Stability analysis and snap-through evaluation of the cable-driven continuum robots

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar, Iran

2 حکیم سبزواری-فنی و مهندسی- گروه مهندسی مکانیک

Abstract

Most of the continuum robots have flexible backbones that are deformed under the internal and external loads and a considerable amount of potential energy may be stored in the backbone. Hence, the continuum robots are exposed to instability issues such as snap-through. The snap-through instability occurs when, with changes in the applied forces, the robot reaches the boundary of its stable region and then moves toward a stable configuration in an uncontrolled manner. Snap-through instability is harmful to the continuum robots and its prediction is important for the design and control of the robot. However, most of the studies focused on design, kinematics, and dynamics of the continuum robots and there are limited studies worked on stability analysis of these robots. In this paper, the stability analysis of the cable-driven continuum robots is investigated. For this, the static equilibrium configurations of the robot are firstly determined under the internal and external loadings. Then, the stiffness matrix of the robot is obtained and the robot stability and snap-through condition are evaluated. The accuracy of the static equations of the robot is verified using the experimental results and the possibility of snap-through occurrence is modeled through simulations. Besides, the effects of the external loads, robot configuration in space, and cross-section of the backbone on the workspace and snap-through occurrence are studied.

Keywords

Main Subjects


[1] G. Robinson, J.B.C. Davies, Continuum robots-a state of the art, in:  Proceedings 1999 IEEE international conference on robotics and automation (Cat. No. 99CH36288C), IEEE, 1999, pp. 2849-2854.
[2] H. Ohno, S. Hirose, Study on slime robot (proposal of slime robot and design of slim slime robot), in:  Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000)(Cat. No. 00CH37113), IEEE, 2000, pp. 2218-2223.
[3] B.A. Jones, I.D. Walker, Practical kinematics for real-time implementation of continuum robots, IEEE Transactions on Robotics, 22(6) (2006) 1087-1099.
[4] S. Cobos-Guzman, D. Axinte, J. Kell, A Novel Continuum Robot Using Twin-Pivot Compliant Joints: Design, Modeling, and Validation.
[5] Z.Y. Bayraktaroglu, Snake-like locomotion: Experimentations with a biologically inspired wheel-less snake robot, Mechanism and Machine Theory, 44(3) (2009) 591-602.
[6] W. McMahan, B. Jones, I. Walker, V. Chitrakaran, A. Seshadri, D. Dawson, Robotic manipulators inspired by cephalopod limbs, Proceedings of the Canadian Engineering Education Association (CEEA),  (2004).
[7] X. Dong, D. Axinte, D. Palmer, S. Cobos, M. Raffles, A. Rabani, J. Kell, Development of a slender continuum robotic system for on-wing inspection/repair of gas turbine engines, Robotics and Computer-Integrated Manufacturing, 44 (2017) 218-229.
[8] J. Casper, R.R. Murphy, Human-robot interactions during the robot-assisted urban search and rescue response at the world trade center, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 33(3) (2003) 367-385.
[9] A. Wolf, H.B. Brown, R. Casciola, A. Costa, M. Schwerin, E. Shamas, H. Choset, A mobile hyper redundant mechanism for search and rescue tasks, in:  Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003)(Cat. No. 03CH37453), IEEE, 2003, pp. 2889-2895.
[10] J. Burgner-Kahrs, D.C. Rucker, H. Choset, Continuum robots for medical applications: A survey, IEEE Transactions on Robotics, 31(6) (2015) 1261-1280.
[11] N. Simaan, R. Taylor, P. Flint, A dexterous system for laryngeal surgery, in:  IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA'04. 2004, IEEE, 2004, pp. 351-357.
[12] N. Simaan, Snake-like units using flexible backbones and actuation redundancy for enhanced miniaturization, in:  Proceedings of the 2005 IEEE International Conference on Robotics and Automation, IEEE, 2005, pp. 3012-3017.
