-
Notifications
You must be signed in to change notification settings - Fork 0
/
index.html
362 lines (314 loc) · 19.9 KB
/
index.html
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
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<meta name="description" content="Dynamically Feasible Trajectory Generation with Optimization Embedded Networks for Autonomous Flight">
<meta name="keywords" content="Robotics, Deep Learning, Differentiable Trajectory Optimization, Quadrotors">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Dynamically Feasible Trajectory Generation with Optimization Embedded Networks for Autonomous Flight</title>
<link rel="stylesheet" href="./static/css/cyk.css">
<link href="https://fonts.googleapis.com/css?family=Google+Sans|Noto+Sans|Castoro"
rel="stylesheet">
<link rel="stylesheet" href="./static/css/bulma.min.css">
<link rel="stylesheet" href="./static/css/bulma-carousel.min.css">
<link rel="stylesheet" href="./static/css/bulma-slider.min.css">
<link rel="stylesheet" href="./static/css/fontawesome.all.min.css">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/gh/jpswalsh/academicons@1/css/academicons.min.css">
<link rel="stylesheet" href="./static/css/index.css">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
<script defer src="./static/js/fontawesome.all.min.js"></script>
<script src="./static/js/bulma-carousel.min.js"></script>
<script src="./static/js/bulma-slider.min.js"></script>
<script src="./static/js/index.js"></script>
<link rel="icon" href="./favicon.ico">
<!-- <meta property="og:site_name" content="Dynamically Feasible Trajectory Generation with Optimization Embedded Networks for Autonomous Flight" />
<meta property="og:type" content="video.other" />
<meta property="og:title" content="Dynamically Feasible Trajectory Generation with Optimization Embedded Networks for Autonomous Flight" />
<meta property="og:description" content="by Zhichao Han, Long Xu and Fei Gao" />
<meta property="og:url" content="https://learning-agility-adaptation.github.io/" />
<meta property="og:image" content="https://learning-agility-adaptation.github.io/static/images/preview.gif" />
<meta property="og:image:secure" content="https://learning-agility-adaptation.github.io/static/images/preview.gif" />
<meta property="og:video" content="https://www.youtube.com/watch?v=ytRQRj8PaAk" />
<meta property="og:video:secure" content="https://www.youtube.com/watch?v=ytRQRj8PaAk" />
<meta property="og:image:width" content="1280" />
<meta property="og:image:height" content="720" /> -->
<!-- <meta name="twitter:card" content="summary_large_image" />
<meta name="twitter:title" content="Dynamically Feasible Trajectory Generation with Optimization Embedded Networks for Autonomous Flight" />
<meta name="twitter:description" content="by Guangyu Zhao, Tianyue Wu, Yeke Chen and Fei Gao" />
<meta name="twitter:url" content="https://learning-agility-adaptation.github.io/" />
<meta name="twitter:image" content="https://learning-agility-adaptation.github.io/static/images/preview.gif" />
<meta name="twitter:card" content="player" />
<meta name="twitter:player" content="https://www.youtube.com/watch?v=ytRQRj8PaAk" />
<meta name="twitter:player:width" content="1280" />
<meta name="twitter:player:height" content="720" /> -->
<script src="https://www.youtube.com/iframe_api"></script>
</head>
<body>
<section class="hero">
<div class="hero-body">
<div class="container">
<!-- title and authors -->
<div class="columns is-centered">
<div class="column has-text-centered">
<h1 class="title is-1 publication-title">Dynamically Feasible Trajectory Generation with Optimization Embedded Networks for Autonomous Flight</h1>
