| #!/usr/bin/python |
| |
| from frc971.control_loops.python import control_loop |
| from frc971.control_loops.python import controls |
| import numpy |
| import sys |
| import argparse |
| from matplotlib import pylab |
| |
| |
| class CIM(control_loop.ControlLoop): |
| def __init__(self): |
| super(CIM, self).__init__("CIM") |
| # 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 = 4650.0 |
| # Free Current in Amps |
| self.free_current = 2.7 |
| # Moment of inertia of the CIM in kg m^2 |
| self.J = 0.0001 |
| # Resistance of the motor, divided by 2 to account for the 2 motors |
| self.resistance = 12.0 / self.stall_current |
| # Motor velocity constant |
| self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) / |
| (12.0 - self.resistance * self.free_current)) |
| # Torque constant |
| self.Kt = self.stall_torque / self.stall_current |
| # Control loop time step |
| self.dt = 0.005 |
| |
| # State feedback matrices |
| self.A_continuous = numpy.matrix( |
| [[-self.Kt / self.Kv / (self.J * self.resistance)]]) |
| self.B_continuous = numpy.matrix( |
| [[self.Kt / (self.J * self.resistance)]]) |
| self.C = numpy.matrix([[1]]) |
| self.D = numpy.matrix([[0]]) |
| |
| self.A, self.B = self.ContinuousToDiscrete(self.A_continuous, |
| self.B_continuous, self.dt) |
| |
| self.PlaceControllerPoles([0.01]) |
| self.PlaceObserverPoles([0.01]) |
| |
| self.U_max = numpy.matrix([[12.0]]) |
| self.U_min = numpy.matrix([[-12.0]]) |
| |
| self.InitializeState() |
| |
| |
| class Drivetrain(control_loop.ControlLoop): |
| def __init__(self, name="Drivetrain", left_low=True, right_low=True): |
| super(Drivetrain, self).__init__(name) |
| # Number of motors per side |
| self.num_motors = 2 |
| # Stall Torque in N m |
| self.stall_torque = 2.42 * self.num_motors |
| # Stall Current in Amps |
| self.stall_current = 133.0 * self.num_motors |
| # Free Speed in RPM. Used number from last year. |
| self.free_speed = 4650.0 |
| # Free Current in Amps |
| self.free_current = 2.7 * self.num_motors |
| # Moment of inertia of the drivetrain in kg m^2 |
| # Just borrowed from last year. |
| self.J = 4.5 |
| # Mass of the robot, in kg. |
| self.m = 68 |
| # Radius of the robot, in meters (from last year). |
| self.rb = 0.617998644 / 2.0 |
| # Radius of the wheels, in meters. |
| self.r = .04445 |
| # Resistance of the motor, divided by the number of motors. |
| self.resistance = 12.0 / self.stall_current |
| # Motor velocity constant |
| self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) / |
| (12.0 - self.resistance * self.free_current)) |
| # Torque constant |
| self.Kt = self.stall_torque / self.stall_current |
| # Gear ratios |
| self.G_low = 18.0 / 60.0 * 18.0 / 50.0 |
| self.G_high = 28.0 / 50.0 * 18.0 / 50.0 |
| if left_low: |
| self.Gl = self.G_low |
| else: |
| self.Gl = self.G_high |
| if right_low: |
| self.Gr = self.G_low |
| else: |
| self.Gr = self.G_high |
| |
| # Control loop time step |
| self.dt = 0.005 |
| |
| # These describe the way that a given side of a robot will be influenced |
| # by the other side. Units of 1 / kg. |
| self.msp = 1.0 / self.m + self.rb * self.rb / self.J |
