.
fvel = self.FilterVelocity(throttle)
@@ -362,7 +374,7 @@
FF_volts = self.CurrentDrivetrain().FF * self.boxed_R
self.U_ideal = self.CurrentDrivetrain().K * (self.boxed_R - self.X) + FF_volts
else:
- print 'Not all in gear'
+ glog.debug('Not all in gear')
if not self.IsInGear(self.left_gear) and not self.IsInGear(self.right_gear):
# TODO(austin): Use battery volts here.
R_left = self.MotorRPM(self.left_shifter_position, self.X[0, 0])
@@ -383,7 +395,7 @@
# TODO(austin): Model the robot as not accelerating when you shift...
# This hack only works when you shift at the same time.
- if True or self.IsInGear(self.left_gear) and self.IsInGear(self.right_gear):
+ if self.IsInGear(self.left_gear) and self.IsInGear(self.right_gear):
self.X = self.CurrentDrivetrain().A * self.X + self.CurrentDrivetrain().B * self.U
self.left_gear, self.left_shifter_position = self.SimShifter(
@@ -391,37 +403,36 @@
self.right_gear, self.right_shifter_position = self.SimShifter(
self.right_gear, self.right_shifter_position)
- print "U is", self.U[0, 0], self.U[1, 0]
- print "Left shifter", self.left_gear, self.left_shifter_position, "Right shifter", self.right_gear, self.right_shifter_position
+ glog.debug('U is %s %s', str(self.U[0, 0]), str(self.U[1, 0]))
+ glog.debug('Left shifter %s %d Right shifter %s %d',
+ self.left_gear, self.left_shifter_position,
+ self.right_gear, self.right_shifter_position)
def main(argv):
+ argv = FLAGS(argv)
+
vdrivetrain = VelocityDrivetrain()
- if len(argv) != 7:
- print "Expected .h file name and .cc file name"
- else:
- dog_loop_writer = control_loop.ControlLoopWriter(
- "VelocityDrivetrain", [vdrivetrain.drivetrain_low_low,
- vdrivetrain.drivetrain_low_high,
- vdrivetrain.drivetrain_high_low,
- vdrivetrain.drivetrain_high_high],
- namespaces=['y2014_bot3', 'control_loops'])
-
- if argv[1][-3:] == '.cc':
- dog_loop_writer.Write(argv[2], argv[1])
+ if not FLAGS.plot:
+ if len(argv) != 5:
+ glog.fatal('Expected .h file name and .cc file name')
else:
+ namespaces = ['y2014_bot3', 'control_loops', 'drivetrain']
+ dog_loop_writer = control_loop.ControlLoopWriter(
+ "VelocityDrivetrain", [vdrivetrain.drivetrain_low_low,
+ vdrivetrain.drivetrain_low_high,
+ vdrivetrain.drivetrain_high_low,
+ vdrivetrain.drivetrain_high_high],
+ namespaces=namespaces)
+
dog_loop_writer.Write(argv[1], argv[2])
- cim_writer = control_loop.ControlLoopWriter(
- "CIM", [drivetrain.CIM()],
- namespaces=['y2014_bot3', 'control_loops'])
+ cim_writer = control_loop.ControlLoopWriter(
+ "CIM", [drivetrain.CIM()])
- if argv[5][-3:] == '.cc':
- cim_writer.Write(argv[6], argv[5])
- else:
- cim_writer.Write(argv[5], argv[6])
- return
+ cim_writer.Write(argv[3], argv[4])
+ return
vl_plot = []
vr_plot = []
@@ -436,16 +447,16 @@
vdrivetrain.left_gear = VelocityDrivetrain.LOW
vdrivetrain.right_gear = VelocityDrivetrain.LOW
- print "K is", vdrivetrain.CurrentDrivetrain().K
+ glog.debug('K is %s', str(vdrivetrain.CurrentDrivetrain().K))
if vdrivetrain.left_gear is VelocityDrivetrain.HIGH:
- print "Left is high"
+ glog.debug('Left is high')
else:
- print "Left is low"
+ glog.debug('Left is low')
if vdrivetrain.right_gear is VelocityDrivetrain.HIGH:
- print "Right is high"
+ glog.debug('Right is high')
else:
- print "Right is low"
+ glog.debug('Right is low')
for t in numpy.arange(0, 1.7, vdrivetrain.dt):
if t < 0.5:
@@ -469,22 +480,6 @@
else:
radius_plot.append(turn_velocity / fwd_velocity)
- cim_velocity_plot = []
- cim_voltage_plot = []
- cim_time = []
- cim = drivetrain.CIM()
- R = numpy.matrix([[300]])
- for t in numpy.arange(0, 0.5, cim.dt):
- U = numpy.clip(cim.K * (R - cim.X) + R / cim.Kv, cim.U_min, cim.U_max)
- cim.Update(U)
- cim_velocity_plot.append(cim.X[0, 0])
- cim_voltage_plot.append(U[0, 0] * 10)
- cim_time.append(t)
- pylab.plot(cim_time, cim_velocity_plot, label='cim spinup')
- pylab.plot(cim_time, cim_voltage_plot, label='cim voltage')
- pylab.legend()
- pylab.show()
