| #!/usr/bin/python |
| |
| from frc971.control_loops.python import control_loop |
| from frc971.control_loops.python import controls |
| import numpy |
| import sys |
| from matplotlib import pylab |
| import glog |
| |
| class DrivetrainParams(object): |
| def __init__(self, J, mass, robot_radius, wheel_radius, G_high, G_low, |
| q_pos_low, q_pos_high, q_vel_low, q_vel_high, |
| motor_type = control_loop.CIM(), num_motors = 2, dt = 0.00505, |
| controller_poles=[0.90, 0.90], observer_poles=[0.02, 0.02]): |
| """Defines all constants of a drivetrain. |
| |
| Args: |
| J: float, Moment of inertia of drivetrain in kg m^2 |
| mass: float, Mass of the robot in kg. |
| robot_radius: float, Radius of the robot, in meters (requires tuning by |
| hand). |
| wheel_radius: float, Radius of the wheels, in meters. |
| G_high: float, Gear ratio for high gear. |
| G_low: float, Gear ratio for low gear. |
| dt: float, Control loop time step. |
| q_pos_low: float, q position low gear. |
| q_pos_high: float, q position high gear. |
| q_vel_low: float, q velocity low gear. |
| q_vel_high: float, q velocity high gear. |
| motor_type: object, class of values defining the motor in drivetrain. |
| num_motors: int, number of motors on one side of drivetrain. |
| controller_poles: array, An array of poles. (See control_loop.py) |
| observer_poles: array, An array of poles. (See control_loop.py) |
| """ |
| |
| self.J = J |
| self.mass = mass |
| self.robot_radius = robot_radius |
| self.wheel_radius = wheel_radius |
| self.G_high = G_high |
| self.G_low = G_low |
| self.dt = dt |
| self.q_pos_low = q_pos_low |
| self.q_pos_high = q_pos_high |
| self.q_vel_low = q_vel_low |
| self.q_vel_high = q_vel_high |
| self.motor_type = motor_type |
| self.num_motors = num_motors |
| self.controller_poles = controller_poles |
| self.observer_poles = observer_poles |
| |
| class Drivetrain(control_loop.ControlLoop): |
| def __init__(self, drivetrain_params, name="Drivetrain", left_low=True, |
| right_low=True): |
| """Defines a base drivetrain for a robot. |
| |
| Args: |
| drivetrain_params: DrivetrainParams, class of values defining the drivetrain. |
| name: string, Name of this drivetrain. |
| left_low: bool, Whether the left is in high gear. |
| right_low: bool, Whether the right is in high gear. |
| """ |
| super(Drivetrain, self).__init__(name) |
| |
| # Moment of inertia of the drivetrain in kg m^2 |
| self.J = drivetrain_params.J |
| # Mass of the robot, in kg. |
| self.mass = drivetrain_params.mass |
| # Radius of the robot, in meters (requires tuning by hand) |
| self.robot_radius = drivetrain_params.robot_radius |
| # Radius of the wheels, in meters. |
| self.r = drivetrain_params.wheel_radius |
| |
| # Gear ratios |
| self.G_low = drivetrain_params.G_low |
| self.G_high = drivetrain_params.G_high |
| 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 = drivetrain_params.dt |
| |
| self.BuildDrivetrain(drivetrain_params.motor_type, drivetrain_params.num_motors); |
| |
| if left_low or right_low: |
| q_pos = drivetrain_params.q_pos_low |
| q_vel = drivetrain_params.q_vel_low |
| else: |
| q_pos = drivetrain_params.q_pos_high |
| q_vel = drivetrain_params.q_vel_high |
| |
| self.BuildDrivetrainController(q_pos, q_vel) |
| |
| self.InitializeState() |
| |
| def BuildDrivetrain(self, motor, num_motors_per_side): |
| self.motor = motor |
| # Number of motors per side |
| self.num_motors = num_motors_per_side |
| # Stall Torque in N m |
| self.stall_torque = motor.stall_torque * self.num_motors * 0.60 |
| # Stall Current in Amps |
| self.stall_current = motor.stall_current * self.num_motors |
| # Free Speed in rad/s |
| self.free_speed = motor.free_speed |
| # Free Current in Amps |
| self.free_current = motor.free_current * self.num_motors |
| |
| # Effective motor resistance in ohms. |
| self.resistance = 12.0 / self.stall_current |
| |
| # Resistance of the motor, divided by the number of motors. |
| # Motor velocity constant |
| self.Kv = (self.free_speed / (12.0 - self.resistance * self.free_current)) |
