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)
qbins = np.linspace(0., 2. * math.pi, 51)
qdotbins = np.linspace(-10., 10., 41)
state_grid = [set(qbins), set(qdotbins)]
input_limit = 2.
input_mesh = [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')
def draw(iteration, mesh, cost_to_go, policy):
# Drawing is slow, don't draw every frame.
if iteration % 20 != 0:
return
plt.title("iteration " + str(iteration))
J = np.reshape(cost_to_go, Q.shape)
surf = ax.plot_surface(Q,
Qdot,
J,
rstride=1,
cstride=1,
cmap=color_map.jet)
plt.pause(0.00001)
surf.remove()
options = DynamicProgrammingOptions()
options.convergence_tol = 1.
options.state_indices_with_periodic_boundary_conditions = {0}
options.visualization_callback = draw
policy, cost_to_go = FittedValueIteration(simulator,
quadratic_regulator_cost,
state_grid, input_mesh,
timestep, options)
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)
surf = ax.plot_surface(Q, Qdot, J, rstride=1, cstride=1, cmap=cm.jet)
Pi = np.reshape(policy, Q.shape)
surf2 = ax2.plot_surface(Q, Qdot, Pi, rstride=1, cstride=1, cmap=cm.jet)
if plt.get_backend() != u"template":
plt.draw_all()
plt.pause(0.00001)
surf.remove()
surf2.remove()
options.visualization_callback = draw
policy, cost_to_go = FittedValueIteration(simulator, cost_function, state_grid,
input_grid, timestep, options)
J = np.reshape(cost_to_go, Q.shape)
surf = ax.plot_surface(Q, Qdot, J, rstride=1, cstride=1, cmap=cm.jet)
Pi = np.reshape(policy.get_output_values(), Q.shape)
surf = ax2.plot_surface(Q, Qdot, Pi, rstride=1, cstride=1, cmap=cm.jet)
# animate the resulting policy.
builder = DiagramBuilder()
plant = builder.AddSystem(DoubleIntegrator())
logger = LogOutput(plant.get_output_port(0), builder)
vi_policy = builder.AddSystem(policy)
builder.Connect(vi_policy.get_output_port(0), plant.get_input_port(0))
builder.Connect(plant.get_output_port(0), vi_policy.get_input_port(0))
diagram = builder.Build()
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
surf = ax.plot_surface(Q, Qdot, J, rstride=1, cstride=1, cmap=cm.jet)
Pi = np.reshape(policy, Q.shape)
surf2 = ax2.plot_surface(Q, Qdot, Pi, rstride=1, cstride=1, cmap=cm.jet)
if plt.get_backend() != u'template':
plt.draw_all()
plt.pause(0.00001)
surf.remove()
surf2.remove()
options.visualization_callback = draw
policy, cost_to_go = FittedValueIteration(simulator, cost_function, state_grid,
input_mesh, timestep, options)
J = np.reshape(cost_to_go, Q.shape)
surf = ax.plot_surface(Q, Qdot, J, rstride=1, cstride=1, cmap=cm.jet)
# Animate the resulting policy.
builder = DiagramBuilder()
pendulum = builder.AddSystem(PendulumPlant())
# TODO(russt): add wrap-around logic to barycentric mesh
# (so the policy has it, too)
class WrapTheta(VectorSystem):
def __init__(self):
VectorSystem.__init__(self, 2, 2)
Pi = np.reshape(policy, Q.shape)
surf2 = ax2.plot_surface(Q, Qdot, Pi, rstride=1, cstride=1, cmap=cm.jet)
if plt.get_backend() != u'template':
plt.draw_all()
plt.pause(0.00001)
surf.remove()
surf2.remove()
options.visualization_callback = draw
policy, cost_to_go = FittedValueIteration(simulator, cost_function,
state_grid, input_grid,
timestep, options)
J = np.reshape(cost_to_go, Q.shape)
surf = ax.plot_surface(Q, Qdot, J, rstride=1, cstride=1,
cmap=cm.jet)
Pi = np.reshape(policy.get_output_values(), Q.shape)
surf = ax2.plot_surface(Q, Qdot, Pi, rstride=1, cstride=1,
cmap=cm.jet)
# Animate the resulting policy.
builder = DiagramBuilder()
pendulum = builder.AddSystem(PendulumPlant())
