Stiffness analysis and experimental validation of robotic systems

Abstract

Stiffness can be considered of primary importance in order to guarantee the successful use of any robotic system for a given task. Therefore, this paper proposes procedures for carrying out both numerical and experimental estimations of stiffness performance for multibody robotic systems. The proposed numerical procedure is based on models with lumped parameters for deriving the Cartesian stiffness matrix. Stiffness performance indices are also proposed for comparing stiffness performance. Then, an experimental procedure for the evaluation stiffness performance is proposed as based on a new measuring system named as Milli-CATRASYS (Milli Cassino Tracking System) and on a trilateration technique. Cases of study are reported to show the soundness and engineering feasibility of both the proposed numerical formulation for stiffness analysis and experimental validation of stiffness performance.

Key words： robotics; stiffness performance; numerical and experimental estimations

References

1 Rivin E I. Stiffness and Damping in Mechanical Design. New York: Marcel Dekker Inc., 1999

2 Nof S Y, ed. Handbook of Industrial Robotics, New York: John Wiley & Sons, 1985

3 Ceccarelli M. Fundamentals of Mechanics of Robotic Manipulation. Dordrecht: Kluwer Academic Publishers, 2004

4 Wikipedia, 2011. Stiffness. Available on-line at http://en.wikipedia.org/wiki/Stiffness

5 Pratt G A, Williamson M M, Dillworth P, Pratt J, Ulland K, Wright A. Stiffness isn’t everything. Preprints of the 4th International Symposium on Experimental Robotics ISER’95, Stanford, 1995. Available on line at http://www.ai.mit.edu/projects/leglab/publications/ sitffness_isnt_everything.pdf

6 Tsumugiwa T, Yokogawa R, Hara K. Variable impedance control with virtual stiffness for human-robot cooperative peg-in-hole task. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots ans Systems IROS’02, Lausanne, 2002, 1075-1081

7 Schimmels J M. Multidirectional compliance and constraint for improved robotic deburring. Part 1: Improved Positioning. Robotics and Computer-integrated Manufacturing, 2001, 17(4): 277-286

8 English C E, Russell D. Mechanics and stiffness limitations of a variable stiffness actuator for use in prosthetic limbs. Mechanism and Machine Theory, 1999, 34(1): 7-25

9 Gosselin C. Stiffness mapping for parallel manipulators. IEEE Transactions on Robotics and Automation, 1990, 6(3): 377-382

10 Tahmasebi F, Tsai L W. Jacobian and stiffness analysis of a novel class of six-DOF parallel minimanipulators. In: Proceedings of the ASME 22nd Biennial Mechanism Conference, Scottsdale, 1992, 47: 95-102

11 Kim H Y, Streit D A. Configuration dependent stiffness of the Puma 560 manipulator: analytical and experimental results. Mechanism and Machine Theory, 1995, 30(8): 1269-1277

12 Duffy J. Statics and Kinematics with Applications to Robotics. Cambridge: Cambridge University Press, 1996, 153-169.

13 Pigoski T, Griffis M, Duffy J. Stiffness mappings employing different frames of reference. Mechanism and Machine Theory, 1998, 33(6): 825-838

14 Tsai L W. Robot Analysis: the Mechanics of Serial and Parallel Manipulators. New York: John Wiley & Sons, 1999, 260-297

15 Ceccarelli M, Carbone G. A stiffness analysis for CaPaMan (Cassino Parallel Manipulator). Mechanism and Machine Theory, 2002, 37(5): 427-439

16 Gosselin C M, Zhang D. Stiffness analysis of parallel mechanisms using a lumped model. International Journal of Robotics and Automation, 2002, 17(1): 17-27

17 Yoon W K, Suehiro T, Tsumaki Y, Uchiyama M. A method for analyzing parallel mechanism stiffness including elastic deformations in the structure. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems IROS’02, Lausanne, 2002, 2875-2880

18 Alici G, Shirinzadeh B. (2003). Exact stiffness analysis and mapping for a 3-SPS+S parallel manipulator. In: Proceedings of the 7th International Conference on Automation Technology AUTOMATION 2003, F120

