Iterative Learning Control with Desired Gravity Compensation under Saturation for a Robotic Machining Manipulator

<div>Applied force for joint <svg height="9.39034pt" id="M328" 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" id="g113-114"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="491" vert-adv-y="491"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.318,3.132)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> using the <svg height="12.5416pt" id="M329" style="vertical-align:-3.25327pt" version="1.1" viewbox="-0.0498162 -9.28833 61.3504 12.5416" width="61.3504pt" 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="M338 322C336 342 324 413 314 436C291 446 264 454 218 454C113 453 50 390 50 312C50 226 131 187 178 164C239 135 253 110 253 81C253 51 231 27 199 27C138 27 91 96 69 159L40 156C40 108 49 38 55 22C76 7 128 -12 181 -12C265 -12 360 37 360 136C360 214 306 249 225 284C174 307 151 330 151 361C151 393 176 415 202 415C249 415 281 374 308 313L338 322Z" id="g13-113"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="383" vert-adv-y="383"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,5.031,0)"><path d="M465 45L455 77C444 72 433 69 421 69C404 69 389 81 389 128V293C389 349 380 392 337 425C310 445 280 454 239 454C182 443 111 409 73 383C51 366 38 353 38 335C38 309 74 285 101 285C121 285 136 293 143 319C151 350 160 374 171 388C180 400 191 406 205 406C241 406 265 371 265 308V278C242 258 165 234 106 212C54 192 30 168 30 116C30 54 81 -12 165 -12C185 -12 232 21 270 46C274 34 281 21 295 9C308 -3 329 -12 356 -12L465 45ZM265 79C249 67 238 63 223 63C200 63 163 84 163 139C163 174 179 192 210 208C231 219 247 229 265 239V79Z" id="g13-95"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="466" vert-adv-y="466"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,10.894,0)"><path d="M329 37L319 72C301 64 285 60 268 60C248 60 212 69 212 147V394H304C320 402 321 431 310 442H212V586L198 593L84 515V442H44L16 406L21 394H84V114C84 24 130 -12 207 -12C214 -12 230 -8 247 -1L329 37Z" id="g13-114"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="339" vert-adv-y="339"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,15.3,0)"><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><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,19.798,0)"><path d="M42 650V615C112 608 121 601 121 516V133C121 48 112 41 37 34V0H347V34C262 41 253 48 253 133V271L321 254C332 254 347 254 362 256C468 269 567 330 567 464C567 529 540 579 493 611C453 639 397 650 318 650H42ZM253 570C253 585 255 595 262 601C268 606 280 611 299 611C360 611 423 574 423 461C423 326 343 300 307 300C286 300 265 305 253 310V570Z" id="g13-78"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="599" vert-adv-y="599"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,27.52,0)"><path d="M41 650V615C111 608 121 602 121 516V134C121 48 111 42 32 35V0H289C413 0 518 27 592 83C668 141 717 229 717 351C717 446 678 517 628 564C564 625 467 650 341 650H41ZM255 540C255 569 257 586 265 595C272 602 292 609 328 609C397 609 450 589 491 547C537 502 566 426 566 331C566 152 474 43 340 43C270 43 255 68 255 140V540Z" id="g13-66"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="761" vert-adv-y="761"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,37.452,0)"><path d="M541 58L519 60C477 65 472 69 472 126V703C421 688 341 674 277 667V636C338 628 344 624 344 570V449C322 452 311 454 303 454C147 454 29 343 29 207C29 58 147 -12 233 -12C244 -12 259 -9 283 6L344 45V-13C423 10 517 22 541 26V58ZM344 80C322 66 307 64 289 64C243 64 171 111 171 234C171 386 248 412 271 412C301 412 328 395 344 360V80Z" id="g13-98"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="547" vert-adv-y="547"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,44.563,0)"><path d="M494 439C454 435 401 429 349 428C312 446 283 454 242 454H241C152 454 48 402 48 290C48 228 85 177 146 157C127 139 95 112 44 91C43 77 48 53 58 37C73 16 92 -3 133 -18C108 -34 82 -48 58 -68C38 -84 27 -100 27 -123C27 -178 85 -244 214 -244C347 -244 481 -153 481 -39C481 66 390 84 327 84C295 84 267 82 235 82C187 81 170 103 170 120C170 131 177 140 184 148C199 146 216 143 234 143C332 143 424 195 424 299C424 333 413 356 398 376L455 371C474 382 492 414 498 432L494 439ZM235 417C284 417 305 359 305 294C305 220 284 180 245 180C198 180 176 236 176 306C176 379 205 417 235 417ZM242 -21C280 -21 302 -23 329 -29C361 -38 385 -59 385 -95C385 -148 340 -189 264 -189C185 -189 135 -141 135 -92C135 -72 144 -57 158 -42C172 -26 194 -21 242 -21Z" id="g13-101"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="492" vert-adv-y="492"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,51.038,0)"><path d="M399 120C363 89 334 79 292 79S154 123 154 256C154 363 199 401 238 401C266 401 298 385 339 349C348 341 354 338 361 338C378 338 404 364 404 393C405 407 401 419 386 429C369 443 336 454 300 454H299C261 454 196 440 130 392C67 345 29 274 29 201C29 92 109 -12 246 -12C307 -12 372 31 418 96L399 120Z" id="g13-97"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="422" vert-adv-y="422"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,56.524,0)"><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><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg> control scheme.</div>

Mathematical Problems in Engineering

fig23

Figure 23

Figure 23: Iterative Learning Control with Desired Gravity Compensation under Saturation for a Robotic Machining Manipulator 