Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-13T21:56:40.764Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal spring balancing of robot manipulators in point-to-point motion

Published online by Cambridge University Press:  02 November 2012

A. Nikoobin,
M. Moradi and
A. Esmaili
A. Nikoobin*
Affiliation:
Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran
M. Moradi
Affiliation:
Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
A. Esmaili
Affiliation:
Department of Computer & Electrical Engineering, Semnan University, Semnan, Iran
*
*Corresponding author. E-mail: anikoobin@iust.ac.ir
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

The balancing of robotic systems is an important issue, because it allows significant reduction of torques. However, the literature review shows that the balancing of robotic systems is performed without considering the traveling trajectory. Although in static balancing the gravity effects on the actuators are removed, and in complete balancing the Coriolis, centripetal, gravitational, and cross-inertia terms are eliminated, but it does not mean that the required torque to move the manipulator from one point to another point is minimum. In this paper, “optimal spring balancing” is presented for open-chain robotic system based on indirect solution of open-loop optimal control problem. Indeed, optimal spring balancing is an optimal trajectory planning problem in which states, controls, and all the unknown parameters associated with the springs must be determined simultaneously to minimize the given performance index for a predefined point-to-point task. For this purpose, on the basis of the fundamental theorem of calculus of variations, the necessary conditions for optimality are derived that lead to the optimality conditions associated with Pontryagin's minimum principle and an additional condition associated with the constant parameters. The obtained optimality conditions are developed for a two-link manipulator in detail. Finally, the efficiency of the suggested approach is illustrated by simulation for a two-link manipulator and a PUMA-like robot. The obtained results show that the proposed method has dominant superiority over the previous methods such as static balancing or complete balancing.

Keywords

Optimal balancingRobot manipulatorsTrajectory planningOptimal controlPontryagin minimum principleSprings

Information

Type
Articles
Information
Robotica , Volume 31 , Issue 4 , July 2013, pp. 611 - 621
Copyright
Copyright © Cambridge University Press 2012 

