Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Symbol</td><td class="align_center">Unit</td><td class="align_center">Aircraft 1</td><td class="align_center">Aircraft 2</td><td class="align_center">Aircraft 3</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left"><span style="width: 11.2299ptpx;"><svg height="12.4698pt" id="M224" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 11.2299 12.4698" width="11.2299pt" 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="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.643,3.132)"><path d="M418 650H141L133 618C225 611 232 604 218 531L141 120C126 45 119 37 33 32L24 0H301L308 32C220 37 214 44 227 120L305 531C319 605 325 611 411 618L418 650Z"></path></g></svg></span></td><td class="align_center">m</td><td class="align_center">4176</td><td class="align_center">4170</td><td class="align_center">4194</td></tr><tr><td class="align_left"><span style="width: 10.734ptpx;"><svg height="12.4698pt" id="M225" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 10.734 12.4698" width="10.734pt" 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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"><path d="M418 650H141L133 618C225 611 232 604 218 531L141 120C126 45 119 37 33 32L24 0H301L308 32C220 37 214 44 227 120L305 531C319 605 325 611 411 618L418 650Z"></path></g></svg></span></td><td class="align_center">deg</td><td class="align_center">39.8414</td><td class="align_center">39.8449</td><td class="align_center">39.8458</td></tr><tr><td class="align_left"><span style="width: 12.3521ptpx;"><svg height="12.4698pt" id="M226" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 12.3521 12.4698" width="12.3521pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.132)"><path d="M418 650H141L133 618C225 611 232 604 218 531L141 120C126 45 119 37 33 32L24 0H301L308 32C220 37 214 44 227 120L305 531C319 605 325 611 411 618L418 650Z"></path></g></svg></span></td><td class="align_center">deg</td><td class="align_center">-4.3243</td><td class="align_center">-4.3165</td><td class="align_center">-4.3184</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Positions of the aircraft at conflict region (at time 980 s) without distance constraint for Experiment 2.</div>

International Journal of Aerospace Engineering

tab4

Table 4

Table 4: Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints 