| #!/usr/bin/python |
| |
| from aos.common.util.trapezoid_profile import TrapezoidProfile |
| from frc971.control_loops.python import control_loop |
| from frc971.control_loops.python import controls |
| import numpy |
| import sys |
| import matplotlib |
| 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 + \ |
| 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 = 0.05 |
| q_vel = 10.0 |
| 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 = 0.12 |
| q_vel = 2.00 |
| q_voltage = 3.0 |
| 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 = 0.05 |
| 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.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 xrange(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) |
| |
| 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.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/2.0], [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)) |