Refactor year-agnostic catapult code to frc971
This breaks up the y2022 catapult code into multiple files and moves
them into the frc971 folder. Year-specific parameters are now
provided via the constructors, and the goal message is moved into
frc971 as well.
Signed-off-by: Niko Sohmers <nikolai@sohmers.com>
Change-Id: I4ea720ae62a7c6c229d6c24a1f08edd7bc5b9728
diff --git a/frc971/control_loops/catapult/BUILD b/frc971/control_loops/catapult/BUILD
new file mode 100644
index 0000000..1235044
--- /dev/null
+++ b/frc971/control_loops/catapult/BUILD
@@ -0,0 +1,86 @@
+load("//aos/flatbuffers:generate.bzl", "static_flatbuffer")
+
+package(default_visibility = ["//visibility:public"])
+
+static_flatbuffer(
+ name = "catapult_goal_fbs",
+ srcs = [
+ "catapult_goal.fbs",
+ ],
+ deps = [
+ "//frc971/control_loops:profiled_subsystem_fbs",
+ ],
+)
+
+cc_library(
+ name = "catapult_controller",
+ srcs =
+ [
+ "catapult_controller.cc",
+ ],
+ hdrs =
+ [
+ "catapult_controller.h",
+ ],
+ visibility = ["//visibility:public"],
+ deps =
+ [
+ ":mpc_problem_generator",
+ ],
+)
+
+cc_library(
+ name = "mpc_problem",
+ srcs =
+ [
+ "mpc_problem.cc",
+ ],
+ hdrs =
+ [
+ "mpc_problem.h",
+ ],
+ visibility = ["//visibility:public"],
+ deps =
+ [
+ "//aos:realtime",
+ "//aos/time",
+ "//third_party/osqp-cpp",
+ "@org_tuxfamily_eigen//:eigen",
+ ],
+)
+
+cc_library(
+ name = "mpc_problem_generator",
+ srcs =
+ [
+ "mpc_problem_generator.cc",
+ ],
+ hdrs =
+ [
+ "mpc_problem_generator.h",
+ ],
+ visibility = ["//visibility:public"],
+ deps =
+ [
+ ":mpc_problem",
+ "//frc971/control_loops:state_feedback_loop",
+ ],
+)
+
+cc_library(
+ name = "catapult",
+ srcs = [
+ "catapult.cc",
+ ],
+ hdrs =
+ [
+ "catapult.h",
+ ],
+ visibility = ["//visibility:public"],
+ deps = [
+ ":catapult_controller",
+ "//frc971/control_loops:static_zeroing_single_dof_profiled_subsystem",
+ "//frc971/control_loops/catapult:catapult_goal_fbs",
+ "//frc971/zeroing:pot_and_absolute_encoder",
+ ],
+)
diff --git a/frc971/control_loops/catapult/catapult.cc b/frc971/control_loops/catapult/catapult.cc
new file mode 100644
index 0000000..2e1867c
--- /dev/null
+++ b/frc971/control_loops/catapult/catapult.cc
@@ -0,0 +1,138 @@
+#include "frc971/control_loops/catapult/catapult.h"
+
+namespace frc971::control_loops::catapult {
+
+const flatbuffers::Offset<
+ frc971::control_loops::PotAndAbsoluteEncoderProfiledJointStatus>
+Catapult::Iterate(const CatapultGoal *catapult_goal,
+ const PotAndAbsolutePosition *position,
+ double battery_voltage, double *catapult_voltage, bool fire,
+ flatbuffers::FlatBufferBuilder *fbb) {
+ const frc971::control_loops::StaticZeroingSingleDOFProfiledSubsystemGoal
+ *return_goal =
+ catapult_goal != nullptr && catapult_goal->has_return_position()
+ ? catapult_goal->return_position()
+ : nullptr;
+
+ const bool catapult_disabled =
+ catapult_.Correct(return_goal, position, catapult_voltage == nullptr);
+
+ if (catapult_disabled) {
+ catapult_state_ = CatapultState::PROFILE;
+ } else if (catapult_.running() && catapult_goal != nullptr && fire &&
+ !last_firing_) {
+ catapult_state_ = CatapultState::FIRING;
+ latched_shot_position = catapult_goal->shot_position();
+ latched_shot_velocity = catapult_goal->shot_velocity();
+ }
+
+ // Don't update last_firing_ if the catapult is disabled, so that we actually
+ // end up firing once it's enabled
+ if (catapult_.running() && !catapult_disabled) {
+ last_firing_ = fire;
+ }
+
+ use_profile_ = true;
+
+ switch (catapult_state_) {
+ case CatapultState::FIRING: {
+ // Select the ball controller. We should only be firing if we have a
+ // ball, or at least should only care about the shot accuracy.
+ catapult_.set_controller_index(0);
+ // Ok, so we've now corrected. Next step is to run the MPC.
+ //
+ // Since there is a unit delay between when we ask for a U and the
+ // hardware applies it, we need to run the optimizer for the position at
+ // the *next* control loop cycle.
+
+ Eigen::Vector3d next_X = catapult_.estimated_state();
+ for (int i = catapult_.controller().plant().coefficients().delayed_u;
+ i > 1; --i) {
+ next_X = catapult_.controller().plant().A() * next_X +
+ catapult_.controller().plant().B() *
+ catapult_.controller().observer().last_U(i - 1);
+ }
+
+ catapult_mpc_.SetState(
+ next_X.block<2, 1>(0, 0),
+ Eigen::Vector2d(latched_shot_position, latched_shot_velocity));
+
+ const bool solved = catapult_mpc_.Solve();
+ current_horizon_ = catapult_mpc_.current_horizon();
+ const bool started = catapult_mpc_.started();
+ if (solved || started) {
+ std::optional<double> solution = catapult_mpc_.Next();
+
+ if (!solution.has_value()) {
+ CHECK_NOTNULL(catapult_voltage);
+ *catapult_voltage = 0.0;
+ if (catapult_mpc_.started()) {
+ ++shot_count_;
+ // Finished the catapult, time to fire.
