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Continuum robots are highly miniaturizable, exhibit non-linear shapes with several curves, and are flexible and compliant. In particular, concentric-tube and tendon-driven continuum robots can be designed on a small scale with diameters of below 10 mm. A small diameter-to-length ratio enables insertion of these robots through small entry points in order to reach hardly accessible regions by avoiding obstacles. This scenario can often be found in minimally invasive surgery and technical inspections. However, to reach the target region, a deployment along a narrow tortuous path is often required. Common tendon-driven continuum robots are intrinsically incapable of such deployment and concentric-tube continuum robots require special path conditions and intensive parameter optimization. Other proposed robot types, such as hyper-redundant and pneumatically actuated robots, exhibit less favorable diameter-to-length ratios and are thus not suitable for those tasks. Since the limiting factors are found in the design of continuum robots, we propose a novel tendon-driven continuum robot design, which features an additional degree of freedom in each robot section. The backbone is composed of straight, concentrically arranged tubes, each of which composes a section and is used to adapt its length. We present a three-section continuum robot prototype with a diameter of 7 mm, determine its follow-the-leader capabilities theoretically, and validate the results experimentally using model-based control. For our 165 mm long robot prototype, the repeatability is below 2.38 mm. The model accuracy reaches a median of 3.16% over 25 configurations with respect to robot length. The path-following error over five curvilinear paths results in median errors of 2.59% with respect to robot length.

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Tendon actuation is one of the most prominent actuation principles for continuum robots. To date, a wide variety of modelling approaches has been derived to describe the deformations of tendon-driven continuum robots. Motivated by the need for a comprehensive overview of existing methodologies, this work summarizes and outlines state-of-the-art modelling approaches. In particular, the most relevant models are classified based on backbone representations and kinematic as well as static assumptions. Numerical case studies are conducted to compare the performance of representative modelling approaches from the current state-of-the-art, considering varying robot parameters and scenarios. The approaches show different performances in terms of accuracy and computation time. Guidelines for the selection of the most suitable approach for given designs of tendon-driven continuum robots and applications are deduced from these results.

Path following and follow-the-leader motion is particularly desirable for minimally-invasive surgery in confined spaces which can only be reached using tortuous paths, e.g. through natural orifices. While path following and followthe-leader motion can be achieved by hyper-redundant snake robots, their size is usually not applicable for medical applications. Continuum robots, such as tendon-driven or concentric tube mechanisms, fulfill the size requirements for minimally invasive surgery, but yet follow-the-leader motion is not inherently provided. In fact, parameters of the manipulator's section curvatures and translation have to be chosen wisely a priori.In this paper, we consider a tendon-driven continuum robot with extensible sections. After reformulating the forward kinematics model, we formulate prerequisites for follow-the-leader motion and present a general approach to determine a sequence of robot configurations to achieve follow-the-leader motion along a given 3D path. We evaluate our approach in a series of simulations with 3D paths composed of constant curvature arcs and general 3D paths described by B-spline curves. Our results show that mean path errors <0.4 mm and mean tip errors <1.6 mm can theoretically be achieved for constant curvature paths and <2 mm and <3.1 mm for general B-spline curves respectively.

This paper presents a miniature wrist that can be integrated into needle-sized surgical instruments. The wrist consists of a nitinol tube with asymmetric cutouts that is actuated by a single tendon to provide high distal curvature. We derive and experimentally validate kinematic and static models for the wrist and describe several prototype wrists, illustrating the straightforward fabrication and scalability of the design. We experimentally investigate fatigue life, the concept of tip-first bending, and practical use of the wrist with a concentric tube robot in an endonasal surgical scenario.

Added to their high dexterity and ability to conform to complex shapes, continuum robots can be further improved to provide safer interaction with their environment. Indeed, controlling their stiffness is one of the most challenging yet promising research topics. We propose a tubular stiffening sheath as a replaceable cover for small-diameter continuum robots to temporarily increase the stiffness in a certain configuration. In this article, we assess and compare performances of two different stiffening modalities: granular and layer jamming, provide arguments for material selection and experimental results for stiffness with respect to lateral and axial applied forces. Furthermore, we detected empirically additional effects relating sheath stiffness to material parameters and added to recent investigations in the state of the art, which are based exclusively on material roughness. Finally, we integrated the selected layer jamming material in a miniaturized sheath (13 mm outer diameter, 2.5 mm wall thickness) and covered a tendon-actuated continuum robot with it. Experimental characterization of the behavior with respect to applied external forces was performed via stiffness measurements and proved that the initial tendon-actuated continuum robot stiffness can be improved by a factor up to 24.

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