Flatness-based Finite-Horizon Multi-UAV Formation Trajectory Planning and Directionally Aware Collision Avoidance Tracking

Abstract: Collision-free optimal formation control of unmanned aerial vehicle (UAV) teams is challenging. The state-of-the-art optimal control approaches often rely on numerical methods sensitive to initial guesses. This paper presents an innovative collision-free finite-time formation control scheme for multiple UAVs leveraging the differential flatness of the UAV dynamics, eliminating the need for numerical methods. We formulate a finite-time optimal control problem to plan a formation trajectory for feasible initial states. This formation trajectory planning optimal control problem involves a collective performance index to meet the formation requirements of achieving relative positions and velocity consensus. It is solved by applying Pontryagin's principle. Subsequently, a collision-constrained regulating problem is addressed to ensure collision-free tracking of the planned formation trajectory. The tracking problem incorporates a directionally aware collision avoidance strategy that prioritizes avoiding UAVs in the forward path and relative approach. It assigns lower priority to those on the sides with an oblique relative approach and disregards UAVs behind and not in the relative approach. The simulation results for a four-UAV team (re)formation problem confirm the efficacy of the proposed control scheme.