Trajectory Design and Tracking Control for Nonlinear Underactuated Wheeled Inverted Pendulum

<div>Simulation results of tracking <svg height="12.5794pt" id="M194" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 27.3633 12.5794" width="27.3633pt" 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="M552 399C552 425 539 454 501 454C451 454 411 416 332 310L314 361C295 415 272 454 241 454C202 454 143 409 83 325L106 298C141 343 161 356 170 356C182 356 194 353 216 283L240 205C186 131 142 82 117 82C108 82 103 85 92 94C86 99 78 104 71 104C47 104 21 82 21 48S46 -12 78 -12C135 -12 174 38 256 161L281 89C306 16 325 -12 364 -12S468 27 529 120L509 149C465 97 443 83 430 83C416 83 404 107 392 140L346 271C370 300 392 326 410 343C430 360 443 367 455 367C465 367 474 363 480 356S492 345 500 345C522 345 552 365 552 399Z" id="g5-121"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.477,3.132)"><path d="M636 22C611 29 589 38 560 74C536 104 518 134 495 173L430 300C518 328 592 392 592 492C592 555 563 594 528 618C491 643 435 650 377 650H140L131 618C222 610 223 601 208 518L137 136C121 43 116 40 27 32L18 0H295L300 32C212 40 206 42 223 138L248 279H296C334 279 350 272 369 230C393 174 413 140 441 94C482 24 523 1 626 -8L636 22ZM497 480C497 422 468 374 417 343C387 324 353 315 304 315H255L298 556C303 583 309 598 319 603C331 610 348 613 367 613C448 613 497 573 497 480Z" id="g50-83"></path></g><g transform="matrix(.013,0,0,-0.013,13.784,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,18.282,0)"><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" id="g113-117"></path></g><g transform="matrix(.013,0,0,-0.013,22.716,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg> when considering parameter uncertainties, external disturbances, and input saturation.</div>

Mathematical Problems in Engineering

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Figure 7

Figure 7: Trajectory Design and Tracking Control for Nonlinear Underactuated Wheeled Inverted Pendulum 