Copy back a lot of the 2014 code.
Change-Id: I552292d8bd7bce4409e02d254bef06a9cc009568
diff --git a/y2014/control_loops/python/claw.py b/y2014/control_loops/python/claw.py
new file mode 100755
index 0000000..b5ea6a1
--- /dev/null
+++ b/y2014/control_loops/python/claw.py
@@ -0,0 +1,491 @@
+#!/usr/bin/python
+
+import control_loop
+import controls
+import polytope
+import polydrivetrain
+import numpy
+import sys
+from matplotlib import pylab
+
+class Claw(control_loop.ControlLoop):
+ def __init__(self, name="RawClaw"):
+ super(Claw, self).__init__(name)
+ # Stall Torque in N m
+ self.stall_torque = 2.42
+ # Stall Current in Amps
+ self.stall_current = 133
+ # Free Speed in RPM
+ self.free_speed = 5500.0
+ # Free Current in Amps
+ self.free_current = 2.7
+ # Moment of inertia of the claw in kg m^2
+ self.J_top = 2.8
+ self.J_bottom = 3.0
+
+ # Resistance of the motor
+ self.R = 12.0 / self.stall_current
+ # Motor velocity constant
+ self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) /
+ (13.5 - self.R * self.free_current))
+ # Torque constant
+ self.Kt = self.stall_torque / self.stall_current
+ # Gear ratio
+ self.G = 14.0 / 48.0 * 18.0 / 32.0 * 18.0 / 66.0 * 12.0 / 60.0
+ # Control loop time step
+ self.dt = 0.01
+
+ # State is [bottom position, bottom velocity, top - bottom position,
+ # top - bottom velocity]
+ # Input is [bottom power, top power - bottom power * J_top / J_bottom]
+ # Motor time constants. difference_bottom refers to the constant for how the
+ # bottom velocity affects the difference of the top and bottom velocities.
+ self.common_motor_constant = -self.Kt / self.Kv / (self.G * self.G * self.R)
+ self.bottom_bottom = self.common_motor_constant / self.J_bottom
+ self.difference_bottom = -self.common_motor_constant * (1 / self.J_bottom
+ - 1 / self.J_top)
+ self.difference_difference = self.common_motor_constant / self.J_top
+ # State feedback matrices
+
+ self.A_continuous = numpy.matrix(
+ [[0, 0, 1, 0],
+ [0, 0, 0, 1],
+ [0, 0, self.bottom_bottom, 0],
+ [0, 0, self.difference_bottom, self.difference_difference]])
+
+ self.A_bottom_cont = numpy.matrix(
+ [[0, 1],
+ [0, self.bottom_bottom]])
+
+ self.A_diff_cont = numpy.matrix(
+ [[0, 1],
+ [0, self.difference_difference]])
+
+ self.motor_feedforward = self.Kt / (self.G * self.R)
+ self.motor_feedforward_bottom = self.motor_feedforward / self.J_bottom
+ self.motor_feedforward_difference = self.motor_feedforward / self.J_top
+ self.motor_feedforward_difference_bottom = (
+ self.motor_feedforward * (1 / self.J_bottom - 1 / self.J_top))
+ self.B_continuous = numpy.matrix(
+ [[0, 0],
+ [0, 0],
+ [self.motor_feedforward_bottom, 0],
+ [-self.motor_feedforward_bottom, self.motor_feedforward_difference]])
+
+ print "Cont X_ss", self.motor_feedforward / -self.common_motor_constant
+
+ self.B_bottom_cont = numpy.matrix(
+ [[0],
+ [self.motor_feedforward_bottom]])
+
+ self.B_diff_cont = numpy.matrix(
+ [[0],
+ [self.motor_feedforward_difference]])
+
+ self.C = numpy.matrix([[1, 0, 0, 0],
+ [1, 1, 0, 0]])
+ self.D = numpy.matrix([[0, 0],
+ [0, 0]])
+
+ self.A, self.B = self.ContinuousToDiscrete(
+ self.A_continuous, self.B_continuous, self.dt)
+
+ self.A_bottom, self.B_bottom = controls.c2d(
+ self.A_bottom_cont, self.B_bottom_cont, self.dt)
+ self.A_diff, self.B_diff = controls.c2d(
+ self.A_diff_cont, self.B_diff_cont, self.dt)
+
+ self.K_bottom = controls.dplace(self.A_bottom, self.B_bottom, [.75 + 0.1j, .75 - 0.1j])
+ self.K_diff = controls.dplace(self.A_diff, self.B_diff, [.75 + 0.1j, .75 - 0.1j])
+
+ print "K_diff", self.K_diff
+ print "K_bottom", self.K_bottom
+
+ print "A"
+ print self.A
+ print "B"
+ print self.B
+
+
+ self.Q = numpy.matrix([[(1.0 / (0.10 ** 2.0)), 0.0, 0.0, 0.0],
+ [0.0, (1.0 / (0.06 ** 2.0)), 0.0, 0.0],
+ [0.0, 0.0, 0.10, 0.0],
+ [0.0, 0.0, 0.0, 0.1]])
+
+ self.R = numpy.matrix([[(1.0 / (40.0 ** 2.0)), 0.0],
+ [0.0, (1.0 / (5.0 ** 2.0))]])
+ #self.K = controls.dlqr(self.A, self.B, self.Q, self.R)
+
+ self.K = numpy.matrix([[self.K_bottom[0, 0], 0.0, self.K_bottom[0, 1], 0.0],
+ [0.0, self.K_diff[0, 0], 0.0, self.K_diff[0, 1]]])
+
+ # Compute the feed forwards aceleration term.