+ catapult_state_ = CatapultState::RESETTING;
+ }
+ } else {
+ // TODO(austin): Voltage error?
+ CHECK_NOTNULL(catapult_voltage);
+ if (current_horizon_ == 1) {
+ battery_voltage = 12.0;
+ }
+ *catapult_voltage = std::max(
+ 0.0, std::min(12.0, (*solution - 0.0 * next_X(2, 0)) * 12.0 /
+ std::max(battery_voltage, 8.0)));
+ use_profile_ = false;
+ }
+ } else {
+ if (!fire) {
+ // Eh, didn't manage to solve before it was time to fire. Give up.
+ catapult_state_ = CatapultState::PROFILE;
+ }
+ }
+
+ if (!use_profile_) {
+ catapult_.ForceGoal(catapult_.estimated_position(),
+ catapult_.estimated_velocity());
+ }
+ }
+ if (catapult_state_ != CatapultState::RESETTING) {
+ break;
+ } else {
+ [[fallthrough]];
+ }
+
+ case CatapultState::RESETTING:
+ if (catapult_.controller().R(1, 0) > 7.0) {
+ catapult_.AdjustProfile(7.0, 2000.0);
+ } else if (catapult_.controller().R(1, 0) > 0.0) {
+ catapult_.AdjustProfile(7.0, 1000.0);
+ } else {
+ catapult_state_ = CatapultState::PROFILE;
+ }
+ [[fallthrough]];
+
+ case CatapultState::PROFILE:
+ break;
+ }
+
+ if (use_profile_) {
+ if (catapult_state_ != CatapultState::FIRING) {
+ catapult_mpc_.Reset();
+ }
+ // Select the controller designed for when we have no ball.
+ catapult_.set_controller_index(1);
+
+ current_horizon_ = 0u;
+ const double output_voltage = catapult_.UpdateController(catapult_disabled);
+ if (catapult_voltage != nullptr) {
+ *catapult_voltage = output_voltage;
+ }
+ }
+
+ catapult_.UpdateObserver(catapult_voltage != nullptr
+ ? (*catapult_voltage * battery_voltage / 12.0)
+ : 0.0);
+
+ return catapult_.MakeStatus(fbb);
+}
+
+} // namespace frc971::control_loops::catapult
\ No newline at end of file
diff --git a/frc971/control_loops/catapult/catapult.h b/frc971/control_loops/catapult/catapult.h
new file mode 100644
index 0000000..e84ea88
--- /dev/null
+++ b/frc971/control_loops/catapult/catapult.h
@@ -0,0 +1,79 @@
+#ifndef FRC971_CONTROL_LOOPS_CATAPULT_CATAPULT_H_
+#define FRC971_CONTROL_LOOPS_CATAPULT_CATAPULT_H_
+
+#include "frc971/control_loops/catapult/catapult_controller.h"
+#include "frc971/control_loops/catapult/catapult_goal_generated.h"
+#include "frc971/control_loops/static_zeroing_single_dof_profiled_subsystem.h"
+#include "frc971/zeroing/pot_and_absolute_encoder.h"
+
+namespace frc971 {
+namespace control_loops {
+namespace catapult {
+
+// Class to handle transitioning between both the profiled subsystem and the MPC
+// for shooting.
+class Catapult {
+ public:
+ Catapult(frc971::control_loops::StaticZeroingSingleDOFProfiledSubsystemParams<
+ zeroing::PotAndAbsoluteEncoderZeroingEstimator>
+ catapult_params,
+ StateFeedbackPlant<2, 1, 1> plant)
+ : catapult_(catapult_params), catapult_mpc_(std::move(plant), 30) {}
+
+ using PotAndAbsoluteEncoderSubsystem =
+ ::frc971::control_loops::StaticZeroingSingleDOFProfiledSubsystem<
+ ::frc971::zeroing::PotAndAbsoluteEncoderZeroingEstimator,
+ ::frc971::control_loops::PotAndAbsoluteEncoderProfiledJointStatus>;
+
+ // Resets all state for when WPILib restarts.
+ void Reset() { catapult_.Reset(); }
+
+ void Estop() { catapult_.Estop(); }
+
+ bool zeroed() const { return catapult_.zeroed(); }
+ bool estopped() const { return catapult_.estopped(); }
+ double solve_time() const { return catapult_mpc_.solve_time(); }
+
+ uint8_t mpc_horizon() const { return current_horizon_; }
+
+ bool mpc_active() const { return !use_profile_; }
+
+ // Returns the number of shots taken.
+ int shot_count() const { return shot_count_; }
+
+ // Returns the estimated position
+ double estimated_position() const { return catapult_.estimated_position(); }
+
+ // Runs either the MPC or the profiled subsystem depending on if we are
+ // shooting or not. Returns the status.