-
# TODO(austin):
# Shifting compensation.
diff --git a/y2014_bot3/joystick_reader.cc b/y2014_bot3/joystick_reader.cc
index 6dfcbb4..86f78dc 100644
--- a/y2014_bot3/joystick_reader.cc
+++ b/y2014_bot3/joystick_reader.cc
@@ -11,11 +11,11 @@
#include "aos/common/time.h"
#include "frc971/queues/gyro.q.h"
+#include "frc971/control_loops/drivetrain/drivetrain.q.h"
#include "y2014_bot3/autonomous/auto.q.h"
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.q.h"
#include "y2014_bot3/control_loops/rollers/rollers.q.h"
-using ::y2014_bot3::control_loops::drivetrain_queue;
+using ::frc971::control_loops::drivetrain_queue;
using ::y2014_bot3::control_loops::rollers_queue;
using ::frc971::sensors::gyro_reading;
@@ -30,9 +30,12 @@
// Joystick & button addresses.
const JoystickAxis kSteeringWheel(1, 1), kDriveThrottle(2, 2);
-const ButtonLocation kShiftHigh(2, 3), kShiftLow(2, 1);
+const ButtonLocation kShiftHigh(2, 3), kShiftHigh2(2, 2), kShiftLow(2, 1);
const ButtonLocation kQuickTurn(1, 5);
+const ButtonLocation kTurn1(1, 7);
+const ButtonLocation kTurn2(1, 11);
+
const ButtonLocation kFrontRollersIn(3, 8);
const ButtonLocation kBackRollersIn(3, 7);
const ButtonLocation kFrontRollersOut(3, 6);
@@ -62,15 +65,33 @@
}
void HandleDrivetrain(const ::aos::input::driver_station::Data &data) {
+ bool is_control_loop_driving = false;
+ static double left_goal = 0.0;
+ static double right_goal = 0.0;
const double wheel = -data.GetAxis(kSteeringWheel);
const double throttle = -data.GetAxis(kDriveThrottle);
+ if (data.PosEdge(kTurn1) || data.PosEdge(kTurn2)) {
+ drivetrain_queue.status.FetchLatest();
+ if (drivetrain_queue.status.get()) {
+ left_goal = drivetrain_queue.status->estimated_left_position;
+ right_goal = drivetrain_queue.status->estimated_right_position;
+ }
+ }
+ if (data.IsPressed(kTurn1) || data.IsPressed(kTurn2)) {
+ is_control_loop_driving = true;
+ }
+
if (!drivetrain_queue.goal.MakeWithBuilder()
.steering(wheel)
.throttle(throttle)
- .quickturn(data.IsPressed(kQuickTurn))
- .control_loop_driving(false)
.highgear(is_high_gear_)
+ .quickturn(data.IsPressed(kQuickTurn))
+ .control_loop_driving(is_control_loop_driving)
+ .left_goal(left_goal - wheel * 0.5 + throttle * 0.3)
+ .right_goal(right_goal + wheel * 0.5 + throttle * 0.3)
+ .left_velocity_goal(0)
+ .right_velocity_goal(0)
.Send()) {
LOG(WARNING, "sending stick values failed\n");
}
@@ -79,7 +100,7 @@
is_high_gear_ = false;
}
- if (data.PosEdge(kShiftHigh)) {
+ if (data.PosEdge(kShiftHigh) || data.PosEdge(kShiftHigh2)) {
is_high_gear_ = true;
}
}
diff --git a/y2014_bot3/wpilib/BUILD b/y2014_bot3/wpilib/BUILD
index 5f5319c..8af099f 100644
--- a/y2014_bot3/wpilib/BUILD
+++ b/y2014_bot3/wpilib/BUILD
@@ -10,7 +10,7 @@
