Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-14T20:06:04.463Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinematic model to control the end-effector of a continuum robot for multi-axis processing

Published online by Cambridge University Press:  24 November 2015

Salvador Cobos-Guzman ,
David Palmer  and
Dragos Axinte
Salvador Cobos-Guzman*
Affiliation:
University of Nottingham, Machining and Condition Monitoring Research Group, University Park, Nottingham, NG7 2RD, UK.
David Palmer
Affiliation:
University of Nottingham, Machining and Condition Monitoring Research Group, University Park, Nottingham, NG7 2RD, UK.
Dragos Axinte
Affiliation:
University of Nottingham, Machining and Condition Monitoring Research Group, University Park, Nottingham, NG7 2RD, UK.
*
*Corresponding author. E-mail: Salvador.Cobos_Guzman@nottingham.ac.uk, epxdp1@nottingham.ac.uk, dragos.axinte@nottingham.ac.uk
Get access Rights & Permissions [Opens in a new window]

Summary

This paper presents a novel kinematic approach for controlling the end-effector of a continuum robot for in-situ repair/inspection in restricted and hazardous environments. Forward and inverse kinematic (IK) models have been developed to control the last segment of the continuum robot for performing multi-axis processing tasks using the last six Degrees of Freedom (DoF). The forward kinematics (FK) is proposed using a combination of Euler angle representation and homogeneous matrices. Due to the redundancy of the system, different constraints are proposed to solve the IK for different cases; therefore, the IK model is solved for bending and direction angles between (−π/2 to +π/2) radians. In addition, a novel method to calculate the Jacobian matrix is proposed for this type of hyper-redundant kinematics. The error between the results calculated using the proposed Jacobian algorithm and using the partial derivative equations of the FK map (with respect to linear and angular velocity) is evaluated. The error between the two models is found to be insignificant, thus, the Jacobian is validated as a method of calculating the IK for six DoF.

