Cooperative Path Planning MILP Encoding: Constraints Min JT Receding Horizon Fuel Cost Fn S;≤Wj,etc State Space Constraints S: +I= As+ Bu State Evolution equation X1≤Xmin+My1 my yi< ymin Myi3 Obstacle Avoidance <-ymax My 14 Σyk≤3 At least one enabled Similar constraints for Collision avoidance (for all pairs of vehicles) Encoding Exclusion Constraints Kout ofn constraints hold. At most k ofn hold: f1(x1,x2,…xn)≤d1OR f(x1,x2,…,xn)≤dN where f, are linear expressions LP Encoding Introduce y; to deselect each constraint Constrain K of y; to select constraints ∑y1=N-K ∑y≤N-K Use Big M to turn- off constraint f(x1,--,xn)≤d1+My1 f(x1,--,xn)≤dx+MyNCooperative Path Planning MILP Encoding: Constraints • Min JT Receding Horizon Fuel Cost Fn • sij wij, etc. State Space Constraints • si +1 = Asi + Bui State Evolution Equation • xi xmin + Myi1 -xi -xmax + Myi2 yi ymin + Myi3 Obstacle Avoidance -yi -ymax + Myi4 6 yik 3 At least one enabled • Similar constraints for Collision Avoidance (for all pairs of vehicles) • K out of N constraints hold: f1(x1, x2 ,…xn) < d1 OR : fN(x1, x2 , …, xn ) < dN where fi are linear expressions • LP Encoding: • Introduce yi to deselect each constraint: • Constrain K of yi to select constraints: • Use Big M to turn-off constraint: f1(x1, ---, xn ) < d1 + My1 : fN(x1, ---, xn ) < dN + MyN Encoding Exclusion Constraints ¦ d  N i yi N K 1 • At most K of N hold: ¦  N i yi N K 1