Adaptive Backstepping Sliding Mode Control of Trajectory Tracking for Robotic Manipulators

<div>Trajectory tracking of two-link robotic manipulator. (a) <svg height="11.5773pt" id="M197" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.5275 11.3095 11.5773" width="11.3095pt" 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="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(.0091,0,0,-0.0091,6.24,-5.741)"><path d="M457 455H370L403 612H360L326 455H218L252 612H210L175 455H77L68 394H161L132 257H31L20 196H117L77 19H120L159 196H268L230 19H272L311 196H402L412 257H325L355 394H447L457 455ZM313 394L283 257H175L204 394H313Z"></path></g></svg>link with <span class="nowrap"><svg height="9.39034pt" id="M198" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 11.3878 9.39034" width="11.3878pt" 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 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.318,3.132)"><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"></path></g></svg>.</span> (b) <svg height="11.5773pt" id="M199" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.5275 11.3095 11.5773" width="11.3095pt" 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="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.24,-5.741)"><path d="M457 455H370L403 612H360L326 455H218L252 612H210L175 455H77L68 394H161L132 257H31L20 196H117L77 19H120L159 196H268L230 19H272L311 196H402L412 257H325L355 394H447L457 455ZM313 394L283 257H175L204 394H313Z"></path></g></svg>link with <span class="nowrap"><svg height="9.39034pt" id="M200" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 11.3878 9.39034" width="11.3878pt" 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 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.318,3.132)"><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"></path></g></svg>.</span></div>

Complexity

fig5

Figure 5

Figure 5: Adaptive Backstepping Sliding Mode Control of Trajectory Tracking for Robotic Manipulators 