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

Published online by Cambridge University Press:  24 March 2010

A. Nikoobin*
Affiliation:
Department of Mechanical Engineering, Semnan University, Semnan, Iran
M. Moradi
Affiliation:
Department of Computer & Electrical Engineering, Semnan University, Semnan, Iran
*
*Corresponding author. E-mail: anikoobin@iust.ac.ir

Summary

In this paper, a new balancing approach called “optimal balancing” is presented for open-chain robot manipulators based on open-loop optimal control. In fact, an optimal trajectory planning problem is outlined in which states, controls and the values of counterweights must be determined simultaneously in order to minimize the given performance index for a predefined point-to-point task. Optimal balancing method can be propounded beside the other methods such as unbalancing, static balancing and adaptive balancing, with this superiority that the objective criterion value obtained of proposed method is very lower than the objective criterion value obtained of other methods. For this purpose, the optimal control problem is extended to the case where the performance index, the differential constraints and the prescribed final conditions contain parameters. Using the fundamental theorem of calculus of variations, the necessary conditions for optimality are derived which lead to the optimality conditions associated with the Pontryagin's minimum principle and an additional condition associated with the constant parameters. By developing the obtained optimality conditions for the two-link manipulator, a two-point boundary value problem is achieved which can be solved with bvp4c command in MATLAB®. The obtained results show that optimal balancing in comparison with the previous methods can reduce the performance index significantly. This method can be easily applied to the more complicated manipulator such as a three degrees of freedom articulated manipulator.