+ self.K[1, 0] = -self.B[1, 0] * self.K[0, 0] / self.B[1, 1]
+
+ lstsq_A = numpy.identity(2)
+ lstsq_A[0, :] = self.B[1, :]
+ lstsq_A[1, :] = self.B[3, :]
+ print "System of Equations coefficients:"
+ print lstsq_A
+ print "det", numpy.linalg.det(lstsq_A)
+
+ out_x = numpy.linalg.lstsq(
+ lstsq_A,
+ numpy.matrix([[self.A[1, 2]], [self.A[3, 2]]]))[0]
+ self.K[1, 2] = -lstsq_A[0, 0] * (self.K[0, 2] - out_x[0]) / lstsq_A[0, 1] + out_x[1]
+
+ print "K unaugmented"
+ print self.K
+ print "B * K unaugmented"
+ print self.B * self.K
+ F = self.A - self.B * self.K
+ print "A - B * K unaugmented"
+ print F
+ print "eigenvalues"
+ print numpy.linalg.eig(F)[0]
+
+ self.rpl = .05
+ self.ipl = 0.010
+ self.PlaceObserverPoles([self.rpl + 1j * self.ipl,
+ self.rpl + 1j * self.ipl,
+ self.rpl - 1j * self.ipl,
+ self.rpl - 1j * self.ipl])
+
+ # The box formed by U_min and U_max must encompass all possible values,
+ # or else Austin's code gets angry.
+ self.U_max = numpy.matrix([[12.0], [12.0]])
+ self.U_min = numpy.matrix([[-12.0], [-12.0]])
+
+ # For the tests that check the limits, these are (upper, lower) for both
+ # claws.
+ self.hard_pos_limits = None
+ self.pos_limits = None
+
+ # Compute the steady state velocities for a given applied voltage.
+ # The top and bottom of the claw should spin at the same rate if the
+ # physics is right.
+ X_ss = numpy.matrix([[0], [0], [0.0], [0]])
+
+ U = numpy.matrix([[1.0],[1.0]])
+ A = self.A
+ B = self.B
+ #X_ss[2, 0] = X_ss[2, 0] * A[2, 2] + B[2, 0] * U[0, 0]
+ X_ss[2, 0] = 1 / (1 - A[2, 2]) * B[2, 0] * U[0, 0]
+ #X_ss[3, 0] = X_ss[3, 0] * A[3, 3] + X_ss[2, 0] * A[3, 2] + B[3, 0] * U[0, 0] + B[3, 1] * U[1, 0]
+ #X_ss[3, 0] * (1 - A[3, 3]) = X_ss[2, 0] * A[3, 2] + B[3, 0] * U[0, 0] + B[3, 1] * U[1, 0]
+ X_ss[3, 0] = 1 / (1 - A[3, 3]) * (X_ss[2, 0] * A[3, 2] + B[3, 1] * U[1, 0] + B[3, 0] * U[0, 0])
+ #X_ss[3, 0] = 1 / (1 - A[3, 3]) / (1 - A[2, 2]) * B[2, 0] * U[0, 0] * A[3, 2] + B[3, 0] * U[0, 0] + B[3, 1] * U[1, 0]
+ X_ss[0, 0] = A[0, 2] * X_ss[2, 0] + B[0, 0] * U[0, 0]
+ X_ss[1, 0] = A[1, 2] * X_ss[2, 0] + A[1, 3] * X_ss[3, 0] + B[1, 0] * U[0, 0] + B[1, 1] * U[1, 0]
+
+ print "X_ss", X_ss
+
+ self.InitializeState()
+
+
+class ClawDeltaU(Claw):
+ def __init__(self, name="Claw"):
+ super(ClawDeltaU, self).__init__(name)
+ A_unaugmented = self.A
+ B_unaugmented = self.B
+ C_unaugmented = self.C
+
+ self.A = numpy.matrix([[0.0, 0.0, 0.0, 0.0, 0.0],
+ [0.0, 0.0, 0.0, 0.0, 0.0],
+ [0.0, 0.0, 0.0, 0.0, 0.0],
+ [0.0, 0.0, 0.0, 0.0, 0.0],
+ [0.0, 0.0, 0.0, 0.0, 1.0]])
