Curvature-Bounded Lengthening and Shortening for Restricted Vehicle Path Planning

In this paper, the traditional shortest path planning problem for vehicle is advanced to length-targeted path planning problem, i.e., to plan path with its length being as close to a specified value as possible. Lengthening and shortening of given initial paths are used to solve this problem. Based on an operation set consisting of three basic path homotopies, we build a comprehensive and systematic framework to plan paths with target length, which is a generalization of the existing related studies. Thereby, the expected paths can be independently searched through such deformation processes within topological classes. The proposed framework can produce the largest length coverage in different scenarios and under different conditions, and it can also generate expected paths with arbitrary topological classification in terms of the curvature constraint and the obstacle constraint. Examples show that our lengthening and shortening method can effectively solve the length-targeted path planning problem in environment without or with obstacles. Note to Practitioners—This paper presents a curvature-bounded lengthening and shortening approach for path planning of vehicles. The curvature and obstacle constraints in the path planning problem are handled using the topological technique. In addition, a rigorous classification system is presented to systematically categorize the potential paths. Within a path class, any path can be deformed to other paths while keeping the curvature bounded. Then, the path deformation process is conducted via a series of basic homotopy operations to approach the target length. The length coverage range of this process is reduced when some endpoint conditions are meet or the vehicle is trapped into a closed region.