Make initial bot3 folder and structure.
Change-Id: I9b7e97fe8533b99a28ab15b4ade5e9ac95c7d836
diff --git a/bot3/control_loops/python/drivetrain.py b/bot3/control_loops/python/drivetrain.py
new file mode 100644
index 0000000..8ed62d6
--- /dev/null
+++ b/bot3/control_loops/python/drivetrain.py
@@ -0,0 +1,242 @@
+#!/usr/bin/python
+
+import control_loop
+import controls
+import numpy
+import sys
+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.R = 12.0 / self.stall_current
+ # Motor velocity constant
+ self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) /
+ (12.0 - self.R * 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.R)]])
+ self.B_continuous = numpy.matrix(
+ [[self.Kt / (self.J * self.R)]])
+ 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)
+ # Stall Torque in N m
+ self.stall_torque = 2.42
+ # Stall Current in Amps
+ self.stall_current = 133.0
+ # Free Speed in RPM. Used number from last year.
+ self.free_speed = 4650.0
+ # Free Current in Amps
+ self.free_current = 2.7
+ # Moment of inertia of the drivetrain in kg m^2
+ # Just borrowed from last year.
+ self.J = 10
+ # Mass of the robot, in kg.
+ self.m = 68
+ # Radius of the robot, in meters (from last year).
+ self.rb = 0.9603 / 2.0
+ # Radius of the wheels, in meters.
+ self.r = .0515938
+ # Resistance of the motor, divided by the number of motors.
+ self.R = 12.0 / self.stall_current / 2
+ # Motor velocity constant
+ self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) /
+ (12.0 - self.R * self.free_current))
+ # Torque constant
+ self.Kt = self.stall_torque / self.stall_current
+ # Gear ratios
+ self.G_const = 28.0 / 50.0 * 20.0 / 64.0
+
+ self.G_low = self.G_const
+ self.G_high = self.G_const
+
+ 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.R * self.r * self.r)
+ self.tcr = -self.Kt / self.Kv / (self.Gr * self.Gr * self.R * self.r * self.r)
+ self.mpl = self.Kt / (self.Gl * self.R * self.r)
+ self.mpr = self.Kt / (self.Gr * self.R * 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]])
+
+ #print "THE NUMBER I WANT" + str(numpy.linalg.inv(self.A_continuous) * -self.B_continuous * numpy.matrix([[12.0], [12.0]]))
+ 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])
+ print self.K
+ q_pos = 0.07
+ 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 self.A
+ print self.B
+ 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()
+
+def main(argv):
+ # 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])
+
+ #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])
+
+ #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])
+
+ #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])
+
+ #pylab.plot(range(100), close_loop_left)
+ #pylab.plot(range(100), close_loop_right)
+ #pylab.show()
+
+ # Write the generated constants out to a file.
+ print "Output one"
+ 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)
+
+ if len(argv) != 5:
+ print "Expected .h file name and .cc file name"
+ else:
+ dog_loop_writer = control_loop.ControlLoopWriter(
+ "Drivetrain", [drivetrain_low_low, drivetrain_low_high,
+ drivetrain_high_low, drivetrain_high_high])
+ if argv[1][-3:] == '.cc':
+ dog_loop_writer.Write(argv[2], argv[1])
+ else:
+ dog_loop_writer.Write(argv[1], argv[2])
+
+if __name__ == '__main__':
+ sys.exit(main(sys.argv))
diff --git a/bot3/control_loops/python/elevator.py b/bot3/control_loops/python/elevator.py
new file mode 100644
index 0000000..2d72ff2
--- /dev/null
+++ b/bot3/control_loops/python/elevator.py
@@ -0,0 +1,247 @@
+#!/usr/bin/python
+
+import control_loop
+import controls
+import polytope
+import polydrivetrain
+import numpy
+import sys
+import matplotlib
+from matplotlib import pylab
+
+class Elevator(control_loop.ControlLoop):
+ def __init__(self, name="Elevator", mass=None):
+ super(Elevator, self).__init__(name)
+ # 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
+ # Mass of the elevator
+ # TODO(comran): Get actual value.
+ self.mass = 13.0
+ # Resistance of the motor
+ self.R = 12.0 / self.stall_current
+ # Motor velocity constant
+ self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) /
+ (12.0 - self.R * self.free_current))
+ # Torque constant
+ self.Kt = self.stall_torque / self.stall_current
+ # Gear ratio
+ # TODO(comran): Get actual value.
