Simultaneous Stabilization Control of Position and Orientation for Non-Holonomic Vehicle in 3D Space: Geometric Reference Trajectory

This paper addresses the challenge of simultaneous stabilization control of the position and orientation of the non-holonomic vehicle in three-dimensional (3D) space by constructing a geometric reference trajectory. Firstly, by leveraging the geometric reference trajectory configuration defined on SE(3), a geometric reference trajectory for the desired position and orientation of a vehicle in 3D space is devised. Then, an adjustable trajectory inclination is introduced to provide a safe operational trajectory for a non-holonomic vehicle in the 3D space. Secondly, based on the geometric reference trajectory, a simultaneous stabilization controller for a general non-holonomic vehicle in 3D space is designed to enable the position and orientation to converge simultaneously to the desired configuration along the specified geometric reference trajectory, with convergence proven by a Lyapunov function. Subsequently, a two-phase autonomous landing controller strategy is devised for a fixed-wing Unmanned Aerial Vehicle (UAV), enabling it to safely land without stalling along a geometric reference trajectory that maintains a suitable trajectory inclination. Finally, the designed controllers are validated through numerical simulations.