Determination of an Unknown Unactuated Joint Axis in a Compliant Serial Kinematical Chain Using Force Control and the Krylov Power Iteration Method

The determination of unactuated structural joint axes within a compliant structure by external measurements is a subject of interest in many areas. Most eminently, the issue arises for example in the identification of a human joint axis by non-invasive measures, as is needed in robotics rehabilitation and surgery planning procedures. While most existing non-invasive approaches rely here on external optical tracking systems and/or inertial measurement units (IMU) attached to the skin and hence induce large artifact errors, identification of joint axes through tactile control has not yet been addressed in the literature. This paper presents a novel approach to determine an unknown unactuated joint axis in a compliant embedding using robot force-controlled motion. The approach consists in iteratively imparting a load increment according to the Krylov power iteration method until convergence to the force eigenscrew with largest impedance eigenvalue is achieved. The novelty of the approach consists in applying the Krylov steps directly on the target system, hence avoiding the need to explicitly identify the impedance matrix, which is difficult to obtain. The paper validates the proposed procedure by a mimicry mechanical device of the upper limb, composed of a revolute joint representing the elbow joint and a compliant wrist suspension imitating the local movements of the soft tissue at the wrist. The experiments show a promising perspective of the approach.