Add code for prototyping with the 2012 drivebase
Change-Id: I16b5b2e9982f1911b410c25872eca7a00fa561f3
diff --git a/y2012/control_loops/python/polydrivetrain.py b/y2012/control_loops/python/polydrivetrain.py
new file mode 100755
index 0000000..9948ff2
--- /dev/null
+++ b/y2012/control_loops/python/polydrivetrain.py
@@ -0,0 +1,512 @@
+#!/usr/bin/python
+
+import numpy
+import sys
+from frc971.control_loops.python import polytope
+from y2012.control_loops.python import drivetrain
+from frc971.control_loops.python import control_loop
+from frc971.control_loops.python import controls
+from matplotlib import pylab
+
+import gflags
+import glog
+
+__author__ = 'Austin Schuh (austin.linux@gmail.com)'
+
+FLAGS = gflags.FLAGS
+
+try:
+ gflags.DEFINE_bool('plot', False, 'If true, plot the loop response.')
+except gflags.DuplicateFlagError:
+ pass
+
+def CoerceGoal(region, K, w, R):
+ """Intersects a line with a region, and finds the closest point to R.
+
+ Finds a point that is closest to R inside the region, and on the line
+ defined by K X = w. If it is not possible to find a point on the line,
+ finds a point that is inside the region and closest to the line. This
+ function assumes that
+
+ Args:
+ region: HPolytope, the valid goal region.
+ K: numpy.matrix (2 x 1), the matrix for the equation [K1, K2] [x1; x2] = w
+ w: float, the offset in the equation above.
+ R: numpy.matrix (2 x 1), the point to be closest to.
+
+ Returns:
+ numpy.matrix (2 x 1), the point.
+ """
+ return DoCoerceGoal(region, K, w, R)[0]
+
+def DoCoerceGoal(region, K, w, R):
+ if region.IsInside(R):
+ return (R, True)
+
+ perpendicular_vector = K.T / numpy.linalg.norm(K)
+ parallel_vector = numpy.matrix([[perpendicular_vector[1, 0]],
+ [-perpendicular_vector[0, 0]]])
+
+ # We want to impose the constraint K * X = w on the polytope H * X <= k.
+ # We do this by breaking X up into parallel and perpendicular components to
+ # the half plane. This gives us the following equation.
+ #
+ # parallel * (parallel.T \dot X) + perpendicular * (perpendicular \dot X)) = X
+ #
+ # Then, substitute this into the polytope.
+ #
+ # H * (parallel * (parallel.T \dot X) + perpendicular * (perpendicular \dot X)) <= k
+ #
+ # Substitute K * X = w
+ #
+ # H * parallel * (parallel.T \dot X) + H * perpendicular * w <= k
+ #
+ # Move all the knowns to the right side.
+ #
+ # H * parallel * ([parallel1 parallel2] * X) <= k - H * perpendicular * w
+ #
+ # Let t = parallel.T \dot X, the component parallel to the surface.
+ #
+ # H * parallel * t <= k - H * perpendicular * w
+ #
+ # This is a polytope which we can solve, and use to figure out the range of X
+ # that we care about!
+
+ t_poly = polytope.HPolytope(
+ region.H * parallel_vector,
+ region.k - region.H * perpendicular_vector * w)
+
+ vertices = t_poly.Vertices()
+
+ if vertices.shape[0]:
+ # The region exists!
+ # Find the closest vertex
+ min_distance = numpy.infty
+ closest_point = None
+ for vertex in vertices:
+ point = parallel_vector * vertex + perpendicular_vector * w
+ length = numpy.linalg.norm(R - point)
+ if length < min_distance:
+ min_distance = length
+ closest_point = point
+
+ return (closest_point, True)
+ else:
+ # Find the vertex of the space that is closest to the line.
