def runPendulumExample(args):
    builder = DiagramBuilder()
    plant, scene_graph = AddMultibodyPlantSceneGraph(builder)
    parser = Parser(plant)
    parser.AddModelFromFile(FindResource("pendulum/pendulum.urdf"))
    plant.Finalize()

    pose_bundle_output_port = scene_graph.get_pose_bundle_output_port()
    Tview = np.array([[1., 0., 0., 0.], [0., 0., 1., 0.], [0., 0., 0., 1.]],
                     dtype=np.float64)
    visualizer = builder.AddSystem(
        PlanarSceneGraphVisualizer(scene_graph,
                                   Tview=Tview,
                                   xlim=[-1.2, 1.2],
                                   ylim=[-1.2, 1.2]))
    builder.Connect(pose_bundle_output_port, visualizer.get_input_port(0))

    diagram = builder.Build()
    simulator = Simulator(diagram)
    simulator.Initialize()
    simulator.set_target_realtime_rate(1.0)

    # Fix the input port to zero.
    plant_context = diagram.GetMutableSubsystemContext(
        plant, simulator.get_mutable_context())
    plant_context.FixInputPort(plant.get_actuation_input_port().get_index(),
                               np.zeros(plant.num_actuators()))
    plant_context.SetContinuousState([0.5, 0.1])
    simulator.StepTo(args.duration)
Beispiel #2
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def Simulate2dRamone(x0, duration,
        desired_goal = 0.0,
        print_period = 0.0):

    builder = DiagramBuilder()
    tree = RigidBodyTree()
    AddModelInstanceFromUrdfFile("ramone_act.urdf", FloatingBaseType.kRollPitchYaw, None, tree)

    plant = builder.AddSystem(RigidBodyPlant(tree))

    controller = builder.AddSystem(
        Ramone2dController(tree, 
                           desired_goal=desired_goal, 
                           print_period=print_period))

    builder.Connect(plant.get_output_port(0), controller.get_input_port(0))
    builder.Connect(controller.get_output_port(0), plant.get_input_port(0))

    state_log = builder.AddSystem(SignalLogger(plant.get_num_states()))
    builder.Connect(plant.get_output_port(0), state_log.get_input_port(0))

    diagram = builder.Build()
    simulator = Simulator(diagram)

    simulator.set_target_realtime_rate(1.0)
    simulator.set_publish_every_time_step(True)
    simulator.get_mutable_context().set_accuracy(1e-4)

    state = simulator.get_mutable_context().get_mutable_continuous_state_vector()

    state.SetFromVector(x0)

    simulator.StepTo(duration)

    return tree, controller, state_log, plant
def playbackMotion(data1, data2, data3, data4, times):
    data = np.concatenate((data2, data1, data4, data3), axis=0)
    tree = RigidBodyTree(
        FindResource(
            os.path.dirname(os.path.realpath(__file__)) +
            "/block_pusher2.urdf"), FloatingBaseType.kFixed)

    # Set up a block diagram with the robot (dynamics), the controller, and a
    # visualization block.
    builder = DiagramBuilder()
    robot = builder.AddSystem(Player(data, times))

    Tview = np.array([[1., 0., 0., 0.], [0., 1., 0., 0.], [0., 0., 0., 1.]],
                     dtype=np.float64)
    visualizer = builder.AddSystem(
        PlanarRigidBodyVisualizer(tree,
                                  Tview,
                                  xlim=[-2.8, 4.8],
                                  ylim=[-2.8, 10]))
    #print(robot.get_output_port(0).size())
    builder.Connect(robot.get_output_port(0), visualizer.get_input_port(0))

    logger = builder.AddSystem(
        SignalLogger(tree.get_num_positions() + tree.get_num_velocities()))
    builder.Connect(robot.get_output_port(0), logger.get_input_port(0))

    diagram = builder.Build()

    # Set up a simulator to run this diagram
    simulator = Simulator(diagram)
    simulator.set_target_realtime_rate(1.0)
    simulator.set_publish_every_time_step(True)

    # Simulate for 10 seconds
    simulator.StepTo(times[-1] + 0.5)
Beispiel #4
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def RunSimulation(quadrotor_plant,
                  control_law,
                  x0=np.random.random((8, 1)),
                  duration=30,
                  control_period=0.0333,
                  print_period=1.0,
                  simulation_period=0.0333):

    quadrotor_controller = QuadrotorController(control_law,
                                               control_period=control_period,
                                               print_period=print_period)

    # Create a simple block diagram containing the plant in feedback
    # with the controller.
    builder = DiagramBuilder()
    # The last pendulum plant we made is now owned by a deleted
    # system, so easiest path is for us to make a new one.
    plant = builder.AddSystem(
        QuadrotorPendulum(mb=quadrotor_plant.mb,
                          lb=quadrotor_plant.lb,
                          m1=quadrotor_plant.m1,
                          l1=quadrotor_plant.l1,
                          g=quadrotor_plant.g,
                          input_max=quadrotor_plant.input_max))

    controller = builder.AddSystem(quadrotor_controller)
    builder.Connect(plant.get_output_port(0), controller.get_input_port(0))
    builder.Connect(controller.get_output_port(0), plant.get_input_port(0))

    # Create a logger to capture the simulation of our plant
    input_log = builder.AddSystem(SignalLogger(2))
    input_log._DeclarePeriodicPublish(control_period, 0.0)

    builder.Connect(controller.get_output_port(0), input_log.get_input_port(0))

    state_log = builder.AddSystem(SignalLogger(8))
    state_log._DeclarePeriodicPublish(control_period, 0.0)

    builder.Connect(plant.get_output_port(0), state_log.get_input_port(0))

    diagram = builder.Build()

    # Set the initial conditions for the simulation.
    context = diagram.CreateDefaultContext()
    state = context.get_mutable_continuous_state_vector()
    state.SetFromVector(x0)

    # Create the simulator.
    simulator = Simulator(diagram, context)
    simulator.Initialize()
    simulator.set_publish_every_time_step(True)

    simulator.get_integrator().set_fixed_step_mode(True)
    simulator.get_integrator().set_maximum_step_size(control_period)

    # Simulate for the requested duration.
    simulator.StepTo(duration)

    return input_log, state_log
def simulateRobot(time, B, v_command):
    tree = RigidBodyTree(
        FindResource(
            os.path.dirname(os.path.realpath(__file__)) +
            "/block_pusher2.urdf"), FloatingBaseType.kFixed)