+ const flatbuffers::Offset<
+ frc971::control_loops::PotAndAbsoluteEncoderProfiledJointStatus>
+ Iterate(const CatapultGoal *catapult_goal,
+ const PotAndAbsolutePosition *position, double battery_voltage,
+ double *catapult_voltage, bool fire,
+ flatbuffers::FlatBufferBuilder *fbb);
+
+ private:
+ PotAndAbsoluteEncoderSubsystem catapult_;
+
+ frc971::control_loops::catapult::CatapultController catapult_mpc_;
+
+ enum CatapultState { PROFILE, FIRING, RESETTING };
+
+ CatapultState catapult_state_ = CatapultState::PROFILE;
+
+ double latched_shot_position = 0.0;
+ double latched_shot_velocity = 0.0;
+
+ bool last_firing_ = false;
+ bool use_profile_ = true;
+
+ int shot_count_ = 0;
+ uint8_t current_horizon_ = 0u;
+};
+
+} // namespace catapult
+} // namespace control_loops
+} // namespace frc971
+
+#endif // Y2022_CONTROL_LOOPS_SUPERSTRUCTURE_CATAPULT_CATAPULT_H_
diff --git a/frc971/control_loops/catapult/catapult_controller.cc b/frc971/control_loops/catapult/catapult_controller.cc
new file mode 100644
index 0000000..a4187f7
--- /dev/null
+++ b/frc971/control_loops/catapult/catapult_controller.cc
@@ -0,0 +1,62 @@
+#include "frc971/control_loops/catapult/catapult_controller.h"
+
+namespace frc971::control_loops::catapult {
+
+CatapultController::CatapultController(StateFeedbackPlant<2, 1, 1> plant,
+ size_t horizon)
+ : generator_(std::move(plant), horizon) {
+ problems_.reserve(generator_.horizon());
+ for (size_t i = generator_.horizon(); i > 0; --i) {
+ problems_.emplace_back(generator_.MakeProblem(i));
+ }
+
+ Reset();
+}
+
+void CatapultController::Reset() {
+ current_controller_ = 0;
+ solve_time_ = 0.0;
+}
+
+void CatapultController::SetState(Eigen::Matrix<double, 2, 1> X_initial,
+ Eigen::Matrix<double, 2, 1> X_final) {
+ if (current_controller_ >= problems_.size()) {
+ return;
+ }
+ problems_[current_controller_]->SetState(X_initial, X_final);
+}
+
+bool CatapultController::Solve() {
+ if (current_controller_ >= problems_.size()) {
+ return true;
+ }
+ const bool result = problems_[current_controller_]->Solve();
+ solve_time_ = problems_[current_controller_]->solve_time();
+ return result;
+}
+
+std::optional<double> CatapultController::Next() {
+ if (current_controller_ >= problems_.size()) {
+ return std::nullopt;
+ }
+
+ double u;
+ size_t solution_number = 0;
+ if (current_controller_ == 0u) {
+ while (solution_number < problems_[current_controller_]->horizon() &&
+ problems_[current_controller_]->U(solution_number) < 0.01) {
+ u = problems_[current_controller_]->U(solution_number);
+ ++solution_number;
+ }
+ }
+ u = problems_[current_controller_]->U(solution_number);
+
+ if (current_controller_ + 1u + solution_number < problems_.size()) {
+ problems_[current_controller_ + solution_number + 1]->WarmStart(
+ *problems_[current_controller_]);
+ }
+ current_controller_ += 1u + solution_number;
+ return u;
+}
+
+} // namespace frc971::control_loops::catapult
\ No newline at end of file
diff --git a/frc971/control_loops/catapult/catapult_controller.h b/frc971/control_loops/catapult/catapult_controller.h
new file mode 100644
index 0000000..3a666f9
--- /dev/null
+++ b/frc971/control_loops/catapult/catapult_controller.h
@@ -0,0 +1,65 @@
+#include "frc971/control_loops/catapult/mpc_problem_generator.h"
+// A class to hold all the state needed to manage the catapult MPC solvers for
+// repeated shots.
+//
+// The solver may take a couple of cycles to get everything converged and ready.
+// The flow is as follows:
+// 1) Reset() the state for the new problem.
+// 2) Update to the current state with SetState()
+// 3) Call Solve(). This will return true if it is ready to be executed, false
+// if it needs more iterations to fully converge.
+// 4) Next() returns the current optimal control output and advances the
+// pointers to the next problem.
+// 5) Go back to 2 for the next cycle.
+
+namespace frc971 {
+namespace control_loops {
+namespace catapult {
+
+class CatapultController {
+ public:
+ CatapultController(StateFeedbackPlant<2, 1, 1> plant, size_t horizon);
+
+ // Starts back over at the first controller.
+ void Reset();
+
+ // Updates our current and final states for the current controller.
+ void SetState(Eigen::Matrix<double, 2, 1> X_initial,
+ Eigen::Matrix<double, 2, 1> X_final);
+
+ // Solves! Returns true if the solution converged and osqp was happy.
+ bool Solve();
+
+ // Returns the time in seconds it last took Solve to run.
+ double solve_time() const { return solve_time_; }
+
+ // Returns the horizon of the current controller.
+ size_t current_horizon() const {
+ if (current_controller_ >= problems_.size()) {
+ return 0u;
+ } else {
+ return problems_[current_controller_]->horizon();
+ }
+ }
+
+ // Returns the controller value if there is a controller to run, or nullopt if
+ // we finished the last controller. Advances the controller pointer to the
+ // next controller and warms up the next controller.
+ std::optional<double> Next();
+
+ // Returns true if Next has been called and a controller has been used. Reset
+ // starts over.
+ bool started() const { return current_controller_ != 0u; }
+
+ private:
+ CatapultProblemGenerator generator_;
+
+ std::vector<std::unique_ptr<MPCProblem>> problems_;
+
+ size_t current_controller_ = 0;
+ double solve_time_ = 0.0;
+};
+
+} // namespace catapult
+} // namespace control_loops
+} // namespace frc971
\ No newline at end of file
diff --git a/frc971/control_loops/catapult/catapult_goal.fbs b/frc971/control_loops/catapult/catapult_goal.fbs
new file mode 100644
index 0000000..3e59455
--- /dev/null
+++ b/frc971/control_loops/catapult/catapult_goal.fbs
@@ -0,0 +1,17 @@
+include "frc971/control_loops/profiled_subsystem.fbs";
+
+namespace frc971.control_loops.catapult;
+
+table CatapultGoal {
+ // Old fire flag, only kept for backwards-compatability with logs.