+ region_vertices = region.Vertices()
+ min_distance = numpy.infty
+ closest_point = None
+ for vertex in region_vertices:
+ point = vertex.T
+ length = numpy.abs((perpendicular_vector.T * point)[0, 0])
+ if length < min_distance:
+ min_distance = length
+ closest_point = point
+
+ return (closest_point, False)
+
+
+class VelocityDrivetrainModel(control_loop.ControlLoop):
+ def __init__(self, left_low=True, right_low=True, name="VelocityDrivetrainModel"):
+ super(VelocityDrivetrainModel, self).__init__(name)
+ self._drivetrain = drivetrain.Drivetrain(left_low=left_low,
+ right_low=right_low)
+ self.dt = 0.005
+ self.A_continuous = numpy.matrix(
+ [[self._drivetrain.A_continuous[1, 1], self._drivetrain.A_continuous[1, 3]],
+ [self._drivetrain.A_continuous[3, 1], self._drivetrain.A_continuous[3, 3]]])
+
+ self.B_continuous = numpy.matrix(
+ [[self._drivetrain.B_continuous[1, 0], self._drivetrain.B_continuous[1, 1]],
+ [self._drivetrain.B_continuous[3, 0], self._drivetrain.B_continuous[3, 1]]])
+ self.C = numpy.matrix(numpy.eye(2))
+ self.D = numpy.matrix(numpy.zeros((2, 2)))
+
+ self.A, self.B = self.ContinuousToDiscrete(self.A_continuous,
+ self.B_continuous, self.dt)
+
+ # FF * X = U (steady state)
+ self.FF = self.B.I * (numpy.eye(2) - self.A)
+
+ self.PlaceControllerPoles([0.8, 0.8])
+ self.PlaceObserverPoles([0.02, 0.02])
+
+ self.G_high = self._drivetrain.G_high
+ self.G_low = self._drivetrain.G_low
+ self.R = self._drivetrain.R
+ self.r = self._drivetrain.r
+ self.Kv = self._drivetrain.Kv
+ self.Kt = self._drivetrain.Kt
+
+ self.U_max = self._drivetrain.U_max
+ self.U_min = self._drivetrain.U_min
+
+
+class VelocityDrivetrain(object):
+ HIGH = 'high'
+ LOW = 'low'
+ SHIFTING_UP = 'up'
+ SHIFTING_DOWN = 'down'
+
+ def __init__(self):
+ self.drivetrain_low_low = VelocityDrivetrainModel(
+ left_low=True, right_low=True, name='VelocityDrivetrainLowLow')
+ self.drivetrain_low_high = VelocityDrivetrainModel(left_low=True, right_low=False, name='VelocityDrivetrainLowHigh')
+ self.drivetrain_high_low = VelocityDrivetrainModel(left_low=False, right_low=True, name = 'VelocityDrivetrainHighLow')
+ self.drivetrain_high_high = VelocityDrivetrainModel(left_low=False, right_low=False, name = 'VelocityDrivetrainHighHigh')
+
+ # X is [lvel, rvel]
+ self.X = numpy.matrix(
+ [[0.0],
+ [0.0]])
+
+ self.U_poly = polytope.HPolytope(
+ numpy.matrix([[1, 0],
+ [-1, 0],
+ [0, 1],
+ [0, -1]]),
+ numpy.matrix([[12],
+ [12],
+ [12],
+ [12]]))
+
+ self.U_max = numpy.matrix(
+ [[12.0],
+ [12.0]])
+ self.U_min = numpy.matrix(
+ [[-12.0000000000],
+ [-12.0000000000]])
+
+ self.dt = 0.005
+
+ self.R = numpy.matrix(
+ [[0.0],
+ [0.0]])
+
+ # ttrust is the comprimise between having full throttle negative inertia,
+ # and having no throttle negative inertia. A value of 0 is full throttle
+ # inertia. A value of 1 is no throttle negative inertia.
