def test_saturation(self):
system = Saturation((0., -1., 3.), (1., 2., 4.))
context = system.CreateDefaultContext()
output = system.AllocateOutput()
def mytest(input, expected):
system.get_input_port(0).FixValue(context, input)
system.CalcOutput(context, output)
self.assertTrue(np.allclose(output.get_vector_data(
0).CopyToVector(), expected))
mytest((-5., 5., 4.), (0., 2., 4.))
mytest((.4, 0., 3.5), (.4, 0., 3.5))
def main():
parser = argparse.ArgumentParser(description=__doc__)
parser.add_argument(
"--num_samples",
type=int,
default=50,
help="Number of Monte Carlo samples to use to estimate performance.")
parser.add_argument("--torque_limit",
type=float,
default=2.0,
help="Torque limit of the pendulum.")
args = parser.parse_args()
if args.torque_limit < 0:
raise InvalidArgumentError("Please supply a nonnegative torque limit.")
# Assemble the Pendulum plant.
builder = DiagramBuilder()
pendulum = builder.AddSystem(MultibodyPlant(0.0))
file_name = FindResourceOrThrow("drake/examples/pendulum/Pendulum.urdf")
Parser(pendulum).AddModelFromFile(file_name)
pendulum.WeldFrames(pendulum.world_frame(),
pendulum.GetFrameByName("base"))
pendulum.Finalize()
# Set the pendulum to start at uniformly random
# positions (but always zero velocity).
elbow = pendulum.GetMutableJointByName("theta")
upright_theta = np.pi
theta_expression = Variable(name="theta",
type=Variable.Type.RANDOM_UNIFORM) * 2. * np.pi
elbow.set_random_angle_distribution(theta_expression)
# Set up LQR, with high position gains to try to ensure the
# ROA is close to the theoretical torque-limited limit.
Q = np.diag([100., 1.])
R = np.identity(1) * 0.01
linearize_context = pendulum.CreateDefaultContext()
linearize_context.SetContinuousState(np.array([upright_theta, 0.]))
actuation_port = pendulum.get_actuation_input_port()
actuation_port.FixValue(linearize_context, 0)
controller = builder.AddSystem(
LinearQuadraticRegulator(pendulum, linearize_context, Q, R,
np.zeros(0), actuation_port.get_index()))
# Apply the torque limit.
torque_limit = args.torque_limit
torque_limiter = builder.AddSystem(
Saturation(min_value=np.array([-torque_limit]),
max_value=np.array([torque_limit])))
builder.Connect(controller.get_output_port(0),
torque_limiter.get_input_port(0))
builder.Connect(torque_limiter.get_output_port(0),
pendulum.get_actuation_input_port())
builder.Connect(pendulum.get_state_output_port(),
controller.get_input_port(0))
diagram = builder.Build()
# Perform the Monte Carlo simulation.
def make_simulator(generator):
''' Create a simulator for the system
using the given generator. '''
simulator = Simulator(diagram)
simulator.set_target_realtime_rate(0)
simulator.Initialize()
return simulator
def calc_wrapped_error(system, context):
''' Given a context from the end of the simulation,
calculate an error -- which for this stabilizing
task is the distance from the
fixed point. '''
state = diagram.GetSubsystemContext(
pendulum, context).get_continuous_state_vector()
error = state.GetAtIndex(0) - upright_theta
# Wrap error to [-pi, pi].
return (error + np.pi) % (2 * np.pi) - np.pi
num_samples = args.num_samples
results = MonteCarloSimulation(make_simulator=make_simulator,
output=calc_wrapped_error,
final_time=1.0,
num_samples=num_samples,
generator=RandomGenerator())
# Compute results.
# The "success" region is fairly large since some "stabilized" trials
# may still be oscillating around the fixed point. Failed examples are
# consistently much farther from the fixed point than this.
binary_results = np.array([abs(res.output) < 0.1 for res in results])
passing_ratio = float(sum(binary_results)) / len(results)
# 95% confidence interval for the passing ratio.
passing_ratio_var = 1.96 * np.sqrt(passing_ratio *
(1. - passing_ratio) / len(results))
print("Monte-Carlo estimated performance across %d samples: "
"%.2f%% +/- %0.2f%%" %
(num_samples, passing_ratio * 100, passing_ratio_var * 100))
# Analytically compute the best possible ROA, for comparison, but
# calculating where the torque needed to lift the pendulum exceeds
# the torque limit.
arm_radius = 0.5
arm_mass = 1.0
# torque = r x f = r * (m * 9.81 * sin(theta))
# theta = asin(torque / (r * m))
if torque_limit <= (arm_radius * arm_mass * 9.81):
roa_half_width = np.arcsin(torque_limit /
(arm_radius * arm_mass * 9.81))
else:
roa_half_width = np.pi
roa_as_fraction_of_state_space = roa_half_width / np.pi
print("Max possible ROA = %0.2f%% of state space, which should"
" match with the above estimate." %
(100 * roa_as_fraction_of_state_space))
