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In paper the fundamental question about optimal interaction between the controlling stimuli generated by the active (powered) and the passive (unpowered) drives of the robotic systems have been studied. A mathematical statement of the problem has been proposed that is suitable to study this question for the semi-passively actuated n-degree-of-freedom robotic systems. The problem is formulated as an optimal control problem for n-degree-of-freedom mechanical system models a semi-passively actuated robot. We take into account the interaction between the external controlling stimuli acting on the robotic system and the control forces exerting by its passive drives. It is made by introducing the additional constraints imposed both on the phase coordinates of the system and the controlling stimuli of passive drives. These constraints describe the inherent dynamics of passive drives that have been incorporated into the structure of robotic system. Closed-form solutions of considered problem have been obtained for two cases. First, for an arbitrary robotic system having n degree-of-freedom without any restrictions on the controlling stimuli of its passive drives. Second, for a robotic system with one degree-of-freedom having viscoelastic damper-like passive drive. The obtained results can help to design the optimal structure of passive drives for robotic systems.

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