+ self.G = (56.0 / 12.0) * (84.0 / 14.0)
+ # Pulley diameter
+ # TODO(comran): Get actual value.
+ self.r = 32 * 0.005 / numpy.pi / 2.0
+ # Control loop time step
+ self.dt = 0.005
+
+ # Elevator spring constant (N/m)
+ # TODO(comran): Get actual value.
+ self.spring = 800.0
+
+ # State is [average position, average velocity]
+ # Input is [V]
+
+ # TODO(comran): Change everything below.
+
+ C1 = self.spring / (self.mass * 0.5)
+ C2 = self.Kt * self.G / (self.mass * 0.5 * self.r * self.R)
+ C3 = self.G * self.G * self.Kt / (
+ self.R * self.r * self.r * self.mass * 0.5 * self.Kv)
+
+ self.A_continuous = numpy.matrix(
+ [[0, 1, 0, 0],
+ [0, -C3, 0, 0],
+ [0, 0, 0, 1],
+ [0, 0, -C1 * 2.0, -C3]])
+
+ print "Full speed is", C2 / C3 * 12.0
+
+ # Start with the unmodified input
+ self.B_continuous = numpy.matrix(
+ [[0, 0],
+ [C2 / 2.0, C2 / 2.0],
+ [0, 0],
+ [C2 / 2.0, -C2 / 2.0]])
+
+ self.C = numpy.matrix([[1, 0, 1, 0],
+ [1, 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)
+
+ print self.A
+
+ controlability = controls.ctrb(self.A, self.B);
+ print "Rank of augmented controlability matrix.", numpy.linalg.matrix_rank(
+ controlability)
+
+ q_pos = 0.02
+ q_vel = 0.400
+ q_pos_diff = 0.01
+ q_vel_diff = 0.45
+ 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_diff ** 2.0)), 0.0],
+ [0.0, 0.0, 0.0, (1.0 / (q_vel_diff ** 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 self.K
+
+ print numpy.linalg.eig(self.A - self.B * self.K)[0]
+
+ self.rpl = 0.20
+ self.ipl = 0.05
+ self.PlaceObserverPoles([self.rpl + 1j * self.ipl,
+ self.rpl + 1j * self.ipl,
+ self.rpl - 1j * self.ipl,
+ self.rpl - 1j * self.ipl])
+
+ # 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], [12.0]])
+ self.U_min = numpy.matrix([[-12.0], [-12.0]])
+
+ self.InitializeState()
+
+
+def CapU(U):
+ if U[0, 0] - U[1, 0] > 24:
+ return numpy.matrix([[12], [-12]])
+ elif U[0, 0] - U[1, 0] < -24:
+ return numpy.matrix([[-12], [12]])
+ else:
+ max_u = max(U[0, 0], U[1, 0])
+ min_u = min(U[0, 0], U[1, 0])
+ if max_u > 12:
+ return U - (max_u - 12)
+ if min_u < -12:
+ return U - (min_u + 12)
+ return U
+
+
+def run_test(elevator, initial_X, goal, max_separation_error=0.01,
+ show_graph=True, iterations=200, controller_elevator=None,
+ observer_elevator=None):
+ """Runs the elevator plant with an initial condition and goal.
+
+ The tests themselves are not terribly sophisticated; I just test for
+ whether the goal has been reached and whether the separation goes
+ outside of the initial and goal values by more than max_separation_error.
+ Prints out something for a failure of either condition and returns
+ False if tests fail.
+ Args:
+ elevator: elevator object to use.
+ initial_X: starting state.
+ goal: goal state.
+ show_graph: Whether or not to display a graph showing the changing
+ states and voltages.
+ iterations: Number of timesteps to run the model for.
+ controller_elevator: elevator object to get K from, or None if we should
+ use elevator.
+ observer_elevator: elevator object to use for the observer, or None if we
+ should use the actual state.
+ """
+
+ elevator.X = initial_X
+
+ if controller_elevator is None:
+ controller_elevator = elevator
+
+ if observer_elevator is not None:
+ observer_elevator.X_hat = initial_X + 0.01
+ observer_elevator.X_hat = initial_X
+
+ # Various lists for graphing things.
