def test_fitted_value_iteration_pendulum(self):
plant = PendulumPlant()
simulator = Simulator(plant)
def quadratic_regulator_cost(context):
x = context.get_continuous_state_vector().CopyToVector()
x[0] = x[0] - math.pi
u = plant.EvalVectorInput(context, 0).CopyToVector()
return x.dot(x) + u.dot(u)
# Note: intentionally under-sampled to keep the problem small
qbins = np.linspace(0., 2.*math.pi, 11)
qdotbins = np.linspace(-10., 10., 11)
state_grid = [set(qbins), set(qdotbins)]
input_limit = 2.
input_mesh = [set(np.linspace(-input_limit, input_limit, 5))]
timestep = 0.01
num_callbacks = [0]
def callback(iteration, mesh, cost_to_go, policy):
# Drawing is slow, don't draw every frame.
num_callbacks[0] += 1
options = DynamicProgrammingOptions()
options.convergence_tol = 1.
options.periodic_boundary_conditions = [
PeriodicBoundaryCondition(0, 0., 2.*math.pi)
]
options.visualization_callback = callback
options.input_port_index = InputPortSelection.kUseFirstInputIfItExists
options.assume_non_continuous_states_are_fixed = False
policy, cost_to_go = FittedValueIteration(simulator,
quadratic_regulator_cost,
state_grid, input_mesh,
timestep, options)
self.assertGreater(num_callbacks[0], 0)
def VI(u_cost=180.**2):
tree = RigidBodyTree("/opt/underactuated/src/cartpole/cartpole.urdf",
FloatingBaseType.kFixed)
plant = RigidBodyPlant(tree)
simulator = Simulator(plant)
options = DynamicProgrammingOptions()
def min_time_cost(context):
x = context.get_continuous_state_vector().CopyToVector()
u = plant.EvalVectorInput(context, 0).CopyToVector()
x[1] = x[1] - math.pi
if x.dot(x) < .1: # seeks get x to (math.pi, 0., 0., 0.)
return 0.
return 1. + 2*x.dot(x)/(10**2+math.pi**2+10**2+math.pi**2) + u.dot(u)/(u_cost)
def quadratic_regulator_cost(context):
x = context.get_continuous_state_vector().CopyToVector()
x[1] = x[1] - math.pi
u = plant.EvalVectorInput(context, 0).CopyToVector()
return 2*x.dot(x)/(10**2+math.pi**2+10**2+math.pi**2) + u.dot(u)/(u_cost)
if (True):
cost_function = min_time_cost
input_limit = 360.
options.convergence_tol = 0.001
state_steps = 19
input_steps = 19
else:
cost_function = quadratic_regulator_cost
input_limit = 250.
options.convergence_tol = 0.01
state_steps = 19
input_steps = 19
####### SETTINGS ####### My cartpole linspaces are off??????
# State: (x, theta, x_dot, theta_dot)
# Previous Best... (min. time) (3)
xbins = np.linspace(-10., 10., state_steps)
thetabins = np.hstack((np.linspace(0., math.pi-0.2, 8), np.linspace(math.pi-0.2, math.pi+0.2, 11), np.linspace(math.pi+0.2, 8, 2*math.pi)))
xdotbins = np.linspace(-10., 10., state_steps)
thetadotbins = np.linspace(-10., 10., state_steps)
timestep = 0.01
# Test 1 (4)
xbins = np.linspace(-10., 10., state_steps)
thetabins = np.hstack((np.linspace(0., math.pi-0.12, 8), np.linspace(math.pi-0.12, math.pi+0.12, 11), np.linspace(math.pi+0.12, 8, 2*math.pi)))
xdotbins = np.linspace(-10., 10., state_steps+2)
thetadotbins = np.hstack((np.linspace(-10., -1.5, 9), np.linspace(-1.5, 1.5, 11), np.linspace(1.5, 10., 9)))
# timestep = 0.001 <- wasn't active...
# Test 2 - Test 1 was worse? WOW I HAD A BUG! - in my last np.linspace (5) SWEET!!!
xbins = np.linspace(-10., 10., state_steps)
thetabins = np.hstack((np.linspace(0., math.pi-0.2, 10), np.linspace(math.pi-0.2, math.pi+0.2, 9), np.linspace(math.pi+0.2, 2*math.pi, 10)))
xdotbins = np.linspace(-10., 10., state_steps+2)
thetadotbins = np.linspace(-10., 10., state_steps)
timestep = 0.01
input_limit = 1000. # test_stabilize_top7 for the higher input_limit version
options.periodic_boundary_conditions = [
PeriodicBoundaryCondition(1, 0., 2.*math.pi),
]
state_grid = [set(xbins), set(thetabins), set(xdotbins), set(thetadotbins)]
input_grid = [set(np.linspace(-input_limit, input_limit, input_steps))] # Input: x force
print("VI with u_cost={} beginning".format(u_cost))
policy, cost_to_go = FittedValueIteration(simulator, cost_function,
state_grid, input_grid,
timestep, options)
print("VI with u_cost={} completed!".format(u_cost))
save_policy("u_cost={:.0f}_torque_limit={:.0f}".format(u_cost, input_limit), policy, cost_to_go, state_grid)
return policy, cost_to_go
if (True):
cost_function = min_time_cost
input_limit = 3.
options.convergence_tol = 0.001
else:
cost_function = quadratic_regulator_cost
input_limit = 3.
options.convergence_tol = 0.1
qbins = np.linspace(0., 2. * math.pi, 51)
qdotbins = np.linspace(-10., 10., 51)
state_grid = [set(qbins), set(qdotbins)]
options.periodic_boundary_conditions = [
PeriodicBoundaryCondition(0, 0., 2. * math.pi),
]
input_grid = [set(np.linspace(-input_limit, input_limit, 9))]
timestep = 0.01
[Q, Qdot] = np.meshgrid(qbins, qdotbins)
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlabel("theta")
ax.set_ylabel("thetadot")
ax.set_title("Cost-to-Go")
fig2 = plt.figure()
ax2 = fig2.gca(projection='3d')
ax2.set_xlabel("q")
ax2.set_ylabel("qdot")