+ // Use the fire flag in the root Goal instead
+ fire:bool (id: 0, deprecated);
+
+ // The target shot position and velocity. If these are provided before fire
+ // is called, the optimizer can pre-compute the trajectory.
+ shot_position:double (id: 1);
+ shot_velocity:double (id: 2);
+
+ // The target position to return the catapult to when not shooting.
+ return_position:frc971.control_loops.StaticZeroingSingleDOFProfiledSubsystemGoal (id: 3);
+}
\ No newline at end of file
diff --git a/frc971/control_loops/catapult/mpc.tex b/frc971/control_loops/catapult/mpc.tex
new file mode 100644
index 0000000..b7110fe
--- /dev/null
+++ b/frc971/control_loops/catapult/mpc.tex
@@ -0,0 +1,202 @@
+\documentclass[a4paper,12pt]{article}
+\usepackage{amsmath}
+\usepackage{graphicx}
+\begin{document}
+
+TODO(austin): Now that the python matches the original problem and solves, confirm the paper matches what got implemented.
+
+osqp!
+
+\section{Catapult MPC}
+We want to phrase our problem as trying to solve for the set of control inputs
+which get us closest to the destination, but minimizes acceleration.
+Specifically, we want to minimize acceleration close to the end.
+We also have a voltage limit.
+
+Our model is
+
+\begin{equation}
+\label{cost}
+ \begin{bmatrix} x_1 \\ v_1 \end{bmatrix} =
+ \begin{bmatrix} a_{00} & a_{01} \\ 0 & a_{11} \end{bmatrix}
+ \begin{bmatrix} x_0 \\ v_0 \end{bmatrix} +
+ \begin{bmatrix} b_{0} \\ b_{1} \end{bmatrix} \begin{bmatrix} u_0 \end{bmatrix}
+\end{equation}
+
+Our acceleration can be measured as:
+
+\begin{equation}
+\label{accel}
+ \frac{ \left( \boldsymbol{X_1(1)} - \boldsymbol{X_1(0)} \right)}{\Delta t}
+\end{equation}
+
+This simplifies to:
+
+\begin{equation}
+ \frac{a_{11} v_0 + b_1 u_0 - v_0}{\Delta t}
+\end{equation}
+
+and finally
+
+\begin{equation}
+ \frac{(a_{11} - 1) v_0 + b_1 u_0}{\Delta t}
+\end{equation}
+
+
+We can also compute our state matrix as a function of inital state and the control inputs.
+
+\begin{equation}
+\label{all_x}
+ \begin{bmatrix} X_1 \\ X_2 \\ X_3 \\ \vdots \end{bmatrix} =
+ \begin{bmatrix} A \\
+ A^2 \\
+ A^3 \\
+ \vdots \end{bmatrix}
+ X_0 +
+ \begin{bmatrix} B & 0 & 0 & 0 \\
+ A B & B & 0 & 0 \\
+ A^2 B & A B & B & 0 \\
+ \vdots & \ddots & & \hdots \end{bmatrix}
+ \begin{bmatrix} U_0 \\ U_1 \\ U_2 \\ \vdots \end{bmatrix}
+\end{equation}
+
+\section{MPC problem formulation}
+
+We want to penalize both final state and intermediate acceleration.
+
+\begin{equation}
+C = \sum_{n=0}^{39} \frac{\left(v(n + 1) - v(n)\right)^2}{\Delta t} \pi_n + (X_{40} - X_{final})^T Q_{final} (X_{40} - X_{final})
+\end{equation}
+
+where $\pi_n$ is a constant only dependent on $n$, and designed such that it depends on the distance to the end of the sequence, not the distance from the start.
+
+In order to use OSQP, which has a code generator, we need to get this into the form of
+
+\begin{tabular}{ l l }
+minimize & $ \frac{1}{2} X^T P X + q^T X $ \\
+subject to & $ l <= A X <= u $ \\
+\end{tabular}
+
+This is the simplest form of a constrained quadratic program that we can solve efficiently.
+Luckily for us, the problem statement above fits that definition.
+
+\section{Manipulating the formulation}
+
+We need to separate constant factors from things dependent on U (or X in OSQP parlance) so we can create these matrices easier.
+
+\subsection{Terminal cost}
+
+Next step is to compute $X_{40}$ using equation \ref{all_x}.
+We can do this by only computing the final row of the matrix.
+
+\begin{equation}
+\label{x40}
+ X_{40} = \begin{bmatrix} A^{39} B & A^{38} B & \hdots & B \end{bmatrix}
+ \begin{bmatrix} U_0 \\
+ \vdots \\
+ U_{39}
+ \end{bmatrix} + A^{40} X_0 = B_f \boldsymbol{U} + A^{40} X_0
+\end{equation}
+
+We can substitute equation \ref{x40} into equation \ref{cost}.
+
+\begin{equation}
+\label{final_cost}
+\begin{aligned}[t]
+ C_f = & \boldsymbol{U}^T B_f^T Q_{final} B_f \boldsymbol{U} \\
+ & + 2 (A^{40} X_0 - X_{final})^T Q_{final} B_f \boldsymbol{U} \\
+ & + (A^{40} X_0 - X_{final})^T Q_{final} (A^{40} X_0 - X_{final})
+\end{aligned}
+\end{equation}
+
+\subsection{Acceleration costs}
+
+We can compute a velocity matrix for all the times by stripping out the positions from equation \ref{all_x} by using every other row.
+We can use this to then compute the accelerations for each time slice and then penalize them.
+
+\begin{equation}
+ \begin{bmatrix} v_1 \\ v_2 \\ \vdots \\ v_{40} \end{bmatrix} =
+ M \boldsymbol{U} + \begin{bmatrix} a_{11} \\ a^2_{11} \\ \vdots \\ a^{40}_{11} \end{bmatrix} v_0 =
+ M \boldsymbol{U} + m v_0
+\end{equation}
+
+We can then use equation \ref{accel} in matrix form to convert a velocity matrix to an acceleration matrix.
