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66c9c8a | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 | # Copyright (c) 2022 NVIDIA CORPORATION. All rights reserved.
# 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 Jacobian
#
# Demonstrates how to compute the Jacobian of a multi-valued function.
# Here, we use the simulation of a cartpole to differentiate
# through the kinematics function. We instantiate multiple copies of the
# cartpole and compute the Jacobian of the state of each cartpole in parallel
# in order to perform inverse kinematics via Jacobian transpose.
#
###########################################################################
import math
import os
import numpy as np
import warp as wp
import warp.sim
import warp.sim.render
wp.init()
@wp.kernel
def compute_endeffector_position(
body_q: wp.array(dtype=wp.transform),
num_links: int,
ee_link_index: int,
ee_link_offset: wp.vec3,
ee_pos: wp.array(dtype=wp.vec3),
):
tid = wp.tid()
ee_pos[tid] = wp.transform_point(body_q[tid * num_links + ee_link_index], ee_link_offset)
class Example:
def __init__(self, stage=None, enable_rendering=True, num_envs=1, device=None):
builder = wp.sim.ModelBuilder()
self.num_envs = num_envs
self.device = device
self.frame_dt = 1.0 / 60.0
self.render_time = 0.0
# step size to use for the IK updates
self.step_size = 0.1
articulation_builder = wp.sim.ModelBuilder()
wp.sim.parse_urdf(
os.path.join(os.path.dirname(__file__), "assets/cartpole.urdf"),
articulation_builder,
xform=wp.transform_identity(),
floating=False,
density=0,
armature=0.1,
stiffness=0.0,
damping=0.0,
shape_ke=1.0e4,
shape_kd=1.0e2,
shape_kf=1.0e2,
shape_mu=1.0,
limit_ke=1.0e4,
limit_kd=1.0e1,
)
builder = wp.sim.ModelBuilder()
self.num_links = len(articulation_builder.joint_type)
# use the last link as the end-effector
self.ee_link_index = self.num_links - 1
self.ee_link_offset = wp.vec3(0.0, 0.0, 1.0)
self.dof = len(articulation_builder.joint_q)
self.target_origin = []
for i in range(num_envs):
builder.add_builder(
articulation_builder,
xform=wp.transform(
wp.vec3(i * 2.0, 4.0, 0.0), wp.quat_from_axis_angle(wp.vec3(1.0, 0.0, 0.0), -math.pi * 0.5)
),
)
self.target_origin.append((i * 2.0, 4.0, 0.0))
# joint initial positions
builder.joint_q[-3:] = np.random.uniform(-0.5, 0.5, size=3)
self.target_origin = np.array(self.target_origin)
# finalize model
self.model = builder.finalize(device)
self.model.ground = True
self.model.joint_q.requires_grad = True
self.model.body_q.requires_grad = True
self.model.joint_attach_ke = 1600.0
self.model.joint_attach_kd = 20.0
self.integrator = wp.sim.SemiImplicitIntegrator()
self.enable_rendering = enable_rendering
self.renderer = None
if enable_rendering:
self.renderer = wp.sim.render.SimRenderer(self.model, stage)
self.ee_pos = wp.zeros(self.num_envs, dtype=wp.vec3, device=device, requires_grad=True)
self.state = self.model.state(requires_grad=True)
self.targets = self.target_origin.copy()
self.profiler = {}
def compute_ee_position(self):
# computes the end-effector position from the current joint angles
wp.sim.eval_fk(self.model, self.model.joint_q, self.model.joint_qd, None, self.state)
wp.launch(
compute_endeffector_position,
dim=self.num_envs,
inputs=[self.state.body_q, self.num_links, self.ee_link_index, self.ee_link_offset],
outputs=[self.ee_pos],
device=self.device,
)
return self.ee_pos
def compute_jacobian(self):
# our function has 3 outputs (EE position), so we need a 3xN jacobian per environment
jacobians = np.empty((self.num_envs, 3, self.dof), dtype=np.float32)