+ t = []
+ x_avg = []
+ x_sep = []
+ x_hat_avg = []
+ x_hat_sep = []
+ v_avg = []
+ v_sep = []
+ u_left = []
+ u_right = []
+
+ sep_plot_gain = 100.0
+
+ for i in xrange(iterations):
+ X_hat = elevator.X
+ if observer_elevator is not None:
+ X_hat = observer_elevator.X_hat
+ x_hat_avg.append(observer_elevator.X_hat[0, 0])
+ x_hat_sep.append(observer_elevator.X_hat[2, 0] * sep_plot_gain)
+ U = controller_elevator.K * (goal - X_hat)
+ U = CapU(U)
+ x_avg.append(elevator.X[0, 0])
+ v_avg.append(elevator.X[1, 0])
+ x_sep.append(elevator.X[2, 0] * sep_plot_gain)
+ v_sep.append(elevator.X[3, 0])
+ if observer_elevator is not None:
+ observer_elevator.PredictObserver(U)
+ elevator.Update(U)
+ if observer_elevator is not None:
+ observer_elevator.Y = elevator.Y
+ observer_elevator.CorrectObserver(U)
+
+ t.append(i * elevator.dt)
+ u_left.append(U[0, 0])
+ u_right.append(U[1, 0])
+
+ print numpy.linalg.inv(elevator.A)
+ print "delta time is ", elevator.dt
+ print "Velocity at t=0 is ", x_avg[0], v_avg[0], x_sep[0], v_sep[0]
+ print "Velocity at t=1+dt is ", x_avg[1], v_avg[1], x_sep[1], v_sep[1]
+
+ if show_graph:
+ pylab.subplot(2, 1, 1)
+ pylab.plot(t, x_avg, label='x avg')
+ pylab.plot(t, x_sep, label='x sep')
+ if observer_elevator is not None:
+ pylab.plot(t, x_hat_avg, label='x_hat avg')
+ pylab.plot(t, x_hat_sep, label='x_hat sep')
+ pylab.legend()
+
+ pylab.subplot(2, 1, 2)
+ pylab.plot(t, u_left, label='u left')
+ pylab.plot(t, u_right, label='u right')
+ pylab.legend()
+ pylab.show()
+
+
+def main(argv):
+ loaded_mass = 25
+ #loaded_mass = 0
+ elevator = Elevator(mass=13 + loaded_mass)
+ elevator_controller = Elevator(mass=13 + 15)
+ observer_elevator = Elevator(mass=13 + 15)
+ #observer_elevator = None
+
+ # Test moving the elevator with constant separation.
+ initial_X = numpy.matrix([[0.0], [0.0], [0.01], [0.0]])
+ #initial_X = numpy.matrix([[0.0], [0.0], [0.00], [0.0]])
+ R = numpy.matrix([[1.0], [0.0], [0.0], [0.0]])
+ run_test(elevator, initial_X, R, controller_elevator=elevator_controller,
+ observer_elevator=observer_elevator)
+
+ # Write the generated constants out to a file.
+ if len(argv) != 3:
+ print "Expected .h file name and .cc file name for the elevator."
+ else:
+ elevator = Elevator("Elevator")
+ loop_writer = control_loop.ControlLoopWriter("Elevator", [elevator])
+ 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))
diff --git a/bot3/control_loops/python/polydrivetrain.py b/bot3/control_loops/python/polydrivetrain.py
new file mode 100644
index 0000000..a62c8c8
--- /dev/null
+++ b/bot3/control_loops/python/polydrivetrain.py
@@ -0,0 +1,504 @@
+#!/usr/bin/python
+
+import numpy
+import sys
+import polytope
+import drivetrain
+import control_loop
+import controls
+from matplotlib import pylab
+
+__author__ = 'Austin Schuh (austin.linux@gmail.com)'
+
+
+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 = 0.01
+ 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([0.6, 0.6])
+ 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 = 0.01
+
+ 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 = 1.1
+
+ 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):
+ print gear_name, 'Not in gear.'
+ return current_gear
+ else:
+ is_high = current_gear is VelocityDrivetrain.HIGH
+ if is_high != goal_gear_is_high:
+ if goal_gear_is_high:
+ print gear_name, 'Shifting up.'
+ return VelocityDrivetrain.SHIFTING_UP
+ else:
+ print gear_name, 'Shifting down.'