+ self.ttrust = 1.0
+
+ self.left_gear = VelocityDrivetrain.LOW
+ self.right_gear = VelocityDrivetrain.LOW
+ self.left_shifter_position = 0.0
+ self.right_shifter_position = 0.0
+ self.left_cim = drivetrain.CIM()
+ self.right_cim = drivetrain.CIM()
+
+ def IsInGear(self, gear):
+ return gear is VelocityDrivetrain.HIGH or gear is VelocityDrivetrain.LOW
+
+ def MotorRPM(self, shifter_position, velocity):
+ if shifter_position > 0.5:
+ return (velocity / self.CurrentDrivetrain().G_high /
+ self.CurrentDrivetrain().r)
+ else:
+ return (velocity / self.CurrentDrivetrain().G_low /
+ self.CurrentDrivetrain().r)
+
+ def CurrentDrivetrain(self):
+ if self.left_shifter_position > 0.5:
+ if self.right_shifter_position > 0.5:
+ return self.drivetrain_high_high
+ else:
+ return self.drivetrain_high_low
+ else:
+ if self.right_shifter_position > 0.5:
+ return self.drivetrain_low_high
+ else:
+ return self.drivetrain_low_low
+
+ def SimShifter(self, gear, shifter_position):
+ if gear is VelocityDrivetrain.HIGH or gear is VelocityDrivetrain.SHIFTING_UP:
+ shifter_position = min(shifter_position + 0.5, 1.0)
+ else:
+ shifter_position = max(shifter_position - 0.5, 0.0)
+
+ if shifter_position == 1.0:
+ gear = VelocityDrivetrain.HIGH
+ elif shifter_position == 0.0:
+ gear = VelocityDrivetrain.LOW
+
+ return gear, shifter_position
+
+ def ComputeGear(self, wheel_velocity, should_print=False, current_gear=False, gear_name=None):
+ high_omega = (wheel_velocity / self.CurrentDrivetrain().G_high /
+ self.CurrentDrivetrain().r)
+ low_omega = (wheel_velocity / self.CurrentDrivetrain().G_low /
+ self.CurrentDrivetrain().r)
+ #print gear_name, "Motor Energy Difference.", 0.5 * 0.000140032647 * (low_omega * low_omega - high_omega * high_omega), "joules"
+ high_torque = ((12.0 - high_omega / self.CurrentDrivetrain().Kv) *
+ self.CurrentDrivetrain().Kt / self.CurrentDrivetrain().R)
+ low_torque = ((12.0 - low_omega / self.CurrentDrivetrain().Kv) *
+ self.CurrentDrivetrain().Kt / self.CurrentDrivetrain().R)
+ high_power = high_torque * high_omega
+ low_power = low_torque * low_omega
+ #if should_print:
+ # print gear_name, "High omega", high_omega, "Low omega", low_omega
+ # print gear_name, "High torque", high_torque, "Low torque", low_torque
+ # print gear_name, "High power", high_power, "Low power", low_power
+
+ # Shift algorithm improvements.
+ # TODO(aschuh):
+ # It takes time to shift. Shifting down for 1 cycle doesn't make sense
+ # because you will end up slower than without shifting. Figure out how
+ # to include that info.
+ # If the driver is still in high gear, but isn't asking for the extra power
+ # from low gear, don't shift until he asks for it.
+ goal_gear_is_high = high_power > low_power
+ #goal_gear_is_high = True
+
+ if not self.IsInGear(current_gear):
+ glog.debug('%s Not in gear.', gear_name)
+ return current_gear
+ else:
+ is_high = current_gear is VelocityDrivetrain.HIGH
+ if is_high != goal_gear_is_high:
+ if goal_gear_is_high:
+ glog.debug('%s Shifting up.', gear_name)
+ return VelocityDrivetrain.SHIFTING_UP
+ else:
+ glog.debug('%s Shifting down.', gear_name)
+ return VelocityDrivetrain.SHIFTING_DOWN
+ else:
+ return current_gear
+
+ def FilterVelocity(self, throttle):
+ # Invert the plant to figure out how the velocity filter would have to work
+ # out in order to filter out the forwards negative inertia.