| self.msn = 1.0 / self.m - self.rb * self.rb / self.J |
| # The calculations which we will need for A and B. |
| self.tcl = -self.Kt / self.Kv / (self.Gl * self.Gl * self.resistance * self.r * self.r) |
| self.tcr = -self.Kt / self.Kv / (self.Gr * self.Gr * self.resistance * self.r * self.r) |
| self.mpl = self.Kt / (self.Gl * self.resistance * self.r) |
| self.mpr = self.Kt / (self.Gr * self.resistance * self.r) |
| |
| # State feedback matrices |
| # X will be of the format |
| # [[positionl], [velocityl], [positionr], velocityr]] |
| self.A_continuous = numpy.matrix( |
| [[0, 1, 0, 0], |
| [0, self.msp * self.tcl, 0, self.msn * self.tcr], |
| [0, 0, 0, 1], |
| [0, self.msn * self.tcl, 0, self.msp * self.tcr]]) |
| self.B_continuous = numpy.matrix( |
| [[0, 0], |
| [self.msp * self.mpl, self.msn * self.mpr], |
| [0, 0], |
| [self.msn * self.mpl, self.msp * self.mpr]]) |
| self.C = numpy.matrix([[1, 0, 0, 0], |
| [0, 0, 1, 0]]) |
| self.D = numpy.matrix([[0, 0], |
| [0, 0]]) |
| |
| self.A, self.B = self.ContinuousToDiscrete( |
| self.A_continuous, self.B_continuous, self.dt) |
| |
| # Poles from last year. |
| self.hp = 0.65 |
| self.lp = 0.83 |
| self.PlaceControllerPoles([self.hp, self.lp, self.hp, self.lp]) |
| |
| q_pos = 0.12 |
| q_vel = 1.0 |
| self.Q = numpy.matrix([[(1.0 / (q_pos ** 2.0)), 0.0, 0.0, 0.0], |
| [0.0, (1.0 / (q_vel ** 2.0)), 0.0, 0.0], |
| [0.0, 0.0, (1.0 / (q_pos ** 2.0)), 0.0], |
| [0.0, 0.0, 0.0, (1.0 / (q_vel ** 2.0))]]) |
| |
| self.R = numpy.matrix([[(1.0 / (12.0 ** 2.0)), 0.0], |
| [0.0, (1.0 / (12.0 ** 2.0))]]) |
| self.K = controls.dlqr(self.A, self.B, self.Q, self.R) |
| |
| print "DT K", name |
| print self.K |
| print numpy.linalg.eig(self.A - self.B * self.K)[0] |
| |
| self.hlp = 0.3 |
| self.llp = 0.4 |
| self.PlaceObserverPoles([self.hlp, self.hlp, self.llp, self.llp]) |
| |
| self.U_max = numpy.matrix([[12.0], [12.0]]) |
| self.U_min = numpy.matrix([[-12.0], [-12.0]]) |
| self.InitializeState() |
| |
| |
| class KFDrivetrain(Drivetrain): |
| def __init__(self, name="KFDrivetrain", left_low=True, right_low=True): |
| super(KFDrivetrain, self).__init__(name, left_low, right_low) |
| |
| self.unaugmented_A_continuous = self.A_continuous |
| self.unaugmented_B_continuous = self.B_continuous |
| |
| # The states are |
| # The practical voltage applied to the wheels is |
| # V_left = U_left + left_voltage_error |
| # |
| # [left position, left velocity, right position, right velocity, |
| # left voltage error, right voltage error, angular_error] |
| self.A_continuous = numpy.matrix(numpy.zeros((7, 7))) |
| self.B_continuous = numpy.matrix(numpy.zeros((7, 2))) |
| self.A_continuous[0:4,0:4] = self.unaugmented_A_continuous |
| self.A_continuous[0:4,4:6] = self.unaugmented_B_continuous |
| self.B_continuous[0:4,0:2] = self.unaugmented_B_continuous |
| |
| self.A, self.B = self.ContinuousToDiscrete( |
| self.A_continuous, self.B_continuous, self.dt) |
| |
| self.C = numpy.matrix([[1, 0, 0, 0, 0, 0, self.rb], |
| [0, 0, 1, 0, 0, 0, -self.rb], |
| [0, -2.0 / self.rb, 0, 2.0 / self.rb, 0, 0, 0]]) |
| |
| self.D = numpy.matrix([[0, 0], |
| [0, 0], |
| [0, 0]]) |
| |
| q_pos = 0.08 |