'//aos/common:stl_mutex',
'//aos/common/logging',
'//third_party/allwpilib_2016:wpilib',
- '//y2014_bot3/control_loops/drivetrain:drivetrain_queue',
+ '//frc971/control_loops/drivetrain:drivetrain_queue',
'//aos/common/controls:control_loop',
'//aos/common/util:log_interval',
'//aos/common:time',
@@ -29,7 +29,7 @@
'//frc971/wpilib:pdp_fetcher',
'//frc971/wpilib:dma',
'//y2014_bot3/autonomous:auto_queue',
- '//y2014_bot3/control_loops/drivetrain:drivetrain_lib',
'//y2014_bot3/control_loops/rollers:rollers_lib',
+ '//y2014_bot3/control_loops/drivetrain:drivetrain_base',
],
)
diff --git a/y2014_bot3/wpilib/wpilib_interface.cc b/y2014_bot3/wpilib/wpilib_interface.cc
index e1e07a0..5692465 100644
--- a/y2014_bot3/wpilib/wpilib_interface.cc
+++ b/y2014_bot3/wpilib/wpilib_interface.cc
@@ -27,10 +27,10 @@
#include "aos/linux_code/init.h"
#include "aos/common/messages/robot_state.q.h"
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.q.h"
+#include "frc971/control_loops/drivetrain/drivetrain.q.h"
+#include "y2014_bot3/control_loops/drivetrain/drivetrain_base.h"
#include "y2014_bot3/control_loops/rollers/rollers.q.h"
#include "y2014_bot3/autonomous/auto.q.h"
-#include "y2014_bot3/control_loops/drivetrain/drivetrain.h"
#include "y2014_bot3/control_loops/rollers/rollers.h"
#include "frc971/wpilib/joystick_sender.h"
@@ -48,7 +48,7 @@
#endif
using ::aos::util::SimpleLogInterval;
-using ::y2014_bot3::control_loops::drivetrain_queue;
+using ::frc971::control_loops::drivetrain_queue;
using ::y2014_bot3::control_loops::rollers_queue;
using ::frc971::wpilib::BufferedPcm;
using ::frc971::wpilib::BufferedSolenoid;
@@ -61,13 +61,13 @@
double drivetrain_translate(int32_t in) {
return static_cast<double>(in) / (256.0 /*cpr*/ * 4.0 /*4x*/) *
- ::y2014_bot3::control_loops::kDrivetrainEncoderRatio *
+ ::y2014_bot3::control_loops::drivetrain::kDrivetrainEncoderRatio *
(4 /*wheel diameter*/ * 2.54 / 100.0 * M_PI);
}
double drivetrain_velocity_translate(double in) {
return (1.0 / in) / 256.0 /*cpr*/ *
- ::y2014_bot3::control_loops::kDrivetrainEncoderRatio *
+ ::y2014_bot3::control_loops::drivetrain::kDrivetrainEncoderRatio *
(4 /*wheel diameter*/ * 2.54 / 100.0 * M_PI);
}
@@ -154,7 +154,7 @@
public:
SolenoidWriter(const ::std::unique_ptr<::frc971::wpilib::BufferedPcm> &pcm)
: pcm_(pcm),
- drivetrain_(".y2014_bot3.control_loops.drivetrain_queue.output"),
+ drivetrain_(".frc971.control_loops.drivetrain_queue.output"),
rollers_(".y2014_bot3.control_loops.rollers_queue.output") {}
void set_pressure_switch(::std::unique_ptr<DigitalInput> pressure_switch) {
@@ -249,7 +249,7 @@
::std::unique_ptr<DigitalInput> pressure_switch_;
::std::unique_ptr<Relay> compressor_relay_;