Type
Article
Copyright
Copyright © Cambridge University Press 2010

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References

1.Chettibi, T., Lehtihet, H. E., Haddad, M. and Hanchi, S., “Minimum cost trajectory planning for industrial robots,” Eur. J. Mech. 23 (4), 703715 (2004).CrossRefGoogle Scholar
2.Hull, D. G., “Conversion of optimal control problems into parameter optimization problems,” J. Guid. Control Dyn. 20 (1), 5760 (1997).CrossRefGoogle Scholar
3.Betts, J. T., “Survey of numerical methods for trajectory optimization,” J. Guid. Control Dyn. 21 (2), 193207 (1998).CrossRefGoogle Scholar
4.Callies, R. and Rentrop, P., “Optimal control of rigid-link manipulators by indirect methods,” GAMM-Mitteilungen 31 (1), 2758 (2008).CrossRefGoogle Scholar
5.Chen, Y. C., “Solving robot trajectory planning problems with uniform cubic B-splines,” Optim. Control Appl. Methods 12 (4), 247262 (1991).CrossRefGoogle Scholar
6.Gill, P. E., Murray, W. and Saunders, A., “Large-Scale SQP Methods and Their Application in Trajectory Optimization,” In: Computational Optimal Control (Birkhauser Verlag, Basel, Switzerland, 1994) pp. 2942.CrossRefGoogle Scholar
7.Wächter, A. and Biegler, L. T., “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Math. Program. 106 (1), 2557 (2006).CrossRefGoogle Scholar
8.Ge, X-S. and Chen, L-Q., “Optimal motion planning for nonholonomic systems using genetic algorithm with wavelet approximation,” Appl. Math. Comput. 180, 7685 (2006).Google Scholar
9.Ravichandran, T., Wang, D. and Heppler, G., “Simultaneous plant-controller design optimization of a two-link planar manipulator,” Mechatronics 16 (3), 233242 (2006).CrossRefGoogle Scholar
10.Saravanan, R., Ramabalan, S. and Balamurugan, C., “Multiobjective trajectory planner for industrial robots with payload constraints,” Robotica 26 (6), 753765 (2008).CrossRefGoogle Scholar
11.Arora, J., Introduction to Optimum Design (Elsevier Academic Press, San Diego, CA, 2004).Google Scholar
12.Kirk, D. E., Optimal Control Theory, an Introduction (Prentice-Hall, Englewood Cliffs, NJ, 1970).Google Scholar
13.Shiller, Z. and Dubowsky, S., “Robot path planning with obstacles, actuators, gripper and payload constraints,” Int. J. Robot. Res. 8 (6), 318 (1986).CrossRefGoogle Scholar
14.Shiller, Z., “Time-energy optimal control of articulated systems with geometric path constraints,” IEEE Int. Conf. Robot. Autom. 4, 26802685 (1994).Google Scholar
15.Fotouhi, R. and Szyszkowski, W., “An algorithm for time optimal control problems,” J. Guid. Control Dyn. 120, 414418 (1998).Google Scholar
16.Bessonnet, G. and Chessé, S., “Optimal dynamics of actuated kinematic chains. Part 2. Problem statements and computational aspects,” Eur. J. Mech. 24, 472490 (2005).CrossRefGoogle Scholar
17.Bertolazzi, E., Biral, F. and Da Lio, M., “Symbolic–numeric indirect method for solving optimal control problems for large multibody systems,” Multibody Syst. Dyn. 13 (2), 233252, (2005).CrossRefGoogle Scholar
18.Sentinella, M. R. and Casalino, L., “Genetic Algorithm and Indirect Method Coupling for Low-Thrust Trajectory Optimization,” 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, California (July 9–12, 2006).Google Scholar
19.Furuno, S., Yamamoto, M. and Mohri, A., “Trajectory planning of mobile manipulator with stability considerations,” IEEE Int. Conf. Robot. Autom. 3, 34033408 (2003).Google Scholar
20.Korayem, M. H. and Nikoobin, A., “Maximum payload for flexible joint manipulators in point-to-point task using optimal control approach,” Int. J. Adv. Manuf. Technol. 38 (9–10), 10451060 (2008).CrossRefGoogle Scholar
21.Korayem, M. H., Nikoobin, A. and Azimirad, V., “Trajectory optimization of flexible link manipulators in point-to-point motion,” Robot. J. 27 (6), 825840 (2009).CrossRefGoogle Scholar
22.Korayem, M. H. and Nikoobin, A., “Maximum-payload path planning for redundant manipulator using indirect solution of optimal control problem,” Int. J. Adv. Manuf. Technol. 44 (7–8), 725736 (2009).CrossRefGoogle Scholar
23.Rivin, E. I., Mechanical Design of Robots (McGraw-Hill, New York, 1988).Google Scholar
24.Park, J., Haan, J. and Park, F. C., “Convex optimization algorithms for active balancing of humanoid robots,” IEEE Trans. Robot. 23 (4), 817822 (2007).CrossRefGoogle Scholar
25.Chung, W. K. and Cho, H. S., “On the dynamic characteristics of a balanced PUMA-760 robot,” IEEE Trans. Ind. Electron. 35 (2), 222230 (1988).CrossRefGoogle Scholar
26.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, 871881 (2004).CrossRefGoogle Scholar
27.Kamenskii, V. A., “On the problem of the number of counterweights in the balancing of plane linkages,” J. Mech. 3, 323333 (1968).CrossRefGoogle Scholar
28.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), 5970 (1998).CrossRefGoogle Scholar
29.Saravanan, R., Ramabalan, S. and Babu, P. D., “Optimum static balancing of an industrial robot mechanism,” Eng. Appl. Artif. Intell. 21 (6), 824834 (2008).CrossRefGoogle Scholar
30.Santangelo, B. G. and Sinatra, R., “Static balancing of a six-degree-of freedom parallel mechanism with six two-link revolute legs,” Int. J. Robot. Autom. 20 (4), 206216 (2005).Google Scholar
31.Hull, D. G., “Sufficiency for optimal control problems involving parameters,” J. Optim. Theory Appl. 97 (3), 579590 (1998).CrossRefGoogle Scholar
32.Herman, P., “Dynamical couplings reduction for rigid manipulators using generalized velocity components,” Mech. Res. Commun. 35, 553561 (2008).CrossRefGoogle Scholar