Pose and Shape Reconstruction of a Noncooperative Spacecraft Using Camera and Range Measurements

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/ijae/volume-2017/4535316/figures/4535316.fig.008a.svgz" name="4535316.fig.008a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b><svg height="10.7187pt" id="M184" style="vertical-align:-4.679521pt" version="1.1" viewbox="-0.0498162 -6.03918 23.2477 10.7187" width="23.2477pt" 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="M534 -230V-198C472 -191 467 -186 467 -127V336C467 404 469 422 470 442L465 446C441 437 423 434 414 434C403 434 396 435 381 440C370 444 350 451 309 454C158 455 29 343 29 201C29 103 99 -12 259 -12L339 22V-126C339 -187 330 -190 260 -198V-230H534ZM339 58C327 52 317 50 303 50C247 50 170 115 170 235C170 358 226 413 271 413C293 413 319 398 339 372V58Z" id="g13-111"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.968,3.132)"><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" id="g50-67"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.501,3.132)"><path d="M381 704H317L48 -163H112L381 704Z" id="g50-48"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.408,3.132)"><path d="M690 629C653 643 577 667 483 667C225 667 24 528 24 292C24 92 174 -17 367 -17C448 -17 534 1 570 10C592 34 642 131 658 174C648 180 639 186 629 192C562 89 499 21 382 21C223 21 130 138 130 298C130 467 255 627 462 627C582 627 643 589 650 462L686 466C689 517 688 580 690 629Z" id="g50-68"></path></g></svg> error</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/ijae/volume-2017/4535316/figures/4535316.fig.008b.svgz" name="4535316.fig.008b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b><svg height="10.7448pt" id="M185" style="vertical-align:-4.6795pt" version="1.1" viewbox="-0.0498162 -6.0653 24.8657 10.7448" width="24.8657pt" 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="M639 301C639 404 592 454 551 454C530 454 509 447 504 443L496 426C521 401 554 359 554 260C554 144 510 62 444 62C415 62 400 94 400 134C400 187 435 310 447 350L442 358L315 348C309 297 296 229 284 179C266 106 243 73 207 73C177 73 153 99 153 164C153 282 201 370 272 429L255 460C123 402 21 296 21 152C21 51 69 -12 136 -12C200 -12 253 33 291 90C300 20 331 -12 388 -12C423 -12 460 4 500 31C582 86 639 198 639 301Z" id="g5-246"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.612,3.132)"><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" id="g50-67"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.145,3.132)"><path d="M381 704H317L48 -163H112L381 704Z" id="g50-48"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.053,3.132)"><path d="M690 629C653 643 577 667 483 667C225 667 24 528 24 292C24 92 174 -17 367 -17C448 -17 534 1 570 10C592 34 642 131 658 174C648 180 639 186 629 192C562 89 499 21 382 21C223 21 130 138 130 298C130 467 255 627 462 627C582 627 643 589 650 462L686 466C689 517 688 580 690 629Z" id="g50-68"></path></g></svg> error</td></tr></table>

