y2014/control_loops/python/claw.py

#!/usr/bin/python

from frc971.control_loops.python import control_loop
from frc971.control_loops.python import controls
from frc971.control_loops.python import polytope
from y2014.control_loops.python import polydrivetrain
import numpy
import sys
from matplotlib import pylab
import gflags
import glog

FLAGS = gflags.FLAGS

try:
    gflags.DEFINE_bool('plot', False, 'If true, plot the loop response.')
except gflags.DuplicateFlagError:
    pass


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 = 0.005

        # 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
                                          ]])

        glog.debug('Cont X_ss %f',
                   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,
                                        [0.87 + 0.05j, 0.87 - 0.05j])
        self.K_diff = controls.dplace(self.A_diff, self.B_diff,
                                      [0.85 + 0.05j, 0.85 - 0.05j])

        glog.debug('K_diff %s', str(self.K_diff))
        glog.debug('K_bottom %s', str(self.K_bottom))

        glog.debug('A')
        glog.debug(self.A)
        glog.debug('B')
        glog.debug(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, :]
        glog.debug('System of Equations coefficients:')
        glog.debug(str(lstsq_A))
        glog.debug('det %s', str(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]

        glog.debug('K unaugmented')
        glog.debug(str(self.K))
        glog.debug('B * K unaugmented')
        glog.debug(str(self.B * self.K))
        F = self.A - self.B * self.K
        glog.debug('A - B * K unaugmented')
        glog.debug(str(F))
        glog.debug('eigenvalues')
        glog.debug(str(numpy.linalg.eig(F)[0]))

        self.rpl = .09
        self.ipl = 0.030
        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])

        glog.debug('X_ss %s', str(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]])

        controllability = controls.ctrb(self.A, self.B)
        glog.debug('Rank of augmented controllability matrix: %d',
                   numpy.linalg.matrix_rank(controllability))

        glog.debug('K')
        glog.debug(str(self.K))
        glog.debug('Placed controller poles are')
        glog.debug(str(numpy.linalg.eig(self.A - self.B * self.K)[0]))
        glog.debug(
            str([
                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=True,
             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
            glog.info('Claw separation was %f', claw.X[1, 0])
            glog.info("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
            glog.info('Claws at %f and %f', claw.X[0, 0],
                      claw.X[0, 0] + claw.X[1, 0])
            glog.info("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
        glog.error('X was %s Expected %s', str(claw.X), str(goal))

    return tests_passed


def main(argv):
    argv = FLAGS(argv)

    claw = Claw()
    if FLAGS.plot:
        # 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:
        glog.fatal('Expected .h file name and .cc file name for the claw.')
    else:
        namespaces = ['y2014', 'control_loops', 'claw']
        claw = Claw('Claw')
        loop_writer = control_loop.ControlLoopWriter(
            'Claw', [claw], namespaces=namespaces)
        loop_writer.AddConstant(
            control_loop.Constant('kClawMomentOfInertiaRatio', '%f',
                                  claw.J_top / claw.J_bottom))
        loop_writer.AddConstant(control_loop.Constant('kDt', '%f', claw.dt))
        loop_writer.Write(argv[1], argv[2])


if __name__ == '__main__':
    sys.exit(main(sys.argv))