A virtual target approach for trajectory optimization of a general class of constrained vehicles

This paper addresses the computation of (local) optimal feasible trajectories that best approximate in L2 sense any given desired maneuver for a general class of constrained robotic vehicles. For trajectory tracking and geometric tracking approaches, we propose a trajectory optimization strategy using a Virtual Target Vehicle (VTV) perspective where the virtual target plays the role of an additional control input. This extra flexibility can improve the numerical performance of the optimal control solver, which is based on a nonlinear projection operator Newton method, as well as enforce a trajectory-tracking or an only path-following behaviour of the resulting optimal trajectory. As an application scenario we apply the proposed approach to Unmanned Aerial Vehicles (UAVs). We provide numerical computations based on the loiter maneuver that illustrates the benefits of VTV design procedure and highlights interesting features of the proposed trajectory tracking and geometric tracking optimal control strategies.