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

This article addresses the challenge of simultaneous stabilization control of the position and orientation of the nonholonomic vehicle in three-dimensional (3-D) space by constructing a geometric reference trajectory. First, by leveraging the geometric reference trajectory configuration defined on $\mathit{\text{SE}}(3)$, a geometric reference trajectory for the desired position and orientation of a vehicle in 3-D space is devised. Then, an adjustable trajectory inclination is introduced to provide a safe operational trajectory for a nonholonomic vehicle in the 3-D space. Second, based on the geometric reference trajectory, a simultaneous stabilization controller for a general nonholonomic vehicle in 3-D 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 autonomous aerial vehicle, 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.