+ # This math assumes that the left and right power and velocity are equal.
+
+ # The throttle filter should filter such that the motor in the highest gear
+ # should be controlling the time constant.
+ # Do this by finding the index of FF that has the lowest value, and computing
+ # the sums using that index.
+ FF_sum = self.CurrentDrivetrain().FF.sum(axis=1)
+ min_FF_sum_index = numpy.argmin(FF_sum)
+ min_FF_sum = FF_sum[min_FF_sum_index, 0]
+ min_K_sum = self.CurrentDrivetrain().K[min_FF_sum_index, :].sum()
+ # Compute the FF sum for high gear.
+ high_min_FF_sum = self.drivetrain_high_high.FF[0, :].sum()
+
+ # U = self.K[0, :].sum() * (R - x_avg) + self.FF[0, :].sum() * R
+ # throttle * 12.0 = (self.K[0, :].sum() + self.FF[0, :].sum()) * R
+ # - self.K[0, :].sum() * x_avg
+
+ # R = (throttle * 12.0 + self.K[0, :].sum() * x_avg) /
+ # (self.K[0, :].sum() + self.FF[0, :].sum())
+
+ # U = (K + FF) * R - K * X
+ # (K + FF) ^-1 * (U + K * X) = R
+
+ # Scale throttle by min_FF_sum / high_min_FF_sum. This will make low gear
+ # have the same velocity goal as high gear, and so that the robot will hold
+ # the same speed for the same throttle for all gears.
+ adjusted_ff_voltage = numpy.clip(throttle * 12.0 * min_FF_sum / high_min_FF_sum, -12.0, 12.0)
+ return ((adjusted_ff_voltage + self.ttrust * min_K_sum * (self.X[0, 0] + self.X[1, 0]) / 2.0)
+ / (self.ttrust * min_K_sum + min_FF_sum))
+
+ def Update(self, throttle, steering):
+ # Shift into the gear which sends the most power to the floor.
+ # This is the same as sending the most torque down to the floor at the
+ # wheel.
+
+ self.left_gear = self.right_gear = True
+ if True:
+ self.left_gear = self.ComputeGear(self.X[0, 0], should_print=True,
+ current_gear=self.left_gear,
+ gear_name="left")
+ self.right_gear = self.ComputeGear(self.X[1, 0], should_print=True,
+ current_gear=self.right_gear,
+ gear_name="right")
+ if self.IsInGear(self.left_gear):
+ self.left_cim.X[0, 0] = self.MotorRPM(self.left_shifter_position, self.X[0, 0])
+
+ if self.IsInGear(self.right_gear):
+ self.right_cim.X[0, 0] = self.MotorRPM(self.right_shifter_position, self.X[0, 0])
+
+ if self.IsInGear(self.left_gear) and self.IsInGear(self.right_gear):
+ # Filter the throttle to provide a nicer response.
+ fvel = self.FilterVelocity(throttle)
+
+ # Constant radius means that angualar_velocity / linear_velocity = constant.
+ # Compute the left and right velocities.
