End-Effector Trajectory Tracking Control of Space Robot with <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.199599pt" id="M1" height="16.0985pt" version="1.1" viewBox="-0.0657574 -11.8989 22.9551 16.0985" width="22.9551pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g198-13" d="M608 643C551 682 486 687 443 687C299 687 188 608 188 504C188 361 341 312 465 312C483 312 501 313 518 315C454 195 366 93 314 59C255 82 201 109 141 109C73 109 33 83 33 52C33 13 76 -9 159 -9C218 -9 267 -1 314 15C354 0 402 -15 478 -15C575 -15 671 36 759 141L740 155C657 63 571 16 475 16C448 16 411 26 372 39C458 74 565 199 627 333C806 381 931 499 931 587C931 634 908 669 848 669C767 669 671 582 620 506C591 462 569 411 534 347C503 343 490 342 471 342C330 342 229 399 229 500C229 603 346 657 451 657C486 657 540 657 596 624L608 643ZM890 588C890 519 822 457 747 414C712 395 678 378 643 369C683 484 760 632 841 632C873 632 890 615 890 588ZM266 35C235 24 200 21 161 21C103 21 74 32 74 54C74 75 122 79 141 79C172 79 209 69 266 36V35Z"/><glyph.data ascent="687" descent="-226" horiz-adv-x="946" vert-adv-y="946"/></g><g transform="matrix(.012,0,0,-0.012,16.233,4.134)"><path id="g50-51" 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"/><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"/></g></svg> Gain Performance

<div>The estimate of the optimal weight matrix (<svg height="15.3197pt" id="M214" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -12.0286 54.3199 15.3197" width="54.3199pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.868,-3.001)"><path d="M846 558C704 595 559 633 434 679H412C288 633 141 595 0 558L8 532L423 607L838 532L846 558Z" id="g119-106"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="846" vert-adv-y="846"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z" id="g13-85"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="979" vert-adv-y="979"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.727,3.132)"><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><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,21.353,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,32.616,0)"><path d="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z" id="g13-85"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="979" vert-adv-y="979"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,45.343,3.132)"><path d="M398 365C398 411 356 451 297 451C250 451 198 430 151 397C65 336 24 230 24 139C24 14 97 -12 148 -12C198 -12 284 7 373 104L355 130C306 84 246 53 198 53C132 53 111 109 111 163V189C209 211 398 261 398 365ZM317 351C317 308 273 262 117 225C134 338 189 383 221 399C230 404 249 407 263 407C295 407 317 389 317 351Z" id="g50-102"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="422" vert-adv-y="422"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,49.183,3.132)"><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><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> and <svg height="15.3197pt" id="M215" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -12.0286 54.3199 15.3197" width="54.3199pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.868,-3.001)"><path d="M846 558C704 595 559 633 434 679H412C288 633 141 595 0 558L8 532L423 607L838 532L846 558Z" id="g119-106"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="846" vert-adv-y="846"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z" id="g13-85"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="979" vert-adv-y="979"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.727,3.132)"><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><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,21.353,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,32.616,0)"><path d="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z" id="g13-85"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="979" vert-adv-y="979"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,45.343,3.132)"><path d="M398 365C398 411 356 451 297 451C250 451 198 430 151 397C65 336 24 230 24 139C24 14 97 -12 148 -12C198 -12 284 7 373 104L355 130C306 84 246 53 198 53C132 53 111 109 111 163V189C209 211 398 261 398 365ZM317 351C317 308 273 262 117 225C134 338 189 383 221 399C230 404 249 407 263 407C295 407 317 389 317 351Z" id="g50-102"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="422" vert-adv-y="422"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,49.183,3.132)"><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><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>) in the absence of external disturbances.</div>

Mathematical Problems in Engineering

fig12

Figure 12

Figure 12: End-Effector Trajectory Tracking Control of Space Robot with <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.199599pt" id="M1" height="16.0985pt" version="1.1" viewBox="-0.0657574 -11.8989 22.9551 16.0985" width="22.9551pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g198-13" d="M608 643C551 682 486 687 443 687C299 687 188 608 188 504C188 361 341 312 465 312C483 312 501 313 518 315C454 195 366 93 314 59C255 82 201 109 141 109C73 109 33 83 33 52C33 13 76 -9 159 -9C218 -9 267 -1 314 15C354 0 402 -15 478 -15C575 -15 671 36 759 141L740 155C657 63 571 16 475 16C448 16 411 26 372 39C458 74 565 199 627 333C806 381 931 499 931 587C931 634 908 669 848 669C767 669 671 582 620 506C591 462 569 411 534 347C503 343 490 342 471 342C330 342 229 399 229 500C229 603 346 657 451 657C486 657 540 657 596 624L608 643ZM890 588C890 519 822 457 747 414C712 395 678 378 643 369C683 484 760 632 841 632C873 632 890 615 890 588ZM266 35C235 24 200 21 161 21C103 21 74 32 74 54C74 75 122 79 141 79C172 79 209 69 266 36V35Z"/><glyph.data ascent="687" descent="-226" horiz-adv-x="946" vert-adv-y="946"/></g><g transform="matrix(.012,0,0,-0.012,16.233,4.134)"><path id="g50-51" 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"/><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"/></g></svg> Gain Performance 

Mathematical Problems in Engineering

End-Effector Trajectory Tracking Control of Space Robot with Gain Performance

Figure 12