Adaptation Algorithm of Geometric Graphs for Robot Motion Planning in Dynamic Environments

<div>Neighbor node and sensing node. (a) Neighbor node for neighbor radius <svg height="11.4899pt" id="M49" style="vertical-align:-5.52899pt" version="1.1" viewbox="-0.0498162 -5.96091 10.1024 11.4899" width="10.1024pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z" id="g113-115"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="422" vert-adv-y="422"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"><path d="M478 400C478 445 461 451 447 451C425 451 399 442 369 425C316 395 241 339 172 252H170L191 340C198 371 203 395 203 412C203 439 194 451 178 451C147 451 81 411 24 351L43 324C68 349 101 371 111 371C117 371 122 363 115 334L35 -4L42 -11C61 -4 87 3 117 9C130 72 144 130 158 181C241 296 342 379 383 379C398 379 404 370 384 285L330 60C302 -58 282 -164 282 -190S323 -257 354 -257L361 -243C357 -223 359 -177 382 -73L464 303C474 347 478 378 478 400Z" id="g50-229"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="502" vert-adv-y="502"></glyph.data></g></svg>; (b) sensing nodes around node <svg height="9.33029pt" id="M50" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.03918 10.1494 9.33029" width="10.1494pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M534 -230V-198C472 -191 467 -186 467 -127V336C467 404 469 422 470 442L465 446C441 437 423 434 414 434C403 434 396 435 381 440C370 444 350 451 309 454C158 455 29 343 29 201C29 103 99 -12 259 -12L339 22V-126C339 -187 330 -190 260 -198V-230H534ZM339 58C327 52 317 50 303 50C247 50 170 115 170 235C170 358 226 413 271 413C293 413 319 398 339 372V58Z" id="g13-111"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="536" vert-adv-y="536"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.968,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data></g></svg> for sensing radius <svg height="9.25202pt" id="M51" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 8.99722 9.25202" width="8.99722pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z" id="g113-115"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="422" vert-adv-y="422"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,4.901,3.132)"><path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z" id="g50-116"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="381" vert-adv-y="381"></glyph.data></g></svg>.</div>

Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: Adaptation Algorithm of Geometric Graphs for Robot Motion Planning in Dynamic Environments 