# Design of a three-segment continuum robot for minimally invasive surgery

- Bo Ouyang
^{1}Email authorView ORCID ID profile, - Yunhui Liu
^{2}and - Dong Sun
^{1}

**Received: **28 February 2016

**Accepted: **9 March 2016

**Published: **24 March 2016

## Abstract

Continuum robot, as known as snake-like robot, usually does not include rigid links and has the ability to reach into a confined space by shaping itself into smooth curves. This paper presents the design of a three-segment continuum robot for minimally invasive surgery. The continuum robot employs a single super-elastic nitinol rod as the backbone and concentric disks assembled on the backbone for tendons attachment. Each segment is driven by four tendons and controlled by two linear actuators. The length of each segment is optimized based on the surgical workspace. A visual servo system is designed to assist the surgeon in operating the robot. Simulation experiment is conducted to demonstrate the proposed design.

### Keywords

Continuum robot Dimensional synthesis Visual servo Medical robot## Background

A continuum robot is a flexible robot inspired by caterpillars, elephant trunks, octopus arms, and mammalian tongues. The robot can vary its nature shape because of the materials flexibility and is capable of reaching into a complex environment. Therefore, the continuum robot has the potential in single-port access surgery and natural orifice transluminal.

It is generally assumed that the segment of continuum robot bends with constant curvature [5]. The kinematics of multi-segment continuum robot can be formulated by a Denavit–Hartenberg-type approach [1]. Although there are various ways for kinematic modeling, the piecewise constant curvature is assumed finally [6]. Variable curvature continuum robot has been also developed [7]. However, the kinematic modeling is extremely hard.

Control of continuum robot possesses a great challenge because of the compliance of continuum robot. The dynamic model of a planar continuum robot has been introduced [8]. The dynamics of a spatial continuum robot has also been reported based on the principle of virtual power [9]. The statics and dynamics of variable curvature continuum robot have been presented by the classical Cosserat rod model [10]. However, the design of a controller is still a difficult issue because of the material flexibility. A neural network controller has been tried, where a hypothesis dynamic model is estimated online [11]. A model-less feedback control has been proposed without using the constant curvature kinematic frameworks [12].

A three-segment continuum robot for minimally invasive surgery has been developed in this study. The robot employs a single super-elastic nitinol rod as the backbone. Twelve tendons passing through the concentric disks are used to operate the robot. These tendons are divided into three groups. Each group has two pairs of tendons and is controlled by two linear actuators. The segment length is determined by the cable nodes in the group, which can be adjusted by varying the position of the nodes. Moreover, the approximate boundary of reachable workspace is formulated. A unique method is proposed to minimize the length of continuum robot. Finally, a visual servo system is designed.

## Mechanical structure

*z*-axis (\(\phi\)) and

*y*-axis (\(\theta\)), based on the constant curvature kinematics frameworks. The number of tendons is at least three for driving one segment, because tendons must be work in tension. This property brings a disadvantage for the kinematic control of continuum robot with three tendons. Because the shape of one segment is determined by two tendons, the tension of the third tendon is extremely large as the translation error of the third tendon is positive. The third tendon would be snapped. The designed continuum robot with each segment driven by four tendons and controlled by two linear actuators is developed to compensate this disadvantage.

*n*is the number of disks. Equation (1) indicates that one tendon works in tension and the other one is slack in each pair, which is exactly the requirement of the continuum robot control. Therefore, one just needs to change the moving direction of linear motor based on \(\phi\) for the operation of the continuum robot. On the other side, multiple segments are employed to provide sufficient DOF for accomplishing complex surgical tasks. Twelve tendons and six linear motors are used to operate the robot finally. The tendons are divided into three groups (\(H_{1}\), \(H_{2}\), and \(H_{3}\)), and each group has two pairs (\(H_{ix}\), \(H_{iy}\), and \(i = 1, 2, 3\)). The length of each segment (\(l_{i}\)) is defined by the cable nodes. Thus, the length of each segment can be adjusted based on the surgical requirement.

