Stabilization Control for Nonholonomic Vehicles with Second Order Dynamics

This paper investigated the stabilization control problem for the nonholonomic vehicle with second order dynamics, which evolves in Lie group SE(2). At first, we designed the control law for the vehicle by dint of the exponential coordinates in Lie algebra, and then proved the stability of the closed loop system by choosing an appropriate Lyapunov function. The greatest novelty of the proposed control law was the global convergence property. In other words, the vehicle was able to be stabilized to the identity configuration from any position with arbitrary orientation. Furthermore, the initial attitude angle specified as pi or -pi would correspond to different trajectories, which provided choices in case of limitations imposed by surroundings. In order to demonstrate the effectiveness of the control law, numerical simulations were presented at the end. To the best of our knowledge, it is the first time that a global stabilization control algorithm for nonholonomic vehicles is proposed directly based on second order dynamics without using the backstepping technique.