- ::aos::Queue<::y2014_bot3::control_loops::DrivetrainQueue::Output>
+ ::aos::Queue<::frc971::control_loops::DrivetrainQueue::Output>
drivetrain_;
::aos::Queue<::y2014_bot3::control_loops::RollersQueue::Output> rollers_;
@@ -269,11 +269,11 @@
private:
virtual void Read() override {
- ::y2014_bot3::control_loops::drivetrain_queue.output.FetchAnother();
+ ::frc971::control_loops::drivetrain_queue.output.FetchAnother();
}
virtual void Write() override {
- auto &queue = ::y2014_bot3::control_loops::drivetrain_queue.output;
+ auto &queue = ::frc971::control_loops::drivetrain_queue.output;
LOG_STRUCT(DEBUG, "will output", *queue);
left_drivetrain_talon_->Set(-queue->left_voltage / 12.0);
right_drivetrain_talon_->Set(queue->right_voltage / 12.0);
@@ -373,9 +373,9 @@
// Outputs
DrivetrainWriter drivetrain_writer;
drivetrain_writer.set_left_drivetrain_talon(
- ::std::unique_ptr<Talon>(new Talon(2)));
- drivetrain_writer.set_right_drivetrain_talon(
::std::unique_ptr<Talon>(new Talon(5)));
+ drivetrain_writer.set_right_drivetrain_talon(
+ ::std::unique_ptr<Talon>(new Talon(2)));
::std::thread drivetrain_writer_thread(::std::ref(drivetrain_writer));
RollersWriter rollers_writer;
diff --git a/y2016/constants.cc b/y2016/constants.cc
index 974a82d..6e33055 100644
--- a/y2016/constants.cc
+++ b/y2016/constants.cc
@@ -81,8 +81,7 @@
5.0, // drivetrain max speed
// Intake
- {
- // Value to add to the pot reading for the intake.
+ {// Value to add to the pot reading for the intake.
-4.550531 + 150.40906362 * M_PI / 180.0 + 0.5098 - 0.0178 - 0.0725,
{Values::kZeroingSampleSize, Values::kIntakeEncoderIndexDifference,
// Location of an index pulse.
@@ -90,8 +89,7 @@
},
// Shoulder
- {
- // Value to add to the pot reading for the shoulder.
+ {// Value to add to the pot reading for the shoulder.
-1.0 - 0.0822 + 0.06138835 * M_PI / 180.0 - 0.0323 - 0.1057 +
0.0035 + 0.0055 - 0.001 - 0.0103 + 0.0032 - 0.0755,
{Values::kZeroingSampleSize, Values::kShoulderEncoderIndexDifference,
@@ -99,10 +97,10 @@
},
// Wrist
- {
- // Value to add to the pot reading for the wrist.
+ {// Value to add to the pot reading for the wrist.
3.2390714288298668 + -0.06138835 * M_PI / 180.0 + 0.0078 - 0.0548 -
- 0.0167 + 0.002 - 0.0026 - 0.1040 - 0.0035 - 0.0012 + 0.0166 - 0.017 + 0.148 + 0.004,
+ 0.0167 + 0.002 - 0.0026 - 0.1040 - 0.0035 - 0.0012 + 0.0166 -
+ 0.017 + 0.148 + 0.004,
{Values::kZeroingSampleSize, Values::kWristEncoderIndexDifference,
-0.354946, 2.5},
},
@@ -116,10 +114,9 @@
5.0, // drivetrain max speed
// Intake
- {
- // Hard stop is 164.2067247 degrees.
- -4.2193 + (164.2067247 * M_PI / 180.0 + 0.02 - 0.0235) + 0.0549 -
- 0.104 + 0.019 - 0.938 + 0.660 - 0.002,
+ {// Hard stop is 160.0185751389329 degrees.
