Directional Critical Load Index: A Distance-to-Instability Metric for Continuum Robots

Equilibrium stability assessment is a primary issue in continuum robots (CRs). The possible stable-to-unstable transitions that CRs may admit complicate the use of CRs in tasks where safety and human–robot interactions are mandatory. In this context, metrics measuring the distance from instability are essential but rarely developed. Existing metrics are frequently based on the evaluation of matrices involving mixed units, thus resulting in unit-dependent metrics. Moreover, the physical meaning of existing metric is hard to interpretate. This article proposes to use the magnitude of a force that brings instability to the CR equilibrium as a measure of the distance to instability. The major advantages of this metric are the intrinsic physical meaning, the practical interpretation of the results, and the well-defined unit of the measurements. The proposed metric (named directional critical load index) is based on the linearization of the eigenvalues of the reduced Hessian matrix of the total potential energy, which can be achieved regardless of the employed discretization technique. Three different case studies illustrate and demonstrate the main results of this article.