y2017/control_loops/python/hood.py

#!/usr/bin/python

from aos.util.trapezoid_profile import TrapezoidProfile
from frc971.control_loops.python import control_loop
from frc971.control_loops.python import controls
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 Hood(control_loop.ControlLoop):

    def __init__(self, name='Hood'):
        super(Hood, self).__init__(name)
        # Stall Torque in N m
        self.stall_torque = 0.43
        # Stall Current in Amps
        self.stall_current = 53.0
        self.free_speed_rpm = 13180.0
        # Free Speed in rotations/second.
        self.free_speed = self.free_speed_rpm / 60
        # Free Current in Amps
        self.free_current = 1.8

        # Resistance of the motor
        self.R = 12.0 / self.stall_current
        # Motor velocity constant
        self.Kv = ((self.free_speed * 2.0 * numpy.pi) /
                   (12.0 - self.R * self.free_current))
        # Torque constant
        self.Kt = self.stall_torque / self.stall_current
        # First axle gear ratio off the motor
        self.G1 = (12.0 / 60.0)
        # Second axle gear ratio off the motor
        self.G2 = self.G1 * (14.0 / 36.0)
        # Third axle gear ratio off the motor
        self.G3 = self.G2 * (14.0 / 36.0)
        # The last gear reduction (encoder -> hood angle)
        self.last_G = (20.0 / 345.0)
        # Gear ratio
        self.G = (12.0 / 60.0) * (14.0 / 36.0) * (14.0 / 36.0) * self.last_G

        # 36 tooth gear inertia in kg * m^2
        self.big_gear_inertia = 0.5 * 0.039 * ((36.0 / 40.0 * 0.025)**2)

        # Motor inertia in kg * m^2
        self.motor_inertia = 0.000006
        glog.debug(self.big_gear_inertia)

        # Moment of inertia, measured in CAD.
        # Extra mass to compensate for friction is added on.
        self.J = 0.08 + 2.3 + \
                 self.big_gear_inertia * ((self.G1 / self.G) ** 2) + \
                 self.big_gear_inertia * ((self.G2 / self.G) ** 2) + \
                 self.motor_inertia * ((1.0 / self.G) ** 2.0)
        glog.debug('J effective %f', self.J)

        # Control loop time step
        self.dt = 0.005

        # State is [position, velocity]
        # Input is [Voltage]

        C1 = self.Kt / (self.R * self.J * self.Kv * self.G * self.G)
        C2 = self.Kt / (self.J * self.R * self.G)

        self.A_continuous = numpy.matrix([[0, 1], [0, -C1]])

        # Start with the unmodified input
        self.B_continuous = numpy.matrix([[0], [C2]])

        self.C = numpy.matrix([[1, 0]])
        self.D = numpy.matrix([[0]])

        self.A, self.B = self.ContinuousToDiscrete(self.A_continuous,
                                                   self.B_continuous, self.dt)

        controllability = controls.ctrb(self.A, self.B)

        glog.debug('Free speed is %f',
                   -self.B_continuous[1, 0] / self.A_continuous[1, 1] * 12.0)
        glog.debug(repr(self.A_continuous))

        # Calculate the LQR controller gain
        q_pos = 0.015
        q_vel = 0.40
        self.Q = numpy.matrix([[(1.0 / (q_pos**2.0)), 0.0],
                               [0.0, (1.0 / (q_vel**2.0))]])

        self.R = numpy.matrix([[(5.0 / (12.0**2.0))]])
        self.K = controls.dlqr(self.A, self.B, self.Q, self.R)