+ -4.2193 + (160.0185751389329 * M_PI / 180.0 + 0.02 - 0.0235) +
+ 0.0549 - 0.104 + 0.019 - 0.938 + 0.660 - 0.002 - 0.2081,
{Values::kZeroingSampleSize, Values::kIntakeEncoderIndexDifference,
0.332370, 1.3},
},
@@ -135,7 +132,8 @@
// Wrist
{
3.326328571170133 - 0.06138835 * M_PI / 180.0 - 0.177 + 0.0323 -
- 0.023 + 0.0488 + 0.0120 - 0.0005 - 0.0784 - 0.0010 - 0.080 + 0.1245,
+ 0.023 + 0.0488 + 0.0120 - 0.0005 - 0.0784 - 0.0010 - 0.080 +
+ 0.1245,
{Values::kZeroingSampleSize, Values::kWristEncoderIndexDifference,
-0.263227, 1.3},
},
diff --git a/y2016/plotting/responsive_plotter.js b/y2016/plotting/responsive_plotter.js
new file mode 100644
index 0000000..0840e1d
--- /dev/null
+++ b/y2016/plotting/responsive_plotter.js
@@ -0,0 +1,238 @@
+"use strict";
+
+// Create anonymous namespace to avoid leaking these functions.
+(function() {
+// Convenience function that fetches a file and extracts the array buffer.
+function fetch_ArrayBuffer(url) { // returns Promise<ArrayBuffer>
+ return fetch(url).then(function(val) { return val.arrayBuffer(); });
+}
+
+// Two dimensional vector.
+class Point2d {
+ constructor(x, y) {
+ this.x = x;
+ this.y = y;
+ }
+ sub(o) { return new Point2d(this.x - o.x, this.y - o.y); }
+ add(o) { return new Point2d(this.x + o.x, this.y + o.y); }
+};
+
+// Drag event object for updating a Point2d class by reference.
+class PointDrag {
+ constructor(point) { // point : Point2d
+ this.point = point;
+ }
+ doDrag(delta) {
+ this.point.x += delta.x;
+ this.point.y += delta.y;
+ }
+ doMouseUp(e) { return null; }
+}
+
+// Takes in a canvas and adds the ability to click and drag the offset point.
+// scaleX and scaleY are allowed to be locked or not-locked as the scroll events
+// must be handled by the user of this class.
+//
+// offset.x and offset.y are defined in reference to the model-scale, not the viewport.
+// Thus to move the viewport you need to use offset.x * scaleX, etc.
+//
+// scaleX and scaleY aren't automatically applied to the rendering context because
+// differing x and y scales mess up the line width rendering.
+class ClickDrag {
+ constructor(canvas) {
+ canvas.addEventListener('selectstart', function(e) { e.preventDefault(); return false; }, false);
+ canvas.addEventListener('mousemove', this.handleMouseMove.bind(this), true);
+ canvas.addEventListener('mousedown', this.handleMouseDown.bind(this), true);
+ canvas.addEventListener('mouseup', this.handleMouseUp.bind(this), true);
+ this.canvas = canvas;
+ this.dragger = null;
+ this.offset = new Point2d(0, 0);
+ this.scaleX = 1.0;
+ this.scaleY = 1.0;
+ this.old_point = null;
+ this.on_redraw = null;
+ }
+ translateContext(ctx) { // ctx : CanvasRenderingContext2D
+ ctx.translate(this.offset.x * this.scaleX, this.offset.y * this.scaleY);
+ }
+ handleMouseMove(e) { // e : MouseEvent
+ let pos = new Point2d(e.offsetX / this.scaleX, e.offsetY / this.scaleY);
+ if (this.old_point !== null && this.dragger !== null) {
+ this.dragger.doDrag(pos.sub(this.old_point));
+ if (this.on_redraw !== null) { this.on_redraw(); }
+ }
+ this.old_point = pos;
+ }
+ get width() { return this.canvas.width; }
+ handleMouseDown(e) { // e : MouseEvent
+ this.dragger = new PointDrag(this.offset);
+ }
+ handleMouseUp(e) { // e : MouseEvent
+ if (this.dragger === null) { return; }
+ if (this.dragger.doMouseUp !== undefined) {
+ this.dragger = this.dragger.doMouseUp(e);
+ if (this.on_redraw !== null) { this.on_redraw(); }
+ }
+ }
+ multiplyScale(evt, dx, dy) {
+ let x_cur = evt.offsetX / this.scaleX - this.offset.x;
+ let y_cur = evt.offsetY / this.scaleY - this.offset.y;
+ this.scaleX *= dx;
+ this.scaleY *= dy;
+ this.offset.x = evt.offsetX / this.scaleX - x_cur;
+ this.offset.y = evt.offsetY / this.scaleY - y_cur;
+ if (this.on_redraw !== null) { this.on_redraw(); }
+ }
+};
+
+// This represents a particular downsampling of a timeseries dataset.
