Shorter Path Design and Control for an Underactuated Satellite

<div>The minimum number of maneuvers given arbitrary target attitudes (<svg height="14.2262pt" id="M149" style="vertical-align:-3.429501pt" version="1.1" viewbox="-0.0498162 -10.7967 40.0984 14.2262" width="40.0984pt" 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="M642 419L635 448C586 435 552 411 532 392C518 379 509 351 496 304C484 260 462 196 445 150C424 93 388 40 314 30L413 508L406 510L344 491L257 36C205 46 175 84 175 169C175 195 180 241 185 277C189 304 190 331 190 358C190 413 175 448 141 448C111 448 69 429 23 373L30 347C51 365 68 375 81 375C93 375 108 368 108 327C108 307 104 268 101 239C98 211 95 180 95 155C95 33 159 -8 248 -14L213 -186C206 -220 221 -254 230 -261L261 -230L306 -11C339 -4 366 6 389 20C431 46 473 87 503 155C533 224 557 286 571 325C586 367 606 393 642 419Z" id="g113-245"></path></g><g transform="matrix(.013,0,0,-0.013,12.136,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,23.399,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path></g><g transform="matrix(.013,0,0,-0.013,29.639,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.0091,0,0,-0.0091,35.926,-5.741)"><path d="M339 262C339 340 273 403 193 403S48 340 48 262S113 121 193 121S339 184 339 262ZM283 262C283 210 242 168 193 168S104 210 104 262S144 356 193 356S283 314 283 262Z" id="g54-73"></path></g></svg>).</div>

International Journal of Aerospace Engineering

Shorter Path Design and Control for an Underactuated Satellite

Figure 6