        # Calculate the feed forwards gain.
        q_pos_ff = 0.005
        q_vel_ff = 1.0
        self.Qff = numpy.matrix([[(1.0 / (q_pos_ff**2.0)), 0.0],
                                 [0.0, (1.0 / (q_vel_ff**2.0))]])

        self.Kff = controls.TwoStateFeedForwards(self.B, self.Qff)

        glog.debug('K %s', repr(self.K))
        glog.debug('Poles are %s',
                   repr(numpy.linalg.eig(self.A - self.B * self.K)[0]))

        q_pos = 0.10
        q_vel = 1.65
        self.Q = numpy.matrix([[(q_pos**2.0), 0.0], [0.0, (q_vel**2.0)]])

        r_volts = 0.025
        self.R = numpy.matrix([[(r_volts**2.0)]])

        self.KalmanGain, self.Q_steady = controls.kalman(
            A=self.A, B=self.B, C=self.C, Q=self.Q, R=self.R)

        glog.debug('Kal %s', repr(self.KalmanGain))
        self.L = self.A * self.KalmanGain
        glog.debug('KalL is %s', repr(self.L))

        # 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]])
        self.U_min = numpy.matrix([[-12.0]])

        self.InitializeState()


class IntegralHood(Hood):

    def __init__(self, name='IntegralHood'):
        super(IntegralHood, self).__init__(name=name)

        self.A_continuous_unaugmented = self.A_continuous
        self.B_continuous_unaugmented = self.B_continuous

        self.A_continuous = numpy.matrix(numpy.zeros((3, 3)))
        self.A_continuous[0:2, 0:2] = self.A_continuous_unaugmented
        self.A_continuous[0:2, 2] = self.B_continuous_unaugmented

        self.B_continuous = numpy.matrix(numpy.zeros((3, 1)))
        self.B_continuous[0:2, 0] = self.B_continuous_unaugmented

        self.C_unaugmented = self.C
        self.C = numpy.matrix(numpy.zeros((1, 3)))
        self.C[0:1, 0:2] = self.C_unaugmented

        self.A, self.B = self.ContinuousToDiscrete(self.A_continuous,
                                                   self.B_continuous, self.dt)

        q_pos = 0.01
        q_vel = 4.0
        q_voltage = 4.0
        self.Q = numpy.matrix([[(q_pos**2.0), 0.0, 0.0],
                               [0.0, (q_vel**2.0), 0.0],
                               [0.0, 0.0, (q_voltage**2.0)]])

        r_pos = 0.001
        self.R = numpy.matrix([[(r_pos**2.0)]])

        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

        self.K_unaugmented = self.K
        self.K = numpy.matrix(numpy.zeros((1, 3)))
        self.K[0, 0:2] = self.K_unaugmented
        self.K[0, 2] = 1

        self.Kff = numpy.concatenate(
            (self.Kff, numpy.matrix(numpy.zeros((1, 1)))), axis=1)

        self.InitializeState()


class ScenarioPlotter(object):

    def __init__(self):
        # Various lists for graphing things.
        self.t = []
        self.x = []
        self.v = []
        self.v_hat = []
        self.a = []
        self.x_hat = []
        self.u = []
        self.offset = []

    def run_test(self,
                 hood,
                 end_goal,
                 controller_hood,
                 observer_hood=None,
                 iterations=200):
        """Runs the hood plant with an initial condition and goal.

        Args:
            hood: hood object to use.
            end_goal: end_goal state.
            controller_hood: Hood object to get K from, or None if we should
                use hood.
            observer_hood: Hood object to use for the observer, or None if we should
                use the actual state.
            iterations: Number of timesteps to run the model for.
        """

        if controller_hood is None:
            controller_hood = hood

        vbat = 12.0

        if self.t:
            initial_t = self.t[-1] + hood.dt
        else:
            initial_t = 0

        goal = numpy.concatenate((hood.X, numpy.matrix(numpy.zeros((1, 1)))),
                                 axis=0)

        profile = TrapezoidProfile(hood.dt)
        profile.set_maximum_acceleration(10.0)
        profile.set_maximum_velocity(1.0)
        profile.SetGoal(goal[0, 0])