| q_vel = 0.40 |
| q_voltage = 6.0 |
| q_gyro = 0.1 |
| |
| self.Q = numpy.matrix([[(q_pos ** 2.0), 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], |
| [0.0, (q_vel ** 2.0), 0.0, 0.0, 0.0, 0.0, 0.0], |
| [0.0, 0.0, (q_pos ** 2.0), 0.0, 0.0, 0.0, 0.0], |
| [0.0, 0.0, 0.0, (q_vel ** 2.0), 0.0, 0.0, 0.0], |
| [0.0, 0.0, 0.0, 0.0, (q_voltage ** 2.0), 0.0, 0.0], |
| [0.0, 0.0, 0.0, 0.0, 0.0, (q_voltage ** 2.0), 0.0], |
| [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, (q_gyro ** 2.0)]]) |
| |
| r_pos = 0.05 |
| r_gyro = 0.001 |
| self.R = numpy.matrix([[(r_pos ** 2.0), 0.0, 0.0], |
| [0.0, (r_pos ** 2.0), 0.0], |
| [0.0, 0.0, (r_gyro ** 2.0)]]) |
| |
| # Solving for kf gains. |
| 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 |
| |
| # We need a nothing controller for the autogen code to be happy. |
| self.K = numpy.matrix(numpy.zeros((self.B.shape[1], self.A.shape[0]))) |
| |
| |
| def main(argv): |
| parser = argparse.ArgumentParser(description='Calculate drivetrain.') |
| parser.add_argument('--plot', action='store_true', default=False, help='If true, plot') |
| parser.add_argument('drivetrainh') |
| parser.add_argument('drivetraincc') |
| parser.add_argument('kalman_drivetrainh') |
| parser.add_argument('kalman_drivetraincc') |
| |
| args = parser.parse_args(argv[1:]) |
| |
| # Simulate the response of the system to a step input. |
| drivetrain = Drivetrain() |
| simulated_left = [] |
| simulated_right = [] |
| for _ in xrange(100): |
| drivetrain.Update(numpy.matrix([[12.0], [12.0]])) |
| simulated_left.append(drivetrain.X[0, 0]) |
| simulated_right.append(drivetrain.X[2, 0]) |
| |
| if args.plot: |
| pylab.plot(range(100), simulated_left) |
| pylab.plot(range(100), simulated_right) |
| pylab.show() |
| |
| # Simulate forwards motion. |
| drivetrain = Drivetrain() |
| close_loop_left = [] |
| close_loop_right = [] |
| R = numpy.matrix([[1.0], [0.0], [1.0], [0.0]]) |
| for _ in xrange(100): |
| U = numpy.clip(drivetrain.K * (R - drivetrain.X_hat), |
| drivetrain.U_min, drivetrain.U_max) |
| drivetrain.UpdateObserver(U) |
| drivetrain.Update(U) |
| close_loop_left.append(drivetrain.X[0, 0]) |
| close_loop_right.append(drivetrain.X[2, 0]) |
| |
| if args.plot: |
| pylab.plot(range(100), close_loop_left) |
| pylab.plot(range(100), close_loop_right) |
| pylab.show() |
| |
| # Try turning in place |
| drivetrain = Drivetrain() |
| close_loop_left = [] |
| close_loop_right = [] |
| R = numpy.matrix([[-1.0], [0.0], [1.0], [0.0]]) |
| for _ in xrange(100): |
| U = numpy.clip(drivetrain.K * (R - drivetrain.X_hat), |
| drivetrain.U_min, drivetrain.U_max) |
| drivetrain.UpdateObserver(U) |
| drivetrain.Update(U) |
| close_loop_left.append(drivetrain.X[0, 0]) |
| close_loop_right.append(drivetrain.X[2, 0]) |
| |
| if args.plot: |
| pylab.plot(range(100), close_loop_left) |
| pylab.plot(range(100), close_loop_right) |
| pylab.show() |
| |
| # Try turning just one side. |
| drivetrain = Drivetrain() |
| close_loop_left = [] |
| close_loop_right = [] |
| R = numpy.matrix([[0.0], [0.0], [1.0], [0.0]]) |
| for _ in xrange(100): |
| U = numpy.clip(drivetrain.K * (R - drivetrain.X_hat), |
