Humanoid Motion Control by Compliance Optimization Explicitly Considering its Positive Definiteness

This article discusses a compliance optimization approach that satisfies positive definiteness. Physical human–robot interactions are an important topic in robotics, for which force or compliance control is a key technology. Operational space control (OSC) is one of the most common approaches for robot force control with redundant degrees of freedom. By linearizing OSC, we can derive joint stiffness and viscosity matrices equivalent to the OSC. For an appropriate control, it is important that these matrices are positive definite. However, the stiffness matrix equivalent to the OSC is not always positive definite. In this case, a high kinetic energy is required, which is a problem in terms of the control performance. Therefore, the control performance can be improved by explicitly considering the positive definiteness of the stiffness or compliance. In this article, the authors derive a dynamically consistent compliance formulation and propose a compliance optimization that satisfies positive definiteness. The space of the symmetric positive definite matrix is a Riemannian manifold. We show that minimizing the Riemaniann geodesic distance results in a better performance compared with using OSC. The proposed method is validated via forward dynamics simulations and experiments using a hydrostatically driven humanoid Hydra.