    # Set up a block diagram with the robot (dynamics), the controller, and a
    # visualization block.
    builder = DiagramBuilder()
    robot = builder.AddSystem(RigidBodyPlant(tree))

    controller = builder.AddSystem(DController(tree, B, v_command))
    builder.Connect(robot.get_output_port(0), controller.get_input_port(0))
    builder.Connect(controller.get_output_port(0), robot.get_input_port(0))

    Tview = np.array([[1., 0., 0., 0.], [0., 1., 0., 0.], [0., 0., 0., 1.]],
                     dtype=np.float64)
    visualizer = builder.AddSystem(
        PlanarRigidBodyVisualizer(tree,
                                  Tview,
                                  xlim=[-2.8, 4.8],
                                  ylim=[-2.8, 10]))
    builder.Connect(robot.get_output_port(0), visualizer.get_input_port(0))

    logger = builder.AddSystem(
        SignalLogger(tree.get_num_positions() + tree.get_num_velocities()))
    builder.Connect(robot.get_output_port(0), logger.get_input_port(0))

    diagram = builder.Build()

    # Set up a simulator to run this diagram
    simulator = Simulator(diagram)
    simulator.set_target_realtime_rate(1.0)
    simulator.set_publish_every_time_step(True)

    # Set the initial conditions
    context = simulator.get_mutable_context()
    state = context.get_mutable_continuous_state_vector()
    start1 = 3 * np.pi / 16
    start2 = 15 * np.pi / 16
    #np.pi/6 - eps, 2*np.pi/3 + eps, -np.pi/6 + eps, -2*np.pi/3 - eps,    np.pi/6 - eps, 2*np.pi/3 + eps, -np.pi/6 + eps, -2*np.pi/3 - eps
    state.SetFromVector(
        (start1, start2, -start1, -start2, np.pi + start1, start2,
         np.pi - start1, -start2, 1, 1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
         0., 0.))  # (theta1, theta2, theta1dot, theta2dot)

    # Simulate for 10 seconds
    simulator.StepTo(time)
    #import pdb; pdb.set_trace()
    return (logger.data()[8:11, :], logger.data()[:8, :],
            logger.data()[19:22, :], logger.data()[11:19, :],
            logger.sample_times())
Beispiel #6
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def RunSimulation(pendulum_plant,
                  control_law,
                  x0=np.random.random((4, 1)),
                  duration=30):
    pendulum_controller = PendulumController(control_law)

    # Create a simple block diagram containing the plant in feedback
    # with the controller.
    builder = DiagramBuilder()
    # The last pendulum plant we made is now owned by a deleted
    # system, so easiest path is for us to make a new one.
    plant = builder.AddSystem(
        InertialWheelPendulum(m1=pendulum_plant.m1,
                              l1=pendulum_plant.l1,
                              m2=pendulum_plant.m2,
                              l2=pendulum_plant.l2,
                              r=pendulum_plant.r,
                              g=pendulum_plant.g,
                              input_max=pendulum_plant.input_max))

    controller = builder.AddSystem(pendulum_controller)
    builder.Connect(plant.get_output_port(0), controller.get_input_port(0))
    builder.Connect(controller.get_output_port(0), plant.get_input_port(0))

    # Create a logger to capture the simulation of our plant
    input_log = builder.AddSystem(SignalLogger(1))
    input_log._DeclarePeriodicPublish(0.033333, 0.0)
    builder.Connect(controller.get_output_port(0), input_log.get_input_port(0))

    state_log = builder.AddSystem(SignalLogger(4))
    state_log._DeclarePeriodicPublish(0.033333, 0.0)
    builder.Connect(plant.get_output_port(0), state_log.get_input_port(0))

    diagram = builder.Build()

    # Set the initial conditions for the simulation.
    context = diagram.CreateDefaultContext()
    state = context.get_mutable_continuous_state_vector()
    state.SetFromVector(x0)

    # Create the simulator.
    simulator = Simulator(diagram, context)
    simulator.Initialize()
    simulator.set_publish_every_time_step(False)
    simulator.get_integrator().set_fixed_step_mode(True)
    simulator.get_integrator().set_maximum_step_size(0.005)

    # Simulate for the requested duration.
    simulator.StepTo(duration)

    return input_log, state_log
Beispiel #7
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def Simulate2dBallAndBeam(x0, duration):

    builder = DiagramBuilder()

    # Load in the ball and beam from a description file.
    tree = RigidBodyTree()
    AddModelInstancesFromSdfString(
        open("ball_and_beam.sdf", 'r').read(), FloatingBaseType.kFixed, None,
        tree)

    # A RigidBodyPlant wraps a RigidBodyTree to allow
    # forward dynamical simulation.
    plant = builder.AddSystem(RigidBodyPlant(tree))

    # Spawn a controller and hook it up
    controller = builder.AddSystem(BallAndBeam2dController(tree))
    builder.Connect(plant.get_output_port(0), controller.get_input_port(0))
    builder.Connect(controller.get_output_port(0), plant.get_input_port(0))

    # Create a logger to log at 30hz
    state_log = builder.AddSystem(SignalLogger(plant.get_num_states()))
    state_log._DeclarePeriodicPublish(0.0333, 0.0)  # 30hz logging
    builder.Connect(plant.get_output_port(0), state_log.get_input_port(0))

    # Create a simulator
    diagram = builder.Build()
    simulator = Simulator(diagram)

    # Don't limit realtime rate for this sim, since we
    # produce a video to render it after simulating the whole thing.
    #simulator.set_target_realtime_rate(100.0)
    simulator.set_publish_every_time_step(False)

    # Force the simulator to use a fixed-step integrator,
    # which is much faster for this stiff system. (Due to the
    # spring-model of collision, the default variable-timestep
    # integrator will take very short steps. I've chosen the step
    # size here to be fast while still being stable in most situations.)
    integrator = simulator.get_mutable_integrator()
    integrator.set_fixed_step_mode(True)
    integrator.set_maximum_step_size(0.001)

    # Set the initial state
    state = simulator.get_mutable_context(
    ).get_mutable_continuous_state_vector()
    state.SetFromVector(x0)

