Error Modeling in Distance and Rotation for Self-Calibration of Space Robots on Orbit

<div>Schematic of the relative pose error model. The robot moves from the configuration <svg height="11.8957pt" id="M53" style="vertical-align:-3.18152pt" version="1.1" viewbox="-0.0498162 -8.71418 17.0092 11.8957" width="17.0092pt" 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="M388 665C159 665 42 485 42 321C42 132 178 -15 377 -15C566 -15 718 122 718 333C718 528 570 665 388 665ZM371 622C490 622 565 502 565 303C565 116 493 29 397 29C268 29 196 170 196 343C196 515 269 622 371 622ZM494 222V451H459C452 394 446 389 408 389H353C313 390 306 395 299 451H265V222H299C307 279 314 285 352 285H407C446 285 452 279 460 222H494Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.917,3.132)"><path d="M722 32C646 41 636 48 622 116L544 496L509 667L472 658L153 123C106 45 93 42 27 32L18 0H259L268 32C178 40 172 48 204 107L272 233H509C523 180 533 137 540 96C548 50 546 39 466 32L457 0H714L722 32ZM502 283H299L448 547H450L502 283Z"></path></g></svg> to <span class="nowrap"><svg height="11.8957pt" id="M54" style="vertical-align:-3.18152pt" version="1.1" viewbox="-0.0498162 -8.71418 16.0683 11.8957" width="16.0683pt" 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="M388 665C159 665 42 485 42 321C42 132 178 -15 377 -15C566 -15 718 122 718 333C718 528 570 665 388 665ZM371 622C490 622 565 502 565 303C565 116 493 29 397 29C268 29 196 170 196 343C196 515 269 622 371 622ZM494 222V451H459C452 394 446 389 408 389H353C313 390 306 395 299 451H265V222H299C307 279 314 285 352 285H407C446 285 452 279 460 222H494Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.917,3.132)"><path d="M598 511C598 627 497 650 401 650H141L131 618C219 611 222 606 210 538L130 119C117 43 108 39 25 32L18 0H236C324 0 396 5 456 30C531 59 585 119 585 193C585 285 520 331 428 351V353C529 373 598 423 598 511ZM502 508C502 418 431 368 330 368H263L298 559C303 584 308 595 317 600C329 608 345 612 369 612C428 612 502 595 502 508ZM483 197C483 95 404 39 309 39C225 39 206 58 219 139L256 330H317C395 330 483 301 483 197Z"></path></g></svg>,</span> and its nominal end-effector pose changes from the frame <svg height="11.5564pt" id="M55" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 18.3287 11.5564" width="18.3287pt" 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="M293 -169V-141C218 -131 209 -90 209 -44C209 19 222 85 222 152C222 207 198 255 139 269V273C199 286 222 334 222 388C222 454 209 523 209 588C209 632 218 671 293 681V709C234 709 148 695 148 577C147 513 155 438 155 372C155 337 152 291 64 285V256C152 250 155 204 155 169C156 105 148 31 148 -41C148 -157 234 -169 293 -169Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.511,0)"><path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.646,0)"><path d="M283 255V284C195 290 192 337 192 375C192 436 200 508 200 580C200 696 116 709 54 709V681C127 671 139 634 139 588C138 524 125 452 125 387C125 333 149 286 209 272V268C148 253 125 206 125 151C126 87 139 16 139 -47C139 -92 127 -131 54 -141V-169C115 -169 200 -152 200 -41C200 32 192 104 192 164C192 202 195 249 283 255Z"></path></g></svg> to <span class="nowrap"><svg height="11.5564pt" id="M56" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 16.9977 11.5564" width="16.9977pt" 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="M293 -169V-141C218 -131 209 -90 209 -44C209 19 222 85 222 152C222 207 198 255 139 269V273C199 286 222 334 222 388C222 454 209 523 209 588C209 632 218 671 293 681V709C234 709 148 695 148 577C147 513 155 438 155 372C155 337 152 291 64 285V256C152 250 155 204 155 169C156 105 148 31 148 -41C148 -157 234 -169 293 -169Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.511,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.324,0)"><path d="M283 255V284C195 290 192 337 192 375C192 436 200 508 200 580C200 696 116 709 54 709V681C127 671 139 634 139 588C138 524 125 452 125 387C125 333 149 286 209 272V268C148 253 125 206 125 151C126 87 139 16 139 -47C139 -92 127 -131 54 -141V-169C115 -169 200 -152 200 -41C200 32 192 104 192 164C192 202 195 249 283 255Z"></path></g></svg>.</span></div>

International Journal of Aerospace Engineering

fig3

Figure 3

Figure 3: Error Modeling in Distance and Rotation for Self-Calibration of Space Robots on Orbit 