Backstepping Control of Tendon-Driven Continuum Robots in Large Deflections Using the Cosserat Rod Model

TL;DR

The paper addresses the challenge of controlling tendon-driven continuum robots under large deflections by employing a Cosserat rod-based dynamic model to capture nonlinear behavior. It proposes a backstepping control design and validates it through both numerical simulations and experimental tests, showing smoother trajectories, shorter settling times, and lower overshoot than a traditional sliding-mode controller. The results demonstrate robustness to external forces and disturbances, highlighting backstepping as a practical approach for reliable large-deflection manipulation in continuum robotics. Overall, the work provides a viable control strategy for TDCRs with significant bending, enabling safer and more precise operation in unstructured environments.

Abstract

This paper presents a study on the backstepping control of tendon-driven continuum robots for large deflections using the Cosserat rod model. Continuum robots are known for their flexibility and adaptability, making them suitable for various applications. However, modeling and controlling them pose challenges due to their nonlinear dynamics. To model their dynamics, the Cosserat rod method is employed to account for significant deflections, and a numerical solution method is developed to solve the resulting partial differential equations. Previous studies on controlling tendon-driven continuum robots using Cosserat rod theory focused on sliding mode control and were not tested for large deflections, lacking experimental validation. In this paper, backstepping control is proposed as an alternative to sliding mode control for achieving a significant bending. The numerical results are validated through experiments in this study, demonstrating that the proposed backstepping control approach is a promising solution for achieving large deflections with smoother trajectories, reduced settling time, and lower overshoot. Furthermore, two scenarios involving external forces and disturbances were introduced to further highlight the robustness of the backstepping control approach.

Figures (14)

• Figure 1: Schematic configuration of a single-section tendon-driven continuum robot.
• Figure 2: A section of a rod subjected to distributed forces $\mathbf{f}(s)$ and moments $\mathbf{l}(s)$ at a given time $t$.
• Figure 3: A tendon-driven continuum robot used in the test setup. Markers 1-3 indicate base markers, 4-7 denote CR's tip markers, 8 represents the backbone, 9 stands for tendon, and 10 indicates the spacer disk.
• Figure 4: Comparison of backstepping and sliding mode control under normal conditions: (a) x-component of the robot's tip vs. iteration, (b) z-component of the robot's tip vs. iteration, (c) tendon displacement, and (d) position error.
• Figure 5: Comparison of the robot's configuration under different control methods, (a) backstepping control, and (b) sliding mode control.