    # Simulate!
    simulator.StepTo(duration)

    return tree, controller, state_log
def simulate_acrobot():
    builder = DiagramBuilder()

    acrobot = builder.AddSystem(AcrobotPlant())
    saturation = builder.AddSystem(Saturation(min_value=[-10], max_value=[10]))
    builder.Connect(saturation.get_output_port(0), acrobot.get_input_port(0))
    wrapangles = WrapToSystem(4)
    wrapangles.set_interval(0, 0, 2. * math.pi)
    wrapangles.set_interval(1, -math.pi, math.pi)
    wrapto = builder.AddSystem(wrapangles)
    builder.Connect(acrobot.get_output_port(0), wrapto.get_input_port(0))
    controller = builder.AddSystem(BalancingLQR())
    builder.Connect(wrapto.get_output_port(0), controller.get_input_port(0))
    builder.Connect(controller.get_output_port(0),
                    saturation.get_input_port(0))

    tree = RigidBodyTree(FindResource("acrobot/acrobot.urdf"),
                         FloatingBaseType.kFixed)
    visualizer = builder.AddSystem(
        PlanarRigidBodyVisualizer(tree, xlim=[-4., 4.], ylim=[-4., 4.]))
    builder.Connect(acrobot.get_output_port(0), visualizer.get_input_port(0))

    diagram = builder.Build()
    simulator = Simulator(diagram)
    simulator.set_target_realtime_rate(1.0)
    simulator.set_publish_every_time_step(False)
    context = simulator.get_mutable_context()

    state = context.get_mutable_continuous_state_vector()

    parser = argparse.ArgumentParser()
    parser.add_argument("-N",
                        "--trials",
                        type=int,
                        help="Number of trials to run.",
                        default=5)
    parser.add_argument("-T",
                        "--duration",
                        type=float,
                        help="Duration to run each sim.",
                        default=4.0)
    args = parser.parse_args()

    print(AcrobotPlant)

    for i in range(args.trials):
        context.set_time(0.)
        state.SetFromVector(UprightState().CopyToVector() +
                            0.05 * np.random.randn(4, ))
        simulator.StepTo(args.duration)
    def RunSimulation(self, real_time_rate=1.0):
        '''
        Here we test using the NNSystem in a Simulator to drive
        an acrobot.
        '''
        sdf_file = "assets/acrobot.sdf"
        urdf_file = "assets/acrobot.urdf"

        builder = DiagramBuilder()
        plant, scene_graph = AddMultibodyPlantSceneGraph(builder)
        parser = Parser(plant=plant, scene_graph=scene_graph)
        parser.AddModelFromFile(sdf_file)
        plant.Finalize(scene_graph)

        # Add
        nn_system = NNSystem(self.pytorch_nn_object)
        builder.AddSystem(nn_system)

        # NN -> plant
        builder.Connect(nn_system.NN_out_output_port,
                        plant.get_actuation_input_port())
        # plant -> NN
        builder.Connect(plant.get_continuous_state_output_port(),
                        nn_system.NN_in_input_port)

        # Add meshcat visualizer
        meshcat = MeshcatVisualizer(scene_graph)
        builder.AddSystem(meshcat)
        # builder.Connect(scene_graph.GetOutputPort("lcm_visualization"),
        builder.Connect(scene_graph.get_pose_bundle_output_port(),
                        meshcat.GetInputPort("lcm_visualization"))

        # build diagram
        diagram = builder.Build()
        meshcat.load()
        # time.sleep(2.0)
        RenderSystemWithGraphviz(diagram)

        # construct simulator
        simulator = Simulator(diagram)

        # context = diagram.GetMutableSubsystemContext(
        #     self.station, simulator.get_mutable_context())

        simulator.set_publish_every_time_step(False)
        simulator.set_target_realtime_rate(real_time_rate)
        simulator.Initialize()
        sim_duration = 5.
        simulator.StepTo(sim_duration)
        print("stepping complete")
Beispiel #10
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def Simulate2dHopper(x0,
                     duration,
                     desired_lateral_velocity=0.0,
                     print_period=0.0):
    builder = DiagramBuilder()

    plant = builder.AddSystem(MultibodyPlant(0.0005))
    scene_graph = builder.AddSystem(SceneGraph())
    plant.RegisterAsSourceForSceneGraph(scene_graph)
    builder.Connect(plant.get_geometry_poses_output_port(),
                    scene_graph.get_source_pose_port(plant.get_source_id()))
    builder.Connect(scene_graph.get_query_output_port(),
                    plant.get_geometry_query_input_port())

    # Build the plant
    parser = Parser(plant)
    parser.AddModelFromFile("raibert_hopper_2d.sdf")
    plant.WeldFrames(plant.world_frame(), plant.GetFrameByName("ground"))
    plant.AddForceElement(UniformGravityFieldElement())
    plant.Finalize()

    # Create a logger to log at 30hz
    state_dim = plant.num_positions() + plant.num_velocities()
    state_log = builder.AddSystem(SignalLogger(state_dim))
    state_log.DeclarePeriodicPublish(0.0333, 0.0)  # 30hz logging
    builder.Connect(plant.get_continuous_state_output_port(),
                    state_log.get_input_port(0))

    # The controller
    controller = builder.AddSystem(
        Hopper2dController(plant,
                           desired_lateral_velocity=desired_lateral_velocity,
                           print_period=print_period))
    builder.Connect(plant.get_continuous_state_output_port(),
                    controller.get_input_port(0))
    builder.Connect(controller.get_output_port(0),
                    plant.get_actuation_input_port())

    # The diagram
    diagram = builder.Build()
    simulator = Simulator(diagram)
    simulator.Initialize()

    plant_context = diagram.GetMutableSubsystemContext(
        plant, simulator.get_mutable_context())
    plant_context.get_mutable_discrete_state_vector().SetFromVector(x0)

    simulator.StepTo(duration)
    return plant, controller, state_log
Beispiel #11
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def animate_cartpole(policy, duration=10.):
    # Animate the resulting policy.
    builder = DiagramBuilder()
    tree = RigidBodyTree("/opt/underactuated/src/cartpole/cartpole.urdf",
                         FloatingBaseType.kFixed)
    plant = RigidBodyPlant(tree)
    plant_system = builder.AddSystem(plant)

    # TODO(russt): add wrap-around logic to barycentric mesh
    # (so the policy has it, too)
    class WrapTheta(VectorSystem):
        def __init__(self):
            VectorSystem.__init__(self, 4, 4)

        def _DoCalcVectorOutput(self, context, input, state, output):
            output[:] = input
            twoPI = 2.*math.pi
            output[1] = output[1] - twoPI * math.floor(output[1] / twoPI)


    wrap = builder.AddSystem(WrapTheta())
    builder.Connect(plant_system.get_output_port(0), wrap.get_input_port(0))
    vi_policy = builder.AddSystem(policy)
    builder.Connect(wrap.get_output_port(0), vi_policy.get_input_port(0))
    builder.Connect(vi_policy.get_output_port(0), plant_system.get_input_port(0))

    logger = builder.AddSystem(SignalLogger(4))
    logger._DeclarePeriodicPublish(0.033333, 0.0)
    builder.Connect(plant_system.get_output_port(0), logger.get_input_port(0))

    diagram = builder.Build()
    simulator = Simulator(diagram)
    simulator.set_publish_every_time_step(False)

    state = simulator.get_mutable_context().get_mutable_continuous_state_vector()
    state.SetFromVector([-1., math.pi-1, 1., -1.])

