Robot group formations: a dynamic programming approach for a shortest path computation

Rigid formations of mobile robots are to be used for special missions in which the task-execution requires a tight cooperation of all units in the group so as to constrain them to keep preassigned mutual distances. In the paper an algorithm for the optimal path-planning of rigid formations of mobile robots is considered for a case in which the path cost index is given by the sum of all distances covered by the robots in the group. The proposed solution method provides an approximate solution to the problem based on a discretization of the configuration space of the formation. A dynamic programming algorithm is used then to find the optimal path in configuration space. Several examples are introduced to show the effectiveness of the proposed dynamic programming method as compared to three heuristic strategies which are also devised in the paper