A symplectic method for trajectory planning of general tractor-trailer systems

Abstract

Trajectory planning is a key issue in the motion control of tractor-trailer system. In this paper, a unified differential-algebraic equation approach to establish the kinematic models of general tractor-trailer systems is developed. By analyzing practical physical limitations and transportation requirements, the trajectory planning of tractor-trailer system is formulated as a nonlinear constrained optimal control problem. Aiming at efficient numerical solution, a novel symplectic method is proposed. In the proposed method, a symplectic discretization is first implemented to transform the necessary conditions for the original optimal control problem into a set of non-smooth equations. Then, a composite strategy that integrates preconditioned iteration techniques is employed for robust solution. The proposed symplectic method is validated by three examples with different system configurations. Simulation results demonstrate that our method outperforms pseudospectral methods in computational efficiency and robustness to initial guesses. Specifically, a multi-stage strategy can be adopted to achieve robust solution in the presence of obstacles, making the system successfully travel across narrow corridors. An animation of the simulation results is available at www.bilibili.com/video/BV1EN4y1P7Ar.