Optimal paths for robot group formations based on dynamic programming

Rigid formations of mobile robots are used for special missions in which the assigned task requires tight cooperation of all units in the group so to constrain them to keep preassigned mutual distances. In this article an algorithm for the optimal path planning of rigid formations of mobile robots is considered, where the path cost index is given by the maximum of all distances covered by the robots in the group. An approximate optimal solution is found by discretizing the formation configuration space and applying a dynamic programming algorithm. Several examples are introduced to show the effectiveness of the proposed dynamic programming method as compared to four heuristic strategies that are also devised in the article. The influence of the discretization accuracy on the cost and on the computational complexity is discussed.