<div>(a) Quaternions estimation errors in components: <svg height="14.007pt" id="M182" style="vertical-align:-4.67952pt" version="1.1" viewbox="-0.0498162 -9.32748 59.8663 14.007" width="59.8663pt" 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="M534 -230V-198C472 -191 467 -186 467 -127V336C467 404 469 422 470 442L465 446C441 437 423 434 414 434C403 434 396 435 381 440C370 444 350 451 309 454C158 455 29 343 29 201C29 103 99 -12 259 -12L339 22V-126C339 -187 330 -190 260 -198V-230H534ZM339 58C327 52 317 50 303 50C247 50 170 115 170 235C170 358 226 413 271 413C293 413 319 398 339 372V58Z" id="g13-111"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.968,3.132)"><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" id="g50-67"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.501,3.132)"><path d="M381 704H317L48 -163H112L381 704Z" id="g50-48"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.408,3.132)"><path d="M690 629C653 643 577 667 483 667C225 667 24 528 24 292C24 92 174 -17 367 -17C448 -17 534 1 570 10C592 34 642 131 658 174C648 180 639 186 629 192C562 89 499 21 382 21C223 21 130 138 130 298C130 467 255 627 462 627C582 627 643 589 650 462L686 466C689 517 688 580 690 629Z" id="g50-68"></path></g><g transform="matrix(.013,0,0,-0.013,26.027,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path></g><g transform="matrix(.013,0,0,-0.013,36.994,-.3)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z" id="g119-17"></path></g><g transform="matrix(.013,0,0,-0.013,36.564,0)"><path d="M534 -230V-198C472 -191 467 -186 467 -127V336C467 404 469 422 470 442L465 446C441 437 423 434 414 434C403 434 396 435 381 440C370 444 350 451 309 454C158 455 29 343 29 201C29 103 99 -12 259 -12L339 22V-126C339 -187 330 -190 260 -198V-230H534ZM339 58C327 52 317 50 303 50C247 50 170 115 170 235C170 358 226 413 271 413C293 413 319 398 339 372V58Z" id="g13-111"></path></g><g transform="matrix(.0091,0,0,-0.0091,43.532,3.132)"><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" id="g50-67"></path></g><g transform="matrix(.0091,0,0,-0.0091,49.065,3.132)"><path d="M381 704H317L48 -163H112L381 704Z" id="g50-48"></path></g><g transform="matrix(.0091,0,0,-0.0091,52.972,3.132)"><path d="M690 629C653 643 577 667 483 667C225 667 24 528 24 292C24 92 174 -17 367 -17C448 -17 534 1 570 10C592 34 642 131 658 174C648 180 639 186 629 192C562 89 499 21 382 21C223 21 130 138 130 298C130 467 255 627 462 627C582 627 643 589 650 462L686 466C689 517 688 580 690 629Z" id="g50-68"></path></g></svg>. (b) Target’s angular velocity estimation error in components: <svg height="17.4897pt" id="M183" style="vertical-align:-5.331901pt" version="1.1" viewbox="-0.0498162 -12.1578 77.6621 17.4897" width="77.6621pt" 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="M639 301C639 404 592 454 551 454C530 454 509 447 504 443L496 426C521 401 554 359 554 260C554 144 510 62 444 62C415 62 400 94 400 134C400 187 435 310 447 350L442 358L315 348C309 297 296 229 284 179C266 106 243 73 207 73C177 73 153 99 153 164C153 282 201 370 272 429L255 460C123 402 21 296 21 152C21 51 69 -12 136 -12C200 -12 253 33 291 90C300 20 331 -12 388 -12C423 -12 460 4 500 31C582 86 639 198 639 301Z" id="g5-246"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.612,-5.741)"><path d="M384 354C435 370 515 408 515 502C515 549 494 593 459 616C426 639 384 650 308 650H45V618C127 613 130 606 130 524V127C130 45 125 38 37 33V0H262C342 0 409 12 461 40C521 73 558 124 558 192C558 295 481 336 384 352V354ZM217 365V556C217 587 221 597 229 604C238 611 261 615 288 615C382 615 421 558 421 490C421 406 374 365 266 365H217ZM217 327H264C384 327 457 284 457 183C457 80 383 38 301 38C235 38 217 55 217 127V327Z" id="g58-64"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.026,-5.741)"><path d="M43 650V617C122 612 130 606 130 522V128C130 44 122 37 34 32V0H275C400 0 497 25 573 82C652 142 698 229 698 350C698 445 662 518 613 565C549 625 456 650 327 650H43ZM217 544C217 580 220 591 229 599C240 607 264 613 311 613C380 613 437 599 482 570C561 523 598 436 598 336C598 177 511 40 324 40C248 40 217 61 217 135V544Z" id="g58-66"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.733,-5.741)"><path d="M639 21C616 28 593 39 566 68C542 92 523 117 486 170C457 215 415 282 397 314C472 346 524 398 524 485C524 545 497 590 456 617C417 641 369 650 296 650H43V617C122 612 130 608 130 523V129C130 45 122 38 38 33V0H306V33C225 38 216 45 216 129V282H249C302 282 319 270 336 243C365 195 401 132 436 84C483 18 525 -5 597 -8C610 -9 622 -9 635 -9L639 21ZM216 319V559C216 586 219 596 227 603S250 613 281 613C356 613 429 576 429 469C429 416 413 379 374 348C349 327 316 319 265 