Optimal trajectory planning for a quadrotor via a Gauss Pseudo-spectrum Method

The quadrotor, as a kind of Unmanned Aerial Vehicles (UAVs), has become a hot research topic, due to its small size, easy configuration, good stealthy characteristics, etc. It is a typical nonlinear system with coupling multi-variables. Therefore, it is difficult to optimize trajectory in real-time and its trajectory optimization research is limited so far. In this paper, we firstly establish a quadrotor dynamic model by Newton-Euler equations and simplify it properly. Then a Gauss Pseudo-spectrum Method (GPM) with the hp-Adaptive mesh refinement algorithm is proposed to solve the problem which is a nonlinear optimal control problem with path and boundary constraints. The results verify that the method can effectively generate satisfied optimal trajectories for the aircraft and it provides mathematical foundation for the further engineering applications.