Smooth Path Planning for Robot Docking in Unknown Environment with Obstacles

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/4359036/figures/4359036.fig.006a.svgz" name="4359036.fig.006a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Initial environment (<span class="nowrap"><svg height="8.555213pt" id="M314" style="vertical-align:-0.2063942pt" version="1.1" viewbox="-0.049816 -8.348819 46.131146 8.555213" width="46.131146pt" 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="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.081,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.373,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.636,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.611,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,34.875,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,41.138,0)"><path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z"></path></g></svg>)</span></td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/4359036/figures/4359036.fig.006b.svgz" name="4359036.fig.006b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Path replanning to avoid <svg height="11.81741pt" id="M315" style="vertical-align:-3.181505pt" version="1.1" viewbox="-0.049816 -8.635905 14.141048 11.81741" width="14.141048pt" 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="M699 369C699 549 575 666 407 666C186 666 23 488 23 278C23 101 145 -16 312 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22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,41.138,0)"><path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z"></path></g></svg>)</span></td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/4359036/figures/4359036.fig.006c.svgz" name="4359036.fig.006c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Path replanning for docking (<span class="nowrap"><svg height="8.555213pt" id="M317" style="vertical-align:-0.2063942pt" version="1.1" viewbox="-0.049816 -8.348819 46.131146 8.555213" 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38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z"></path></g></svg>)</span></td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/4359036/figures/4359036.fig.006d.svgz" name="4359036.fig.006d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>Path replanning for docking (<span class="nowrap"><svg height="8.555213pt" id="M318" style="vertical-align:-0.2063942pt" version="1.1" viewbox="-0.049816 -8.348819 52.394539 8.555213" width="52.394539pt" 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="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 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class="fig-caption"><td><b>(e) </b>Path replanning for docking (<span class="nowrap"><svg height="8.555213pt" id="M319" style="vertical-align:-0.2063942pt" version="1.1" viewbox="-0.049816 -8.348819 52.394539 8.555213" width="52.394539pt" 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="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.081,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.373,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.636,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 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602Z"></path></g><g transform="matrix(.013,0,0,-0.013,47.402,0)"><path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z"></path></g></svg>)</span></td></tr><tr class="fig-image" id="f"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/4359036/figures/4359036.fig.006f.svgz" name="4359036.fig.006f" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(f) </b>Docking successfully (<span class="nowrap"><svg height="8.555213pt" id="M320" style="vertical-align:-0.2063942pt" version="1.1" viewbox="-0.049816 -8.348819 52.394539 8.555213" width="52.394539pt" xmlns="http://www.w3.org/2000/svg" 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<div>Simulation results of the smooth path planning approach in unknown environment with both static and moving obstacles.</div>

Complexity

fig6

Figure 6

Figure 6: Smooth Path Planning for Robot Docking in Unknown Environment with Obstacles 