Physical flexibility plays a significant role not only in human motions but also in robot motions. For example, a humanoid robot with passive and flexible elements, which can be regarded as a rigid--soft hybrid-link system, has the advantages of storing energy and mitigating impact in a dynamic motion. However, the motion design and control of a hybrid-link system are challenging to achieve and have only been discussed in the literature. In this study, we propose the framework of inverse kinematics and compliance optimization-based control for a hybrid-link humanoid system that represents the continuous deformation of a flexible structure using the piece-wise constant strain (PCS) model. The proposed method was validated using forward dynamics simulations for standing, jumping, and walking motions. Then, we built an experimental setup using a biped humanoid robot with leaf-spring type prosthesis leg, in which the prosthesis deformation was measured by a motion capture system. Using this setup, we experimentally validated the proposed method for standing balance control in both double- and single-support cases.

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