| # Torque constant |
| self.Kt = self.stall_torque / self.stall_current |
| |
| # 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.mass + self.robot_radius * self.robot_radius / self.J |
| self.msn = 1.0 / self.mass - self.robot_radius * self.robot_radius / 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) |
| |
| def BuildDrivetrainController(self, q_pos, q_vel): |
| # Tune the LQR controller |
| 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) |
| |
| glog.debug('DT q_pos %f q_vel %s %s', q_pos, q_vel, self._name) |
| glog.debug(str(numpy.linalg.eig(self.A - self.B * self.K)[0])) |
| glog.debug('K %s', repr(self.K)) |
| |
| 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]]) |
| |
| class KFDrivetrain(Drivetrain): |
| def __init__(self, drivetrain_params, name="KFDrivetrain", |
| left_low=True, right_low=True): |
| """Kalman filter values of a drivetrain. |
| |
| Args: |
| drivetrain_params: DrivetrainParams, class of values defining the drivetrain. |
| name: string, Name of this drivetrain. |
| left_low: bool, Whether the left is in high gear. |
| right_low: bool, Whether the right is in high gear. |
| """ |
| super(KFDrivetrain, self).__init__(drivetrain_params, name, left_low, right_low) |
| |
| self.unaugmented_A_continuous = self.A_continuous |
| self.unaugmented_B_continuous = self.B_continuous |
| |
| # The practical voltage applied to the wheels is |
| # V_left = U_left + left_voltage_error |
| # |
| # The states are |
| # [left position, left velocity, right position, right velocity, |
| # left voltage error, right voltage error, angular_error] |
| # |
| # The left and right positions are filtered encoder positions and are not |
| # adjusted for heading error. |
| # The turn velocity as computed by the left and right velocities is |
| # adjusted by the gyro velocity. |
| # The angular_error is the angular velocity error between the wheel speed |
| # and the gyro speed. |
| 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_continuous[0,6] = 1 |
| self.A_continuous[2,6] = -1 |
| |
| self.A, self.B = self.ContinuousToDiscrete( |
| self.A_continuous, self.B_continuous, self.dt) |
| |
| self.C = numpy.matrix([[1, 0, 0, 0, 0, 0, 0], |
| [0, 0, 1, 0, 0, 0, 0], |
| [0, -0.5 / drivetrain_params.robot_radius, 0, 0.5 / drivetrain_params.robot_radius, 0, 0, 0]]) |
| |
| self.D = numpy.matrix([[0, 0], |
| [0, 0], |
| [0, 0]]) |
| |
| q_pos = 0.05 |
| q_vel = 1.00 |
| q_voltage = 10.0 |
| q_encoder_uncertainty = 2.00 |
| |
| 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_encoder_uncertainty ** 2.0)]]) |
| |
| r_pos = 0.0001 |
| r_gyro = 0.000001 |
| 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 |
| |
| unaug_K = self.K |
| |
| # Implement a nice closed loop controller for use by the closed loop |
| # controller. |
| self.K = numpy.matrix(numpy.zeros((self.B.shape[1], self.A.shape[0]))) |
| self.K[0:2, 0:4] = unaug_K |
| self.K[0, 4] = 1.0 |
| self.K[1, 5] = 1.0 |
| |
| self.Qff = numpy.matrix(numpy.zeros((4, 4))) |
| qff_pos = 0.005 |
| qff_vel = 1.00 |
| self.Qff[0, 0] = 1.0 / qff_pos ** 2.0 |
| self.Qff[1, 1] = 1.0 / qff_vel ** 2.0 |
| self.Qff[2, 2] = 1.0 / qff_pos ** 2.0 |
| self.Qff[3, 3] = 1.0 / qff_vel ** 2.0 |
| self.Kff = numpy.matrix(numpy.zeros((2, 7))) |
| self.Kff[0:2, 0:4] = controls.TwoStateFeedForwards(self.B[0:4,:], self.Qff) |
| |
| self.InitializeState() |
| |
| |
| def WriteDrivetrain(drivetrain_files, kf_drivetrain_files, year_namespace, |
| drivetrain_params): |
| |
| # Write the generated constants out to a file. |
| drivetrain_low_low = Drivetrain(name="DrivetrainLowLow", |
| left_low=True, right_low=True, drivetrain_params=drivetrain_params) |
| drivetrain_low_high = Drivetrain(name="DrivetrainLowHigh", |
| left_low=True, right_low=False, drivetrain_params=drivetrain_params) |
| drivetrain_high_low = Drivetrain(name="DrivetrainHighLow", |
| left_low=False, right_low=True, drivetrain_params=drivetrain_params) |
| drivetrain_high_high = Drivetrain(name="DrivetrainHighHigh", |