+ 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 False:
+ 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])
+
+ steering *= 2.3
+ if True or 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:
+ print '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 True or 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)
+
+ print "U is", self.U[0, 0], self.U[1, 0]
+ print "Left shifter", self.left_gear, self.left_shifter_position, "Right shifter", self.right_gear, self.right_shifter_position
+
+
+def main(argv):
+ vdrivetrain = VelocityDrivetrain()
+
+ if len(argv) != 7:
+ print "Expected .h file name and .cc file name"
+ else:
+ dog_loop_writer = control_loop.ControlLoopWriter(
+ "VelocityDrivetrain", [vdrivetrain.drivetrain_low_low,
+ vdrivetrain.drivetrain_low_high,
+ vdrivetrain.drivetrain_high_low,
+ vdrivetrain.drivetrain_high_high])
+
+ if argv[1][-3:] == '.cc':
+ dog_loop_writer.Write(argv[2], argv[1])
+ else:
+ dog_loop_writer.Write(argv[1], argv[2])
+
+ cim_writer = control_loop.ControlLoopWriter(
+ "CIM", [drivetrain.CIM()])
+
+ if argv[5][-3:] == '.cc':
+ cim_writer.Write(argv[6], argv[5])
+ else:
+ cim_writer.Write(argv[5], argv[6])
+ 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
+
+ print "K is", vdrivetrain.CurrentDrivetrain().K
+
+ if vdrivetrain.left_gear is VelocityDrivetrain.HIGH:
+ print "Left is high"
+ else:
+ print "Left is low"
+ if vdrivetrain.right_gear is VelocityDrivetrain.HIGH:
+ print "Right is high"
+ else:
+ print "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))
diff --git a/bot3/control_loops/python/polydrivetrain_test.py b/bot3/control_loops/python/polydrivetrain_test.py
new file mode 100644
index 0000000..434cdca
--- /dev/null
+++ b/bot3/control_loops/python/polydrivetrain_test.py
@@ -0,0 +1,82 @@
+#!/usr/bin/python
+
+import polydrivetrain
+import numpy
+from numpy.testing import *
+import polytope
+import unittest
+
+__author__ = 'Austin Schuh (austin.linux@gmail.com)'
+
+
+class TestVelocityDrivetrain(unittest.TestCase):
+ def MakeBox(self, x1_min, x1_max, x2_min, x2_max):
+ H = numpy.matrix([[1, 0],
+ [-1, 0],
+ [0, 1],
+ [0, -1]])
+ K = numpy.matrix([[x1_max],
+ [-x1_min],
+ [x2_max],
+ [-x2_min]])
+ return polytope.HPolytope(H, K)
+
+ def test_coerce_inside(self):
+ """Tests coercion when the point is inside the box."""
+ box = self.MakeBox(1, 2, 1, 2)
+
+ # x1 = x2
+ K = numpy.matrix([[1, -1]])
+ w = 0
+
+ assert_array_equal(polydrivetrain.CoerceGoal(box, K, w,
+ numpy.matrix([[1.5], [1.5]])),
+ numpy.matrix([[1.5], [1.5]]))
+
+ def test_coerce_outside_intersect(self):
+ """Tests coercion when the line intersects the box."""
+ box = self.MakeBox(1, 2, 1, 2)
+
+ # x1 = x2
+ K = numpy.matrix([[1, -1]])
+ w = 0
+
+ assert_array_equal(polydrivetrain.CoerceGoal(box, K, w, numpy.matrix([[5], [5]])),
+ numpy.matrix([[2.0], [2.0]]))
+
+ def test_coerce_outside_no_intersect(self):
+ """Tests coercion when the line does not intersect the box."""
+ box = self.MakeBox(3, 4, 1, 2)
+
+ # x1 = x2
+ K = numpy.matrix([[1, -1]])
+ w = 0
+
+ assert_array_equal(polydrivetrain.CoerceGoal(box, K, w, numpy.matrix([[5], [5]])),
+ numpy.matrix([[3.0], [2.0]]))
+
+ def test_coerce_middle_of_edge(self):
+ """Tests coercion when the line intersects the middle of an edge."""
+ box = self.MakeBox(0, 4, 1, 2)
+
+ # x1 = x2
+ K = numpy.matrix([[-1, 1]])
+ w = 0
+
+ assert_array_equal(polydrivetrain.CoerceGoal(box, K, w, numpy.matrix([[5], [5]])),
+ numpy.matrix([[2.0], [2.0]]))
+
+ def test_coerce_perpendicular_line(self):
+ """Tests coercion when the line does not intersect and is in quadrant 2."""
+ box = self.MakeBox(1, 2, 1, 2)
+
+ # x1 = -x2
+ K = numpy.matrix([[1, 1]])
+ w = 0
+
+ assert_array_equal(polydrivetrain.CoerceGoal(box, K, w, numpy.matrix([[5], [5]])),
+ numpy.matrix([[1.0], [1.0]]))
+
+
+if __name__ == '__main__':
+ unittest.main()