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# NVIDIA CORPORATION and its licensors retain all intellectual property
# and proprietary rights in and to this software, related documentation
# and any modifications thereto. Any use, reproduction, disclosure or
# distribution of this software and related documentation without an express
# license agreement from NVIDIA CORPORATION is strictly prohibited.
###########################################################################
# Example Trajectory Optimization
#
# Shows how to optimize torque trajectories for a simple planar environment
# using Warp's provided Adam optimizer.
#
###########################################################################
import os
import numpy as np
import warp as wp
import warp.sim
import warp.sim.render
from warp.optim import Adam
wp.init()
@wp.kernel
def loss_l2(
states: wp.array2d(dtype=wp.float32), targets: wp.array2d(dtype=wp.float32), loss: wp.array(dtype=wp.float32)
):
i, j = wp.tid()
diff = states[i, j] - targets[i, j]
l = diff * diff
wp.atomic_add(loss, 0, l)
@wp.kernel
def apply_torque(torques: wp.array(dtype=wp.float32), start_index: int, body_f: wp.array(dtype=wp.spatial_vector)):
fx = torques[start_index + 0]
fz = torques[start_index + 1]
body_f[0] = wp.spatial_vector(0.0, 0.0, 0.0, fx, 0.0, fz)
@wp.kernel
def save_state(body_q: wp.array(dtype=wp.transform), write_index: int, states: wp.array2d(dtype=wp.float32)):
pos = wp.transform_get_translation(body_q[0])
states[write_index, 0] = pos[0]
states[write_index, 1] = pos[2]
class Example:
def __init__(self, stage, device=None, verbose=False):
self.verbose = verbose
self.frame_dt = 1.0 / 60.0
self.episode_frames = 100
self.sim_substeps = 1
self.sim_dt = self.frame_dt / self.sim_substeps
self.render_time = 0.0
self.iter = 0
builder = wp.sim.ModelBuilder()
self.device = device
# add planar joints
builder = wp.sim.ModelBuilder(gravity=0.0)
builder.add_articulation()
b = builder.add_body(origin=wp.transform())
builder.add_shape_box(pos=wp.vec3(0.0, 0.0, 0.0), hx=0.5, hy=0.5, hz=0.5, density=100.0, body=b)
# compute reference trajectory
rad = np.linspace(0.0, np.pi * 2, self.episode_frames)
self.ref_traj = np.stack([np.cos(rad), np.sin(rad)], axis=1)
# set initial joint configuration to first reference state
builder.body_q[0] = wp.transform(p=[self.ref_traj[0][0], 0.0, self.ref_traj[0][1]])
self.ref_traj = wp.array(self.ref_traj, dtype=wp.float32, device=self.device, requires_grad=True)
self.last_traj = wp.empty_like(self.ref_traj)
# finalize model
self.model = builder.finalize(device, requires_grad=True)
self.builder = builder
self.model.ground = False
self.dof_q = self.model.joint_coord_count
self.dof_qd = self.model.joint_dof_count
self.num_bodies = self.model.body_count
self.action_dim = 2
self.state_dim = 2
assert self.ref_traj.shape == (self.episode_frames, self.state_dim)
self.integrator = wp.sim.SemiImplicitIntegrator()
# initial guess
self.actions = wp.array(
np.zeros(self.episode_frames * self.action_dim) * 100.0,
dtype=wp.float32,
device=self.device,
requires_grad=True,
)
self.optimizer = Adam([self.actions], lr=1e2)
self.loss = wp.zeros(1, dtype=wp.float32, device=self.device, requires_grad=True)
self.renderer = wp.sim.render.SimRenderer(self.model, stage, scaling=100.0)
# allocate sim states for trajectory
self.states = []
for _ in range(self.episode_frames + 1):
self.states.append(self.model.state(requires_grad=True))
def compute_loss(self):
"""
Advances the system dynamics given the rigid-body state in maximal coordinates and generalized joint torques
[body_q, body_qd, tau].
"""
self.last_traj.zero_()
for i in range(self.episode_frames):
state = self.states[i]
for _ in range(self.sim_substeps):
next_state = self.model.state(requires_grad=True)
wp.sim.collide(self.model, state)
# apply generalized torques to rigid body here, instead of planar joints
wp.launch(
apply_torque,
1,
inputs=[self.actions, i * self.action_dim],
outputs=[state.body_f],
device=self.device,
)
state = self.integrator.simulate(self.model, state, next_state, self.sim_dt, requires_grad=True)
self.states[i + 1] = state
# save state
wp.launch(
save_state,
dim=1,
inputs=[self.states[i + 1].body_q, i],
outputs=[self.last_traj],
device=self.device,
)
# compute loss
wp.launch(
loss_l2,
dim=self.last_traj.shape,
inputs=[self.last_traj, self.ref_traj],
outputs=[self.loss],
device=self.device,
)
def update(self):
"""Runs a single optimizer iteration"""
self.loss.zero_()
tape = wp.Tape()
with tape:
self.compute_loss()
if self.verbose and (self.iter + 1) % 10 == 0:
print(f"Iter {self.iter+1} Loss: {self.loss.numpy()[0]:.3f}")
tape.backward(loss=self.loss)
# print("action grad", self.actions.grad.numpy())
assert not np.isnan(self.actions.grad.numpy()).any(), "NaN in gradient"
self.optimizer.step([self.actions.grad])
tape.zero()
self.iter = self.iter + 1
def render(self):
for i in range(self.episode_frames):
self.renderer.begin_frame(self.render_time)
self.renderer.render(self.states[i + 1])
self.renderer.end_frame()
self.render_time += self.frame_dt
if __name__ == "__main__":
import matplotlib.pyplot as plt
stage_path = os.path.join(os.path.dirname(__file__), "outputs/example_sim_trajopt.usd")
example = Example(stage_path, device=wp.get_preferred_device(), verbose=True)
# Optimize
num_iter = 250
for i in range(num_iter):
example.update()
# Render every 25 iters
if i % 25 == 0:
example.render()
example.renderer.save()
np_states = example.last_traj.numpy()
np_ref = example.ref_traj.numpy()
plt.plot(np_ref[:, 0], np_ref[:, 1], label="Reference Trajectory")
plt.plot(np_states[:, 0], np_states[:, 1], label="Optimized Trajectory")
plt.grid()
plt.legend()
plt.axis("equal")
plt.show()
#
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