    # Do the sim.
    simulator.StepTo(duration)

    # Visualize the result as a video.
    vis = PlanarRigidBodyVisualizer(tree, xlim=[-12.5, 12.5], ylim=[-1, 2.5])
    ani = vis.animate(logger, repeat=True)

    # plt.show()
    # Things added to get visualizations in an ipynb
    plt.close(vis.fig)
    HTML(ani.to_html5_video())
def RunPendulumSimulation(pendulum_plant,
                          pendulum_controller,
                          x0=[0.9, 0.0],
                          duration=10):
    '''
        Accepts a pendulum_plant (which should be a
        DampedOscillatingPendulumPlant) and simulates it for 
        'duration' seconds from initial state `x0`. Returns a 
        logger object which can return simulated timesteps `
        logger.sample_times()` (N-by-1) and simulated states
        `logger.data()` (2-by-N).
    '''

    # Create a simple block diagram containing the plant in feedback
    # with the controller.
    builder = DiagramBuilder()
    plant = builder.AddSystem(pendulum_plant)
    controller = builder.AddSystem(pendulum_controller)
    builder.Connect(plant.get_output_port(0), controller.get_input_port(0))
    builder.Connect(controller.get_output_port(0), plant.get_input_port(0))

    # Create a logger to capture the simulation of our plant
    # (We tell the logger to expect a 3-variable input,
    # and hook it up to the pendulum plant's 3-variable output.)
    logger = builder.AddSystem(SignalLogger(3))
    logger._DeclarePeriodicPublish(0.033333, 0.0)

    builder.Connect(plant.get_output_port(0), logger.get_input_port(0))

    diagram = builder.Build()

    # Create the simulator.
    simulator = Simulator(diagram)
    simulator.Initialize()
    simulator.set_publish_every_time_step(False)

    # Set the initial conditions for the simulation.
    state = simulator.get_mutable_context().get_mutable_state()\
                     .get_mutable_continuous_state().get_mutable_vector()
    state.SetFromVector(x0)

    # Simulate for the requested duration.
    simulator.StepTo(duration)

    # Return the logger, which stores the output of the
    # plant across the time steps of the simulation.
    return logger
def runManipulationExample(args):
    builder = DiagramBuilder()
    station = builder.AddSystem(ManipulationStation(time_step=0.005))
    station.SetupDefaultStation()
    station.Finalize()

    plant = station.get_multibody_plant()
    scene_graph = station.get_scene_graph()
    pose_bundle_output_port = station.GetOutputPort("pose_bundle")

    # Side-on view of the station.
    Tview = np.array([[1., 0., 0., 0.],
                      [0., 0., 1., 0.],
                      [0., 0., 0., 1.]],
                     dtype=np.float64)
    visualizer = builder.AddSystem(PlanarSceneGraphVisualizer(
        scene_graph, Tview=Tview, xlim=[-0.5, 1.0], ylim=[-1.2, 1.2],
        draw_period=0.1))
    builder.Connect(pose_bundle_output_port,
                    visualizer.get_input_port(0))

    diagram = builder.Build()
    simulator = Simulator(diagram)
    simulator.Initialize()
    simulator.set_target_realtime_rate(1.0)

    # Fix the control inputs to zero.
    station_context = diagram.GetMutableSubsystemContext(
        station, simulator.get_mutable_context())
    station.GetInputPort("iiwa_position").FixValue(
        station_context, station.GetIiwaPosition(station_context))
    station.GetInputPort("iiwa_feedforward_torque").FixValue(
        station_context, np.zeros(7))
    station.GetInputPort("wsg_position").FixValue(
        station_context, np.zeros(1))
    station.GetInputPort("wsg_force_limit").FixValue(
        station_context, [40.0])
    simulator.StepTo(args.duration)
diagram = builder.Build()
simulator = Simulator(diagram)
simulator.set_target_realtime_rate(1.0)
simulator.set_publish_every_time_step(True)

# kinsol = rtree.doKinematics(q)
# com = rtree.centerOfMass(kinsol)
# print com

# nominal standing state
# state = simulator.get_mutable_context().get_mutable_continuous_state_vector()
# state.SetFromVector(q+qd)
cassie.set_state_vector(simulator.get_mutable_context(), x)

simulator.StepTo(1.0)

# simulator.Initialize();
# from bot_lcmgl import lcmgl
# import lcm as true_lcm
# viz_lcmgl = lcmgl("Visualize-Points", true_lcm.LCM())
# cache = rtree.doKinematics(x[:23], x[23:])

# thigh_l = rtree.transformPoints(cache, GetFourBarHipMountPoint(),
#                                 rtree.FindBodyIndex("thigh_left"), 0)
# heel_l = rtree.transformPoints(cache, GetFourBarHeelMountPoint(),
#                                rtree.FindBodyIndex("heel_spring_left"), 0)
# thigh_r = rtree.transformPoints(cache, -GetFourBarHipMountPoint(),
#                                 rtree.FindBodyIndex("thigh_right"), 0)
# heel_r = rtree.transformPoints(cache, GetFourBarHeelMountPoint(),
#                                rtree.FindBodyIndex("heel_spring_right"), 0)
Beispiel #15
0
def RunSimulation(robobee_plantBS,
                  control_law,
                  x0=np.random.random((15, 1)),
                  duration=30):
    robobee_controller = RobobeeController(control_law)

    # Create a simple block diagram containing the plant in feedback
    # with the controller.
    builder = DiagramBuilder()
    # The last pendulum plant we made is now owned by a deleted
    # system, so easiest path is for us to make a new one.
    plant = builder.AddSystem(
        RobobeePlantBS(m=robobee_plantBS.m,
                       Ixx=robobee_plantBS.Ixx,
                       Iyy=robobee_plantBS.Iyy,
                       Izz=robobee_plantBS.Izz,
                       g=robobee_plantBS.g,
                       input_max=robobee_plantBS.input_max))

