Distributed curvature control of a continuum arm with intermittently attached cables

Abstract

This paper presents a dynamics analysis and curvature control approach for a uniform continuum arm. A pair of cables are intermittently attached to the continuum arm at the tip as well as in several spanwise locations. The dynamical model is based on a set of nonlinear coupled partial differential equations, capturing the complex dynamics of the system. We propose a feedforward plus proportional-derivative feedback control law that ensures exponential stability of the regulation error system in both the $L^{\infty }$ and $L^2$ norms. The dynamical model with distributed control successfully describes the continuum system’s ability to achieve both C-shaped and S-shaped configurations, which are crucial for various practical applications. Numerical simulations validate the effectiveness of the proposed strategy, demonstrating precise control over the arm’s bending behavior.