| #!/usr/bin/python |
| |
| 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([0.3, 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), 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 xrange(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)) |