    Rigidbody_selector = builder.AddSystem(RigidBodySelection())

    print("1. Connecting plant and controller\n")
    controller = builder.AddSystem(robobee_controller)
    builder.Connect(plant.get_output_port(0), controller.get_input_port(0))
    builder.Connect(controller.get_output_port(0), plant.get_input_port(0))

    # Create a logger to capture the simulation of our plant
    print("2. Connecting plant to the logger\n")
    set_time_interval = 0.001
    time_interval_multiple = 1000
    publish_period = set_time_interval * time_interval_multiple

    input_log = builder.AddSystem(SignalLogger(4))
    # input_log._DeclarePeriodicPublish(0.033333, 0.0)
    builder.Connect(controller.get_output_port(0), input_log.get_input_port(0))

    state_log = builder.AddSystem(SignalLogger(15))
    # state_log._DeclarePeriodicPublish(0.033333, 0.0)
    builder.Connect(plant.get_output_port(0), state_log.get_input_port(0))

    # Drake visualization
    print("3. Connecting plant output to DrakeVisualizer\n")

    rtree = RigidBodyTree(
        FindResourceOrThrow("drake/examples/robobee/robobee_arena.urdf"),
        FloatingBaseType.kQuaternion)  #robobee_twobar
    lcm = DrakeLcm()
    visualizer = builder.AddSystem(
        DrakeVisualizer(tree=rtree, lcm=lcm, enable_playback=True))

    builder.Connect(plant.get_output_port(0),
                    Rigidbody_selector.get_input_port(0))
    builder.Connect(Rigidbody_selector.get_output_port(0),
                    visualizer.get_input_port(0))

    print("4. Building diagram\n")

    diagram = builder.Build()

    # Set the initial conditions for the simulation.
    context = diagram.CreateDefaultContext()
    state = context.get_mutable_continuous_state_vector()
    state.SetFromVector(x0)

    # Create the simulator.
    print("5. Create simulation\n")

    simulator = Simulator(diagram, context)
    simulator.Initialize()
    # simulator.set_publish_every_time_step(False)

    simulator.set_target_realtime_rate(1)
    simulator.get_integrator().set_fixed_step_mode(True)
    simulator.get_integrator().set_maximum_step_size(0.05)

    # Simulate for the requested duration.
    simulator.StepTo(duration)

    return input_log, state_log
Beispiel #16
0
    def draw(self, context):
        xy = self.EvalVectorInput(context, 0).CopyToVector()
        self.lines.set_xdata(xy[:self.num_particles])
        self.lines.set_ydata(xy[self.num_particles:])
        self.ax.set_title('t = ' + str(context.get_time()))


builder = DiagramBuilder()

num_particles = 5000
xlim = [-2.75, 2.75]
ylim = [-3.25, 3.25]
draw_timestep = .25
sys = builder.AddSystem(VanDerPolParticles(num_particles))
visualizer = builder.AddSystem(
    Particle2DVisualizer(num_particles, xlim, ylim, draw_timestep))
builder.Connect(sys.get_output_port(0), visualizer.get_input_port(0))
AddRandomInputs(.1, builder)

# TODO(russt): Plot nominal limit cycle.

diagram = builder.Build()
simulator = Simulator(diagram)
simulator.set_publish_every_time_step(False)
simulator.get_mutable_integrator().set_fixed_step_mode(True)
simulator.get_mutable_integrator().set_maximum_step_size(0.1)

simulator.StepTo(20)
plt.show()
Beispiel #17
0
def Simulate2dHopper(x0,
                     duration,
                     desired_lateral_velocity=0.0,
                     print_period=0.0):
    builder = DiagramBuilder()

    # Load in the hopper from a description file.
    # It's spawned with a fixed floating base because
    # the robot description file includes the world as its
    # root link -- it does this so that I can create a robot
    # system with planar dynamics manually. (Drake doesn't have
    # a planar floating base type accessible right now that I
    # know about -- it only has 6DOF floating base types.)
    tree = RigidBodyTree()
    AddModelInstancesFromSdfString(
        open("raibert_hopper_2d.sdf", 'r').read(), FloatingBaseType.kFixed,
        None, tree)

    # A RigidBodyPlant wraps a RigidBodyTree to allow
    # forward dynamical simulation. It handles e.g. collision
    # modeling.
    plant = builder.AddSystem(RigidBodyPlant(tree))
    # Alter the ground material used in simulation to make
    # it dissipate more energy (to make the hopping more critical)
    # and stickier (to make the hopper less likely to slip).
    allmaterials = CompliantMaterial()
    allmaterials.set_youngs_modulus(1E8)  # default 1E9
    allmaterials.set_dissipation(1.0)  # default 0.32
    allmaterials.set_friction(1.0)  # default 0.9.
    plant.set_default_compliant_material(allmaterials)

    # Spawn a controller and hook it up
    controller = builder.AddSystem(
        Hopper2dController(tree,
                           desired_lateral_velocity=desired_lateral_velocity,
                           print_period=print_period))
    builder.Connect(plant.get_output_port(0), controller.get_input_port(0))
    builder.Connect(controller.get_output_port(0), plant.get_input_port(0))

    # Create a logger to log at 30hz
    state_log = builder.AddSystem(SignalLogger(plant.get_num_states()))
    state_log._DeclarePeriodicPublish(0.0333, 0.0)  # 30hz logging
    builder.Connect(plant.get_output_port(0), state_log.get_input_port(0))

    # Create a simulator
    diagram = builder.Build()
    simulator = Simulator(diagram)
    # Don't limit realtime rate for this sim, since we
    # produce a video to render it after simulating the whole thing.
    #simulator.set_target_realtime_rate(100.0)
    simulator.set_publish_every_time_step(False)

    # Force the simulator to use a fixed-step integrator,
    # which is much faster for this stiff system. (Due to the
    # spring-model of collision, the default variable-timestep
    # integrator will take very short steps. I've chosen the step
    # size here to be fast while still being stable in most situations.)
    integrator = simulator.get_mutable_integrator()
    integrator.set_fixed_step_mode(True)
    integrator.set_maximum_step_size(0.0005)

    # Set the initial state
    state = simulator.get_mutable_context(
    ).get_mutable_continuous_state_vector()
    state.SetFromVector(x0)

    # Simulate!
    simulator.StepTo(duration)

    return tree, controller, state_log
#Data Logger
logger = LogOutput(plant.get_continuous_state_output_port(), builder)

#Run Simulation
diagram = builder.Build()
simulator = Simulator(diagram)
simulator.set_target_realtime_rate(1.)

