Rolling-horizon trajectory planning for multiple UAVs based on pseudospectral collocation

This paper proposes a method based on a Legendre pseudospectral collocation to generate trajectories in scenarios with multiple aerial vehicles in order to avoid collisions. The method uses a rolling horizon policy in which collision-free trajectories are planned up to a given time horizon, thus considering a much smaller problem space. Then, the system is applied iteratively. Using this approach, the multi-UAV trajectory generation problem can be solved exactly to yield an optimal solution to the sub-problem given by the considered time horizon. The proposed method allows for both changes of speed and heading for each aerial vehicle to guarantee that the safety distance between them is always maintained. Many simulations have been performed to compute the better values for the relevant parameters of the method (i.e. look-ahead time and the number of collocations points). The number of collocation points affects significantly the computation time, so a tradeoff between feasibility and optimality should be reached. The computational load and scalability of the method are also studied in randomly generated scenarios to test its application in real time. Experiments to test the validity of the approach have been also carried out in the multivehicle aerial testbed of the Center for Advanced Aerospace Technologies (Seville, Spain).