Scheduling safe movement of air traffic in crowded air spaces

„his p—per ™onsiders the pro˜lem of gener—ting ™oni™tEfree movement s™hedules for — set of vehi™les th—t —re oper—ting simult—neously in — ™ommon —irsp—™eF sn ˜oth ™ivili—n —ir tr—™ m—n—gement —nd milit—ry —ir ™—mp—ign pl—nning ™ontextsD it is ™ru™i—l th—t the movements of dierent vehi™les ˜e ™oordin—ted so —s to —void ™ollisions —nd ne—r missesF yur —ppro—™h st—rts from — view of —irsp—™e m—n—gement —s — fourEdimension—l resour™e —llo™—tion pro˜lemD where the sp—™e in whi™h vehi™les must m—neuver is itself m—n—ged —s — ™—p—™it—ted resour™eF ‡e introdu™e — line—r o™tree represent—tion of —irsp—™e ™—p—™ity to index ve™torE˜—sed vehi™le routes —nd e™iently dete™t regions of potenti—l ™oni™tF qener—lizing the notion of ™ontentionE˜—sed se—r™h heuristi™sD we next dene — s™heduling —lgorithm th—t pro™eeds ˜y rst solving — rel—xed version of the pro˜lem to ™onstru™t — sp—ti—l ™—p—™ity prole @represented —s —n o™treeAD —nd then using sp—tioEtempor—l regions where dem—nd ex™eeds ™—p—™ity to m—ke ™oni™tE—voiding vehi™le routing —nd s™heduling de™isionsF ‡e illustr—te the utility of this ˜—si™ represent—tion —nd se—r™h —lgorithm in two w—ysF pirstD to demonstr—te the over—ll vi—˜ility of the —ppro—™hD we present experiment—l results using d—t— representing — re—listi™—lly sized —ir ™—mp—ign pl—nning dom—inF ƒe™ondD we dene — more —˜str—™t notion of ’en™ounter set4D whi™h toler—tes some —mount of ™oni™t on the —ssumption th—t onE ˜o—rd de™oni™tion pro™esses ™—n t—ke —ppropri—te —void—n™e m—neuvers —t exe™ution timeD —nd show th—t gener—tion of this more —˜str—™t form of predi™tive guid—n™e ™—n ˜e o˜t—ined without loss in ™omput—tion—l e™ien™yF