  Compliance control is an increasingly employed technique used in the robotic
field. It is known that various mechanical properties can be reproduced
depending on the design of the stiffness matrix, but the design theory that
takes advantage of this high degree of design freedom has not been elucidated.
This paper, therefore, discusses the non-diagonal elements of the stiffness
matrix. We proposed a design method according to the conditions required for
achieving stable motion. Additionally, we analyzed the displacement induced by
the non-diagonal elements in response to an external force and found that to
obtain stable contact with a symmetric matrix, the matrix should be positive
definite, i.e., all eigenvalues must be positive, however its parameter design
is complicated. In this study, we focused on the use of asymmetric matrices in
compliance control and showed that the design of eigenvalues can be simplified
by using a triangular matrix. This approach expands the range of the stiffness
design and enhances the ability of the compliance control to induce motion. We
conducted experiments using the stiffness matrix and confirmed that assembly
could be achieved without complicated trajectory planning.
