Continuous planning with winding constraints using optimal heuristic-driven front propagation

Recent work has produced methods to solve the winding-constrained optimal feedback navigation problem. Given the start and the goal positions and the winding constraints, the solution to this problem is a feedback vector field such that, when integrated from the start, the trajectory is the shortest path connecting the start and the goal which satisfies given constraints. Such constraints intuitively restrict the direction and the number of times the path winds around given planar regions. We formulate a continuous version of this problem that contrasts with the discrete treatments previously presented. This leads to a geometrical characterization of the problem for which simplicial complex approximation is particularly useful. Thus, it yields theoretical insight as well as a practical algorithm for approximating the continuous problem using an efficient and high-accuracy heuristic-driven front propagation method on simplicial meshes. Experimental results are given evaluating the solution quality and efficiency of the method versus methods based on the discrete formulation and without using heuristics.