• Advances in robotics research
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• v.1 no.1
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• pp.41-59
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• 2014

This paper deals with the problem of steering a group of mobile robots along a reference path while maintaining a desired geometric formation. To solve this problem, the overall formation is decomposed into numerous geometric patterns composed of pairs of robots, and the state of the geometric patterns is defined. A control algorithm for the problem is proposed based on the Nash equilibrium strategies incorporating receding horizon control (RHC), also known as model predictive control (MPC). Each robot calculates a control input over a finite prediction horizon and transmits this control input to its neighbor. Considering the motion of the other robots in the prediction horizon, each robot calculates the optimal control strategy to achieve its goals: tracking a reference path and maintaining a desired formation. The performance of the proposed algorithm is validated using numerical simulations.