+
+\begin{equation}
+ \begin{bmatrix} \alpha_1 \\ \alpha_2 \\ \alpha_3 \\ \vdots \\ \alpha_{40} \end{bmatrix} =
+ \frac{1}{\Delta t} \left(
+ \begin{bmatrix} 1 & 0 & 0 & \hdots & 0 \\
+ -1 & 1 & 0 & \hdots & 0 \\
+ 0 & -1 & 1 & \hdots & 0 \\
+ \vdots & & & \ddots & \vdots \\
+ 0 & 0 & \hdots & -1 & 1 \\
+ \end{bmatrix}
+ \begin{bmatrix} v_1 \\ v_2 \\ \vdots \\ v_{40} \end{bmatrix} - \begin{bmatrix} v_0 \\ 0 \\ \vdots \\ 0 \end{bmatrix}
+\right)
+\end{equation}
+
+We can pull some of these terms out to make it easier to work with.
+
+\begin{equation}
+\boldsymbol{\alpha} = W V + w v_0
+\end{equation}
+
+Our acceleration cost function is then:
+
+\begin{equation}
+C_a = \boldsymbol{\alpha}^T
+ \begin{bmatrix} \pi_1 & & 0 \\
+ & \pi_2 & \\
+ 0 & & \ddots \end{bmatrix} \boldsymbol{\alpha} =
+ \boldsymbol{\alpha}^T \Pi \boldsymbol{\alpha}
+\end{equation}
+
+We can substitute everything in to get something as a function of $U$.
+
+\begin{equation}
+C_a = \left(W \left(M \boldsymbol{U} + m v_0 \right) + w v_0 \right)^T \Pi \left(W \left(M \boldsymbol{U} + m v_0 \right) + w v_0 \right)
+\end{equation}
+
+And then simplify this down into the expected form.
+
+\begin{equation}
+ C_a = \left(W M \boldsymbol{U} + (W m + w) v_0 \right)^T \Pi \left(W M \boldsymbol{U} + (W m + w) v_0 \right)
+\end{equation}
+
+\begin{equation}
+\label{accel_cost}
+\begin{aligned}[t]
+C_a = & \boldsymbol{U}^T M^T W^T \Pi W M \boldsymbol{U} \\
+ & + 2 v_0 (W m + w)^T \Pi W M \boldsymbol{U} \\
+& + v_0 (W m + w)^T \Pi \left(W m + w \right) v_0
+\end{aligned}
+\end{equation}
+
+\subsection{Overall cost}
+
+We can combine equations \ref{final_cost} and \ref{accel_cost} to get our overall cost in the correct form.
+
+\begin{equation}
+\begin{aligned}[t]
+C &= \boldsymbol{U}^T \left( M^T W^T \Pi W M + B_f^T Q_{final} B_f \right) \boldsymbol{U} \\
+ &+ \left(2 v_0 (W m + w)^T \Pi W M
+ - 2 X_{final}^T Q_{final} B_f
+\right) \boldsymbol{U} \\
+& + X_{final}^T Q_{final} X_{final}
+ + v_0 (W m + w)^T \Pi \left(W m + w \right) v_0
+\end{aligned}
+\end{equation}
+
+
+\section{Response}
+
+For a reasonable request (11 m/s after 90 degrees), we get the following response
+
+\begin{figure}
+ \centering
+ \includegraphics[width=\linewidth]{response.png}
+\end{figure}
+
+This is well within 1\% error, and avoid saturation and keeps the acceleration down at the end.
+
+\end{document}
diff --git a/frc971/control_loops/catapult/mpc_problem.cc b/frc971/control_loops/catapult/mpc_problem.cc
new file mode 100644
index 0000000..23859cd
--- /dev/null
+++ b/frc971/control_loops/catapult/mpc_problem.cc
@@ -0,0 +1,95 @@
+#include "frc971/control_loops/catapult/mpc_problem.h"
+
+namespace frc971::control_loops::catapult {
+namespace chrono = std::chrono;
+
+namespace {
+osqp::OsqpInstance MakeInstance(
+ size_t horizon, Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> P) {
+ osqp::OsqpInstance instance;
+ instance.objective_matrix = P.sparseView();
+
+ instance.constraint_matrix =
+ Eigen::SparseMatrix<double, Eigen::ColMajor, osqp::c_int>(horizon,
+ horizon);
+ instance.constraint_matrix.setIdentity();
+
+ instance.lower_bounds =
+ Eigen::Matrix<double, Eigen::Dynamic, 1>::Zero(horizon, 1);
+ instance.upper_bounds =
+ Eigen::Matrix<double, Eigen::Dynamic, 1>::Ones(horizon, 1) * 12.0;
+ return instance;
+}
+
+} // namespace
+MPCProblem::MPCProblem(size_t horizon,
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> P,
+ Eigen::Matrix<double, Eigen::Dynamic, 1> accel_q,
+ Eigen::Matrix<double, 2, 2> Af,
+ Eigen::Matrix<double, Eigen::Dynamic, 2> final_q)
+ : horizon_(horizon),
+ accel_q_(std::move(accel_q)),
+ Af_(std::move(Af)),
+ final_q_(std::move(final_q)),
+ instance_(MakeInstance(horizon, std::move(P))) {
+ // Start with a representative problem.
