frc971/control_loops/python/linear_system.py

#!/usr/bin/python

from aos.util.trapezoid_profile import TrapezoidProfile
from frc971.control_loops.python import control_loop
from frc971.control_loops.python import controls
import numpy
from matplotlib import pylab
import glog


class LinearSystemParams(object):

    def __init__(self,
                 name,
                 motor,
                 G,
                 radius,
                 mass,
                 q_pos,
                 q_vel,
                 kalman_q_pos,
                 kalman_q_vel,
                 kalman_q_voltage,
                 kalman_r_position,
                 dt=0.005):
        self.name = name
        self.motor = motor
        self.G = G
        self.radius = radius
        self.mass = mass
        self.q_pos = q_pos
        self.q_vel = q_vel
        self.kalman_q_pos = kalman_q_pos
        self.kalman_q_vel = kalman_q_vel
        self.kalman_q_voltage = kalman_q_voltage
        self.kalman_r_position = kalman_r_position
        self.dt = dt


class LinearSystem(control_loop.ControlLoop):

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

        self.motor = params.motor

        # Gear ratio
        self.G = params.G
        self.radius = params.radius

        # Mass in kg
        self.mass = params.mass + self.motor.motor_inertia / (
            (self.G * self.radius)**2.0)

        # Control loop time step
        self.dt = params.dt

        # State is [position, velocity]
        # Input is [Voltage]
        C1 = self.motor.Kt / (self.G * self.G * self.radius * self.radius *
                              self.motor.resistance * self.mass * self.motor.Kv)
        C2 = self.motor.Kt / (
            self.G * self.radius * self.motor.resistance * self.mass)

        self.A_continuous = numpy.matrix([[0, 1], [0, -C1]])

        # Start with the unmodified input
        self.B_continuous = numpy.matrix([[0], [C2]])
        glog.debug(repr(self.A_continuous))
        glog.debug(repr(self.B_continuous))

        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('Controllability of %d',
                   numpy.linalg.matrix_rank(controllability))
        glog.debug('Mass: %f', self.mass)
        glog.debug('Stall force: %f',
                   self.motor.stall_torque / self.G / self.radius)
        glog.debug('Stall acceleration: %f',
                   self.motor.stall_torque / self.G / self.radius / self.mass)

        glog.debug('Free speed is %f',
                   -self.B_continuous[1, 0] / self.A_continuous[1, 1] * 12.0)

        self.Q = numpy.matrix([[(1.0 / (self.params.q_pos**2.0)), 0.0],
                               [0.0, (1.0 / (self.params.q_vel**2.0))]])

        self.R = numpy.matrix([[(1.0 / (12.0**2.0))]])
        self.K = controls.dlqr(self.A, self.B, self.Q, self.R)

        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]))

        self.Q = numpy.matrix([[(self.params.kalman_q_pos**2.0), 0.0],
                               [0.0, (self.params.kalman_q_vel**2.0)]])

        self.R = numpy.matrix([[(self.params.kalman_r_position**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))

        # 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 IntegralLinearSystem(LinearSystem):

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

        self.Q = numpy.matrix([[(self.params.kalman_q_pos**2.0), 0.0, 0.0],
                               [0.0, (self.params.kalman_q_vel**2.0), 0.0],
                               [0.0, 0.0, (self.params.kalman_q_voltage**2.0)]])

        self.R = numpy.matrix([[(self.params.kalman_r_position**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.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()


def RunTest(plant,
            end_goal,
            controller,
            observer=None,
            duration=1.0,
            use_profile=True,
            kick_time=0.5,
            kick_magnitude=0.0,
            max_velocity=0.3,
            max_acceleration=10.0):
    """Runs the plant with an initial condition and goal.

    Args:
      plant: plant object to use.
      end_goal: end_goal state.
      controller: LinearSystem object to get K from, or None if we should
          use plant.
      observer: LinearSystem object to use for the observer, or None if we
          should use the actual state.
      duration: float, time in seconds to run the simulation for.
      kick_time: float, time in seconds to kick the robot.
      kick_magnitude: float, disturbance in volts to apply.
      max_velocity: float, the max speed in m/s to profile.
      max_acceleration: float, the max acceleration in m/s/s to profile.
    """
    t_plot = []
    x_plot = []
    v_plot = []
    a_plot = []
    x_goal_plot = []
    v_goal_plot = []
    x_hat_plot = []
    u_plot = []
    offset_plot = []

    if controller is None:
        controller = plant

    vbat = 12.0

    goal = numpy.concatenate((plant.X, numpy.matrix(numpy.zeros((1, 1)))),
                             axis=0)

    profile = TrapezoidProfile(plant.dt)
    profile.set_maximum_acceleration(max_acceleration)
    profile.set_maximum_velocity(max_velocity)
    profile.SetGoal(goal[0, 0])

    U_last = numpy.matrix(numpy.zeros((1, 1)))
    iterations = int(duration / plant.dt)
    for i in xrange(iterations):
        t = i * plant.dt
        observer.Y = plant.Y
        observer.CorrectObserver(U_last)

        offset_plot.append(observer.X_hat[2, 0])
        x_hat_plot.append(observer.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.Kff * (next_goal - observer.A * goal)

        if use_profile:
            U_uncapped = controller.K * (goal - observer.X_hat) + ff_U
            x_goal_plot.append(goal[0, 0])
            v_goal_plot.append(goal[1, 0])
        else:
            U_uncapped = controller.K * (end_goal - observer.X_hat)
            x_goal_plot.append(end_goal[0, 0])
            v_goal_plot.append(end_goal[1, 0])

