Planning for dynamic multi-agent planar manipulation with uncertainty: a game theoretic approach

This paper addresses the planning problem for multi-agent dynamic manipulation in the plane. The objective of planning is to design the forces exerted on the object by agents with which the object can follow a given trajectory in spite of the uncertainty on pressure distribution. The main novelty of the proposed approach is the integration of noncooperative game and cooperative game between agents in hierarchical manner. Based on the dynamic model of the pushed object, the coordination problem is solved in two levels. In the lower control level, a fictitious force controller is designed by using minimax technique to achieve the tracking performance. The design procedure is divided into two steps. First, a linear nominal controller is designed via full-state linearization with desired eigenvalue assignment. Next, a minimax control scheme is specified to optimally attenuate the worst-case effect of the uncertainty due to pressure distribution and achieve a minimax tracking performance. In the coordination level, a cooperative game is formulated between agents to distribute the fictitious force, and the objective of the game is to minimize the worst-case interaction force between agents and the object. Simulations are carried out on three-agent manipulations, results demonstrate the effectiveness of the planning method.