319H216Z" id="g58-80"></path></g><g transform="matrix(.0091,0,0,-0.0091,26.548,-5.741)"><path d="M502 500C497 551 492 613 491 650H43V617C122 612 130 606 130 521V129C130 45 122 38 41 33V0H319V33C227 38 217 45 217 129V305H319C411 305 413 295 427 225H461V421H427C414 357 411 348 319 348H217V580C217 609 219 612 250 612H330C401 612 423 605 439 578C452 557 458 539 467 496L502 500Z" id="g58-68"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.612,3.784)"><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" id="g50-67"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.145,3.784)"><path d="M381 704H317L48 -163H112L381 704Z" id="g50-48"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.053,3.784)"><path d="M615 650H141L132 618C223 612 227 607 212 526L136 123C122 42 112 38 27 32L18 0H522C539 33 580 135 592 166L558 179C536 139 512 100 486 75C454 48 420 41 345 41C287 41 252 42 237 55C221 68 220 100 231 158L261 316H357C455 316 455 309 455 235H489L529 437H494C468 366 460 360 369 360H269L305 565C315 609 316 611 357 611H450C525 611 535 599 548 578C559 556 561 526 560 482L595 486L615 650Z" id="g50-70"></path></g><g transform="matrix(.013,0,0,-0.013,34.951,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path></g><g transform="matrix(.013,0,0,-0.013,45.501,-.326)"><path d="M658 557C549 593 437 629 340 673H318C222 629 109 593 0 557L9 532C116 551 225 577 329 602C435 576 543 551 649 532L658 557Z" id="g119-105"></path></g><g transform="matrix(.013,0,0,-0.013,45.488,0)"><path d="M639 301C639 404 592 454 551 454C530 454 509 447 504 443L496 426C521 401 554 359 554 260C554 144 510 62 444 62C415 62 400 94 400 134C400 187 435 310 447 350L442 358L315 348C309 297 296 229 284 179C266 106 243 73 207 73C177 73 153 99 153 164C153 282 201 370 272 429L255 460C123 402 21 296 21 152C21 51 69 -12 136 -12C200 -12 253 33 291 90C300 20 331 -12 388 -12C423 -12 460 4 500 31C582 86 639 198 639 301Z" id="g5-246"></path></g><g transform="matrix(.0091,0,0,-0.0091,54.1,-6.061)"><path d="M384 354C435 370 515 408 515 502C515 549 494 593 459 616C426 639 384 650 308 650H45V618C127 613 130 606 130 524V127C130 45 125 38 37 33V0H262C342 0 409 12 461 40C521 73 558 124 558 192C558 295 481 336 384 352V354ZM217 365V556C217 587 221 597 229 604C238 611 261 615 288 615C382 615 421 558 421 490C421 406 374 365 266 365H217ZM217 327H264C384 327 457 284 457 183C457 80 383 38 301 38C235 38 217 55 217 127V327Z" id="g58-64"></path></g><g transform="matrix(.0091,0,0,-0.0091,59.514,-6.061)"><path d="M43 650V617C122 612 130 606 130 522V128C130 44 122 37 34 32V0H275C400 0 497 25 573 82C652 142 698 229 698 350C698 445 662 518 613 565C549 625 456 650 327 650H43ZM217 544C217 580 220 591 229 599C240 607 264 613 311 613C380 613 437 599 482 570C561 523 598 436 598 336C598 177 511 40 324 40C248 40 217 61 217 135V544Z" id="g58-66"></path></g><g transform="matrix(.0091,0,0,-0.0091,66.221,-6.061)"><path d="M639 21C616 28 593 39 566 68C542 92 523 117 486 170C457 215 415 282 397 314C472 346 524 398 524 485C524 545 497 590 456 617C417 641 369 650 296 650H43V617C122 612 130 608 130 523V129C130 45 122 38 38 33V0H306V33C225 38 216 45 216 129V282H249C302 282 319 270 336 243C365 195 401 132 436 84C483 18 525 -5 597 -8C610 -9 622 -9 635 -9L639 21ZM216 319V559C216 586 219 596 227 603S250 613 281 613C356 613 429 576 429 469C429 416 413 379 374 348C349 327 316 319 265 319H216Z" id="g58-80"></path></g><g transform="matrix(.0091,0,0,-0.0091,72.036,-6.061)"><path d="M502 500C497 551 492 613 491 650H43V617C122 612 130 606 130 521V129C130 45 122 38 41 33V0H319V33C227 38 217 45 217 129V305H319C411 305 413 295 427 225H461V421H427C414 357 411 348 319 348H217V580C217 609 219 612 250 612H330C401 612 423 605 439 578C452 557 458 539 467 496L502 500Z" id="g58-68"></path></g><g transform="matrix(.0091,0,0,-0.0091,54.1,3.784)"><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" id="g50-67"></path></g><g transform="matrix(.0091,0,0,-0.0091,59.633,3.784)"><path d="M381 704H317L48 -163H112L381 704Z" id="g50-48"></path></g><g transform="matrix(.0091,0,0,-0.0091,63.54,3.784)"><path d="M615 650H141L132 618C223 612 227 607 212 526L136 123C122 42 112 38 27 32L18 0H522C539 33 580 135 592 166L558 179C536 139 512 100 486 75C454 48 420 41 345 41C287 41 252 42 237 55C221 68 220 100 231 158L261 316H357C455 316 455 309 455 235H489L529 437H494C468 366 460 360 369 360H269L305 565C315 609 316 611 357 611H450C525 611 535 599 548 578C559 556 561 526 560 482L595 486L615 650Z" id="g50-70"></path></g></svg> (deg/s).</div>

International Journal of Aerospace Engineering

fig8

Figure 8

Figure 8: Pose and Shape Reconstruction of a Noncooperative Spacecraft Using Camera and Range Measurements 