Keywords

Continuous robotsInverse kinematicKinematics modelJacobian for hyper-redundant systems
Type
Articles
Information
Robotica , Volume 35 , Issue 1 , January 2017 , pp. 224 - 240
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Yekutieli, Y., Flash, T. and Hochner, B., Biomechanics: Hydroskeletal. Encyclopedia of Neuroscience (Larry, R. S., ed.) (Elsevier Academic Press, Oxford, UK, 2009), vol. 2, pp. 189–200.Google Scholar
2. Kier, W. M. and Smith, K. K., “Tongues, tentacles and trunks: The biomechanics of movement in muscular-hydrostats,” Zool. J. Linn. Soc. 83, 307–324 (1985).CrossRefGoogle Scholar
3. Jayne, B. C., “kinematics of terrestrial snake locomotion,” Copeia 4, 915–927 (1986).CrossRefGoogle Scholar
4. Transeth, A. A. and Pettersen, K. Y., “A survey on snake robot modeling and locomotion,” Robotica 27 (7), 999–1015 (2009).CrossRefGoogle Scholar
5. Chirikjian, G. S. and Burdick, J. W., “Kinematics of Hyper-Redundant Robot Locomotion with Applications to Grasping,” IEEE International Conference on Robotics and Automation, Sacramento, CA, USA (1991) pp. 720–725.Google Scholar
6. Chirikjian, G. S. and Burdick, J. W., “A modal approach to hyper-redundant manipulator kinematics,” IEEE Trans. Robot. Autom. 10 (3), 343–354 (1994).Google Scholar
7. Anderson, V. C. and Horn, R. C., “Tensor arm manipulator design,” Transactions of the ASME, vol. 67, DE-57 (1967) pp. 1–12.Google Scholar
8. Walker, I. D. and Hannan, M. W., “A Novel Elephant's Trunk Robot,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Atlanta, USA (1999) pp. 410–415.Google Scholar
9. Mahl, T., Hildebrandt, A. and Sawodny, O., “Forward Kinematics of a Compliant Pneumatically Actuated Redundant Manipulator,” 7th IEEE Conference on Industrial Electronics and Applications (ICIEA), Singapore (2012) pp. 1267–1273.Google Scholar
10. Gravagne, I. A. and Walker, I. D., “Manipulability, force, and compliance analysis for planar continuum manipulators,” IEEE Trans. Robot. Autom. 18 (3), 263–273 (2002).CrossRefGoogle ScholarPubMed
11. OC robotics, http://www.ocrobotics.com/.Google Scholar
12. Kim, Y.-J., Cheng, S., Kim, S. and Iagnemma, K., “Design of a Tubular Snake-like Manipulator with Stiffening Capability by Layer Jamming,” IEEE/RSJ International Conference on Intelligent Robots and Systems Vilamoura, Portugal (2012) pp. 4251–4256.Google Scholar
13. Lanteigne, E. and Jnifene, A., “Design of a Link-Less Hyper-Redundant Manipulator and Composite Shape Memory Alloy Actuator,” Conference on Electrical and Computer Engineering, CCECE '06, Ottawa, Canada (2006) pp. 1180–1183.Google Scholar
14. Webster, R. J. III and Jones, B. A., “Design and kinematic modeling of constant curvature continuum robots: A review,” Int. J. Robot. Res. 29 (13), 1661–1683 (2010).Google Scholar
15. Cheng, F.-T., Chen, T.-H. and Sun, Y.-Y., “Inverse Kinematic Solutions for Redundant Manipulators using Compact Formulation,” IEEE/RSJ International Workshop on Intelligent Robots and Systems, Intelligence for Mechanical Systems, Osaka, Japan (1991) pp. 153–158.Google Scholar
16. Zanganeh, K. E. and Angeles, J., “The Inverse Kinematics of Hyper-Redundant Manipulators using Splines,” IEEE International Conference on Robotics and Automation, Nagoya, Japan (1995) pp. 2797–2802.Google Scholar
17. Fahimi, F., Ashrafiuon, H. and Nataraj, C., “An improved inverse kinematic and velocity solution for spatial hyper-redundant robots,” IEEE Trans. Robot. Autom. 18 (1), 103–107 (2002).CrossRefGoogle Scholar
18. Kim, Y. Y., Jang, G.-W. and Nam, S. J., “Inverse kinematics of binary manipulators by using the continuous-variable-based optimization method,” IEEE Trans. Robot. 22 (1), 33–42 (2006).Google Scholar
19. Yahya, S., Mohamed, H. A. F., Moghavvemi, M. and Yang, S. S., “A Geometrical Inverse Kinematics Method for Hyper-Redundant Manipulators,” 10th International Conference on Control, Automation, Robotics and Vision, ICARCV 2008, Hanoi, Vietnam (Dec. 17–20, 2008) pp. 1954–1958.Google Scholar
20. Neppalli, S., Csencsits, M. A., Jones, B. A. and Walker, I. D., “Closed-form inverse kinematics for continuum manipulator,” Adv. Robot. 23 (15), 2077–2091 (2009).CrossRefGoogle Scholar
21. Singla, E., Tripathi, S., Rakesh, V. and Dasgupta, B., “Dimensional synthesis of kinematically redundant serial manipulators for cluttered environments,” Robot. Auton. Syst. 58 (5), 585–595 (2010).Google Scholar
22. Mutlu, R., Alici, G. and Li, W., “An effective methodology to solve inverse kinematics of electroactive polymer actuators modelled as active and soft robotic structures,” Mech. Mach. Theory 67, 94–110 (2013).Google Scholar
23. Zhang, Z., Yang, G. and Yeo, S. H., “Inverse Kinematics of Modular Cable-Driven Snake-Like Robots with Flexible Backbones,” IEEE Conference on Robotics, Automation and Mechatronics (RAM), Qingdao, China (2011) pp. 41–46.Google Scholar
24. He, C., Wang, S., Xing, Y. and Wang, X., “Kinematics analysis of the coupled tendon-driven robot based on the product-of-exponentials formula,” Mech. Mach. Theory 60, 90–111 (2013).Google Scholar
25. Gallardo, J., Lesso, R., Rico, J. M. and Alici, G., “The kinematics of modular spatial hyper-redundant manipulators formed from RPS-type limbs,” Robot. Auton. Syst. 59 (1), 12–21.Google Scholar
26. Falco, P. and Natale, C., “On the stability of closed-loop inverse kinematics algorithms for redundant robots,” IEEE Trans. Robot. 27 (4), 780–784 (2011).Google Scholar
27. Hartenberg, R. S. and Denavit, J., “A kinematic notation for lower pair mechanisms based on matrices,” J. Appl. Mech. 77 (2), 215–221 (1955).Google Scholar
28. Kell, J., Davies, S., McGill, I., Rigg, G., Raffles, M., Daine, M., Kong, M., Axinte, D., Marinescu, I. and Herbert, C., Patent: EP2431140A1 (2012) pp. 1–10, 21.03.Google Scholar
29. Thomas, G. B. and Finney, R. L, Calculus and Analytic Geometry, 9th ed. (Addison Wesley, USA, 1996), ISBN 0-201-53174-7.Google Scholar
30. Palmer, D., Cobos Guzman, S. and Axinte, D., “Real-time method for tip following navigation of continuum snake arm robots,” Robot. Auton. Syst. 62 (10), 1478–1485 (2014).CrossRefGoogle Scholar
31. Chhabra, R. and Emami, M. R., “A generalized exponential formula for forward and differential kinematics of open-chain multi-body systems,” Mech. Mach. Theory 73, 61–75 (2014).CrossRefGoogle Scholar
32. Dong, X., Raffles, M., Cobos Guzman, S., Axinte, D. and Kell, J., “Design and analysis of a family of snake arm robots connected by compliant joints,” Mech. Mach. Theory 77, 73–91 (2014).Google Scholar
33. Chirikjian, G. S. and Ebert-Uphoff, I., “Numerical convolution on the Euclidean group with applications to workspace generation,” IEEE Trans. Robot. Autom. 14 (1), 123–136 (1998).CrossRefGoogle Scholar
34. Wang, Y. and Chirikjian, G. S., “Workspace generation of hyper-redundant manipulators as a diffusion process on SE(N),” IEEE Trans. Robot. Autom. 20 (3), 399–408 (2004).CrossRefGoogle Scholar

Cobos-Guzman supplementary material

Cobos-Guzman supplementary material 1

Download Cobos-Guzman supplementary material(Video)
Video 453.2 KB