y2017/control_loops/python/shooter.py

#!/usr/bin/python3

from frc971.control_loops.python import control_loop
from frc971.control_loops.python import controls
import numpy
import scipy
import sys
from matplotlib import pylab

import gflags
import glog

FLAGS = gflags.FLAGS

gflags.DEFINE_bool('plot', False, 'If true, plot the loop response.')


def PlotDiff(list1, list2, time):
    pylab.subplot(1, 1, 1)
    pylab.plot(time, numpy.subtract(list1, list2), label='diff')
    pylab.legend()


class VelocityShooter(control_loop.HybridControlLoop):

    def __init__(self, name='VelocityShooter'):
        super(VelocityShooter, self).__init__(name)
        # Number of motors
        self.num_motors = 2.0
        # Stall Torque in N m
        self.stall_torque = 0.71 * self.num_motors
        # Stall Current in Amps
        self.stall_current = 134.0 * self.num_motors
        # Free Speed in RPM
        self.free_speed_rpm = 18730.0
        # Free Speed in rotations/second.
        self.free_speed = self.free_speed_rpm / 60.0
        # Free Current in Amps
        self.free_current = 0.7 * self.num_motors
        # Moment of inertia of the shooter wheel in kg m^2
        # 1400.6 grams/cm^2
        # 1.407 *1e-4 kg m^2
        self.J = 0.00120
        # Resistance of the motor, divided by 2 to account for the 2 motors
        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
        # Gear ratio
        self.G = 12.0 / 36.0
        # Control loop time step
        self.dt = 0.00505

        # State feedback matrices
        # [angular velocity]
        self.A_continuous = numpy.matrix(
            [[-self.Kt / (self.Kv * self.J * self.G * self.G * self.R)]])
        self.B_continuous = numpy.matrix(
            [[self.Kt / (self.J * self.G * self.R)]])
        self.C = numpy.matrix([[1]])
        self.D = numpy.matrix([[0]])

        # The states are [unfiltered_velocity]
        self.A, self.B = self.ContinuousToDiscrete(self.A_continuous,
                                                   self.B_continuous, self.dt)

        self.PlaceControllerPoles([.75])

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

        self.PlaceObserverPoles([0.3])

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

        qff_vel = 8.0
        self.Qff = numpy.matrix([[1.0 / (qff_vel**2.0)]])

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


class SecondOrderVelocityShooter(VelocityShooter):

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

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

        self.A_continuous = numpy.matrix(numpy.zeros((2, 2)))
        self.A_continuous[0:1, 0:1] = self.A_continuous_unaugmented
        self.A_continuous[1, 0] = 175.0
        self.A_continuous[1, 1] = -self.A_continuous[1, 0]

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

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

        # The states are [unfiltered_velocity, velocity]
        self.A, self.B = self.ContinuousToDiscrete(self.A_continuous,
                                                   self.B_continuous, self.dt)

        self.PlaceControllerPoles([.70, 0.60])

        q_vel = 40.0
        q_filteredvel = 30.0
        self.Q = numpy.matrix([[(1.0 / (q_vel**2.0)), 0.0],
                               [0.0, (1.0 / (q_filteredvel**2.0))]])

        self.R = numpy.matrix([[(1.0 / (3.0**2.0))]])
        self.K = controls.dlqr(self.A, self.B, self.Q, self.R)

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

        self.PlaceObserverPoles([0.299, 0.301])

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

        qff_vel = 8.0
        self.Qff = numpy.matrix([[1.0 / (qff_vel**2.0), 0.0],
                                 [0.0, 1.0 / (qff_vel**2.0)]])

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


class Shooter(SecondOrderVelocityShooter):

    def __init__(self, name='Shooter'):
        super(Shooter, self).__init__(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[1:3, 1:3] = self.A_continuous_unaugmented
        self.A_continuous[0, 2] = 1

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

        # State feedback matrices
        # [position, unfiltered_velocity, angular velocity]
        self.C = numpy.matrix([[1, 0, 0]])
        self.D = numpy.matrix([[0]])

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

        observeability = controls.ctrb(self.A.T, self.C.T)
        glog.debug('Rank of augmented observability matrix. %d',
                   numpy.linalg.matrix_rank(observeability))

        self.PlaceObserverPoles([0.9, 0.8, 0.7])

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

        self.InitializeState()


class IntegralShooter(Shooter):

    def __init__(self, name='IntegralShooter'):
        super(IntegralShooter, 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((4, 4)))
        self.A_continuous[0:3, 0:3] = self.A_continuous_unaugmented
        self.A_continuous[0:3, 3] = self.B_continuous_unaugmented

        self.B_continuous = numpy.matrix(numpy.zeros((4, 1)))
        self.B_continuous[0:3, 0] = self.B_continuous_unaugmented

        self.C_unaugmented = self.C
        self.C = numpy.matrix(numpy.zeros((1, 4)))
        self.C[0:1, 0:3] = self.C_unaugmented

