Lattice-based motion planning for a general 2-trailer system

Motion planning for a general 2-trailer system poses a hard problem for any motion planning algorithm and previous methods have lacked any completeness or optimality guarantees. In this work we present a lattice-based motion planning framework for a general 2-trailer system that is resolution complete and resolution optimal. The solution will satisfy both differential and obstacle imposed constraints and is intended either as a part of an autonomous system or as a driver support system to automatically plan complicated maneuvers in backward and forward motion. The proposed framework relies on a precomputing step that is performed offline to generate a finite set of kinematically feasible motion primitives. These motion primitives are then used to create a regular state lattice that can be searched for a solution using standard graph-search algorithms. To make this graph-search problem tractable for real-time applications a novel parametrization of the reachable state space is proposed where each motion primitive moves the system from and to a selected set of circular equilibrium configurations. The approach is evaluated over three different scenarios and impressive real-time performance is achieved.

I. Introduction

In this paper we present a resolution complete and resolution optimal motion planning framework for a general 2-trailer system in both forward and backward motion. The general 2-trailer system has complicated dynamics and is even unstable in backward motion which makes path planning for this system challenging. To enable the effective use of graph search algorithms for path planning under the kinematic constraints imposed by this system, a novel parametrization of the state lattice is proposed. By calculating motion primitives that move the system from and to a chosen set of equilibrium configurations, two system states can be directly removed from the state lattice and make realtime use of classical graph search algorithms tractable. The motion planner could be used as a driver support system to plan complex maneuvers in parking scenarios or as a stand alone planner for autonomous maneuvering with trailers. To the best of the author's knowledge this work presents the first resolution complete motion planning framework for a reversing general 2-trailer system. The focus of this paper is to generate paths that are kinematically feasible and resolution optimal. Therefore, the reader is referred to our previous work on path following controllers in order to find techniques to stabilize the system around these paths [1], [2].