tape = wp.Tape()
with tape:
self.compute_ee_position()
for output_index in range(3):
# select which row of the Jacobian we want to compute
select_index = np.zeros(3)
select_index[output_index] = 1.0
e = wp.array(np.tile(select_index, self.num_envs), dtype=wp.vec3, device=self.device)
tape.backward(grads={self.ee_pos: e})
q_grad_i = tape.gradients[self.model.joint_q]
jacobians[:, output_index, :] = q_grad_i.numpy().reshape(self.num_envs, self.dof)
tape.zero()
return jacobians
def compute_fd_jacobian(self, eps=1e-4):
jacobians = np.zeros((self.num_envs, 3, self.dof), dtype=np.float32)
q0 = self.model.joint_q.numpy().copy()
for e in range(self.num_envs):
for i in range(self.dof):
q = q0.copy()
q[e * self.dof + i] += eps
self.model.joint_q.assign(q)
self.compute_ee_position()
f_plus = self.ee_pos.numpy()[e].copy()
q[e * self.dof + i] -= 2 * eps
self.model.joint_q.assign(q)
self.compute_ee_position()
f_minus = self.ee_pos.numpy()[e].copy()
jacobians[e, :, i] = (f_plus - f_minus) / (2 * eps)
return jacobians
def update(self):
with wp.ScopedTimer("jacobian", print=False, active=True, dict=self.profiler):
# compute jacobian
jacobians = self.compute_jacobian()
# jacobians = self.compute_fd_jacobian()
# compute error
self.ee_pos_np = self.compute_ee_position().numpy()
error = self.targets - self.ee_pos_np
self.error = error.reshape(self.num_envs, 3, 1)
# compute Jacobian transpose update
delta_q = np.matmul(jacobians.transpose(0, 2, 1), self.error)
self.model.joint_q = wp.array(
self.model.joint_q.numpy() + self.step_size * delta_q.flatten(),
dtype=wp.float32,
device=self.device,
requires_grad=True,
)
def render(self):
if self.enable_rendering:
self.renderer.begin_frame(self.render_time)
self.renderer.render(self.state)
self.renderer.render_points("targets", self.targets, radius=0.05)
self.renderer.render_points("ee_pos", self.ee_pos_np, radius=0.05)
self.renderer.end_frame()
self.render_time += self.frame_dt
def run(self):
if self.enable_rendering:
print("autodiff:")
print(self.compute_jacobian())
print("finite diff:")
print(self.compute_fd_jacobian())
for _ in range(5):
# select new random target points
self.targets = self.target_origin.copy()
self.targets[:, 1:] += np.random.uniform(-0.5, 0.5, size=(self.num_envs, 2))
for iter in range(50):
self.update()
self.render()
print("iter:", iter, "error:", self.error.mean())
if self.enable_rendering:
self.renderer.save()
avg_time = np.array(self.profiler["jacobian"]).mean()
avg_steps_second = 1000.0 * float(self.num_envs) / avg_time
print(f"envs: {self.num_envs} steps/second {avg_steps_second} avg_time {avg_time}")
return 1000.0 * float(self.num_envs) / avg_time
if __name__ == "__main__":
profile = False
if profile:
env_count = 2
env_times = []
env_size = []
for i in range(12):
example = Example(enable_rendering=False, num_envs=env_count)
steps_per_second = example.run()
env_size.append(env_count)
env_times.append(steps_per_second)
env_count *= 2
# dump times
for i in range(len(env_times)):
print(f"envs: {env_size[i]} steps/second: {env_times[i]}")
# plot
import matplotlib.pyplot as plt
plt.figure(1)
plt.plot(env_size, env_times)
plt.xscale("log")
plt.xlabel("Number of Envs")
plt.yscale("log")
plt.ylabel("Steps/Second")
plt.show()
else:
stage_path = os.path.join(os.path.dirname(__file__), "outputs/example_jacobian_ik.usd")
example = Example(stage_path, enable_rendering=True, num_envs=10)
example.run()
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