+ Eigen::Matrix<double, 2, 1> X_initial(0.0, 0.0);
+ Eigen::Matrix<double, 2, 1> X_final(2.0, 25.0);
+
+ objective_vector_ =
+ X_initial(1, 0) * accel_q_ + final_q_ * (Af_ * X_initial - X_final);
+ instance_.objective_vector = objective_vector_;
+ settings_.max_iter = 25;
+ settings_.check_termination = 5;
+ settings_.warm_start = 1;
+ // TODO(austin): Do we need this scaling thing? It makes it not solve
+ // sometimes... I'm pretty certain by giving it a decently formed problem to
+ // initialize with, it will not try doing crazy things with the scaling
+ // internally.
+ settings_.scaling = 0;
+ auto status = solver_.Init(instance_, settings_);
+ CHECK(status.ok()) << status;
+}
+
+void MPCProblem::SetState(Eigen::Matrix<double, 2, 1> X_initial,
+ Eigen::Matrix<double, 2, 1> X_final) {
+ X_initial_ = X_initial;
+ X_final_ = X_final;
+ // If we mark this noalias(), it won't re-allocate the vector each time.
+ objective_vector_.noalias() =
+ X_initial(1, 0) * accel_q_ + final_q_ * (Af_ * X_initial - X_final);
+
+ auto status = solver_.SetObjectiveVector(objective_vector_);
+ CHECK(status.ok()) << status;
+}
+
+bool MPCProblem::Solve() {
+ const aos::monotonic_clock::time_point start_time =
+ aos::monotonic_clock::now();
+ osqp::OsqpExitCode exit_code = solver_.Solve();
+ const aos::monotonic_clock::time_point end_time = aos::monotonic_clock::now();
+ VLOG(1) << "OSQP solved in "
+ << std::chrono::duration<double>(end_time - start_time).count();
+ solve_time_ = std::chrono::duration<double>(end_time - start_time).count();
+ // TODO(austin): Dump the exit codes out as an enum for logging.
+ //
+ // TODO(austin): The dual problem doesn't appear to be converging on all
+ // problems. Are we phrasing something wrong?
+
+ // TODO(austin): Set a time limit so we can't run forever, and signal back
+ // when we hit our limit.
+ return exit_code == osqp::OsqpExitCode::kOptimal;
+}
+
+void MPCProblem::WarmStart(const MPCProblem &p) {
+ CHECK_GE(p.horizon(), horizon())
+ << ": Can only copy a bigger problem's solution into a smaller problem.";
+ auto status = solver_.SetPrimalWarmStart(p.solver_.primal_solution().block(
+ p.horizon() - horizon(), 0, horizon(), 1));
+ CHECK(status.ok()) << status;
+ status = solver_.SetDualWarmStart(p.solver_.dual_solution().block(
+ p.horizon() - horizon(), 0, horizon(), 1));
+ CHECK(status.ok()) << status;
+}
+
+} // namespace frc971::control_loops::catapult
\ No newline at end of file
diff --git a/frc971/control_loops/catapult/mpc_problem.h b/frc971/control_loops/catapult/mpc_problem.h
new file mode 100644
index 0000000..04e3936
--- /dev/null
+++ b/frc971/control_loops/catapult/mpc_problem.h
@@ -0,0 +1,72 @@
+#include "Eigen/Dense"
+#include "Eigen/Sparse"
+#include "glog/logging.h"
+
+#include "aos/realtime.h"
+#include "aos/time/time.h"
+#include "osqp++.h"
+#include "osqp.h"
+
+namespace frc971 {
+namespace control_loops {
+namespace catapult {
+
+// MPC problem for a specified horizon. This contains all the state for the
+// solver, setters to modify the current and target state, and a way to fetch
+// the solution.
+class MPCProblem {
+ public:
+ MPCProblem(size_t horizon,
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> P,
+ Eigen::Matrix<double, Eigen::Dynamic, 1> accel_q,
+ Eigen::Matrix<double, 2, 2> Af,
+ Eigen::Matrix<double, Eigen::Dynamic, 2> final_q);
+
+ MPCProblem(MPCProblem const &) = delete;
+ void operator=(MPCProblem const &x) = delete;
+
+ // Sets the current and final state. This keeps the problem in tact and
+ // doesn't recreate it, so it will be fast.
+ void SetState(Eigen::Matrix<double, 2, 1> X_initial,
+ Eigen::Matrix<double, 2, 1> X_final);
+
+ // Solves our problem.
+ bool Solve();
+
+ double solve_time() const { return solve_time_; }
+
+ // Returns the solution that the solver found when Solve was last called.
+ double U(size_t i) const { return solver_.primal_solution()(i); }
+
+ // Returns the number of U's to be solved.
+ size_t horizon() const { return horizon_; }
+
+ // Warm starts the optimizer with the provided solution to make it solve
+ // faster.
+ void WarmStart(const MPCProblem &p);
+
+ private:
+ // The number of u's to solve for.
+ const size_t horizon_;
+
+ // The problem statement variables needed by SetState to update q.
+ const Eigen::Matrix<double, Eigen::Dynamic, 1> accel_q_;
+ const Eigen::Matrix<double, 2, 2> Af_;
+ const Eigen::Matrix<double, Eigen::Dynamic, 2> final_q_;
+
+ Eigen::Matrix<double, 2, 1> X_initial_;
+ Eigen::Matrix<double, 2, 1> X_final_;
+
+ Eigen::Matrix<double, Eigen::Dynamic, 1> objective_vector_;
+
+ // Solver state.
