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. Note to Practitioners—This paper is motivated by our experience and practical needs in building continuum robotic platforms. Stiffness, flexibility, and accurate configuration regulation are practically important properties for this class of robots. Even though simultaneous position-and-stiffness control is a mature topic for rigid and softly-actuated robots, it remains an open problem for continuum robots with theoretically guaranteed performance. The intention of this paper is to address this situation by proposing a model-based solution for a class of underactuated tendon-driven continuum robots. Hence, we propose an energy-based model and a passivity-based controller to regulate stiffness and configuration concurrently. We believe that this work can be beneficial for academic and industrial research in the context of control algorithms for continuum robots.

Continuum robots with variable stiffness have gained wide popularity in the last decade. Layer jamming (LJ) has emerged as a simple and efficient technique to achieve tunable stiffness for continuum robots. Despite its merits, the development of a control-oriented dynamical model1tailored for this specific class of robots remains an open problem in the literature. This paper aims to present the first solution, to the best of our knowledge, to close the gap. We propose an energy-based model that is integrated with the LuGre frictional model for LJ-based continuum robots. Then, we take a comprehensive theoretical analysis for this model, focusing on two fundamental characteristics of LJ-based continuum robots: shape locking and adjustable stiffness. To validate the modeling approach and theoretical results, a series of experiments using our OctRobot-I continuum robotic platform was conducted. The results show that the proposed model is capable of interpreting and predicting the dynamical behaviors in LJ-based continuum robots.

Obtaining the shape and size of a robot's workspace is essential for both its design and control. However, determining the accurate workspace of a multi-segment continuum robot by graphic or analytical methods is a challenging task due to its inherent flexibility and complex structure. Existing numerical methods have limitations when applied to a continuum robot. This paper presents an Equivalent Two Section (ETS) method for calculating the workspace of multi-segment continuum robots. This method is based on the forward kinematics and a piecewise constant curvature (PCC) model to determine the boundaries of the workspace. In order to verify the proposed method, simulation experiments are conducted using six different maximum bending angles and seven different number of segments. Results of the ETS method are compared to the true workspaces of these configurations estimated by an exhaustive approach. The results show that the proposed ETS method is both efficient and accurate, and has small estimation errors. Discussions on the advantages and limitations of the proposed ETS method are also presented.