+ self.A[0:4, 0:4] = A_unaugmented
+ self.A[0:4, 4] = B_unaugmented[0:4, 0]
+
+ self.B = numpy.matrix([[0.0, 0.0],
+ [0.0, 0.0],
+ [0.0, 0.0],
+ [0.0, 0.0],
+ [1.0, 0.0]])
+ self.B[0:4, 1] = B_unaugmented[0:4, 1]
+
+ self.C = numpy.concatenate((C_unaugmented, numpy.matrix([[0.0], [0.0]])),
+ axis=1)
+ self.D = numpy.matrix([[0.0, 0.0],
+ [0.0, 0.0]])
+
+ #self.PlaceControllerPoles([0.55, 0.35, 0.55, 0.35, 0.80])
+ self.Q = numpy.matrix([[(1.0 / (0.04 ** 2.0)), 0.0, 0.0, 0.0, 0.0],
+ [0.0, (1.0 / (0.01 ** 2)), 0.0, 0.0, 0.0],
+ [0.0, 0.0, 0.01, 0.0, 0.0],
+ [0.0, 0.0, 0.0, 0.08, 0.0],
+ [0.0, 0.0, 0.0, 0.0, (1.0 / (10.0 ** 2))]])
+
+ self.R = numpy.matrix([[0.000001, 0.0],
+ [0.0, 1.0 / (10.0 ** 2.0)]])
+ self.K = controls.dlqr(self.A, self.B, self.Q, self.R)
+
+ self.K = numpy.matrix([[50.0, 0.0, 10.0, 0.0, 1.0],
+ [50.0, 0.0, 10.0, 0.0, 1.0]])
+ #self.K = numpy.matrix([[50.0, -100.0, 0, -10, 0],
+ # [50.0, 100.0, 0, 10, 0]])
+
+ controlability = controls.ctrb(self.A, self.B);
+ print "Rank of augmented controlability matrix.", numpy.linalg.matrix_rank(controlability)
+
+ print "K"
+ print self.K
+ print "Placed controller poles are"
+ print numpy.linalg.eig(self.A - self.B * self.K)[0]
+ print [numpy.abs(x) for x in numpy.linalg.eig(self.A - self.B * self.K)[0]]
+
+ self.rpl = .05
+ self.ipl = 0.008
+ self.PlaceObserverPoles([self.rpl + 1j * self.ipl, 0.10, 0.09,
+ self.rpl - 1j * self.ipl, 0.90])
+ #print "A is"
+ #print self.A
+ #print "L is"
+ #print self.L
+ #print "C is"
+ #print self.C
+ #print "A - LC is"
+ #print self.A - self.L * self.C
+
+ #print "Placed observer poles are"
+ #print numpy.linalg.eig(self.A - self.L * self.C)[0]
+
+ self.U_max = numpy.matrix([[12.0], [12.0]])
+ self.U_min = numpy.matrix([[-12.0], [-12.0]])
+
+ self.InitializeState()
+
+def ScaleU(claw, U, K, error):
+ """Clips U as necessary.
+
+ Args:
+ claw: claw object containing moments of inertia and U limits.
+ U: Input matrix to clip as necessary.
+ """
+
+ bottom_u = U[0, 0]
+ top_u = U[1, 0]
+ position_error = error[0:2, 0]
+ velocity_error = error[2:, 0]
+
+ U_poly = polytope.HPolytope(
+ numpy.matrix([[1, 0],
+ [-1, 0],
+ [0, 1],
+ [0, -1]]),
+ numpy.matrix([[12],
+ [12],
+ [12],
+ [12]]))
+
+ if (bottom_u > claw.U_max[0, 0] or bottom_u < claw.U_min[0, 0] or
+ top_u > claw.U_max[0, 0] or top_u < claw.U_min[0, 0]):
+
+ position_K = K[:, 0:2]
+ velocity_K = K[:, 2:]
+
+ # H * U <= k
+ # U = UPos + UVel
+ # H * (UPos + UVel) <= k
+ # H * UPos <= k - H * UVel
+ #
+ # Now, we can do a coordinate transformation and say the following.
