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Compliance control is an increasingly employed technique used in the roboticfield. It is known that various mechanical properties can be reproduceddepending on the design of the stiffness matrix, but the design theory thattakes advantage of this high degree of design freedom has not been elucidated.This paper, therefore, discusses the non-diagonal elements of the stiffnessmatrix. We proposed a design method according to the conditions required forachieving stable motion. Additionally, we analyzed the displacement induced bythe non-diagonal elements in response to an external force and found that toobtain stable contact with a symmetric matrix, the matrix should be positivedefinite, i.e., all eigenvalues must be positive, however its parameter designis complicated. In this study, we focused on the use of asymmetric matrices incompliance control and showed that the design of eigenvalues can be simplifiedby using a triangular matrix. This approach expands the range of the stiffnessdesign and enhances the ability of the compliance control to induce motion. Weconducted experiments using the stiffness matrix and confirmed that assemblycould be achieved without complicated trajectory planning.

Design of non-diagonal stiffness matrix for assembly task