Angle constrained Paths

Abstract

The traveling salesman problem (TSP) is a well-known and most widely studied problem in combinatorial optimization. The Dubins TSP is a variant of TSP for curvature-constrained vehicles. In this paper, another variant of TSP, called angle-constrained TSP, is considered for vehicles that can either move straight or turn, i.e., no voluntary curve is possible. The vehicles are only allowed to make on-the-spot turns and straight motions. We impose turn angle constraint on vehicles. Hence, some additional arbitrary points, called stop points, are added to reach an unreachable target. Here, computing the minimum number of stop points walking on the optimal TSP path is presented as the solution of angle-constrained TSP. In addition, we consider two other problems: computing an angle-constrained path on the vertices with the minimum number of stop points and computing an angle-constrained path with the minimum perimeter. In both problems, there is no need to stay on the optimal TSP path. Here, some algorithms are developed to solve these three problems and are examined on some datasets. These algorithms can be used for the path planning of robots with turn angle constraints.