<div class="is-size-5 publication-authors">
<span class="author-block">
<a href="https://scholar.google.com/citations?user=5g-ZhmwAAAAJ">Zhichao Han</a>*
<a href="https://gaolon.github.io/xulong/">Long Xu</a>*
<a href="https://liuaopei.com/">Liuao Pei</a>
<a href="http://zju-fast.com/fei-gao/">Fei Gao</a>
</span>
</div>
</div>
</div>
<!-- logo -->
<div class="my_columns is-centered">
<div class="my_column is-centered">
<image src="./static/images/logo_fastlab.png" style="width: 60%;margin-right: 0%; margin-left: 40%;margin-top: 2.5%;"></image>
</div>
<div class="my_column is-centered">
<image src="./static/images/logo_zju.png" style="width: 60%; margin-left: 0%;margin-right: 40%;margin-top: 0%; "></image>
</div>
</div>
<!-- <div class="is-size-4 publication-authors">
</div>
<div class="is-size-4 publication-authors">
<b style="color:rgb(255, 100, 100);"> </b>
</div> -->
<!-- buttons -->
<div class="my_columns is-centered ">
<div class="column has-text-centered">
<div class="publication-links">
<!-- PDF Link. -->
<!-- <span class="link-block">
<a href="./resources/article.pdf"
class="external-link button is-normal is-rounded is-dark" target="_blank">
<span class="icon">
<i class="fas fa-file-pdf"></i>
</span>
<span>Paper</span>
</a>
</span> -->
<!-- arXiv Link. -->
<!-- <span class="link-block">
<a href="https://arxiv.org/abs/2403.04586"
class="external-link button is-normal is-rounded is-dark" target="_blank">
<span class="icon">
<i class="ai ai-arxiv"></i>
</span>
<span>arXiv</span>
</a>
</span> -->
<!-- OpenReview Link. -->
<!-- <span class="link-block">
<a href="https://openreview.net/TODO"
class="external-link button is-normal is-rounded is-dark" target="_blank">
<span class="icon">
<img src="static/images/openreview.ico"></img>
</span>
<span>OpenReview</span>
</a>
</span> -->
<!-- Video Link. -->
<!-- <span class="link-block">
<a href="https://www.youtube.com/watch?v=ytRQRj8PaAk"
class="external-link button is-normal is-rounded is-dark" target="_blank">
<span class="icon">
<i class="fab fa-youtube"></i>
</span>
<span>Video</span>
</a>
</span> -->
<!-- Bilibili Link. -->
<!-- <span class="link-block">
<a href="https://www.bilibili.com/video/BV1uy421v7S2/?share_source=copy_web&vd_source=bc789affdda03da3613deb9656e7fa4d"
class="external-link button is-normal is-rounded is-dark" target="_blank">
<span class="icon">
<svg style="color: white" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path d="M488.6 104.1C505.3 122.2 513 143.8 511.9 169.8V372.2C511.5 398.6 502.7 420.3 485.4 437.3C468.2 454.3 446.3 463.2 419.9 464H92.02C65.57 463.2 43.81 454.2 26.74 436.8C9.682 419.4 .7667 396.5 0 368.2V169.8C.7667 143.8 9.682 122.2 26.74 104.1C43.81 87.75 65.57 78.77 92.02 78H121.4L96.05 52.19C90.3 46.46 87.42 39.19 87.42 30.4C87.42 21.6 90.3 14.34 96.05 8.603C101.8 2.868 109.1 0 117.9 0C126.7 0 134 2.868 139.8 8.603L213.1 78H301.1L375.6 8.603C381.7 2.868 389.2 0 398 0C406.8 0 414.1 2.868 419.9 8.603C425.6 14.34 428.5 21.6 428.5 30.4C428.5 39.19 425.6 46.46 419.9 52.19L394.6 78L423.9 78C450.3 78.77 471.9 87.75 488.6 104.1H488.6zM449.8 173.8C449.4 164.2 446.1 156.4 439.1 150.3C433.9 144.2 425.1 140.9 416.4 140.5H96.05C86.46 140.9 78.6 144.2 72.47 150.3C66.33 156.4 63.07 164.2 62.69 173.8V368.2C62.69 377.4 65.95 385.2 72.47 391.7C78.99 398.2 86.85 401.5 96.05 401.5H416.4C425.6 401.5 433.4 398.2 439.7 391.7C446 385.2 449.4 377.4 449.8 368.2L449.8 173.8zM185.5 216.5C191.8 222.8 195.2 230.6 195.6 239.7V273C195.2 282.2 191.9 289.9 185.8 296.2C179.6 302.5 171.8 305.7 162.2 305.7C152.6 305.7 144.7 302.5 138.6 296.2C132.5 289.9 129.2 282.2 128.8 273V239.7C129.2 230.6 132.6 222.8 138.9 216.5C145.2 210.2 152.1 206.9 162.2 206.5C171.4 206.9 179.2 210.2 185.5 216.5H185.5zM377 216.5C383.3 222.8 386.7 230.6 387.1 239.7V273C386.7 282.2 383.4 289.9 377.3 296.2C371.2 302.5 363.3 305.7 353.7 305.7C344.1 305.7 336.3 302.5 330.1 296.2C323.1 289.9 320.7 282.2 320.4 273V239.7C320.7 230.6 324.1 222.8 330.4 216.5C336.7 210.2 344.5 206.9 353.7 206.5C362.9 206.9 370.7 210.2 377 216.5H377z" fill="white"></path></svg> </span>
