Simultaneous Position-and-Stiffness Control of Underactuated Antagonistic Tendon-Driven Continuum Robots

TL;DR

This work tackles the challenge of controlling both position and stiffness in underactuated antagonistic tendon-driven continuum robots. It introduces a planar, rigid-link port-Hamiltonian model with a configuration-dependent input matrix to capture open-loop stiffening, and develops a passivity-based controller that shapes a desired potential energy while respecting non-negative tendon tensions. The closed-loop design yields global asymptotic stability to a prescribed configuration and a tunable closed-loop stiffness described by $K_{\tt O} = \gamma \mathbf{1}_{n\times n} + \alpha_2 I_n$, with stability guaranteed under $\gamma < \alpha_2$. Experimental results on OctRobot-I validate the linear relationship between open-loop stiffness and tendon tension, and demonstrate accurate position tracking and stiffness tuning, along with robustness to disturbances and environmental contact. This framework provides a robust, model-informed path toward real-time, simultaneous control of posture and stiffness in continuum robots, with potential extensions to multi-section and 3D configurations.

Abstract

Continuum robots have gained widespread popularity due to their inherent compliance and flexibility, particularly their adjustable levels of stiffness for various application scenarios. Despite efforts to dynamic modeling and control synthesis over the past decade, few studies have incorporated stiffness regulation into their feedback control design; however, this is one of the initial motivations to develop continuum robots. This paper addresses the crucial challenge of controlling both the position and stiffness of underactuated continuum robots actuated by antagonistic tendons. We begin by presenting a rigid-link dynamical model that can analyze the open-loop stiffening of tendon-driven continuum robots. Based on this model, we propose a novel passivity-based position-and-stiffness controller that adheres to the non-negative tension constraint. Comprehensive experiments on our continuum robot validate the theoretical results and demonstrate the efficacy and precision of this approach.

Figures (16)

• Figure 1: (a) A photo of the continuum robot OctRobot-I (b) Mechanical structure of a class of continuum robots
• Figure 2: An illustration of configuration variables (The symbol "$\bullet$" indicates the lumped mass $m_i$; the angle $q_i$ assumes positive values for small counter-clockwise rotations.)
• Figure 3: One-dimensional illustration of traditional continuum robots kim2013stiffness
• Figure 4: Photo of the entire experimental platform
• Figure 5: The linearity between forces and lengths: The length $L_1$ vs the force $u_1$ of the right cable; and the length difference $\Delta L:= L_1 - L_2$ vs the force difference $\tau_1 := u_1 - u_2$ ("$\times$" represents test data, and the dash lines are the fitted functions.)

Theorems & Definitions (13)

• Remark 1
• Remark 2
• Proposition 1
• proof
• Remark 3
• Remark 4
• Remark 5
• Proposition 2
• proof
• Proposition 3