+ steering_velocity = numpy.abs(fvel) * steering
+ left_velocity = fvel - steering_velocity
+ right_velocity = fvel + steering_velocity
+
+ # Write this constraint in the form of K * R = w
+ # angular velocity / linear velocity = constant
+ # (left - right) / (left + right) = constant
+ # left - right = constant * left + constant * right
+
+ # (fvel - steering * numpy.abs(fvel) - fvel - steering * numpy.abs(fvel)) /
+ # (fvel - steering * numpy.abs(fvel) + fvel + steering * numpy.abs(fvel)) =
+ # constant
+ # (- 2 * steering * numpy.abs(fvel)) / (2 * fvel) = constant
+ # (-steering * sign(fvel)) = constant
+ # (-steering * sign(fvel)) * (left + right) = left - right
+ # (steering * sign(fvel) + 1) * left + (steering * sign(fvel) - 1) * right = 0
+
+ equality_k = numpy.matrix(
+ [[1 + steering * numpy.sign(fvel), -(1 - steering * numpy.sign(fvel))]])
+ equality_w = 0.0
+
+ self.R[0, 0] = left_velocity
+ self.R[1, 0] = right_velocity
+
+ # Construct a constraint on R by manipulating the constraint on U
+ # Start out with H * U <= k
+ # U = FF * R + K * (R - X)
+ # H * (FF * R + K * R - K * X) <= k
+ # H * (FF + K) * R <= k + H * K * X
+ R_poly = polytope.HPolytope(
+ self.U_poly.H * (self.CurrentDrivetrain().K + self.CurrentDrivetrain().FF),
+ self.U_poly.k + self.U_poly.H * self.CurrentDrivetrain().K * self.X)
+
+ # Limit R back inside the box.
+ self.boxed_R = CoerceGoal(R_poly, equality_k, equality_w, self.R)
+
+ FF_volts = self.CurrentDrivetrain().FF * self.boxed_R
+ self.U_ideal = self.CurrentDrivetrain().K * (self.boxed_R - self.X) + FF_volts
+ else:
+ glog.debug('Not all in gear')
+ if not self.IsInGear(self.left_gear) and not self.IsInGear(self.right_gear):
+ # TODO(austin): Use battery volts here.
+ R_left = self.MotorRPM(self.left_shifter_position, self.X[0, 0])
+ self.U_ideal[0, 0] = numpy.clip(
+ self.left_cim.K * (R_left - self.left_cim.X) + R_left / self.left_cim.Kv,
+ self.left_cim.U_min, self.left_cim.U_max)
+ self.left_cim.Update(self.U_ideal[0, 0])
+
+ R_right = self.MotorRPM(self.right_shifter_position, self.X[1, 0])
+ self.U_ideal[1, 0] = numpy.clip(
+ self.right_cim.K * (R_right - self.right_cim.X) + R_right / self.right_cim.Kv,
+ self.right_cim.U_min, self.right_cim.U_max)
+ self.right_cim.Update(self.U_ideal[1, 0])
+ else:
+ assert False
+
+ self.U = numpy.clip(self.U_ideal, self.U_min, self.U_max)
+
+ # TODO(austin): Model the robot as not accelerating when you shift...
+ # This hack only works when you shift at the same time.
+ if self.IsInGear(self.left_gear) and self.IsInGear(self.right_gear):
+ self.X = self.CurrentDrivetrain().A * self.X + self.CurrentDrivetrain().B * self.U
+
+ self.left_gear, self.left_shifter_position = self.SimShifter(
+ self.left_gear, self.left_shifter_position)
+ self.right_gear, self.right_shifter_position = self.SimShifter(
+ self.right_gear, self.right_shifter_position)
+
+ glog.debug('U is %s %s', str(self.U[0, 0]), str(self.U[1, 0]))
+ glog.debug('Left shifter %s %d Right shifter %s %d',
+ self.left_gear, self.left_shifter_position,
+ self.right_gear, self.right_shifter_position)
+
+
+def main(argv):
+ argv = FLAGS(argv)
+