+ #
+ # UPos = position_K * position_error
+ # (H * position_K) * position_error <= k - H * UVel
+ #
+ # Add in the constraint that 0 <= t <= 1
+ # Now, there are 2 ways this can go. Either we have a region, or we don't
+ # have a region. If we have a region, then pick the largest t and go for it.
+ # If we don't have a region, we need to pick a good comprimise.
+
+ pos_poly = polytope.HPolytope(
+ U_poly.H * position_K,
+ U_poly.k - U_poly.H * velocity_K * velocity_error)
+
+ # The actual angle for the line we call 45.
+ angle_45 = numpy.matrix([[numpy.sqrt(3), 1]])
+ if claw.pos_limits and claw.hard_pos_limits and claw.X[0, 0] + claw.X[1, 0] > claw.pos_limits[1]:
+ angle_45 = numpy.matrix([[1, 1]])
+
+ P = position_error
+ L45 = numpy.multiply(numpy.matrix([[numpy.sign(P[1, 0]), -numpy.sign(P[0, 0])]]), angle_45)
+ if L45[0, 1] == 0:
+ L45[0, 1] = 1
+ if L45[0, 0] == 0:
+ L45[0, 0] = 1
+ w45 = numpy.matrix([[0]])
+
+ if numpy.abs(P[0, 0]) > numpy.abs(P[1, 0]):
+ LH = numpy.matrix([[0, 1]])
+ else:
+ LH = numpy.matrix([[1, 0]])
+ wh = LH * P
+ standard = numpy.concatenate((L45, LH))
+ W = numpy.concatenate((w45, wh))
+ intersection = numpy.linalg.inv(standard) * W
+ adjusted_pos_error_h, is_inside_h = polydrivetrain.DoCoerceGoal(pos_poly,
+ LH, wh, position_error)
+ adjusted_pos_error_45, is_inside_45 = polydrivetrain.DoCoerceGoal(pos_poly,
+ L45, w45, intersection)
+ if pos_poly.IsInside(intersection):
+ adjusted_pos_error = adjusted_pos_error_h
+ else:
+ if is_inside_h:
+ if numpy.linalg.norm(adjusted_pos_error_h) > numpy.linalg.norm(adjusted_pos_error_45):
+ adjusted_pos_error = adjusted_pos_error_h
+ else:
+ adjusted_pos_error = adjusted_pos_error_45
+ else:
+ adjusted_pos_error = adjusted_pos_error_45
+ #print adjusted_pos_error
+
+ #print "Actual power is ", velocity_K * velocity_error + position_K * adjusted_pos_error
+ return velocity_K * velocity_error + position_K * adjusted_pos_error
+
+ #U = Kpos * poserror + Kvel * velerror
+
+ #scalar = claw.U_max[0, 0] / max(numpy.abs(top_u), numpy.abs(bottom_u))
+
+ #top_u *= scalar
+ #bottom_u *= scalar
+
+ return numpy.matrix([[bottom_u], [top_u]])
+
+def run_test(claw, initial_X, goal, max_separation_error=0.01, show_graph=False, iterations=200):
+ """Runs the claw plant on a given claw (claw) with an initial condition (initial_X) and goal (goal).
+
+ The tests themselves are not terribly sophisticated; I just test for
+ whether the goal has been reached and whether the separation goes
+ outside of the initial and goal values by more than max_separation_error.
+ Prints out something for a failure of either condition and returns
+ False if tests fail.
+ Args:
+ claw: claw object to use.
+ initial_X: starting state.
+ goal: goal state.
+ show_graph: Whether or not to display a graph showing the changing
+ states and voltages.
+ iterations: Number of timesteps to run the model for."""
+
+ claw.X = initial_X
+
+ # Various lists for graphing things.
+ t = []
+ x_bottom = []
+ x_top = []
+ u_bottom = []
+ u_top = []
+ x_separation = []
+
+ tests_passed = True
+
+ # Bounds which separation should not exceed.