plant_context = diagram.GetMutableSubsystemContext(
    plant, simulator.get_mutable_context())
print plant_context.get_mutable_discrete_state_vector()
plant_context.get_mutable_discrete_state_vector().SetFromVector(x0)

simulator.Initialize()
simulator.StepTo(duration)

#print('sample_times',logger.sample_times()) #nx1 array
print('Final State: ', logger.data()[:, -1])  #nxm array
x_log = logger.data()[4, :]
data = logger.data()
theta_log = np.asarray([
    math.asin(2 * (data[0, i] * data[2, i] - data[1, i] * data[3, i]))
    for i in range(data.shape[1])
])
#theta = math.asin(2*(x[0]*x[2] - x[1]*x[3]))
print('Cost: ', np.matmul(theta_log, theta_log.T))
'''
#print('x evolution: ',logger.data()[1,:]) #nxm array
#print('y evolution: ',logger.data()[2,:]) #nxm array
#print('z evolution: ',logger.data()[3,:]) #nxm array
Beispiel #19
0
class DrakeEnv(gym.Env):
    metadata = {'render.modes': ['human']}

    def __init__(self):
        '''
        Sets up the System diagram and creates a drake visualizer object to
        send LCM messages to during the render method.

        Subclasses must implement the methods below that throw a
        NotImplementedError
        '''

        # Create the Diagram.
        self.system = self.plant_system()
        self.context = self.system.CreateDefaultContext()

        # Create the simulator.
        self.simulator = Simulator(self.system, self.context)
        self.simulator.set_publish_every_time_step(False)

    def seed(self, seed=None):
        self.np_random, seed = seeding.np_random(seed)
        return [seed]

    def plant_system(self):
        '''
        Returns the fully constructed MDP diagram which is connected to the
        vector source for simulation. Each subclass should implement this
        method.
        '''
        raise NotImplementedError

    def get_input_port_action(self):
        '''
        Returns the system input port that corresponds to the action
        '''
        raise NotImplementedError

    def get_observation(self):
        '''
        Returns the system output port that corresponds to the observation
        '''
        raise NotImplementedError

    def get_state(self):
        '''
        Returns the system output port that corresponds to the observation
        '''
        raise NotImplementedError

    @property
    def action_space(self):
        '''
        Specifies the limits of tha action space. This must be overridden by subclasses.
        '''
        raise NotImplementedError

    @property
    def observation_space(self):
        '''
        Specifies the limits of tha action space. This must be overridden by subclasses.
        '''
        raise NotImplementedError

    def get_reward(self, state, action):
        '''
        Computes the reward from the state and an action
        '''
        raise NotImplementedError

    def reset_state(self):
        '''
        Computes the reward from the state and an action
        '''
        raise NotImplementedError

    def step(self, action):
        '''
        Simulates the system diagram for a short period of time
        '''
        # Only allow valid actions from the action space
        action = validate_action(action, self.action_space)

        # Fix input port with action and simulate
        action_fixed_input_port_value = self.context.FixInputPort(
            self.get_input_port_action().get_index(), action)
        self.simulator.StepTo(self.context.get_time() + self.dt)

        # Get the observation, reward, and terminal conditions
        state = self.get_state()
        observation = self.get_observation()
        reward = self.get_reward(state, action)
        done = self.is_done()
        info = {}

        return observation, reward, done, info

    def reset(self):
        '''
        Resets the state in the system diagram
        '''
        self.context.set_time(0)
        self.reset_state()
        return self.get_observation()

    def render(self, mode='human', close=False):
        '''
        Notifies the visualizer to draw the current state. Different implementations based on MultiBodyPlant and RigidBodyTree
        '''
        raise NotImplementedError
logger_x = builder.AddSystem(SignalLogger(n))
logger_u = builder.AddSystem(SignalLogger(m))

builder.Connect(controller.get_output_port(0), quad.get_input_port(0))
builder.Connect(quad.get_output_port(0), logger_x.get_input_port(0))
builder.Connect(quad.get_output_port(0), controller.get_input_port(0))
builder.Connect(controller.get_output_port(0), logger_u.get_input_port(0))
diagram = builder.Build()

# Create the simulator.
simulator = Simulator(diagram)

# Set the initial conditions, x(0).
state = simulator.get_mutable_context().get_mutable_continuous_state_vector()
x0 = np.zeros(n)
x0[0:3] = 0.5
x0[5] = np.pi / 2
state.SetFromVector(x0)

# Simulate
simulator.StepTo(5.0)

#%% plot
PlotTraj(logger_x.data().T, None, None, logger_x.sample_times())

#%% open meshcat
vis = meshcat.Visualizer()
vis.open()

#%% meshcat animation
PlotTrajectoryMeshcat(logger_x.data().T, logger_x.sample_times(), vis)
builder.Connect(quad.get_output_port(0), controller.get_input_port(0))
builder.Connect(controller.get_output_port(0), logger_u.get_input_port(0))
diagram = builder.Build()

# Create the simulator.
simulator = Simulator(diagram)

# if __name__ == '__main__':
# Set the initial conditions, x(0).
state = simulator.get_mutable_context().get_mutable_continuous_state_vector()
state.SetFromVector(traj_specs.x0)
input_vector = simulator.get_mutable_context(
).get_mutable_discrete_state_vector()
input_vector.SetFromVector(traj_specs.u0)
#%% Simulate
simulator.StepTo(h * 300)

#%% plot
PlotTraj(logger_x.data().T,
         dt=None,
         xw_list=traj_specs.xw_list,
         t=logger_x.sample_times())

#%% open meshcat
vis = meshcat.Visualizer()
vis.open()

#%% meshcat animation
wpts_list = np.zeros((len(traj_specs.xw_list) + 1, 3))
for i, xw in enumerate(traj_specs.xw_list):
    wpts_list[i] = xw.x[0:3]
Beispiel #22
0
integrator.set_fixed_step_mode(True)
integrator.set_maximum_step_size(0.001)

#%%

# simulate
context = simulator.get_mutable_context()
x0 = np.array([0., 0., 3., 0.])

# since the ZOH block at t=0 returns its internal state, I have to compute the first feedback "offline"
state_c = context.get_mutable_continuous_state_vector()
state_c.SetFromVector(x0)
state_d = context.get_mutable_discrete_state_vector()
u0 = np.empty(pwa.nu)
controller._DoCalcVectorOutput(context, x0, None, u0)
state_d.SetFromVector(u0)

# run sim
simulator.StepTo(3.)

#%%

# visualize
viz = PlanarRigidBodyVisualizer(tree, xlim=[-1, 1], ylim=[-2.5, 3.])
viz.fig.set_size_inches(10, 5)
ani = viz.animate(state_log, 30, repeat=True)
plt.close(viz.fig)
HTML(ani.to_html5_video())

# print 'hi Ash'
Beispiel #23
0
def SimulateHand(duration=10.,
                 num_fingers=3,
                 mu=0.5,
                 manipuland_sdf="models/manipuland_box.sdf",
                 initial_manipuland_pose=np.array([1.5, 0., 0.]),
                 n_grasp_search_iters=100,
                 manipuland_trajectory_callback=None,
                 control_period=0.0333,
                 print_period=1.0):
    ''' Given a great many passthrough arguments
        (see docs for HandController and
        usage example in set_5_mpc.ipynb), constructs
        a simulation of a num_fingers-fingered hand
        and simulates it for duration seconds from
        a specified initial manipuland pose. 
        