[13] G.S. Chirikjian, A general numerical method for hyper-redundant manipulator inverse kinematics, in:  [1993] Proceedings IEEE International Conference on Robotics and Automation, IEEE, 1993, pp. 107-112.
[14] I.A. Gravagne, I.D. Walker, On the kinematics of remotely-actuated continuum robots, in:  Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No. 00CH37065), IEEE, 2000, pp. 2544-2550.
[15] I.A. Gravagne, I.D. Walker, Kinematic transformations for remotely-actuated planar continuum robots, in:  Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No. 00CH37065), IEEE, 2000, pp. 19-26.
[16] R.J. Webster III, B.A. Jones, Design and kinematic modeling of constant curvature continuum robots: A review, The International Journal of Robotics Research, 29(13) (2010) 1661-1683.
[17] F. Qi, F. Ju, D. Bai, Y. Wang, B. Chen, Kinematic analysis and navigation method of a cable‐driven continuum robot used for minimally invasive surgery, The International Journal of Medical Robotics and Computer Assisted Surgery, 15(4) (2019) e2007.
[18] S. Sara, Farid, T. pour, G. rad, Cinematic modeling of continuum robot arm inspired by origami with curved-fixed elements, Modares Mechanical Engineering, 19(11)  0-0.(in persian)
[19] T. Mahl, A. Hildebrandt, O. Sawodny, A variable curvature continuum kinematics for kinematic control of the bionic handling assistant, IEEE transactions on robotics, 30(4) (2014) 935-949.
[20] D.C. Rucker, B.A. Jones, R.J. Webster III, A geometrically exact model for externally loaded concentric-tube continuum robots, IEEE Transactions on Robotics, 26(5) (2010) 769-780.
[21] H. Yuan, L. Zhou, W. Xu, A comprehensive static model of cable-driven multi-section continuum robots considering friction effect, Mechanism and Machine Theory, 135 (2019) 130-149.
[22] D.C. Rucker, R.J. Webster III, Statics and dynamics of continuum robots with general tendon routing and external loading, IEEE Transactions on Robotics, 27(6) (2011) 1033-1044.
[23] F. Renda, M. Cianchetti, M. Giorelli, A. Arienti, C. Laschi, A 3D steady-state model of a tendon-driven continuum soft manipulator inspired by the octopus arm, Bioinspiration & biomimetics, 7(2) (2012) 025006.
[24] Dehghani, Mosavian, A. akbari, Dynamic modeling of continuum robots with curved-fixed elements without singularity computational states, Modares Mechanical Engineering, 14(15) (2015) 231-240. (in persian)
[25] W.S. Rone, P. Ben-Tzvi, Continuum robot dynamics utilizing the principle of virtual power, IEEE Transactions on Robotics, 30(1) (2013) 275-287.
[26] A. Ehsani-Seresht, S. Hashemi-Pour Moosavi, Dynamic Modeling of the Cable-Driven Continuum Robots in Hybrid Position-Force Actuation Mode, Journal of Mechanisms and Robotics, 12(5) (2020).
[27] A. Amouri, C. Mahfoudi, A. Zaatri, Dynamic Modeling of a Spatial Cable-Driven Continuum Robot Using Euler-Lagrange Method, International Journal of Engineering and Technology Innovation, 10(1) (2019) 60.
[28] A. Amouri, A. Zaatri, C. Mahfoudi, Dynamic modeling of a class of continuum manipulators in fixed orientation, Journal of Intelligent & Robotic Systems, 91(3-4) (2018) 413-424.
[29] R.J. Webster III, J.M. Romano, N.J. Cowan, Mechanics of precurved-tube continuum robots, IEEE Transactions on Robotics, 25(1) (2008) 67-78.
[30] Q. Peyron, K. Rabenorosoa, N. Andreff, P. Renaud, A numerical framework for the stability and cardinality analysis of concentric tube robots: Introduction and application to the follow-the-leader deployment, Mechanism and Machine Theory, 132 (2019) 176-192.
[31] J. Till, D.C. Rucker, Elastic stability of Cosserat rods and parallel continuum robots, IEEE Transactions on Robotics, 33(3) (2017) 718-733.
[32] X. Wang, D. Zhuang, S. Geng, Y. Liu, R. Kang, Stability Analysis of Rod-Driven Continuum Robots Based on Finite Element Models to Avoid Buckling, in:  2019 IEEE 9th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER), IEEE, 2019, pp. 215-220.
[33] L. Cedolin, Stability of structures: elastic, inelastic, fracture and damage theories, World Scientific, 2010.
[34] M. Ohsaki, K. Ikeda, Stability and optimization of structures: generalized sensitivity analysis, Springer Science & Business Media, 2007.