### Dimensional synthesis

The three-segment continuum robot developed in this paper has six DOFs. The workspace of each segment is determined by three parameters: \(\phi_{i}\), \(\theta_{i}\), and \(l_{i}\), \(i = 1,2,3\). The range of rotation angle \(\phi_{i}\) is 0°–360°. Note that the rotation angle \(\theta_{i}\) is limited because of the constant curvature kinematics. In general, the range of rotation angle \(\theta_{i}\) is ranged 0°–90° or 0°–120°. The entire attitude space is independent of the arc length \(l_{i}\). However, the position of end effector depends on \(l_{i}\). The arc length of each segment should be optimized based on surgical workspace.

*θ*. Therefore, the length should be minimized to improve the dexterity of the continuum robot. The dimensional synthesis can be described as the following optimization problem:

## Visual servo system design

After the mechanical structure of continuum robot is developed, the next step is to design an interactive system for assisting surgeon in controlling the robot in a user-friendly way.

### Simulation experiment

## Conclusion

This paper presents the design of a three-segment continuum robot. The approximate boundary of workspace is formulated. The configuration of each segment is determined. In the future, the visual servo control system will be developed, and the controller will be improved.

## Declarations

### Authors’ contributions

A three-segment continuum robot is designed. The boundary of workspace is formulated. Moreover, a method for determining the configurations of each segment is proposed based on monocular vision. All authors read and approved the final manuscript.

### Acknowledgements

The work was also supported by a grant from Research Grants Council of the Hong Kong Special Administrative Region, China (Reference No. CUHK6/CRF/13G assigned to CityU).

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

## References

- Jones BA, Walker ID. Kinematics for multisection continuum robots. IEEE Trans Rob. 2006;22(1):43–55.View ArticleGoogle Scholar
- Xu K, Simaan N. Actuation compensation for flexible surgical snake-like robots with redundant remote actuation. In: IEEE international conference on robotics and automation. 2006. p. 4148–53.Google Scholar
- Simaan N, Xu K, Wei W, Kapoor A, Kazanzides P, Taylor R. Design and integration of a telerobotic system for minimally invasive surgery of the throat. Int J Robot Res. 2009;28:1134–53.View ArticleGoogle Scholar
- Dupont PE, Lock J, Itkowitz B, Butler E. Design and control of concentric-tube robots. IEEE Trans Robot. 2010;26(2):209–25.View ArticleGoogle Scholar
- Gravagne IA, Rahn CD, Walker ID. Large deflection dynamics and control for planar continuum robots. IEEE ASME Trans Mechatron. 2003;8(2):299–307.View ArticleGoogle Scholar
- Webster RJ III, Jones BA. Design and kinematic modeling of constant curvature continuum robots: a review. Int J Robot Res. 2010;29(13):1661–83.View ArticleGoogle Scholar
- Mahl T, Hildebrandt A, Sawodny O. A variable curvature continuum kinematics for kinematic control of the bionic handling assistant. IEEE Trans Robot. 2014;30(4):935–49.View ArticleGoogle Scholar
- Gravagne IA, Walker ID. Manipulability, force, and compliance analysis for planar continuum manipulators. IEEE Trans Robot Autom. 2002;18(3):263–73.View ArticleGoogle Scholar
- Rone WS, Ben-Tzvi P. Continuum robot dynamics utilizing the principle of virtual power. IEEE Trans Robot. 2014;30(1):275–87.View ArticleGoogle Scholar
- Rucker DC, Webster RJ III. Statics and dynamics of continuum robots with general tendon routing and external loading. IEEE Trans Robot. 2011;27(6):1033–44.View ArticleGoogle Scholar
- Braganza D, Dawson DM, Walker ID, Nath N. A neural network controller for continuum robots. IEEE Trans Robot. 2007;23(5):1270–7.View ArticleGoogle Scholar
- Yip MC, Camarillo DB. Model-less feedback control of continuum manipulators in constrained environments. IEEE Trans Robot. 2014;30(4):880–9.View ArticleGoogle Scholar