        Returns:
        (hand, plant, controller, state_log, contact_log)
        hand: The RigidBodyTree of the complete hand.
        plant: The RigidBodyPlant that owns the hand RBT
        controller: The HandController object
        state_log: A SignalLogger that has logged the output
        of the state output port of plant.
        contact_log: A PlanarHandContactLogger object that
        has logged the output of the contact results output
        port of the plant. '''
    builder = DiagramBuilder()

    tree = BuildHand(num_fingers, manipuland_sdf)
    num_finger_links = 3  # from sdf
    num_hand_q = num_finger_links * num_fingers

    # Generate the nominal posture for the hand
    # First link wide open, next links at right angles
    x_nom = np.zeros(2 * num_finger_links * num_fingers + 6)
    for i in range(num_fingers):
        if i < num_fingers / 2:
            x_nom[(num_finger_links*i):(num_finger_links*(i+1))] = \
                np.array([2, 1.57, 1.57])
        else:
            x_nom[(num_finger_links*i):(num_finger_links*(i+1))] = \
                -np.array([2, 1.57, 1.57])

    # Drop in the initial manipuland location
    x_nom[num_hand_q:(num_hand_q + 3)] = initial_manipuland_pose

    # A RigidBodyPlant wraps a RigidBodyTree to allow
    # forward dynamical simulation. It handles e.g. collision
    # modeling.
    plant = builder.AddSystem(RigidBodyPlant(tree))
    # Alter the ground material used in simulation to make
    # it dissipate more energy (to make the object less bouncy)
    # and stickier (to make it easier to hold) and softer
    # (again to make it less bouncy)
    allmaterials = CompliantMaterial()
    allmaterials.set_youngs_modulus(1E6)  # default 1E9
    allmaterials.set_dissipation(1.0)  # default 0.32
    allmaterials.set_friction(0.9)  # default 0.9.
    plant.set_default_compliant_material(allmaterials)

    # Spawn a controller and hook it up
    controller = builder.AddSystem(
        HandController(
            tree,
            x_nom=x_nom,
            num_fingers=num_fingers,
            mu=mu,
            n_grasp_search_iters=n_grasp_search_iters,
            manipuland_trajectory_callback=manipuland_trajectory_callback,
            control_period=control_period,
            print_period=print_period))

    nq = controller.nq
    qinit, info = controller.ComputeTargetPosture(x_nom,
                                                  x_nom[(nq - 3):nq],
                                                  backoff_distance=0.0)
    if info != 1:
        print "Warning: initial condition IK solve returned info ", info
    xinit = np.zeros(x_nom.shape)
    xinit[0:(nq - 3)] = qinit[0:-3]
    xinit[(nq - 3):nq] = x_nom[(nq - 3):nq]
    builder.Connect(plant.get_output_port(0), controller.get_input_port(0))
    for i in range(num_fingers):
        builder.Connect(controller.get_output_port(i), plant.get_input_port(i))

    # Create a state logger to log at 30hz
    state_log = builder.AddSystem(SignalLogger(plant.get_num_states()))
    state_log.DeclarePeriodicPublish(0.0333, 0.0)  # 30hz logging
    builder.Connect(plant.get_output_port(0), state_log.get_input_port(0))

    # And a contact result logger, same rate
    contact_log = builder.AddSystem(PlanarHandContactLogger(controller, plant))
    contact_log.DeclarePeriodicPublish(0.0333, 0.0)
    builder.Connect(plant.contact_results_output_port(),
                    contact_log.get_input_port(0))

    # Create a simulator
    diagram = builder.Build()
    simulator = Simulator(diagram)
    # Don't limit realtime rate for this sim, since we
    # produce a video to render it after simulating the whole thing.
    # simulator.set_target_realtime_rate(100.0)
    simulator.set_publish_every_time_step(False)

    # Force the simulator to use a fixed-step integrator,
    # which is much faster for this stiff system. (Due to the
    # spring-model of collision, the default variable-timestep
    # integrator will take very short steps. I've chosen the step
    # size here to be fast while still being stable in most situations.)
    integrator = simulator.get_mutable_integrator()
    integrator.set_fixed_step_mode(True)
    integrator.set_maximum_step_size(0.005)

    # Set the initial state
    state = simulator.get_mutable_context().\
        get_mutable_continuous_state_vector()
    state.SetFromVector(xinit)

    # Simulate!
    simulator.StepTo(duration)

    return tree, plant, controller, state_log, contact_log
def getPredictedMotion(B, v_command, time):
    #object_positions = object_positions + 0.1
    #manipulator_positions = manipulator_positions + 0.1
    #object_velocities = object_velocities + 0.1
    #manipulator_velocities = manipulator_velocities + 0.1

    #object_positions = object_positions[:, range(0,object_positions.shape[1],2)]
    #manipulator_positions = manipulator_positions[:, range(0,manipulator_positions.shape[1],2)]
    #object_velocities = object_velocities[:, range(0,object_velocities.shape[1],2)]
    #manipulator_velocities = manipulator_velocities[:, range(0,manipulator_velocities.shape[1],2)]
    #times = times[range(0,times.size,2)]
    #import pdb; pdb.set_trace()
    step = 0.01
    A = 10 * np.eye(3)

    tree = RigidBodyTree(
        FindResource(
            os.path.dirname(os.path.realpath(__file__)) +
            "/block_pusher2.urdf"), FloatingBaseType.kFixed)