| left_low=False, right_low=False, drivetrain_params=drivetrain_params) |
| |
| kf_drivetrain_low_low = KFDrivetrain(name="KFDrivetrainLowLow", |
| left_low=True, right_low=True, drivetrain_params=drivetrain_params) |
| kf_drivetrain_low_high = KFDrivetrain(name="KFDrivetrainLowHigh", |
| left_low=True, right_low=False, drivetrain_params=drivetrain_params) |
| kf_drivetrain_high_low = KFDrivetrain(name="KFDrivetrainHighLow", |
| left_low=False, right_low=True, drivetrain_params=drivetrain_params) |
| kf_drivetrain_high_high = KFDrivetrain(name="KFDrivetrainHighHigh", |
| left_low=False, right_low=False, drivetrain_params=drivetrain_params) |
| |
| namespaces = [year_namespace, '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("kFreeSpeed", "%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.mass)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kRobotRadius", "%f", |
| drivetrain_low_low.robot_radius)) |
| 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.AddConstant(control_loop.Constant("kLowGearRatio", "%f", |
| drivetrain_low_low.G_low)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kHighGearRatio", "%f", |
| drivetrain_high_high.G_high)) |
| dog_loop_writer.AddConstant(control_loop.Constant("kHighOutputRatio", "%f", |
| drivetrain_high_high.G_high * drivetrain_high_high.r)) |
| |
| dog_loop_writer.Write(drivetrain_files[0], drivetrain_files[1]) |
| |
| 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(kf_drivetrain_files[0], kf_drivetrain_files[1]) |
| |
| def PlotDrivetrainMotions(drivetrain_params): |
| # Simulate the response of the system to a step input. |
| drivetrain = Drivetrain(left_low=False, right_low=False, drivetrain_params=drivetrain_params) |
| 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]) |
| |
| pylab.rc('lines', linewidth=4) |
| pylab.plot(range(100), simulated_left, label='left position') |
| pylab.plot(range(100), simulated_right, 'r--', label='right position') |
| pylab.suptitle('Acceleration Test\n12 Volt Step Input') |
| pylab.legend(loc='lower right') |
| pylab.show() |
| |
| # Simulate forwards motion. |
| drivetrain = Drivetrain(left_low=False, right_low=False, drivetrain_params=drivetrain_params) |
| close_loop_left = [] |
| close_loop_right = [] |
| left_power = [] |
| right_power = [] |
| R = numpy.matrix([[1.0], [0.0], [1.0], [0.0]]) |
| for _ in xrange(300): |
| 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]) |
| left_power.append(U[0, 0]) |
| right_power.append(U[1, 0]) |
| |
| pylab.plot(range(300), close_loop_left, label='left position') |
| pylab.plot(range(300), close_loop_right, 'm--', label='right position') |
| pylab.plot(range(300), left_power, label='left power') |
| pylab.plot(range(300), right_power, '--', label='right power') |
| pylab.suptitle('Linear Move\nLeft and Right Position going to 1') |
| pylab.legend() |
| pylab.show() |
| |
| # Try turning in place |
| drivetrain = Drivetrain(drivetrain_params=drivetrain_params) |
| close_loop_left = [] |
| close_loop_right = [] |
| R = numpy.matrix([[-1.0], [0.0], [1.0], [0.0]]) |
| for _ in xrange(200): |
| 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]) |
| |
| pylab.plot(range(200), close_loop_left, label='left position') |
| pylab.plot(range(200), close_loop_right, label='right position') |
| pylab.suptitle('Angular Move\nLeft position going to -1 and right position going to 1') |
| pylab.legend(loc='center right') |
| pylab.show() |
| |
| # Try turning just one side. |
| drivetrain = Drivetrain(drivetrain_params=drivetrain_params) |
| close_loop_left = [] |
| close_loop_right = [] |
| R = numpy.matrix([[0.0], [0.0], [1.0], [0.0]]) |
| for _ in xrange(300): |
| 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]) |
| |
| pylab.plot(range(300), close_loop_left, label='left position') |
| pylab.plot(range(300), close_loop_right, label='right position') |
| pylab.suptitle('Pivot\nLeft position not changing and right position going to 1') |
| pylab.legend(loc='center right') |
| pylab.show() |