References

1.Park, J., Haan, J. and Park, F. C., “Convex optimization algorithms for active balancing of humanoid robots,” IEEE Trans. Robot. 23 (4), 817–822 (2007).CrossRefGoogle Scholar
2.Chung, W. K. and Cho, H. S., “On the dynamic characteristics of a balanced PUMA-760 Robot,” IEEE Trans. Ind. Electron. 35 (2), 222–230 (1988).CrossRefGoogle Scholar
3.Coelho, T. A. H., Yong, L. and Alves, V. F. A., “Decoupling of dynamic equations by means of adaptive balancing of 2-dof open-loop mechanism,” Mech. Mach. Theory 39, 871–881 (2004).CrossRefGoogle Scholar
4.Pons, J. L., Ceres, R. and Jimenez, A. R., “Quasi exact linear spring counter gravity system for robotic manipulators,” Mech. Mach. Theory 33 (1–2), 59–70 (1998).CrossRefGoogle Scholar
5.Arakelian, V. and Ghazaryan, S., “Improvement of balancing accuracy of robotic systems: Application to leg orthosis for rehabilitation devices,” Mech. Mach. Theory 43, 565–575 (2008).CrossRefGoogle Scholar
6.Streit, D. A. and Gilmore, B. J., “Perfect spring equilibrators for rotatable bodies,” ASME Trans. J. Mech. Transm. Autom. Des. 111 (4), 451–458 (1989).CrossRefGoogle Scholar
7.Vrijlandt, N. and Herder, J. L., “Seating unit for supporting a body or part of a body,” Patent, NL1018178, Dec 3, (2002).Google Scholar
8.Agrawal, S. K. and Fattah, A., “Gravity-balancing of spatial robotic manipulators,” Mech. Mach. Theory 39, 1331–1344 (2004).CrossRefGoogle Scholar
9.Kondrin, A. T., Petrov, L. N. and Polishchuk, N. F., “Pivoted arm balancing mechanism,” Patent, SU1596154, Sep 30, (1990).Google Scholar
10.Gvozdev, Y. F., “Manipulator,” Patent, SU1777993, Nov 30, (1992).Google Scholar
11.Ulrich, N. and Kumar, V., “Passive Mechanical Gravity Compensation for Robot Manipulators,” Proceedings of the International Conference on Robotics and Automation, Sacramento, California (Apr 1991) vol. 2, pp. 1536–1541.Google Scholar
12.Kolarski, M., Vukobratovic, M. and Borovac, B., “Dynamic analysis of balanced robot mechanisms,” Mech. Mach. Theory 29 (3), 427–454 (1994).CrossRefGoogle Scholar
13.Banala, S. K., Agrawal, S. K., Fattah, A., Krishnamoorthy, V., Hsu, W. L., Scholz, J. and Rudolph, K., “Gravity-balancing leg orthosis and its performance evaluation,” IEEE Trans. Robot. 22 (6), 1228–1239 (2006).CrossRefGoogle Scholar
14.Fattah, A. and Agrawal, S. K., “Gravity-Balancing of Classes of Industrial Robots,” Proceedings of the IEEE International Conference on Robotics and Automation, Orlando, Florida (May 2006) pp. 2872–2877.Google Scholar
15.Barents, R., Schenk, M., van Dorsser, W. D., Wisse, B. M. and Herder, J. L., “Spring-To-Spring Balancing As Energy-free Adjustment Method In Gravity Equilibrator,” 33rd Mechanism and Robotics Conference, Parts A and B, San Diego, California (Aug–Sep 2009) vol. 7, pp. 689–700.Google Scholar
16.Simionescu, I. and Ciupitu, L., “The static balancing of the industrial arms. Part I: Discrete balancing,” Mech. Mach. Theory 35, 1287–1298 (2000).CrossRefGoogle Scholar
17.Kochev, I. S., “General theory of complete shaking moment balancing of planar linkages: A critical review,” Mech. Mach. Theory 35, 1501–1514 (2000).CrossRefGoogle Scholar
18.Moradi, M., Nikoobin, A. and Azadi, S., “Adaptive decoupling for open chain planar robots,” Iranica Sci. 17 (5B), 376–386 (2010).Google Scholar
19.Saravanan, R., Ramabalan, S. and Babu, P. D., “Optimum static balancing of an industrial robot mechanism,” Eng. Appl. Artif. Intell. 21 (6), 824–834 (2008).CrossRefGoogle Scholar
20.Ravichandran, T., Wang, D. and Heppler, G., “Simultaneous plant-controller design optimization of a two-link planar manipulator,” Mechatronics 16, 233–242 (2006).CrossRefGoogle Scholar
21.Nikoobin, A. and Moradi, M., “Optimal balancing of robot manipulators in point-to-point motions,” Robotica 29 (2), 233–244 (2011).CrossRefGoogle Scholar
22.Gosselin, C. M., Vollmer, F., Cote, G. and Wu, Y., “Synthesis and design of reactionless three-degree-of-freedom parallel mechanisms,” IEEE Trans. Robot. Autom. 20 (2), 191–199 (2004).CrossRefGoogle Scholar
23.Cheng, L., Lin, Y., Hou, Z. G., Tan, M., Huang, J. and Zhang, W. J., “Integrated design of machine body and control algorithm for improving the robustness of a closed-chain five-bar machine,” IEEE/ASME Trans. Mechatronics 17 (3), 587–591 (2012).CrossRefGoogle Scholar
24.Cheng, L., Hou, Z. G., Tan, M. and Zhang, W. J., “Tracking control of a closed-chain five-bar robot with two degrees of freedom by integration of approximation-based approach and mechanical design,” IEEE Trans. Syst. Man Cybern. Part B: Cybernetics 42 (5), 1470–1479 (2012).CrossRefGoogle ScholarPubMed
25.Chettibi, T., Lehtihet, H. E., Haddad, M. and Hanchi, S., “Minimum cost trajectory planning for industrial robots,” Eur. J. Mech. Part A :Solids 23 (4), 703–715 (2004).CrossRefGoogle Scholar
26.Hull, D. G., “Conversion of optimal control problems into parameter optimization problems,” J. Guid. Control Dyn. 20 (1), 57–60 (1997).CrossRefGoogle Scholar
27.Callies, R. and Rentrop, P., “Optimal control of rigid-link manipulators by indirect methods,” GAMM-Mitteilungen 31 (1), 27–58 (2008).CrossRefGoogle Scholar
28.Betts, J. T., “Survey of numerical methods for trajectory optimization,” J. Guid. Control Dyn. 21 (2), 193–207 (1998).CrossRefGoogle Scholar
29.Korayem, M. H. and Nikoobin, A., “Formulation and numerical solution of robot manipulators in point-to-point motion with maximum load carrying capacity,” Scientia Iranica J. 16 (1), 101–109 (2009).Google Scholar
30.Hull, D. G., “Sufficiency for optimal control problems involving parameters,” J. Optim. Theory Appl. 97 (3), 579–590 (1998).CrossRefGoogle Scholar
31.Korayem, M. H., Nikoobin, A. and Azimirad, V., “Maximum load carrying capacity of mobile manipulators: Optimal control approach,” Robotica 27, 147–159 (2009).CrossRefGoogle Scholar
32.Kirk, D. E., Optimal Control Theory: An Introduction (Prentice-Hall, Englewood Cliffs, NJ, 1970).Google Scholar