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25 | 25 | <script src="./static/js/bulma-carousel.min.js"></script> |
26 | 26 | <script src="./static/js/bulma-slider.min.js"></script> |
27 | 27 | <script src="./static/js/index.js"></script> |
| 28 | + <link rel=" stylesheet" href=" https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css" integrity=" sha384-wcIxkf4k558AjM3Yz3BBFQUbk/zgIYC2R0QpeeYb+TwlBVMrlgLqwRjRtGZiK7ww" crossorigin=" anonymous" > |
| 29 | + <script defer src=" https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.js" integrity=" sha384-hIoBPJpTUs74ddyc4bFZSM1TVlQDA60VBbJS0oA934VSz82sBx1X7kSx2ATBDIyd" crossorigin=" anonymous" ></script> |
| 30 | + <script defer src=" https://cdn.jsdelivr.net/npm/[email protected]/dist/contrib/auto-render.min.js" integrity=" sha384-43gviWU0YVjaDtb/GhzOouOXtZMP/7XUzwPTstBeZFe/+rCMvRwr4yROQP43s0Xk" crossorigin=" anonymous" onload=" renderMathInElement(document.body);" ></script> |
28 | 31 | </head> |
29 | 32 | <body> |
30 | 33 |
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@@ -188,28 +191,50 @@ <h2 class="title is-3">Abstract</h2> |
188 | 191 | </div> |
189 | 192 | </div> |
190 | 193 | <!--/ Abstract. --> |
191 | | - <!-- Benchmarks. --> |
192 | | - <h2 class="title is-3">Whole-body NMPC on SOLO-12</h2> |
193 | | - <div class="columns is-centered has-text-centered"> |
194 | | - <div class="column is-max-desktop"> |
| 194 | + |
| 195 | + <!-- Results. --> |
| 196 | + <h2 class="title is-3">Results</h2> |
| 197 | + <div> |
| 198 | + <h3 class="title is-4">Whole-body NMPC on SOLO-12</h3> |
| 199 | + <div class="columns is-centered has-text-centered"> |
| 200 | + <div class="column is-max-desktop"> |
195 | 201 | <div class="columns is-centered"> |
196 | 202 | <div class="column content"> |
197 | 203 | <p>Computational timings for P=2 threads</p> |
198 | 204 | <image src="./static/images/solo_timings_2cpu.png" |
199 | 205 | alt="WBNMPC on SOLO-12, P=2 threads." |
200 | | - style="width:90%"></image> |
| 206 | + style="width:100%"></image> |
201 | 207 | </div> |
202 | 208 | <div class="column content"> |
203 | 209 | <p>Computational timings for P=6 threads</p> |
204 | 210 | <image src="./static/images/solo_timings_6cpu.png" |
205 | 211 | alt="WBNMPC on SOLO-12, P=6 threads." |
206 | | - style="width:90%"></image> |
| 212 | + style="width:100%"></image> |
207 | 213 | </div> |
208 | 214 | </div> |
209 | 215 | </div> |
210 | 216 | </div> |
| 217 | + |
| 218 | + <div> |
| 219 | + <h3 class="title is-4">Solving cyclic LQ problems</h3> |
| 220 | + <p>One of the side-effects of our formulation, is the ability to tackle linear-quadratic problems with cyclical constraints of the form \(G_0x_0 + G_Nx_N + g = 0\).</p> |
| 221 | + <p> |
| 222 | + The following is a two-dimensional LQ problem over \(N = 20\) steps with no initial condition but a cyclical condition \(x_0 = x_N\), and some transient costs that steer the generated trajectory close to two points \(\bar{x}_5\) and \(\bar{x}_{15}\). |
| 223 | + </p> |
| 224 | + <div class="content has-text-centered"> |
| 225 | + <img src="./static/images/gar-cyclic-lqr-2d.png" alt="2D cyclic LQ problem" |
| 226 | + style="width: 60%;"> |
| 227 | + </div> |
| 228 | + </div> |
| 229 | + |
| 230 | + <h3 class="title is-4">Synthetic benchmark on M1 Mac Studio Ultra</h3> |
| 231 | + <div class="content has-text-centered"> |
| 232 | + <p>We solve an unconstrained LQ problem with the same dimensions as the SOLO-12 NMPC experiment.</p> |
| 233 | + <img src="./static/images/mac-gar-bench-timings.png" alt="" style="width: 50%;"> |
| 234 | + </div> |
| 235 | + </div> |
211 | 236 |
|
212 | | - <!--/ Benchmarks. --> |
| 237 | + <!--/ Results. --> |
213 | 238 | </div> |
214 | 239 | </section> |
215 | 240 |
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