frc971/control_loops/python/wrist.py

#!/usr/bin/python

import control_loop
import numpy
import sys
from matplotlib import pylab

class Wrist(control_loop.ControlLoop):
  def __init__(self, name="RawWrist"):
    super(Wrist, self).__init__(name)
    # Stall Torque in N m
    self.stall_torque = 1.4
    # Stall Current in Amps
    self.stall_current = 86
    # Free Speed in RPM
    self.free_speed = 6200.0
    # Free Current in Amps
    self.free_current = 1.5
    # Moment of inertia of the wrist in kg m^2
    # TODO(aschuh): Measure this in reality.  It doesn't seem high enough.
    # James measured 0.51, but that can't be right given what I am seeing.
    self.J = 2.0
    # Resistance of the motor
    self.R = 12.0 / self.stall_current + 0.024 + .003
    # Motor velocity constant
    self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) /
               (13.5 - self.R * self.free_current))
    # Torque constant
    self.Kt = self.stall_torque / self.stall_current
    # Gear ratio
    self.G = 1.0 / ((84.0 / 20.0) * (50.0 / 14.0) * (40.0 / 14.0) * (40.0 / 12.0))
    # Control loop time step
    self.dt = 0.01

    # State feedback matrices
    self.A_continuous = numpy.matrix(
        [[0, 1],
         [0, -self.Kt / self.Kv / (self.J * self.G * self.G * self.R)]])
    self.B_continuous = numpy.matrix(
        [[0],
         [self.Kt / (self.J * self.G * self.R)]])
    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)

    self.PlaceControllerPoles([0.85, 0.45])

    self.rpl = .05
    self.ipl = 0.008
    self.PlaceObserverPoles([self.rpl + 1j * self.ipl,
                             self.rpl - 1j * self.ipl])

    self.U_max = numpy.matrix([[12.0]])
    self.U_min = numpy.matrix([[-12.0]])

    self.InitializeState()


class WristDeltaU(Wrist):
  def __init__(self, name="Wrist"):
    super(WristDeltaU, self).__init__(name)
    A_unaugmented = self.A
    B_unaugmented = self.B

    self.A = numpy.matrix([[0.0, 0.0, 0.0],
                           [0.0, 0.0, 0.0],
                           [0.0, 0.0, 1.0]])
    self.A[0:2, 0:2] = A_unaugmented
    self.A[0:2, 2] = B_unaugmented

    self.B = numpy.matrix([[0.0],
                           [0.0],
                           [1.0]])

    self.C = numpy.matrix([[1.0, 0.0, 0.0]])
    self.D = numpy.matrix([[0.0]])

    self.PlaceControllerPoles([0.60, 0.37, 0.80])

    print "K"
    print self.K
    print "Placed controller poles are"
    print numpy.linalg.eig(self.A - self.B * self.K)[0]

    self.rpl = .05
    self.ipl = 0.008
    self.PlaceObserverPoles([self.rpl + 1j * self.ipl,
                             self.rpl - 1j * self.ipl, 0.15])
    print "Placed observer poles are"
    print numpy.linalg.eig(self.A - self.L * self.C)[0]

    self.U_max = numpy.matrix([[12.0]])
    self.U_min = numpy.matrix([[-12.0]])

    self.InitializeState()


def ClipDeltaU(wrist, delta_u):
  old_u = numpy.matrix([[wrist.X[2, 0]]])
  new_u = numpy.clip(old_u + delta_u, wrist.U_min, wrist.U_max)
  return new_u - old_u

def main(argv):
  # Simulate the response of the system to a step input.
  wrist = WristDeltaU()
  simulated_x = []
  for _ in xrange(100):
    wrist.Update(numpy.matrix([[12.0]]))
    simulated_x.append(wrist.X[0, 0])

  pylab.plot(range(100), simulated_x)
  pylab.show()

  # Simulate the closed loop response of the system to a step input.
  wrist = WristDeltaU()
  close_loop_x = []
  close_loop_u = []
  R = numpy.matrix([[1.0], [0.0], [0.0]])
  wrist.X[2, 0] = -5
  for _ in xrange(100):
    U = numpy.clip(wrist.K * (R - wrist.X_hat), wrist.U_min, wrist.U_max)
    U = ClipDeltaU(wrist, U)
    wrist.UpdateObserver(U)
    wrist.Update(U)
    close_loop_x.append(wrist.X[0, 0] * 10)
    close_loop_u.append(wrist.X[2, 0])

  pylab.plot(range(100), close_loop_x)
  pylab.plot(range(100), close_loop_u)
  pylab.show()

  # Write the generated constants out to a file.
  if len(argv) != 5:
    print "Expected .h file name and .cc file name for"
    print "both the plant and unaugmented plant"
  else:
    unaug_wrist = Wrist("RawWrist")
    unaug_loop_writer = control_loop.ControlLoopWriter("RawWrist",
                                                       [unaug_wrist])
    if argv[3][-3:] == '.cc':
      unaug_loop_writer.Write(argv[4], argv[3])
    else:
      unaug_loop_writer.Write(argv[3], argv[4])

    loop_writer = control_loop.ControlLoopWriter("Wrist", [wrist])
    if argv[1][-3:] == '.cc':
      loop_writer.Write(argv[2], argv[1])
    else:
      loop_writer.Write(argv[1], argv[2])

if __name__ == '__main__':
  sys.exit(main(sys.argv))