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.Note to Practitioners—This work is motivated by the concept of robot motion primitives. While direct segmented planning based on dynamical system movement is feasible for robots with multiple degrees of freedom, it cannot be directly applied to wheeled vehicles with non-holonomic constraints. In this paper, we propose a method that utilizes the differential flatness properties of wheeled vehicles to bridge the gap between these two application objects. By converting the trajectory planning problem of the mobile vehicles into an optimal control problem, we can obtain a satisfactory optimal trajectory. Solving the optimal control problem involves an iterative process due to its nature as an initial value problem. While some learning-based method offer end-to-end learning capabilities and can perform real-time optimal control, they requires a substantial number of training dataset (different optimal trajectories) and lack convergence validation. The foundation of this work is the imitation learning paradigm. Although learning-based approaches are also capable of directly learning from demonstrations, our approach realizes a combination of Lyapunov theory, which allows us to extract the planning task’s potential properties from a limited number of demonstrations, and the vehicle’s differential flat properties to construct a framework with analytical solution. The framework can effectively re-plan obstacle-free trajectories, even in scenarios with obstacles not given in learning phase. This effectively compensates for the shortcomings of learning-based methods in terms of data reliance, convergence, and interpretability.