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In this article, we consider the path-planning problem of a cooperativehomogeneous robotic system with rigid formation. An optimal controller isdesigned for each agent in such rigid systems based on Pontryagin's minimumprinciple theory. We found that the optimal control for each agent isequivalent to the optimal control for the Center of Mass (CoM). Thisequivalence is then proved by using some analytical mechanics. Three examplesare finally simulated to illustrate our theoretical results. One applicationcould be utilizing this equivalence to simplify the original multi-agentoptimal control problem.

Optimal path planning of multi-agent cooperative systems with rigid formation