File size: 6,960 Bytes
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
# 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 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()
#