Kinematics optimization and static analysis of a modular continuum robot used for minimally invasive surgery

Abstract

For the outstanding compliance and dexterity of continuum robot, it is increasingly used in minimally invasive surgery. The wide workspace, high dexterity and strong payload capacity are essential to the continuum robot. In this article, we investigate the workspace of a cable-driven continuum robot that we proposed. The influence of section number on the workspace is discussed when robot is operated in narrow environment. Meanwhile, the structural parameters of this continuum robot are optimized to achieve better kinematic performance. Moreover, an indicator based on the dexterous solid angle for evaluating the dexterity of robot is introduced and the distal end dexterity is compared for the three-section continuum robot with different range of variables. Results imply that the wider range of variables achieve the better dexterity. Finally, the static model of robot based on the principle of virtual work is derived to analyze the relationship between the bending shape deformation and the driven force. The simulations and experiments for plane and spatial motions are conducted to validate the feasibility of model, respectively. Results of this article can contribute to the real-time control and movement and can be a design reference for cable-driven continuum robot.

Keywords

Surgical robot cable-driven workspace dexterity kinematics and statics

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References

Liu

Sun

(eds). Biologically inspired robotics. Boca Raton, FL: CRC Press, 2012.

Casper

Murphy

RR.

Human-robot interactions during the robot-assisted urban search and rescue response at the World Trade Center. IEEE T Syst Man Cyb 2003; 33(3): 367–385.

Ghanbari

Noorani

Optimal trajectory planning for design of a crawling gait in a robot using genetic algorithm. Int J Adv Robot Syst 2011; 8(1): 29–36.

Burgner

Rucker

Gilbert

et al . A telerobotic system for transnasal surgery. IEEE/ASME T Mech 2014; 19(3): 996–1006.

Yang

Dong

Kinematics modeling and performance optimization of a kinematic-mechanics coupled continuum manipulator. Mechatronics 2015; 31: 196–204.

Trivedi

Rahn

Kier

et al . Soft robotics: biological inspiration, state of the art, and future research. Appl Bionics Biomech 2008; 5(3): 99–117.

Jones

Walker

ID.

Kinematics for multisection continuum robots. IEEE T Robot 2006; 22(1): 43–55.

Walker

Carreras

McDonnell

et al . Extension versus bending for continuum robots. Int J Adv Robot Syst 2006; 3(2): 171–178.

Simaan

. Snake-like units using flexible backbones and actuation redundancy for enhanced miniaturization. In: Proceedings of the IEEE international conference on robotics and automation, Barcelona, 18–22 April 2005, pp.3012–3017. New York: IEEE.

10.

Chen

Pham

Redarce

Sensor-based guidance control of a continuum robot for semi-autonomous colonoscopy. Robot Auton Syst 2009; 57(6–7): 712–722.

11.

Choi

Kim

WK.

Design of a spring backbone micro endoscope. In: Proceedings of IEEE/RSJ international conference on intelligent robots and systems, 2007, pp.1815–1821. IEEE.

12.

Webster Iii

Romano

Cowan

NJ.

Mechanics of precurved-tube continuum robots. IEEE T Robot 2009; 25(1): 67–78.

13.

Ren

Chiu

PWY

et al . A novel constrained wire-driven flexible mechanism and its kinematic analysis. Mech Mach Theory 2016; 95: 59–75.

14.

Dore

Smoljkic

Poorten

et al . Catheter navigation based on probabilistic fusion of electromagnetic tracking and physically-based simulation. In: IEEE/RSJ international conference on intelligent robots and systems, Vilamoura, 7–12 October 2012, pp.3806–3811. New York: IEEE.

15.

Hannan

Walker

ID.

Analysis and experiments with an elephant’s trunk robot. Adv Robot 2001; 15(8): 847–858.

16.

Jones

Walker

ID.

Practical kinematics for real-time implementation of continuum robots. IEEE T Robot 2006; 22(6): 1087–1099.

17.

Simaan

Taylor

Flint

. A dexterous system for laryngeal surgery. In: IEEE international conference on robotics & automation, New Orleans, LA, 26 April–1 May 2004, pp.351–357. New York: IEEE.

18.

Haiyan

HU.

Kinematic analysis and simulation for cable-driven continuum robot. J Mech Eng 2010; 46(19): 1.

19.

Rucker

Jones

Webster Iii

. A geometrically exact model for externally loaded concentric-tube continuum robots. IEEE T Robot 2010; 26(5): 769–780.

20.

Simaan

Analytic formulation for kinematics, statics, and shape restoration of multibackbone continuum robots via elliptic integrals. J Mech Robot 2010; 2: 011006.

21.

Rone

Ben-Tzvi

. Continuum manipulator statics based on the principle of virtual work. In: ASME 2012 international mechanical engineering congress and exposition, Houston, TX, 9–15 November 2012, pp.321–328. New York: ASME.

22.

Yoshikawa

Manipulability of robotic mechanisms. Int J Robot Res 1985; 4(4): 3–9.

23.

Salisbury

Craig

JJ.

Articulated hands: force control and kinematic issues. Int J Robot Res 1981; 1(1): 4–17.

24.

Lenarcic

Bajd

Stanišić

MM.

Robot mechanisms. Amsterdam: Springer, 2013.

25.

Webster Iii

Jones

. Design and kinematic modeling of constant curvature continuum robots: a review. Int J Robot Res 2010; 29(13): 1661–1683.

26.

Chen

Zhang

et al . Inverse kinematic analysis for cable-driven humanoid arm. Chin J Mech Eng 2007; 43(4): 12–20.

27.

Zhao

Zheng

Configuration comparison among kinematically optimized continuum manipulators for robotic surgeries through a single access port. Robotica 2015; 33(10): 1–20.

28.

Ren

et al . Kinematic comparison of surgical tendon-driven manipulators and concentric tube manipulators. Mech Mach Theory 2017; 107: 148–165.

29.

Song

Lei

Wang

The end-effector angle and manipulator dexterous workspaces. J Mech Design 1990; 112(3): 278–288.

30.

Abdel-Malek

Paul

. The dexterous solid angle of robotic manipulators with a spherical wrist. In: The 23rd Biennial Mechanisms Conference, Minneapolis, Minnesota, 11–14 September 1994, Design Engineering Division, American Society of Mechanical Engineers.

31.

Badescu

Mavroidis

New performance indices and workspace analysis of reconfigurable hyper-redundant robotic arms. Int J Robot Res 2004; 23(6): 643–659.

32.

Crawford

Roberts

Dexterity analysis of three 6-DOF continuum robots combining concentric tube mechanisms and cable-driven mechanisms. IEEE Robot Autom Lett 2017; 2(2): 514–521.

33.

Rucker

Webster Iii

. Statics and dynamics of continuum robots with general tendon routing and external loading. IEEE T Robot 2011; 27(6): 1033–1044.

34.

Rone

Ben-Tzvi

Continuum robot dynamics utilizing the principle of virtual power. IEEE T Robot 2014; 30(1): 275–287.