    # Set up a block diagram with the robot (dynamics), the controller, and a
    # visualization block.
    builder = DiagramBuilder()
    #robot = builder.AddSystem(RigidBodyPlant(tree))
    robot = builder.AddSystem(
        QuasiStaticRigidBodyPlant(tree, step, A, np.linalg.inv(B)))

    controller = builder.AddSystem(QController(tree, v_command, step))
    #builder.Connect(robot.get_output_port(0), controller.get_input_port(0))
    builder.Connect(controller.get_output_port(0), robot.get_input_port(0))

    Tview = np.array([[1., 0., 0., 0.], [0., 1., 0., 0.], [0., 0., 0., 1.]],
                     dtype=np.float64)
    visualizer = builder.AddSystem(
        PlanarRigidBodyVisualizer(tree,
                                  Tview,
                                  xlim=[-2.8, 4.8],
                                  ylim=[-2.8, 10]))
    builder.Connect(robot.get_output_port(0), visualizer.get_input_port(0))

    logger = builder.AddSystem(
        SignalLogger(tree.get_num_positions() + tree.get_num_velocities()))
    builder.Connect(robot.get_output_port(0), logger.get_input_port(0))

    diagram = builder.Build()

    # Set up a simulator to run this diagram
    simulator = Simulator(diagram)
    simulator.set_target_realtime_rate(1.0)
    simulator.set_publish_every_time_step(True)

    # Set the initial conditions
    context = simulator.get_mutable_context()
    state = context.get_mutable_discrete_state_vector()
    start1 = 3 * np.pi / 16
    start2 = 15 * np.pi / 16
    #np.pi/6 - eps, 2*np.pi/3 + eps, -np.pi/6 + eps, -2*np.pi/3 - eps,    np.pi/6 - eps, 2*np.pi/3 + eps, -np.pi/6 + eps, -2*np.pi/3 - eps
    state.SetFromVector(
        (start1, start2, -start1, -start2, np.pi + start1, start2,
         np.pi - start1, -start2, 1, 1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
         0., 0.))  # (theta1, theta2, theta1dot, theta2dot)
    # Simulate for 10 seconds
    simulator.StepTo(time)
    #import pdb; pdb.set_trace()
    return (logger.data()[8:11, :], logger.data()[:8, :],
            logger.data()[19:22, :], logger.data()[11:19, :],
            logger.sample_times())
import matplotlib.pyplot as plt
from pydrake.all import (DiagramBuilder, SignalLogger, Simulator)
from simple_continuous_time_system import *

# Create a simple block diagram containing our system.
builder = DiagramBuilder()
system = builder.AddSystem(SimpleContinuousTimeSystem())
logger = builder.AddSystem(SignalLogger(1))
builder.Connect(system.get_output_port(0), logger.get_input_port(0))
diagram = builder.Build()

# Create the simulator.
simulator = Simulator(diagram)

# Set the initial conditions, x(0).
state = simulator.get_mutable_context().get_mutable_continuous_state_vector()
state.SetFromVector([0.9])

# Simulate for 10 seconds.
simulator.StepTo(10)

# Plot the results.
plt.plot(logger.sample_times(), logger.data().transpose())
plt.xlabel('t')
plt.ylabel('x(t)')
plt.show()
Beispiel #26
0
# Create a simple block diagram containing our system.
controller = builder.AddSystem(QuadLqrController())
logger_x = builder.AddSystem(SignalLogger(n))
logger_u = builder.AddSystem(SignalLogger(m))

builder.Connect(controller.get_output_port(0), quad.get_input_port(0))
builder.Connect(quad.get_output_port(0), logger_x.get_input_port(0))
builder.Connect(quad.get_output_port(0), controller.get_input_port(0))
builder.Connect(controller.get_output_port(0), logger_u.get_input_port(0))
diagram = builder.Build()

# Create the simulator.
simulator = Simulator(diagram)

# Set the initial conditions, x(0).
state = simulator.get_mutable_context().get_mutable_continuous_state_vector()
state.SetFromVector(traj_specs.x0)

# Simulate
simulator.StepTo(traj_specs.h * traj_specs.N)

#%% plot
PlotTraj(logger_x.data().T, None, None, logger_x.sample_times())

#%% open meshcat 
vis = meshcat.Visualizer()
vis.open()

#%% meshcat animation
PlotTrajectoryMeshcat(logger_x.data().T, logger_x.sample_times(), vis)
tree.compile()

builder = DiagramBuilder()
compass_gait = builder.AddSystem(CompassGait())

parser = argparse.ArgumentParser()
parser.add_argument("-T",
                    "--duration",
                    type=float,
                    help="Duration to run sim.",
                    default=10.0)
args = parser.parse_args()

visualizer = builder.AddSystem(
    PlanarRigidBodyVisualizer(tree,
                              xlim=[-1., 5.],
                              ylim=[-1., 2.],
                              figsize_multiplier=2))
builder.Connect(compass_gait.get_output_port(1), visualizer.get_input_port(0))

diagram = builder.Build()
simulator = Simulator(diagram)
simulator.set_target_realtime_rate(1.0)

context = simulator.get_mutable_context()
diagram.Publish(context)  # draw once to get the window open
context.set_accuracy(1e-4)
context.SetContinuousState([0., 0., 0.4, -2.])

simulator.StepTo(args.duration)
Beispiel #28
0
    source = builder.AddSystem(TrajectorySource(q_traj, output_derivative_order=1))

    # controller
    kp = 100 * np.ones(7)
    kd = 10 * np.ones(7)
    ki = 0 * np.ones(7)
    controller = builder.AddSystem(InverseDynamicsController(robot=tree_1, kp=kp, ki=ki, kd=kd, has_reference_acceleration=False))
    
    # plant
    plant = RigidBodyPlant(tree_2, 0.0005)
    kuka = builder.AddSystem(plant)

    # visualizer
    lcm = DrakeLcm()
    visualizer = builder.AddSystem(DrakeVisualizer(tree=tree_1, lcm=lcm, enable_playback=True))
    visualizer.set_publish_period(.001)

    # build the diagram
    builder.Connect(source.get_output_port(0), controller.get_input_port(1))
    builder.Connect(controller.get_output_port(0), kuka.get_input_port(0))
    builder.Connect(kuka.get_output_port(0), visualizer.get_input_port(0))
    builder.Connect(kuka.get_output_port(0), controller.get_input_port(0))
    diagram = builder.Build()

    # run the simulator
    simulator = Simulator(diagram)
    simulator.set_target_realtime_rate(1.0)
    simulator.set_publish_every_time_step(True)
    kuka.set_state_vector(simulator.get_mutable_context(), x_init)
    simulator.StepTo(tspan[-1])