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lqr.py
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lqr.py
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# %% [markdown]
# # Triple cart-pole
# %%
from pydrake.all import (
AddMultibodyPlantSceneGraph,
DiagramBuilder,
LinearQuadraticRegulator,
Parser,
PlanarSceneGraphVisualizer,
Simulator,
Linearize,
LogVectorOutput,
StartMeshcat,
SceneGraph,
MeshcatVisualizerCpp,
RigidTransform,
RotationMatrix,
)
import os
import numpy as np
import pandas as pd
import seaborn as sns
from matplotlib import pyplot as plt
import matplotlib
from IPython.display import display, clear_output, SVG, HTML
# %%
def simulate_triple_cartpole(sim_time=10):
# make visualization larger
matplotlib.rcParams["figure.figsize"] = (10, 10)
# start construction site of our block diagram
builder = DiagramBuilder()
# instantiate the cart-pole and the scene graph
plant, scene_graph = AddMultibodyPlantSceneGraph(builder, time_step=0.0)
Parser(plant).AddModelFromFile("triple_cartpole.urdf")
plant.Finalize()
# set initial unstable equilibrium point
context = plant.CreateDefaultContext()
x_star = [0, np.pi, 0, 0, 0, 0, 0, 0]
context.get_mutable_continuous_state_vector().SetFromVector(x_star)
# weight matrices for the lqr controller
Q = np.diag((10.0, 10.0, 10.0, 10.0, 1.0, 1.0, 1.0, 1.0))
R = np.eye(1)
# Setup input
plant.get_actuation_input_port().FixValue(context, [0])
input_i = plant.get_actuation_input_port().get_index()
lqr = LinearQuadraticRegulator(plant, context, Q, R, input_port_index=int(input_i))
lqr = builder.AddSystem(lqr)
builder.Connect(plant.get_state_output_port(), lqr.get_input_port(0))
builder.Connect(lqr.get_output_port(0), plant.get_actuation_input_port())
# Add loggers
state_logger = LogVectorOutput(plant.get_state_output_port(), builder)
state_logger.set_name("state logger")
input_logger = LogVectorOutput(lqr.get_output_port(), builder)
input_logger.set_name("input logger")
# Add visualizer
visualizer = builder.AddSystem(
PlanarSceneGraphVisualizer(
scene_graph, xlim=[-4.0, 1.0], ylim=[-0.5, 3.2], show=False
)
)
visualizer.set_name("visualizer")
builder.Connect(scene_graph.get_query_output_port(), visualizer.get_input_port(0))
# finish building the block diagram
diagram = builder.Build()
# instantiate a simulator
simulator = Simulator(diagram)
simulator.set_publish_every_time_step(False) # makes sim faster
context = simulator.get_mutable_context()
context.SetTime(0)
context.SetContinuousState(
np.array([-2, 0.95 * np.pi, 0.05 * np.pi, 0.02 * np.pi, 0, 0, 0, 0])
)
# run simulation
visualizer.start_recording()
simulator.Initialize()
simulator.set_target_realtime_rate(1.0)
simulator.AdvanceTo(sim_time)
# show visualization
visualizer.stop_recording()
ani = visualizer.get_recording_as_animation()
ani.save("lqr.mp4", fps=60)
display(HTML(ani.to_jshtml()))
visualizer.reset_recording()
# return the state and input over time
state_log = state_logger.FindLog(simulator.get_context())
input_log = input_logger.FindLog(simulator.get_context())
state_names = list(
[
"x",
"theta_1",
"theta_2",
"theta_3",
"x_dot",
"theta_1_dot",
"theta_2_dot",
"theta_3_dot",
]
)
df = pd.DataFrame(state_log.data().T, columns=state_names)
df["time"] = state_log.sample_times()
df["u"] = input_log.data().T
return df
results = simulate_triple_cartpole()
# %%
# Create a plot of the showing the evolution of state variables over time
fig, (ax1, ax2, ax3, ax4) = plt.subplots(4, 1, figsize=(10, 9))
sns.lineplot(data=results, x="time", y="x", ax=ax1)
ax1.set(ylabel="Cart Position (m)")
results["theta_1_minus_pi"] = results["theta_1"] - np.pi
sns.lineplot(data=results, x="time", y="theta_1_minus_pi", ax=ax2)
sns.lineplot(data=results, x="time", y="theta_2", ax=ax2)
sns.lineplot(data=results, x="time", y="theta_3", ax=ax2)
ax2.set(ylabel="Joint Angles (rad)")
sns.lineplot(data=results, x="time", y="theta_1_dot", ax=ax3)
sns.lineplot(data=results, x="time", y="theta_2_dot", ax=ax3)
sns.lineplot(data=results, x="time", y="theta_3_dot", ax=ax3)
ax3.set(ylabel="Joint Velocities (rad/sec)")
sns.lineplot(data=results, x="time", y="u", ax=ax4)
ax4.set(ylabel="Input (N)")
plt.show()
# %%
# %%
# An example of a phase portait which could be used for showing ROA slices
sns.lineplot(data=results, x="theta_1", y="theta_1_dot", sort=False)
# %%