Rapid Solution of Cosserat Rod Equations via a Nonlinear Partial Observer

The Cosserat rod equations are used to model continuum and soft robots. Solving these equations are computationally expensive, particularly due to mixed boundary values and kinematic constraints. In this paper, we present a novel nonlinear observer that can rapidly estimate the solution of the Cosserat rod equations. We present details of the observer design and analyse its convergence and stability. Furthermore, we compare the accuracy and performance of the observer with common solvers used in the literature. Our results show that the proposed observer can significantly improve the computational efficiency of continuum robots' models and estimates the solution of the Cosserat rod equations 7 times faster than common solvers.