Exact derivative propagation method to compute the generalized compliance matrix for continuum robots: Application to concentric tubes continuum robots

This paper introduces the concept of Generalized Compliance for continuum robots, specifically for those modeled with the Cosserat Rod theory. Unlike existing models based on tip compliance, the proposed approach considers interactions along the entire body of the flexible robot. The paper also presents a novel method referred to as the Low-Level Derivative Propagation Method, which is designed for the computationally efficient derivation of the Generalized Compliance matrix. The proposed method streamlines calculations and reduces integration time. The presented method, which is general and applies to various types of continuum robot models, is demonstrated on the case of a Concentric Tubes Continuum Robot. We provide detailed derivations of the equations and computation techniques leading to the derivation of the Generalized Compliance matrix, as well as a large-scale numerical validation of the method. The code used in this paper is available on the following GitHub website: https://github.com/benoitrosa/Generalized-Compliance-Computation-for-Continuum-Robots.