A Lyapunov-Based Framework for Trajectory Planning of Wheeled Vehicle Using Imitation Learning

Trajectory planning with a learning-based approach has emerged as a crucial element in autonomous unmanned systems and has attracted substantial interest from both academia and industry. However, unresolved issues persist concerning data efficiency, safety, convergence, and generalization within the control pipeline. To address this gap, this work presents a trajectory planning method that combines the differential flatness of wheeled vehicle with global convergence property. Our proposed framework transforms the trajectory planning problem, integrating kinematic constraints into a motion planning paradigm. This transformation significantly reduces the state space associated with trajectory planning. Initially, Gaussian mixture regression (GMR) is employed to learn the nonlinear mapping from flat input, leveraging a limited number of demonstrations solved by the optimal control method. Subsequently, we design an asymmetric quadratic Lyapunov function that incorporates both random barrier information and the potential convergence property of the demonstration trajectories. Based on the optimized parameterized Lyapunov function incorporating the convergence and safety criteria, the analytical supplementary control is subsequently obtained by solving a quadratic programming problem to compensate for the prediction errors of GMR, which make the framework complete. Both numerical and real-world experiments are performed to validate the effectiveness of our framework.