A Memory-based SO(3) Parameterization: Theory and Application to 6D Impedance Control with Radially Unbounded Potential Function

Abstract

This paper proposes a parameterization method to represent SO (3) over multiple turns. This method is called a memory-based parameterization, because the idea is to integrate the past trajectory of exponential coordinates. The parameterization is consistent in the sense that the true rotation matrix can be reconstructed by using the exponential map. As an application of the proposed method, a 6D impedance controller is designed with a radially unbounded potential function. Consequently, in contrast to the conventional methods, an arbitrarily large angular deflection can be accommodated, resulting in a more realistic impedance behavior. The proposed schemes are validated through simulations and experiments.