Inverse Dynamics Based Optimal Fuzzy Controller for a Robot Manipulator via Particle Swarm Optimization

<table class="fixed-width table-group" id="tab4"><tr><td><table class="table"><colgroup><col style="width:2.96em"/><col style="width:5.07em"/><col style="width:4.98em"/><col style="width:3.67em"/></colgroup><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left"><span style="width: 22.0084ptpx;"><svg height="9.49471pt" id="M72" style="vertical-align:-0.1933298pt" version="1.1" viewbox="-0.0498162 -9.30138 22.0084 9.49471" width="22.0084pt" 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="M266 661C273 695 269 703 255 703C237 703 167 670 61 664L56 635L93 631C134 627 135 619 124 564L36 129C12 9 33 -12 62 -12C98 -12 180 25 249 96L232 127C203 101 166 81 158 81C152 81 151 93 157 124L266 661Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.849,0)"><path d="M284 605C284 641 263 668 223 668C170 668 145 620 145 593C145 549 171 526 208 526C253 526 284 564 284 605ZM276 102L256 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260 107 281 60C304 9 330 -12 359 -12C391 -12 452 11 509 84L489 114C462 86 440 74 430 74C409 74 384 131 339 235C324 269 315 288 305 307C332 339 376 361 411 361C438 361 457 356 467 351C471 349 476 351 485 359C499 372 513 395 513 415Z"></path></g></svg></span></td><td class="align_center"><b><i>Position</i></b></td><td class="align_center"><b><i>Velocity</i></b></td><td class="align_center"><span style="width: 12.8048ptpx;"><svg height="15.4736pt" id="M73" style="vertical-align:-3.233701pt" version="1.1" viewbox="-0.0498162 -12.2399 12.8048 15.4736" width="12.8048pt" 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="M503 438L486 441C451 449 386 454 374 454C354 454 329 450 304 444C256 432 180 399 146 372C70 311 21 208 21 111C21 38 54 -12 105 -12C143 -12 190 13 228 45C259 71 293 105 333 154H335L281 -113C266 -186 255 -192 208 -204L196 -207L188 -241L466 -230L470 -193L441 -190C403 -186 396 -175 407 -108L465 233C476 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width="6.36303pt" 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></svg></span></td><td class="align_center">30°</td><td class="align_center"><span style="width: 6.62401ptpx;"><svg height="8.48998pt" id="M75" style="vertical-align:-0.2324896pt" version="1.1" viewbox="-0.0498162 -8.25749 6.62401 8.48998" width="6.62401pt" 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="M252 635C85 635 28 460 28 311C28 167 82 -12 250 -12C419 -12 472 166 472 312C472 457 419 635 252 635ZM248 594C314 594 335 455 335 314C335 174 318 29 252 29S165 180 165 315S181 594 248 594Z"></path></g></svg></span></td><td class="align_center"><b>10</b>°</td></tr><tr><td class="align_left"><span style="width: 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<div>The initial conditions of the location and velocity and the desired values (<span class="nowrap"><svg height="15.287pt" id="M71" style="vertical-align:-3.1293pt" version="1.1" viewbox="-0.0498162 -12.1577 12.232 15.287" width="12.232pt" 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="M515 -240V-213C445 -206 438 -202 438 -132V332C438 399 440 418 441 439L437 442C421 434 408 431 402 431C394 430 389 431 375 435C363 440 342 445 306 449C168 450 38 341 38 197C38 101 108 -12 253 -12L359 30V-130C359 -201 353 -207 274 -213V-240H515ZM359 60C340 51 316 44 285 44C211 44 128 109 128 230C128 348 194 408 262 408C294 408 336 392 359 366V60Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.695,-5.741)"><path d="M526 56L493 58C457 61 448 68 448 119V710C411 697 344 682 288 675V646C362 641 367 639 367 573V439C344 448 315 451 300 451C164 451 40 342 40 202C40 61 147 -12 227 -12C239 -12 266 -7 305 16L367 53V-12C427 10 505 21 526 26V56ZM367 88C342 69 306 54 271 54C207 54 133 111 133 229C133 373 219 409 264 409C301 409 342 394 367 359V88Z"></path></g></svg>)</span> of each of the links.</div>

Journal of Robotics

tab4

Table 4

Table 4: Inverse Dynamics Based Optimal Fuzzy Controller for a Robot Manipulator via Particle Swarm Optimization 