This paper proposes a fast method for obtaining mathematically optimal trajectories for UAVs while avoiding collisions. A comparison of the proposed method with previously used Mixed Integer Linear Programming (MILP) to find the optimal collision-free path UAVs, aircraft, and spacecraft show the effectiveness and performance of this method. Here, the UAV path planning problem is formulated in the new framework named MILP-Tropical optimization that exploits tropical mathematics for obtaining solution and then casted in a novel branch-and-bound method. Various constraints including UAV dynamics are incorporated in the proposed Tropical framework and a solution methodology is presented. An extensive numerical study shows that the proposed method provides faster solution. The proposed technique can be extended to distributed control for multiple vehicles and multiple way-points.

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