19 Simaan N, Shoham M. Stiffness synthesis of a variable geometry six-degrees-of-freedom double planar parallel robot. International Journal of Robotics Research, 2003, 22(9): 757-775

20 Carbone G, Ceccarelli M. A stiffness analysis for a hybrid parallel-serial manipulator. Robotica. International Journal (Toronto, Ont.), 2004, 22: 567-576

21 Ceccarelli M, Carbone G. Numerical and experimental analysis of the stiffness performance of parallel manipulators. 2nd International Colloquium Collaborative Research Centre 562, Braunschweig, 2005, 21-35

22 Lim H O, Setiawan S A, Takanishi A. Balance and impedance control for biped humanoid robot locomotion. In: Proceedings of IEEE 7RSJ International Conference on Intelligent Robots and Systems IROS 2001, Maui, 2001, 494-499

23 Svinin M M, Hosoe S, Uchiyama M, Luo Z W. On the stiffness and stiffness control of redundant manipulators. In: Proceedings of IEEE International Conference on Robotics & Automation ICRA 2002, Washington DC, 2002, 2393-2399

24 Chakarov D. Optimization synthesis of parallel manipulators with desired stiffness. Journal of Theoretical and Applied Mechanics, 1998, 28(4). Avaliable on-line at http://www.imbm.bas.bg/IMBM/LMS/Chakarov/TPM98.pdf

25 Liu X J, Jin Z L, Gao F. Optimum design of 3-DOF spherical parallel manipulators with respect to the conditioning and stiffness indices. Mechanism and Machine Theory, 2000, 35(9): 1257-1267

26 Carbone G, Ceccarelli M, Ogura Y, Lim H O, Takanishi A. Numerical simulation for an optimum design of a humanoid leg through stiffness analysis. 3rd IEEE International Conference on Humanoid Robots HUMANOIDS, München and Karlsruhe, 2003, 3bWalking03

27 Carbone G, Ottaviano E, Ceccarelli M. An optimum design procedure for both serial and parallel manipulators. Journal of Mechanical Engineering Science, 2007, 221(7): 829-843

28 Huang S, Schimmels J M. The bounds and realization of spatial compliances achieved with simple springs connected in parallel. IEEE Transactions on Robotics and Automation, 2000, 14(3): 466-475

29 Zefran M, Kumar V. Affine connections for the cartesian stiffness matrix. In: Proceedings of the IEEE International Conference on Robotics and Automation ICRA’97, Albuquerque, 1997, 2:1376-1381

30 Howard S, Zefran M, Kumar V. On the 6×6 cartesian stiffness matrix for three-dimensional motions. Mechanism and Machine Theory, 1998, 33(4): 389-408

31 Chen S F, Kao I. Geometrical method for modeling of asymmetric 6×6 cartesian stiffness matrix. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems IROS2000, Takamatsu, 2000, 1217-1222

32 Vaishnav R N, Magrab E B. A general procedure to evaluate robot positioning errors. International Journal of Robotics Research, 1987, 6(1): 59-74

33 American National Standards Institute. American National Standard for Industrial Robots and Robot Systems: Point-to-Point and Static Performance Characteristics - Evaluation. New York, 1990, 15.05-1-1990

34 UNI, Italian National Institute for Standards. Manipulating Industrial Robots: Performance Criteria and Related Test Methods. Milan, UNI EN, 1995, 29283 (= ISO 9283)

35 Kardestuncer H. Elementary Matrix Analysis of Structures. Tokyo: McGraw-Hill Kogakusha, 1974

36 Carbone G, Ceccarelli M. A comparison of indices for stiffness performance evaluation. Frontiers of Mechanical Engineering in China, 2010, 5(3): 270-278

37 Merlet J P. Parallel Robots. Dordrecht: Springer Verlag, 2006

38 Patterson T, Lipkin H. A classification of robot compliance. ASME Journal of Mechanical Design., 1993, 115(3): 581-584

39 Gosselin C, Angeles J. A global performance index for the kinematic optimization of robotic manipulators. Transaction of the ASME Journal of Mechanical Design., 1991, 113(3): 220-226