+ vdrivetrain = VelocityDrivetrain()
+
+ if len(argv) != 5:
+ glog.fatal('Expected .h file name and .cc file name')
+ else:
+ namespaces = ['y2012', 'control_loops', 'drivetrain']
+ dog_loop_writer = control_loop.ControlLoopWriter(
+ "VelocityDrivetrain", [vdrivetrain.drivetrain_low_low,
+ vdrivetrain.drivetrain_low_high,
+ vdrivetrain.drivetrain_high_low,
+ vdrivetrain.drivetrain_high_high],
+ namespaces=namespaces)
+
+ dog_loop_writer.Write(argv[1], argv[2])
+
+ cim_writer = control_loop.ControlLoopWriter(
+ "CIM", [drivetrain.CIM()])
+
+ cim_writer.Write(argv[3], argv[4])
+ return
+
+ vl_plot = []
+ vr_plot = []
+ ul_plot = []
+ ur_plot = []
+ radius_plot = []
+ t_plot = []
+ left_gear_plot = []
+ right_gear_plot = []
+ vdrivetrain.left_shifter_position = 0.0
+ vdrivetrain.right_shifter_position = 0.0
+ vdrivetrain.left_gear = VelocityDrivetrain.LOW
+ vdrivetrain.right_gear = VelocityDrivetrain.LOW
+
+ glog.debug('K is %s', str(vdrivetrain.CurrentDrivetrain().K))
+
+ if vdrivetrain.left_gear is VelocityDrivetrain.HIGH:
+ glog.debug('Left is high')
+ else:
+ glog.debug('Left is low')
+ if vdrivetrain.right_gear is VelocityDrivetrain.HIGH:
+ glog.debug('Right is high')
+ else:
+ glog.debug('Right is low')
+
+ for t in numpy.arange(0, 1.7, vdrivetrain.dt):
+ if t < 0.5:
+ vdrivetrain.Update(throttle=0.00, steering=1.0)
+ elif t < 1.2:
+ vdrivetrain.Update(throttle=0.5, steering=1.0)
+ else:
+ vdrivetrain.Update(throttle=0.00, steering=1.0)
+ t_plot.append(t)
+ vl_plot.append(vdrivetrain.X[0, 0])
+ vr_plot.append(vdrivetrain.X[1, 0])
+ ul_plot.append(vdrivetrain.U[0, 0])
+ ur_plot.append(vdrivetrain.U[1, 0])
+ left_gear_plot.append((vdrivetrain.left_gear is VelocityDrivetrain.HIGH) * 2.0 - 10.0)
+ right_gear_plot.append((vdrivetrain.right_gear is VelocityDrivetrain.HIGH) * 2.0 - 10.0)
+
+ fwd_velocity = (vdrivetrain.X[1, 0] + vdrivetrain.X[0, 0]) / 2
+ turn_velocity = (vdrivetrain.X[1, 0] - vdrivetrain.X[0, 0])
+ if abs(fwd_velocity) < 0.0000001:
+ radius_plot.append(turn_velocity)
+ else:
+ radius_plot.append(turn_velocity / fwd_velocity)
+
+ cim_velocity_plot = []
+ cim_voltage_plot = []
+ cim_time = []
+ cim = drivetrain.CIM()
+ R = numpy.matrix([[300]])
+ for t in numpy.arange(0, 0.5, cim.dt):
+ U = numpy.clip(cim.K * (R - cim.X) + R / cim.Kv, cim.U_min, cim.U_max)
+ cim.Update(U)
+ cim_velocity_plot.append(cim.X[0, 0])
+ cim_voltage_plot.append(U[0, 0] * 10)
+ cim_time.append(t)
+ pylab.plot(cim_time, cim_velocity_plot, label='cim spinup')
+ pylab.plot(cim_time, cim_voltage_plot, label='cim voltage')
+ pylab.legend()
+ pylab.show()
+
+ # TODO(austin):
+ # Shifting compensation.
+
+ # Tighten the turn.
+ # Closed loop drive.
+
+ pylab.plot(t_plot, vl_plot, label='left velocity')
+ pylab.plot(t_plot, vr_plot, label='right velocity')
+ pylab.plot(t_plot, ul_plot, label='left voltage')
+ pylab.plot(t_plot, ur_plot, label='right voltage')
+ pylab.plot(t_plot, radius_plot, label='radius')
+ pylab.plot(t_plot, left_gear_plot, label='left gear high')
+ pylab.plot(t_plot, right_gear_plot, label='right gear high')
+ pylab.legend()
+ pylab.show()
+ return 0
+
+if __name__ == '__main__':
+ sys.exit(main(sys.argv))