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

In this article, we consider the path-planning problem of a cooperative homogeneous robotic system with rigid formation. An optimal controller is designed for each agent in such rigid systems based on Pontryagin's minimum principle theory. We found that the optimal control for each agent is equivalent to the optimal control for the Center of Mass (CoM). This equivalence is then proved by using some analytical mechanics. Three examples are finally simulated to illustrate our theoretical results. One application could be utilizing this equivalence to simplify the original multi-agent optimal control problem.