Tractor-Trailer Vehicle Trajectory Planning in Narrow Environments With a Progressively Constrained Optimal Control Approach

Trajectory planning for a tractor-trailer vehicle is challenging due to the non-convex collision avoidance constraints and the unstable kinematics. This article aims to plan precise and optimal trajectory for a car-like tractor that tows standard or general N-trailers in an environment with static obstacles. This trajectory planning scheme can be formulated as a unified optimal control problem, but numerically solving that problem is difficult. Two efforts are made to address the difficulty. First, an extended hybrid A^* search algorithm is proposed to provide an initial guess for the numerical optimization. Second, the numerical optimization process is eased through adopting a progressively constrained optimization strategy, which is about sequentially handling the kinematics, collision avoidance constraints, and boundary conditions. Particularly in dealing with the collision avoidance constraints, an adaptively homotopic warm-starting algorithm is proposed, which defines a sequence of subproblems with the obstacle areas adaptively increase towards their nominal scales. Through solving these subproblems in a sequence, the whole collision avoidance difficulties are dispersed and gradually tackled. Comparative simulations are conducted to validate the efficacy of the proposed trajectory planner.

I. Introduction

Light commercial vehicles have vast applications in various industrial areas. If additional wheeled platforms (called the trailers) are connected to the towing vehicle (called the tractor), a tractor-trailer system is formed [1]. Using a tractor-trailer vehicle helps to decrease the gross number of vehicles because the trailers need not their own drivers [2]. Also, a tractor-trailer system is scalable subject to adding or removing the trailers to meet various hauling demands. In addition, the swept area of a tractor-trailer vehicle is significantly smaller than that of the same-length rigid-body vehicle when turning around. This feature enables a tractor-trailer vehicle to travel agilely in the narrow space [3].