Routing of curves with piecewise constant curvature applied to routing of preformed hoses
We present a method for routing of a preformed hose in a static surrounding of obstacles. Routing of a preformed hose is the process of finding a preformed design of the hose that connects a start and a goal point in a collision-free way. A preformed hose design is in this paper represented by a center curve on the form of a sequence of straight line segments joined by circular arcs. The method generates a set of center curves that are collision-free and satisfy minimum allowed straight length and radius of curvature constraints. Each center curve takes a topologically different path with respect to the surrounding geometry and is locally of minimum length. The main scientific contribution is the coupling of a generalized bi-directional grid search with local curve optimization and curve filtering. The method was applied to a set of benchmark cases from the automotive industry and relevant routing solutions were generated in the magnitude of seconds.