Finding a short path for mobile robot arm coverage of a point set

This paper introduces the problem of Mobile Robot Arm Covering (MRAC) along with a three-step procedure to solve it. In Mobile Robot Arm Covering one seeks the shortest path of a mobile robot equipped with a manipulator such that the manipulator workspace covers a given set of geometric entities. In this paper we consider the problem of covering a set of points. This is solved by a three-step procedure: the search space is first discretized into a finite set of robot poses; then the resulting combinatorial problem is solved by a memetic algorithm and, finally, the given solution is improved in the continuous space. Two popular discretization schemes developed for the related Close Enough Traveling Salesman Problem (CETSP) are evaluated in the MRAC context. Furthermore, a new memetic algorithm to solve MRAC and CETSP instances is developed. This algorithm overcomes the limitations of the approaches based on General Traveling Salesman Problem (GTSP) solvers, namely, the difficulty in handling large problems and the large computational times required to solve them.