+// For the base level, data = min = max.
+// This is required
+class MipMapLevel {
+ // All arrays should be the same size.
+ constructor(data, min, max, scale) { // data : Float32Array, min : Float32Array, max : Float32Array, scale : Integer
+ this.data = data;
+ this.min = min;
+ this.max = max;
+ this.scale = scale;
+ }
+ get length() { return this.data.length; }
+ // Uses box filter to downsample. Guassian may be an improvement.
+ downsample() {
+ let new_length = (this.data.length / 2) | 0;
+ let data = new Float32Array(new_length);
+ let min = new Float32Array(new_length);
+ let max = new Float32Array(new_length);
+ for (let i = 0; i < new_length; i++) {
+ let i1 = i * 2;
+ let i2 = i1 + 1
+ data[i] = (this.data[i1] + this.data[i2]) / 2.0;
+ min[i] = Math.min(this.min[i1], this.min[i2]);
+ max[i] = Math.max(this.max[i1], this.max[i2]);
+ }
+ return new MipMapLevel(data, min, max, this.scale * 2);
+ }
+ static makeBaseLevel(data) { // data : Float32Array
+ return new MipMapLevel(data, data, data, 1);
+ }
+ clipv(v) { // v : Numeric
+ return Math.min(Math.max(v|0, 0), this.length - 1);
+ }
+ draw(ctx, clickDrag) { // ctx : CanvasRenderingContext2D, clickDrag : ClickDrag
+ let scalex = clickDrag.scaleX * this.scale;
+ let scaley = clickDrag.scaleY;
+ let stx = -clickDrag.offset.x / this.scale;
+ let edx = stx + clickDrag.width / scalex;
+ let sti = this.clipv(stx - 2);
+ let edi = this.clipv(edx + 2);
+ ctx.beginPath();
+ ctx.fillStyle="#00ff00";
+ ctx.moveTo(sti * scalex, scaley * this.min[sti]);
+ for (let i = sti + 1; i <= edi; i++) {
+ ctx.lineTo(i * scalex, scaley * this.min[i]);
+ }
+ for (let i = edi; i >= sti; --i) {
+ ctx.lineTo(i * scalex, scaley * this.max[i]);
+ }
+ ctx.fill();
+ ctx.closePath();
+
+ ctx.beginPath();
+ ctx.strokeStyle="#008f00";
+ ctx.moveTo(sti * scalex, scaley * this.data[sti]);
+ for (let i = sti + 1; i <= edi; i++) {
+ ctx.lineTo(i * scalex, scaley * this.data[i]);
+ }
+ ctx.stroke();
+ ctx.closePath();
+ }
+};
+
+// This class represents all downsampled data levels.
+// This must only be used for descrite time-series data.
+class MipMapper {
+ constructor(samples) { // samples : Float32Array
+ this.levels = [];
+ let level = MipMapLevel.makeBaseLevel(samples);
+ this.levels.push(level);
+ while (level.length > 2) {
+ level = level.downsample();
+ this.levels.push(level);
+ }
+ }
+ // Find the level such that samples are spaced at most 2 pixels apart
+ getLevel(scale) { // scale : Float
+ let level = this.levels[0];
+ for (let i = 0; i < this.levels.length; ++i) {
+ // Someone who understands nyquist could probably improve this.
+ if (this.levels[i].scale * scale <= 4.0) {
+ level = this.levels[i];
+ }
+ }
+ return level;
+ }
+}
+
+// Custom HTML element for x-responsive-plotter.
