Trajectory planning for UAVs based on geometric pseudospectral method

This paper studies the geometric pseudospectral method, which refers to the Gauss pseudospectral method that is extended to the special Euclidean group SE(3) for UAVs trajectory planning. On SE(3), a complete left invariant rigidbody dynamical UAV model is established in a body-fixed frame, including kinematical and dynamical models. For the kinematical model, the equivalent Lie algebra equation corresponding to the configuration equation is derived based on the left-trivialized tangent of the local coordinate map. Considering the Lie algebra space is isomorphic to the Euclidean space, the Gauss pseudospectral method is directly used to discretize the dynamical model. The kinematical and dynamical models are considered as the defect equality constraint used for describing the UAVs trajectory planning problem. The simulation results illustrate that the proposed method is effective for planning the UAV trajectory.