Trajectory Planning for a Tractor with Multiple Trailers in Extremely Narrow Environments: A Unified Approach

Trajectory planning for a tractor-trailer vehicle is challenging because the vehicle kinematics consists of underactuated and nonholonomic constraints that are highly coupled. Prevalent sampling-based or search-based planners suitable for rigid-body vehicles are not capable of handling the tractor-trailer vehicle cases. This work aims to deal with generic n-trailer cases in the tiny environments. To this end, an optimal control problem is formulated, which is beneficial in being accurate, straightforward, and unified. An adaptively homotopic warm-starting approach is proposed to facilitate the numerical solution process of the formulated optimal control problem. Compared with the existing sequential warm starting strategies, our proposal can adaptively define the subproblems with the purpose of making the gaps between adjacent subproblems “pleasant” for the solver. Unification and efficiency of the proposed adaptively homotopic warm-starting approach have been investigated in several extremely tiny scenarios. Our planner finds solutions that other existing planners cannot. Online planning opportunities are briefly discussed as well.