<span>Bilibili</span>
</a>
</span> -->
<!-- twitter Link. -->
<!-- <span class="link-block">
<a href="https://twitter.com/Modern_Gangster/status/1766364774689042807"
class="external-link button is-normal is-rounded is-dark" target="_blank">
<span class="icon">
<i class="fab fa-twitter"></i>
</span>
<span>Summary</span>
</a>
</span> -->
<!-- Code Link. -->
<span class="link-block">
<a href="https://github.com/ZJU-FAST-Lab/e2e_opt" class="external-link button is-normal is-rounded is-dark" target="_blank">
<span class="icon">
<svg class="svg-inline--fa fa-github fa-w-16" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="github" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512" data-fa-i2svg=""><path fill="currentColor" d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"></path></svg>
</span>
<span>Code(coming soon)</span>
</a>
</span>
</div>
</div>
</div>
</div>
</div>
</section>
<section class="section">
<div class="columns is-centered">
<div class="column is-full-width is-centered has-text-centered">
<img src="./static/images/pipeline.png" alt="" style="width: 50%;" />
</div>
</div>
<!-- <div class="container">
<div class="columns is-centered">
<div class="column is-full-width is-centered has-text-centered">
<div class="publication-video">
<iframe width="560" height="315" src="https://www.youtube.com/embed/ytRQRj8PaAk?si=ubFX5oKq9VK9VP-3" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" allowfullscreen></iframe>
</div>
</div>
</div>
</div> -->
</section>
<section class="section">
<div class="container">
<!-- Abstract. -->
<div class="columns is-centered has-text-centered">
<div class="column is-two-thirds">
<h2 class="title is-2">Abstract</h2>
<div class="content has-text-justified">
<p>
This paper aims to bridge perception and planning in navigation systems by learning optimal trajectories from depth information in an end-to-end fashion. However, using neural networks as black-box replacements for traditional modules risks scalability and adaptability. Moreover, such methods often fall short in sufficiently incorporating the robot's dynamic constraints, resulting in trajectories that are either inadequately executable or unexpectedly aggressive, diverging from user expectations. In this paper, we fuse the benefits of conventional methods and neural networks by introducing an optimization-embedded network based on a compact trajectory library. The network distills spatial constraints, which are then applied to model-based spatial-temporal trajectory optimization, yielding feasible and optimal solutions. By making the optimization differentiable, our model seamlessly approximates the optimal trajectory. Additionally, the introduced regularized trajectory library permits efficient capture of the spatial distribution of optimal trajectories with minimal storage cost, safeguarding multimodal planning features. Benchmarking demonstrates the outstanding performance of our method in trajectory smoothness, success rate, and constraint satisfaction. Real-world flight experiments with an onboard computer showcase the autonomous quadrotor’s ability to navigate swiftly through dense forests.