+// This should be the main entry-point for this code.
+class ResponsivePlotter extends HTMLElement {
+ createdCallback() {
+ this.data = null;
+ this.canvas = document.createElement("canvas");
+ this.canvas.style["background"] = "inherit";
+ this.canvas.addEventListener("mousewheel", this.doScroll.bind(this), false);
+ this.clickDrag = new ClickDrag(this.canvas);
+ this.clickDrag.on_redraw = this.doRedraw.bind(this);
+ this.clickDrag.offset.y = 160; //320;
+ this.updateInnerData();
+ this.appendChild(this.canvas);
+ }
+ doScroll(e) {
+ let factor = (e.wheelDelta < 0) ? 0.9 : 1.1;
+ this.clickDrag.multiplyScale(e, e.shiftKey ? 1.0 : factor, e.shiftKey ? factor : 1.0);
+ e.preventDefault();
+ }
+ doRedraw() {
+ this.redraw();
+ }
+ updateInnerData() {
+ this.canvas.width = this.getAttribute("width") || 640;
+ this.canvas.height = this.getAttribute("height") || 480;
+ fetch_ArrayBuffer(this.getAttribute("data")).then(this.dataUpdated.bind(this));
+ this.redraw();
+ }
+ attributeChangedCallback(attrName, oldVal, newVal) {
+ if (attrName == "width") {
+ this.canvas.width = this.getAttribute("width") || 640;
+ this.redraw();
+ } else if (attrName == "height") {
+ this.canvas.width = this.getAttribute("height") || 480;
+ this.redraw();
+ } else if (attrName == "data") {
+ // Should this clear out the canvas if a different url is selected?
+ // Well it does.
+ this.data = null;
+ fetch_ArrayBuffer(this.getAttribute("data")).then(this.dataUpdated.bind(this));
+ }
+ }
+ dataUpdated(data) { // data : ArrayBuffer
+ this.data = new MipMapper(new Float32Array(data));
+ this.redraw();
+ }
+ redraw() {
+ let ctx = this.canvas.getContext('2d');
+ ctx.clearRect(0, 0, this.canvas.width, this.canvas.height);
+ ctx.save();
+ this.clickDrag.translateContext(ctx);
+ if (this.data !== null) {
+ let level = this.data.getLevel(this.clickDrag.scaleX);
+ level.draw(ctx, this.clickDrag);
+ }
+ ctx.restore();
+ }
+};
+
+
+// TODO(parker): This is chrome-specific v0 version of this switch to v1 when available.
+document.registerElement('x-responsive-plotter', ResponsivePlotter);
+})();
diff --git a/y2016/plotting/test.html b/y2016/plotting/test.html
new file mode 100644
index 0000000..df278b0
--- /dev/null
+++ b/y2016/plotting/test.html
@@ -0,0 +1,12 @@
+<!DOCTYPE html>
+<html>
+ <head>
+ <meta charset="UTF-8">
+ <script src="/responsive_plotter.js" type="text/javascript"></script>
+ </head>
+
+ <body style=>
+ <x-responsive-plotter width=800 data="/test_data" style="background: lightblue;">
+ </x-responsive-plotter>
+ </body>
+</html>
diff --git a/y2016/plotting/test.rb b/y2016/plotting/test.rb
new file mode 100644
index 0000000..9f2f58a
--- /dev/null
+++ b/y2016/plotting/test.rb
@@ -0,0 +1,29 @@
+require "sinatra"
+
+# Must use sinatra server for this because fetch() in javascript
+# cannot load from the filesystem.
+get '/test.html' do
+ File.read("./test.html")
+end
+
+get '/responsive_plotter.js' do
+ content_type 'text/javascript'
+ File.read("./responsive_plotter.js")
+end
+
+get '/test_data' do
+ content_type 'binary/octet-stream'
+ data = ""
+ # Use ./test_data if it exists. Otherwise random data.
+ if (File.exists?("./test_data"))
+ data = File.read("./test_data")
+ else
+ 1000.times do
+ data += (1024.times.collect do |i|
+ (rand() * 480 - 160)
+ end.pack("F*"))
+ end
+ end
+ data
+end
+