Finite-Time Switched Second-Order Sliding-Mode Control of Nonholonomic Wheeled Mobile Robot Systems

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/1430989/figures/1430989.fig.003a.svgz" name="1430989.fig.003a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Robot circular trajectory in <svg height="10.4342pt" id="M138" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -7.0048 28.4197 10.4342" width="28.4197pt" 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="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 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height="9.49473pt" id="M139" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.59789 9.49473" width="6.59789pt" 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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z" id="g113-230"></path></g></svg> trajectory</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/1430989/figures/1430989.fig.003c.svgz" name="1430989.fig.003c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Control torque <svg height="6.1673pt" id="M140" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 6.40217 6.1673" width="6.40217pt" 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="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z" id="g113-241"></path></g></svg></td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/1430989/figures/1430989.fig.003d.svgz" name="1430989.fig.003d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>Overall trajectory in <svg height="10.1863pt" id="M141" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -7.0048 35.8072 10.1863" width="35.8072pt" xmlns="http://www.w3.org/2000/svg" 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class="fig-caption"><td><b>(e) </b>Zoomed trajectory in <svg height="10.1863pt" id="M142" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -7.0048 35.8072 10.1863" width="35.8072pt" 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="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z" id="g113-123"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g><g transform="matrix(.013,0,0,-0.013,14.001,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path></g><g transform="matrix(.013,0,0,-0.013,24.537,0)"><path d="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z" id="g113-123"></path></g><g transform="matrix(.0091,0,0,-0.0091,30.686,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg> plane</td></tr><tr class="fig-image" id="f"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/1430989/figures/1430989.fig.003f.svgz" name="1430989.fig.003f" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(f) </b>The tracking errors <svg height="9.39034pt" id="M143" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 10.794 9.39034" width="10.794pt" 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="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 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<div>Simulation results of the mobile robot with the proposed controller.</div>

Complexity

fig3

Figure 3

Figure 3: Finite-Time Switched Second-Order Sliding-Mode Control of Nonholonomic Wheeled Mobile Robot Systems 