</p>
</div>
</div>
</div>
</div>
</section>
<section class="section">
<div class="container">
<h2 class="title is-2" style="text-align: center;">Simulation Experiments</h2>
<h2 class="title is-5" style="text-align: center;">(playing speed: 1x)</h2>
<div class="column is-1"></div>
<h2 class="title is-4" style="text-align: center;">Benchmark Comparisons</h2>
<h2 class="title is-4" style="text-align: center;">Maximal speed: 8 m/s; Maximal acceleration: 10 m/s<sup>2</sup></h2>
<div class="columns is-centered has-text-centered">
<div class="column">
<video controls autoplay loop muted playsinline src="./resources/ego.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
Ego-method
</p>
</div>
<div class="column">
<video controls autoplay loop muted playsinline src="./resources/iplanner.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
I-planner
</p>
</div>
</div>
<div class="columns is-centered has-text-centered">
<div class="column">
<video controls autoplay loop muted playsinline src="./resources/proposed.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
Our method
</p>
</div>
</div>
</div>
</section>
<section class="section">
<div class="container">
<h2 class="title is-2" style="text-align: center;">Real-World Experiments</h2>
<h2 class="title is-5" style="text-align: center;">(playing speed: 1x)</h2>
<h2 class="title is-4" style="text-align: center;">Wooden Area</h2>
<h2 class="title is-4" style="text-align: center;">Maximal speed: 5 m/s; Maximal acceleration: 6 m/s<sup>2</sup></h2>
<div class="column is-full-width is-centered has-text-centered">
<video controls autoplay loop muted playsinline src="./resources/real_0.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
Case 0
</p>
</div>
<div class="columns is-centered has-text-centered">
<div class="column">
<video controls autoplay loop muted playsinline src="./resources/real_1.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
Case 1
</p>
</div>
<div class="column">
<video controls autoplay loop muted playsinline src="./resources/real_2.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
Case 2
</p>
</div>
</div>
<div class="columns is-centered has-text-centered">
<div class="column">
<video controls autoplay loop muted playsinline src="./resources/real_3.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
Case 3
</p>
</div>
<div class="column">
<video controls autoplay loop muted playsinline src="./resources/real_4.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
Case 4
</p>
</div>
</div>
<div class="columns is-centered has-text-centered">
<div class="column">
<video controls autoplay loop muted playsinline src="./resources/real_5.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
Case 5
</p>
</div>
<div class="column">
<video controls autoplay loop muted playsinline src="./resources/real_6.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
Case 6
</p>
</div>
</div>
<div class="columns is-centered has-text-centered">
<div class="column">
<video controls autoplay loop muted playsinline src="./resources/real_7.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
Case 7
</p>
</div>
<div class="column">
<video controls autoplay loop muted playsinline src="./resources/real_8.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
<p>
Case 8
</p>
</div>
</div>
<h2 class="title is-4" style="text-align: center;">Flying with Blurred Camera (maximal speed: 5 m/s, maximal acceleration: 6 m/s<sup>2</sup>)</h2>
<h2 class="title is-4" style="text-align: center;">Maximal speed: 5 m/s; Maximal acceleration: 6 m/s<sup>2</sup></h2>
<div class="column is-full-width is-centered has-text-centered">
<video controls autoplay loop muted playsinline src="./resources/robust.mp4" poster="./resources/loading-icon.gif" style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"></video>
</div>
</div>
</section>
<!-- <section class="section" id="BibTeX">
<div class="container content">
<h2 class="titile">BibTeX</h2>
<pre><code>@misc{e2e_opt2024,
title={Dynamically Feasible Trajectory Generation with Optimization Embedded Networks for Autonomous Flight},
author={Zhichao Han and Long Xu and Fei Gao},
year={2024},
eprint={2405.07736},
archivePrefix={arXiv},
primaryClass={cs.RO}
}</code></pre>
</div>
</section> -->
<!-- <footer class="footer">
<div class="container">
<div class="content has-text-centered">
<p>Page template borrowed from <a href="https://nerfies.github.io/"><span class="dnerf">Nerfies</span></a> and <a href="https://manipulation-locomotion.github.io/"><span class="dnerf">Deep-Whole-Body-Control</span></a>.</p>
</div>
</div>
</footer> -->
</body>
</html>