+ osqp::OsqpInstance instance_;
+ osqp::OsqpSolver solver_;
+ osqp::OsqpSettings settings_;
+
+ double solve_time_ = 0;
+};
+
+} // namespace catapult
+} // namespace control_loops
+} // namespace frc971
\ No newline at end of file
diff --git a/frc971/control_loops/catapult/mpc_problem_generator.cc b/frc971/control_loops/catapult/mpc_problem_generator.cc
new file mode 100644
index 0000000..3b36318
--- /dev/null
+++ b/frc971/control_loops/catapult/mpc_problem_generator.cc
@@ -0,0 +1,168 @@
+#include "frc971/control_loops/catapult/mpc_problem_generator.h"
+
+namespace frc971::control_loops::catapult {
+namespace chrono = std::chrono;
+
+CatapultProblemGenerator::CatapultProblemGenerator(
+ StateFeedbackPlant<2, 1, 1> plant, size_t horizon)
+ : plant_(std::move(plant)),
+ horizon_(horizon),
+ Q_final_(
+ (Eigen::DiagonalMatrix<double, 2>().diagonal() << 10000.0, 10000.0)
+ .finished()),
+ As_(MakeAs()),
+ Bs_(MakeBs()),
+ m_(Makem()),
+ M_(MakeM()),
+ W_(MakeW()),
+ w_(Makew()),
+ Pi_(MakePi()),
+ WM_(W_ * M_),
+ Wmpw_(W_ * m_ + w_) {}
+
+std::unique_ptr<MPCProblem> CatapultProblemGenerator::MakeProblem(
+ size_t horizon) {
+ return std::make_unique<MPCProblem>(
+ horizon, P(horizon), accel_q(horizon), Af(horizon),
+ (2.0 * Q_final_ * Bf(horizon)).transpose());
+}
+
+const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>
+CatapultProblemGenerator::P(size_t horizon) {
+ CHECK_GT(horizon, 0u);
+ CHECK_LE(horizon, horizon_);
+ return 2.0 * (WM_.block(0, 0, horizon, horizon).transpose() * Pi(horizon) *
+ WM_.block(0, 0, horizon, horizon) +
+ Bf(horizon).transpose() * Q_final_ * Bf(horizon));
+}
+
+const Eigen::Matrix<double, Eigen::Dynamic, 1> CatapultProblemGenerator::q(
+ size_t horizon, Eigen::Matrix<double, 2, 1> X_initial,
+ Eigen::Matrix<double, 2, 1> X_final) {
+ CHECK_GT(horizon, 0u);
+ CHECK_LE(horizon, horizon_);
+ return 2.0 * X_initial(1, 0) * accel_q(horizon) +
+ 2.0 * ((Af(horizon) * X_initial - X_final).transpose() * Q_final_ *
+ Bf(horizon))
+ .transpose();
+}
+
+const Eigen::Matrix<double, Eigen::Dynamic, 1>
+CatapultProblemGenerator::accel_q(size_t horizon) {
+ return 2.0 * ((Wmpw_.block(0, 0, horizon, 1)).transpose() * Pi(horizon) *
+ WM_.block(0, 0, horizon, horizon))
+ .transpose();
+}
+
+const Eigen::Matrix<double, 2, 2> CatapultProblemGenerator::Af(size_t horizon) {
+ CHECK_GT(horizon, 0u);
+ CHECK_LE(horizon, horizon_);
+ return As_.block<2, 2>(2 * (horizon - 1), 0);
+}
+
+const Eigen::Matrix<double, 2, Eigen::Dynamic> CatapultProblemGenerator::Bf(
+ size_t horizon) {
+ CHECK_GT(horizon, 0u);
+ CHECK_LE(horizon, horizon_);
+ return Bs_.block(2 * (horizon - 1), 0, 2, horizon);
+}
+
+const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>
+CatapultProblemGenerator::Pi(size_t horizon) {
+ CHECK_GT(horizon, 0u);
+ CHECK_LE(horizon, horizon_);
+ return Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>(Pi_).block(
+ horizon_ - horizon, horizon_ - horizon, horizon, horizon);
+}
+
+Eigen::Matrix<double, Eigen::Dynamic, 2> CatapultProblemGenerator::MakeAs() {
+ Eigen::Matrix<double, Eigen::Dynamic, 2> As =
+ Eigen::Matrix<double, Eigen::Dynamic, 2>::Zero(horizon_ * 2, 2);
+ for (size_t i = 0; i < horizon_; ++i) {
+ if (i == 0) {
+ As.block<2, 2>(0, 0) = plant_.A();
+ } else {
+ As.block<2, 2>(i * 2, 0) = plant_.A() * As.block<2, 2>((i - 1) * 2, 0);
+ }
+ }
+ return As;
+}
+
+Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>
+CatapultProblemGenerator::MakeBs() {
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> Bs =
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>::Zero(horizon_ * 2,
+ horizon_);
+ for (size_t i = 0; i < horizon_; ++i) {
+ for (size_t j = 0; j < i + 1; ++j) {
+ if (i == j) {
+ Bs.block<2, 1>(i * 2, j) = plant_.B();
+ } else {
+ Bs.block<2, 1>(i * 2, j) =
+ As_.block<2, 2>((i - j - 1) * 2, 0) * plant_.B();
+ }
+ }
+ }
+ return Bs;
+}
+
+Eigen::Matrix<double, Eigen::Dynamic, 1> CatapultProblemGenerator::Makem() {
+ Eigen::Matrix<double, Eigen::Dynamic, 1> m =
+ Eigen::Matrix<double, Eigen::Dynamic, 1>::Zero(horizon_, 1);
+ for (size_t i = 0; i < horizon_; ++i) {
+ m(i, 0) = As_(1 + 2 * i, 1);
+ }
+ return m;
+}
+
+Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>
+CatapultProblemGenerator::MakeM() {
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> M =
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>::Zero(horizon_,
+ horizon_);
+ for (size_t i = 0; i < horizon_; ++i) {
+ for (size_t j = 0; j < horizon_; ++j) {
+ M(i, j) = Bs_(2 * i + 1, j);
+ }
+ }
+ return M;
+}
+
+Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>
+CatapultProblemGenerator::MakeW() {
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> W =
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>::Identity(horizon_,
+ horizon_);
+ for (size_t i = 0; i < horizon_ - 1; ++i) {
+ W(i + 1, i) = -1.0;
+ }