| drivetrain.U_min, drivetrain.U_max) |
| drivetrain.UpdateObserver(U) |
| drivetrain.Update(U) |
| close_loop_left.append(drivetrain.X[0, 0]) |
| close_loop_right.append(drivetrain.X[2, 0]) |
| |
| if args.plot: |
| pylab.plot(range(100), close_loop_left) |
| pylab.plot(range(100), close_loop_right) |
| pylab.show() |
| |
| # Write the generated constants out to a file. |
| drivetrain_low_low = Drivetrain( |
| name="DrivetrainLowLow", left_low=True, right_low=True) |
| drivetrain_low_high = Drivetrain( |
| name="DrivetrainLowHigh", left_low=True, right_low=False) |
| drivetrain_high_low = Drivetrain( |
| name="DrivetrainHighLow", left_low=False, right_low=True) |
| drivetrain_high_high = Drivetrain( |
| name="DrivetrainHighHigh", left_low=False, right_low=False) |
| |
| kf_drivetrain_low_low = KFDrivetrain( |
| name="KFDrivetrainLowLow", left_low=True, right_low=True) |
| kf_drivetrain_low_high = KFDrivetrain( |
| name="KFDrivetrainLowHigh", left_low=True, right_low=False) |
| kf_drivetrain_high_low = KFDrivetrain( |
| name="KFDrivetrainHighLow", left_low=False, right_low=True) |
| kf_drivetrain_high_high = KFDrivetrain( |
| name="KFDrivetrainHighHigh", left_low=False, right_low=False) |
| |
| if len(argv) != 5: |
| print "Expected .h file name and .cc file name" |
| else: |
| namespaces = ['y2014', 'control_loops', 'drivetrain'] |
| dog_loop_writer = control_loop.ControlLoopWriter( |
| "Drivetrain", [drivetrain_low_low, drivetrain_low_high, |
| drivetrain_high_low, drivetrain_high_high], |
| namespaces = namespaces) |
| dog_loop_writer.AddConstant(control_loop.Constant("kDt", "%f", |
| drivetrain_low_low.dt)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kStallTorque", "%f", |
| drivetrain_low_low.stall_torque)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kStallCurrent", "%f", |
| drivetrain_low_low.stall_current)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kFreeSpeedRPM", "%f", |
| drivetrain_low_low.free_speed)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kFreeCurrent", "%f", |
| drivetrain_low_low.free_current)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kJ", "%f", |
| drivetrain_low_low.J)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kMass", "%f", |
| drivetrain_low_low.m)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kRobotRadius", "%f", |
| drivetrain_low_low.rb)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kWheelRadius", "%f", |
| drivetrain_low_low.r)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kR", "%f", |
| drivetrain_low_low.resistance)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kV", "%f", |
| drivetrain_low_low.Kv)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kT", "%f", |
| drivetrain_low_low.Kt)) |
| |
| dog_loop_writer.Write(args.drivetrainh, args.drivetraincc) |
| |
| kf_loop_writer = control_loop.ControlLoopWriter( |
| "KFDrivetrain", [kf_drivetrain_low_low, kf_drivetrain_low_high, |
| kf_drivetrain_high_low, kf_drivetrain_high_high], |
| namespaces = namespaces) |
| kf_loop_writer.Write(args.kalman_drivetrainh, args.kalman_drivetraincc) |
| |
| if __name__ == '__main__': |
| sys.exit(main(sys.argv)) |