        U_last = numpy.matrix(numpy.zeros((1, 1)))
        for i in range(iterations):
            observer_hood.Y = hood.Y
            observer_hood.CorrectObserver(U_last)

            self.offset.append(observer_hood.X_hat[2, 0])
            self.x_hat.append(observer_hood.X_hat[0, 0])

            next_goal = numpy.concatenate(
                (profile.Update(end_goal[0, 0], end_goal[1, 0]),
                 numpy.matrix(numpy.zeros((1, 1)))),
                axis=0)

            ff_U = controller_hood.Kff * (next_goal - observer_hood.A * goal)

            U_uncapped = controller_hood.K * (goal - observer_hood.X_hat) + ff_U
            U = U_uncapped.copy()
            U[0, 0] = numpy.clip(U[0, 0], -vbat, vbat)
            self.x.append(hood.X[0, 0])

            if self.v:
                last_v = self.v[-1]
            else:
                last_v = 0

            self.v.append(hood.X[1, 0])
            self.a.append((self.v[-1] - last_v) / hood.dt)
            self.v_hat.append(observer_hood.X_hat[1, 0])

            offset = 0.0
            if i > 100:
                offset = 2.0
            hood.Update(U + offset)

            observer_hood.PredictObserver(U)

            self.t.append(initial_t + i * hood.dt)
            self.u.append(U[0, 0])

            ff_U -= U_uncapped - U
            goal = controller_hood.A * goal + controller_hood.B * ff_U

            if U[0, 0] != U_uncapped[0, 0]:
                profile.MoveCurrentState(
                    numpy.matrix([[goal[0, 0]], [goal[1, 0]]]))

        glog.debug('Time: %f', self.t[-1])
        glog.debug('goal_error %s', repr(end_goal - goal))
        glog.debug('error %s', repr(observer_hood.X_hat - end_goal))

    def Plot(self):
        pylab.subplot(3, 1, 1)
        pylab.plot(self.t, self.x, label='x')
        pylab.plot(self.t, self.x_hat, label='x_hat')
        pylab.plot(self.t, self.v, label='v')
        pylab.plot(self.t, self.v_hat, label='v_hat')
        pylab.legend()

        pylab.subplot(3, 1, 2)
        pylab.plot(self.t, self.u, label='u')
        pylab.plot(self.t, self.offset, label='voltage_offset')
        pylab.legend()

        pylab.subplot(3, 1, 3)
        pylab.plot(self.t, self.a, label='a')
        pylab.legend()

        pylab.show()


def main(argv):

    scenario_plotter = ScenarioPlotter()

    hood = Hood()
    hood_controller = IntegralHood()
    observer_hood = IntegralHood()

    # Test moving the hood with constant separation.
    initial_X = numpy.matrix([[0.0], [0.0]])
    R = numpy.matrix([[numpy.pi / 4.0], [0.0], [0.0]])
    scenario_plotter.run_test(
        hood,
        end_goal=R,
        controller_hood=hood_controller,
        observer_hood=observer_hood,
        iterations=200)

    if FLAGS.plot:
        scenario_plotter.Plot()

    # Write the generated constants out to a file.
    if len(argv) != 5:
        glog.fatal(
            'Expected .h file name and .cc file name for the hood and integral hood.'
        )
    else:
        namespaces = ['y2017', 'control_loops', 'superstructure', 'hood']
        hood = Hood('Hood')
        loop_writer = control_loop.ControlLoopWriter(
            'Hood', [hood], namespaces=namespaces)
        loop_writer.AddConstant(
            control_loop.Constant('kFreeSpeed', '%f', hood.free_speed))
        loop_writer.AddConstant(
            control_loop.Constant('kOutputRatio', '%f', hood.G))
        loop_writer.Write(argv[1], argv[2])

        integral_hood = IntegralHood('IntegralHood')
        integral_loop_writer = control_loop.ControlLoopWriter(
            'IntegralHood', [integral_hood], namespaces=namespaces)
        integral_loop_writer.AddConstant(
            control_loop.Constant('kLastReduction', '%f', integral_hood.last_G))
        integral_loop_writer.Write(argv[3], argv[4])


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