+ W /= std::chrono::duration<double>(plant_.dt()).count();
+ return W;
+}
+
+Eigen::Matrix<double, Eigen::Dynamic, 1> CatapultProblemGenerator::Makew() {
+ Eigen::Matrix<double, Eigen::Dynamic, 1> w =
+ Eigen::Matrix<double, Eigen::Dynamic, 1>::Zero(horizon_, 1);
+ w(0, 0) = -1.0 / std::chrono::duration<double>(plant_.dt()).count();
+ return w;
+}
+
+Eigen::DiagonalMatrix<double, Eigen::Dynamic>
+CatapultProblemGenerator::MakePi() {
+ Eigen::DiagonalMatrix<double, Eigen::Dynamic> Pi(horizon_);
+ for (size_t i = 0; i < horizon_; ++i) {
+ Pi.diagonal()(i) =
+ std::pow(0.01, 2.0) +
+ std::pow(0.02 * std::max(0.0, (20 - ((int)horizon_ - (int)i)) / 20.),
+ 2.0);
+ }
+ return Pi;
+}
+
+Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>
+CatapultProblemGenerator::MakeP() {
+ return 2.0 * (M_.transpose() * W_.transpose() * Pi_ * W_ * M_ +
+ Bf(horizon_).transpose() * Q_final_ * Bf(horizon_));
+}
+
+} // namespace frc971::control_loops::catapult
\ No newline at end of file
diff --git a/frc971/control_loops/catapult/mpc_problem_generator.h b/frc971/control_loops/catapult/mpc_problem_generator.h
new file mode 100644
index 0000000..2fbaf66
--- /dev/null
+++ b/frc971/control_loops/catapult/mpc_problem_generator.h
@@ -0,0 +1,69 @@
+#include "frc971/control_loops/catapult/mpc_problem.h"
+#include "frc971/control_loops/state_feedback_loop.h"
+
+namespace frc971 {
+namespace control_loops {
+namespace catapult {
+
+// Decently efficient problem generator for multiple horizons given a max
+// horizon to solve for.
+//
+// The math is documented in mpc.tex
+class CatapultProblemGenerator {
+ public:
+ // Builds a problem generator for the specified max horizon and caches a lot
+ // of the state.
+ CatapultProblemGenerator(StateFeedbackPlant<2, 1, 1> plant, size_t horizon);
+
+ // Returns the maximum horizon.
+ size_t horizon() const { return horizon_; }
+
+ // Makes a problem for the specificed horizon.
+ std::unique_ptr<MPCProblem> MakeProblem(size_t horizon);
+
+ // Returns the P and Q matrices for the problem statement.
+ // cost = 0.5 X.T P X + q.T X
+ const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> P(size_t horizon);
+ const Eigen::Matrix<double, Eigen::Dynamic, 1> q(
+ size_t horizon, Eigen::Matrix<double, 2, 1> X_initial,
+ Eigen::Matrix<double, 2, 1> X_final);
+
+ private:
+ const Eigen::Matrix<double, Eigen::Dynamic, 1> accel_q(size_t horizon);
+
+ const Eigen::Matrix<double, 2, 2> Af(size_t horizon);
+ const Eigen::Matrix<double, 2, Eigen::Dynamic> Bf(size_t horizon);
+ const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> Pi(
+ size_t horizon);
+
+ // These functions are used in the constructor to build up the matrices below.
+ Eigen::Matrix<double, Eigen::Dynamic, 2> MakeAs();
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> MakeBs();
+ Eigen::Matrix<double, Eigen::Dynamic, 1> Makem();
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> MakeM();
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> MakeW();
+ Eigen::Matrix<double, Eigen::Dynamic, 1> Makew();
+ Eigen::DiagonalMatrix<double, Eigen::Dynamic> MakePi();
+ Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> MakeP();
+
+ const StateFeedbackPlant<2, 1, 1> plant_;
+ const size_t horizon_;
+
+ const Eigen::DiagonalMatrix<double, 2> Q_final_;
+
+ const Eigen::Matrix<double, Eigen::Dynamic, 2> As_;
+ const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> Bs_;
+ const Eigen::Matrix<double, Eigen::Dynamic, 1> m_;
+ const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> M_;
+
+ const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> W_;
+ const Eigen::Matrix<double, Eigen::Dynamic, 1> w_;
+ const Eigen::DiagonalMatrix<double, Eigen::Dynamic> Pi_;
+
+ const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> WM_;
+ const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> Wmpw_;
+};
+
+} // namespace catapult
+} // namespace control_loops
+} // namespace frc971
\ No newline at end of file
diff --git a/frc971/control_loops/state_feedback_loop.h b/frc971/control_loops/state_feedback_loop.h
index 3c90434..988aaa9 100644
--- a/frc971/control_loops/state_feedback_loop.h
+++ b/frc971/control_loops/state_feedback_loop.h
@@ -256,8 +256,12 @@
static const int kNumInputs = number_of_inputs;
private:
- Eigen::Matrix<Scalar, number_of_states, 1> X_;
- Eigen::Matrix<Scalar, number_of_outputs, 1> Y_;
+ // X_ and Y_ must be explicitly initialized to avoid having gcc complain about
+ // uninitialized values when using the move constructor.
+ Eigen::Matrix<Scalar, number_of_states, 1> X_ =
+ Eigen::Matrix<Scalar, number_of_states, 1>::Zero();
+ Eigen::Matrix<Scalar, number_of_outputs, 1> Y_ =
+ Eigen::Matrix<Scalar, number_of_outputs, 1>::Zero();
Eigen::Matrix<Scalar, number_of_inputs, Eigen::Dynamic> last_U_;
::std::vector<::std::unique_ptr<StateFeedbackPlantCoefficients<