An energy-efficient control method for stabilizing cooperative periodic motion of multi joint robots, such as manipulators, is proposed. The proposed method is based on the dynamical systems theory and designed to achieve two goals: stabilization of periodic motion and efficient generation of cooperative motion. First, to generate stable periodic motion of an individual robot, we introduce a van-der-Pol-type damping effect and delayed feedback control, which can stabilize the periodic motion with less energy. We also verified the stability of the periodic motion through numerical simulations. Second, to generate the cooperative motion of the robots, we utilize a phenomenon called the frequency synchronization. We employ a theoretical approach based on the phase reduction theory, in which we can characterize the response of a robot to external forcing by the phase sensitivity function. Using the phase sensitivity function, we can optimize the input signal for synchronization and realize the cooperetive control efficiently.
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