Bounded curvature path planning with expected length for Dubins vehicle entering target manifold

Bounded curvature path planning with specified length is a significant technique for single-vehicle assignments and multi-vehicle coordination, especially in the real-time applications. Any existed path can be reached from the curvature-bounded deformation of some other paths. Based on that, this paper proposes a structured homotopy-based (SH-based) planner as an improvement of the conventional path elongation strategy. Not alike path elongation which is driven by initial path, the proposed planner is driven by endpoint condition. It searches expected path within the synthesis of several path homotopies, therefore it has stronger flexibility and adaptability for different endpoint condition than simple elongation. Special homotopy structures which ensure the monotonicity of path length with respect to the homotopy parameter are employed for implementation of fast solution searching. In addition, the proposed method is extended from the point target case to the manifold target case, and the target point transference strategy is adopted to make a trade-off between the path length deviation and the target position value. Static and dynamic cases are respectively simulated for an example of Dubins vehicle, which validate the performance of the proposed method.