Trajectory planning for multi UMVs with reciprocal constraints

In this paper, a special class of trajectory optimization problems is formulized and solved. It involves the optimization of different Unmanned Vehicle (UMV) trajectories, which are coupled through reciprocal constraints. It is shown in the paper that searching for a solution to the problem at hand may stipulate not just planning a longer than the shortest possible path for each UMV, but also choosing slower travel speeds in order to coordinate between the UMVs. Although it seems that solving the problem possesses merits, it has been only partially treated before. Here we suggest solving it by utilizing an evolutionary approach which involves a new algorithmic feature that allows striving towards the desired optimality. The approach is demonstrated and studied through solving and simulating several trajectory planning problems. It is shown that a wide range of problems might be related to that class of problems.