Use of Force-Controlled Compliance-Eigenvector Power-Iterations for Finding an Instantaneous Knee Axis: Mockup Study for a Fixed Hinge

The non-invasive determination of the instantaneous rotation axis of human joints is of high relevance for rehabilitation purposes as well as for medical diagnostics and surgery planning. Current methods rely on skin-attached sensors. However, these lead to errors of up to \(12\,\text {mm}\) offset and \(2^{\circ }\) alignment. This paper analyzes a new concept, previously proposed by the last author et al., based on force control of a robot, to determine the unknown rotation axis by pure tactile motions resulting from on-site compliance-eigenvector power-iterations without the need to determine the compliance matrix. While previous publications viewed only the non-gravitational case in the horizontal plane, here we regard the realistic study of knee flexion in the vertical plane for a mockup setup with fixed hinge including attachment shoe. Described are the theory and the experimental validation. It is shown that the unknown rotation axis can be determined with an offset error below \(2.5\,\text {mm}\) for a lower-leg length of \(496\,\text {mm}\) , and alignment error below \(0.3^{\circ }\) . Further reductions of errors are possible through better post-processing of tracking data and an inclined thigh to avoid singularity around \(90^{\circ }\) flexion angle.