Distance-to-Instability and Distance-to-Singularity Metrics for Continuum Robots

Abstract Existing metrics defined to evaluate the proximity of continuum robots (CRs) to singularities or instability areas are frequently based on matrices involving mixed units, making them sensitive to a change in the unit system. Moreover, their physical meaning is hard to interpret. These metrics are, however, necessary to ensure the best robot performance, as singularities and instability areas may lead to controller instability, or to unstable–stable motions dangerous for the environment. A good metric should be insensitive to the change of units, be bounded, and provide an easily quantifiable information. This is not the case for most metrics used to evaluate the proximity of CRs to singularities or instability areas. Therefore, in this article, we propose new metrics, which can characterize either the distance to instability or to the singularity of any CR. These metrics have a clear physical meaning, have properly defined units (e.g., Newton, meters, radians), and are bounded (they vanish at instability or singularity). They are also generic, i.e., they can be applied to any type of modeling approach (continuous or discrete). Different case studies illustrate our main results.