        U = U_uncapped.copy()
        U[0, 0] = numpy.clip(U[0, 0], -vbat, vbat)
        x_plot.append(plant.X[0, 0])

        if v_plot:
            last_v = v_plot[-1]
        else:
            last_v = 0

        v_plot.append(plant.X[1, 0])
        a_plot.append((v_plot[-1] - last_v) / plant.dt)

        u_offset = 0.0
        if t >= kick_time:
            u_offset = kick_magnitude
        plant.Update(U + u_offset)

        observer.PredictObserver(U)

        t_plot.append(t)
        u_plot.append(U[0, 0])

        ff_U -= U_uncapped - U
        goal = controller.A * goal + controller.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', t_plot[-1])
    glog.debug('goal_error %s', repr(end_goal - goal))
    glog.debug('error %s', repr(observer.X_hat - end_goal))

    pylab.subplot(3, 1, 1)
    pylab.plot(t_plot, x_plot, label='x')
    pylab.plot(t_plot, x_hat_plot, label='x_hat')
    pylab.plot(t_plot, x_goal_plot, label='x_goal')
    pylab.legend()

    pylab.subplot(3, 1, 2)
    pylab.plot(t_plot, u_plot, label='u')
    pylab.plot(t_plot, offset_plot, label='voltage_offset')
    pylab.legend()

    pylab.subplot(3, 1, 3)
    pylab.plot(t_plot, a_plot, label='a')
    pylab.legend()

    pylab.show()


def PlotStep(params, R, plant_params=None):
    """Plots a step move to the goal.

    Args:
      params: LinearSystemParams for the controller and observer
      plant_params: LinearSystemParams for the plant.  Defaults to params if
        plant_params is None.
      R: numpy.matrix(2, 1), the goal"""
    plant = LinearSystem(plant_params or params, params.name)
    controller = IntegralLinearSystem(params, params.name)
    observer = IntegralLinearSystem(params, params.name)

    # Test moving the system.
    initial_X = numpy.matrix([[0.0], [0.0]])
    augmented_R = numpy.matrix(numpy.zeros((3, 1)))
    augmented_R[0:2, :] = R
    RunTest(
        plant,
        end_goal=augmented_R,
        controller=controller,
        observer=observer,
        duration=2.0,
        use_profile=False,
        kick_time=1.0,
        kick_magnitude=0.0)


def PlotKick(params, R, plant_params=None):
    """Plots a step motion with a kick at 1.0 seconds.

    Args:
      params: LinearSystemParams for the controller and observer
      plant_params: LinearSystemParams for the plant.  Defaults to params if
        plant_params is None.
      R: numpy.matrix(2, 1), the goal"""
    plant = LinearSystem(plant_params or params, params.name)
    controller = IntegralLinearSystem(params, params.name)
    observer = IntegralLinearSystem(params, params.name)

    # Test moving the system.
    initial_X = numpy.matrix([[0.0], [0.0]])
    augmented_R = numpy.matrix(numpy.zeros((3, 1)))
    augmented_R[0:2, :] = R
    RunTest(
        plant,
        end_goal=augmented_R,
        controller=controller,
        observer=observer,
        duration=2.0,
        use_profile=False,
        kick_time=1.0,
        kick_magnitude=2.0)


def PlotMotion(params,
               R,
               max_velocity=0.3,
               max_acceleration=10.0,
               plant_params=None):
    """Plots a trapezoidal motion.

    Args:
      params: LinearSystemParams for the controller and observer
      plant_params: LinearSystemParams for the plant.  Defaults to params if
        plant_params is None.
      R: numpy.matrix(2, 1), the goal,
      max_velocity: float, The max velocity of the profile.
      max_acceleration: float, The max acceleration of the profile.
    """
    plant = LinearSystem(plant_params or params, params.name)
    controller = IntegralLinearSystem(params, params.name)
    observer = IntegralLinearSystem(params, params.name)

    # Test moving the system.
    initial_X = numpy.matrix([[0.0], [0.0]])
    augmented_R = numpy.matrix(numpy.zeros((3, 1)))
    augmented_R[0:2, :] = R
    RunTest(
        plant,
        end_goal=augmented_R,
        controller=controller,
        observer=observer,
        duration=2.0,
        use_profile=True,
        max_velocity=max_velocity,
        max_acceleration=max_acceleration)


def WriteLinearSystem(params, plant_files, controller_files, year_namespaces):
    """Writes out the constants for a linear system to a file.

    Args:
      params: LinearSystemParams, the parameters defining the system.
      plant_files: list of strings, the cc and h files for the plant.
      controller_files: list of strings, the cc and h files for the integral
        controller.
      year_namespaces: list of strings, the namespace list to use.
    """
    # Write the generated constants out to a file.
    linear_system = LinearSystem(params, params.name)
    loop_writer = control_loop.ControlLoopWriter(
        linear_system.name, [linear_system], namespaces=year_namespaces)
    loop_writer.AddConstant(
        control_loop.Constant('kFreeSpeed', '%f',
                              linear_system.motor.free_speed))
    loop_writer.AddConstant(
        control_loop.Constant('kOutputRatio', '%f',
                              linear_system.G * linear_system.radius))
    loop_writer.AddConstant(
        control_loop.Constant('kRadius', '%f', linear_system.radius))
    loop_writer.Write(plant_files[0], plant_files[1])

    integral_linear_system = IntegralLinearSystem(params,
                                                  'Integral' + params.name)
    integral_loop_writer = control_loop.ControlLoopWriter(
        integral_linear_system.name, [integral_linear_system],
        namespaces=year_namespaces)
    integral_loop_writer.Write(controller_files[0], controller_files[1])