This paper proposes an energy saving control method of periodic motions composed of multi-frequency components based on adaptive stiffness optimization for mechanical systems. In the case of sinusoidal motions, the concept of resonance can be easily applied to determine an optimal stiffness. This paper tries to extend resonance to deal with periodic motions composed of multi-frequency components. For this purpose, we define a cost function, which represents an amount of actuator torque. Next, an optimal stiffness is defined as the stiffness that minimizes the cost function. The relationship between the optimal stiffness and the desired motions is analytically derived. Based on the preparations, we propose two types of controller. These controllers generate the desired motions using the least amount of actuator torque as possible by optimizing the stiffness adaptively. The controllers work well without using parameters of the objective systems. Stability and effectiveness of the stiffness optimization are proved mathematically. Simulation results demonstrate the effectiveness of the proposed method.
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