        # The states are [position, unfiltered_velocity, velocity, torque_error]
        self.A, self.B = self.ContinuousToDiscrete(self.A_continuous,
                                                   self.B_continuous, self.dt)

        glog.debug('A: \n%s', repr(self.A_continuous))
        glog.debug('eig(A): \n%s', repr(scipy.linalg.eig(self.A_continuous)))
        glog.debug('schur(A): \n%s',
                   repr(scipy.linalg.schur(self.A_continuous)))
        glog.debug('A_dt(A): \n%s', repr(self.A))

        q_pos = 0.01
        q_vel = 5.0
        q_velfilt = 1.5
        q_voltage = 2.0
        self.Q_continuous = numpy.matrix([[(q_pos**2.0), 0.0, 0.0, 0.0],
                                          [0.0, (q_vel**2.0), 0.0, 0.0],
                                          [0.0, 0.0, (q_velfilt**2.0), 0.0],
                                          [0.0, 0.0, 0.0, (q_voltage**2.0)]])

        r_pos = 0.0003
        self.R_continuous = numpy.matrix([[(r_pos**2.0)]])

        _, _, self.Q, self.R = controls.kalmd(A_continuous=self.A_continuous,
                                              B_continuous=self.B_continuous,
                                              Q_continuous=self.Q_continuous,
                                              R_continuous=self.R_continuous,
                                              dt=self.dt)

        self.KalmanGain, self.P_steady_state = 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, 4)))
        self.K[0, 0:3] = self.K_unaugmented
        self.K[0, 3] = 1
        self.Kff_unaugmented = self.Kff
        self.Kff = numpy.matrix(numpy.zeros((1, 4)))
        self.Kff[0, 0:3] = self.Kff_unaugmented

        self.InitializeState()


class ScenarioPlotter(object):

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

    def run_test(self,
                 shooter,
                 goal,
                 iterations=200,
                 controller_shooter=None,
                 observer_shooter=None,
                 hybrid_obs=False):
        """Runs the shooter plant with an initial condition and goal.

        Args:
            shooter: Shooter object to use.
            goal: goal state.
            iterations: Number of timesteps to run the model for.
            controller_shooter: Shooter object to get K from, or None if we should
                use shooter.
            observer_shooter: Shooter object to use for the observer, or None if we
                should use the actual state.
        """

        if controller_shooter is None:
            controller_shooter = shooter

        vbat = 12.0

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

        last_U = numpy.matrix([[0.0]])
        for i in range(iterations):
            X_hat = shooter.X

            if observer_shooter is not None:
                X_hat = observer_shooter.X_hat
                self.x_hat.append(observer_shooter.X_hat[2, 0])

            ff_U = controller_shooter.Kff * (goal - observer_shooter.A * goal)

            U = controller_shooter.K * (goal - X_hat) + ff_U
            U[0, 0] = numpy.clip(U[0, 0], -vbat, vbat)
            self.x.append(shooter.X[0, 0])

            self.diff.append(shooter.X[2, 0] - observer_shooter.X_hat[2, 0])

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

            self.v.append(shooter.X[2, 0])
            self.a.append((self.v[-1] - last_v) / shooter.dt)

            if observer_shooter is not None:
                if i != 0:
                    observer_shooter.Y = shooter.Y
                    observer_shooter.CorrectObserver(U)
                self.offset.append(observer_shooter.X_hat[3, 0])

            applied_U = last_U.copy()
            if i > 60:
                applied_U += 2
            shooter.Update(applied_U)

            if observer_shooter is not None:
                if hybrid_obs:
                    observer_shooter.PredictHybridObserver(last_U, shooter.dt)
                else:
                    observer_shooter.PredictObserver(last_U)
            last_U = U.copy()

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

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


def main(argv):
    scenario_plotter = ScenarioPlotter()

    if FLAGS.plot:
        iterations = 200

        initial_X = numpy.matrix([[0.0], [0.0], [0.0]])
        R = numpy.matrix([[0.0], [100.0], [100.0], [0.0]])

        scenario_plotter_int = ScenarioPlotter()

        shooter = Shooter()
        shooter_controller = IntegralShooter()
        observer_shooter_hybrid = IntegralShooter()

        scenario_plotter_int.run_test(shooter,
                                      goal=R,
                                      controller_shooter=shooter_controller,
                                      observer_shooter=observer_shooter_hybrid,
                                      iterations=iterations,
                                      hybrid_obs=True)

        scenario_plotter_int.Plot()

        pylab.show()

    if len(argv) != 5:
        glog.fatal('Expected .h file name and .cc file name')
    else:
        namespaces = ['y2017', 'control_loops', 'superstructure', 'shooter']
        shooter = Shooter('Shooter')
        loop_writer = control_loop.ControlLoopWriter('Shooter', [shooter],
                                                     namespaces=namespaces)
        loop_writer.AddConstant(
            control_loop.Constant('kFreeSpeed', '%f', shooter.free_speed))
        loop_writer.AddConstant(
            control_loop.Constant('kOutputRatio', '%f', shooter.G))
        loop_writer.Write(argv[1], argv[2])

        integral_shooter = IntegralShooter('IntegralShooter')
        integral_loop_writer = control_loop.ControlLoopWriter(
            'IntegralShooter', [integral_shooter],
            namespaces=namespaces,
            plant_type='StateFeedbackHybridPlant',
            observer_type='HybridKalman')
        integral_loop_writer.Write(argv[3], argv[4])


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