+ lower_bound = (initial_X[1, 0] if initial_X[1, 0] < goal[1, 0]
+ else goal[1, 0]) - max_separation_error
+ upper_bound = (initial_X[1, 0] if initial_X[1, 0] > goal[1, 0]
+ else goal[1, 0]) + max_separation_error
+
+ for i in xrange(iterations):
+ U = claw.K * (goal - claw.X)
+ U = ScaleU(claw, U, claw.K, goal - claw.X)
+ claw.Update(U)
+
+ if claw.X[1, 0] > upper_bound or claw.X[1, 0] < lower_bound:
+ tests_passed = False
+ print "Claw separation was", claw.X[1, 0]
+ print "Should have been between", lower_bound, "and", upper_bound
+
+ if claw.hard_pos_limits and \
+ (claw.X[0, 0] > claw.hard_pos_limits[1] or
+ claw.X[0, 0] < claw.hard_pos_limits[0] or
+ claw.X[0, 0] + claw.X[1, 0] > claw.hard_pos_limits[1] or
+ claw.X[0, 0] + claw.X[1, 0] < claw.hard_pos_limits[0]):
+ tests_passed = False
+ print "Claws at %f and %f" % (claw.X[0, 0], claw.X[0, 0] + claw.X[1, 0])
+ print "Both should be in %s, definitely %s" % \
+ (claw.pos_limits, claw.hard_pos_limits)
+
+ t.append(i * claw.dt)
+ x_bottom.append(claw.X[0, 0] * 10.0)
+ x_top.append((claw.X[1, 0] + claw.X[0, 0]) * 10.0)
+ u_bottom.append(U[0, 0])
+ u_top.append(U[1, 0])
+ x_separation.append(claw.X[1, 0] * 10.0)
+
+ if show_graph:
+ pylab.plot(t, x_bottom, label='x bottom * 10')
+ pylab.plot(t, x_top, label='x top * 10')
+ pylab.plot(t, u_bottom, label='u bottom')
+ pylab.plot(t, u_top, label='u top')
+ pylab.plot(t, x_separation, label='separation * 10')
+ pylab.legend()
+ pylab.show()
+
+ # Test to make sure that we are near the goal.
+ if numpy.max(abs(claw.X - goal)) > 1e-4:
+ tests_passed = False
+ print "X was", claw.X, "Expected", goal
+
+ return tests_passed
+
+def main(argv):
+ claw = Claw()
+
+ # Test moving the claw with constant separation.
+ initial_X = numpy.matrix([[-1.0], [0.0], [0.0], [0.0]])
+ R = numpy.matrix([[1.0], [0.0], [0.0], [0.0]])
+ run_test(claw, initial_X, R)
+
+ # Test just changing separation.
+ initial_X = numpy.matrix([[0.0], [0.0], [0.0], [0.0]])
+ R = numpy.matrix([[0.0], [1.0], [0.0], [0.0]])
+ run_test(claw, initial_X, R)
+
+ # Test changing both separation and position at once.
+ initial_X = numpy.matrix([[0.0], [0.0], [0.0], [0.0]])
+ R = numpy.matrix([[1.0], [1.0], [0.0], [0.0]])
+ run_test(claw, initial_X, R)
+
+ # Test a small separation error and a large position one.
+ initial_X = numpy.matrix([[0.0], [0.0], [0.0], [0.0]])
+ R = numpy.matrix([[2.0], [0.05], [0.0], [0.0]])
+ run_test(claw, initial_X, R)
+
+ # Test a small separation error and a large position one.
+ initial_X = numpy.matrix([[0.0], [0.0], [0.0], [0.0]])
+ R = numpy.matrix([[-0.5], [1.0], [0.0], [0.0]])
+ run_test(claw, initial_X, R)
+
+ # Test opening with the top claw at the limit.
+ initial_X = numpy.matrix([[0.0], [0.0], [0.0], [0.0]])
+ R = numpy.matrix([[-1.5], [1.5], [0.0], [0.0]])
+ claw.hard_pos_limits = (-1.6, 0.1)
+ claw.pos_limits = (-1.5, 0.0)
+ run_test(claw, initial_X, R)
+ claw.pos_limits = None
+
+ # Test opening with the bottom claw at the limit.
+ initial_X = numpy.matrix([[0.0], [0.0], [0.0], [0.0]])
+ R = numpy.matrix([[0], [1.5], [0.0], [0.0]])
+ claw.hard_pos_limits = (-0.1, 1.6)
+ claw.pos_limits = (0.0, 1.6)
+ run_test(claw, initial_X, R)
+ claw.pos_limits = None
+
+ # Write the generated constants out to a file.
+ if len(argv) != 3:
+ print "Expected .h file name and .cc file name for the claw."
+ else:
+ claw = Claw("Claw")
+ loop_writer = control_loop.ControlLoopWriter("Claw", [claw])
+ loop_writer.AddConstant(control_loop.Constant("kClawMomentOfInertiaRatio",
+ "%f", claw.J_top / claw.J_bottom))
+ if argv[1][-3:] == '.cc':
+ loop_writer.Write(argv[2], argv[1])
+ else:
+ loop_writer.Write(argv[1], argv[2])
+
+if __name__ == '__main__':
+ sys.exit(main(sys.argv))