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Solving nonlinear optimal path tracking problem using a new closed loop direct–indirect optimization method: application on mechanical manipulators

  • M. Irani Rahaghi (a1) and F. Barat (a2)
Summary

The purpose of this study is to determine the dynamic load carrying capacity (DLCC) of a manipulator that moves on the specified path using a new closed loop optimal control method. Solution methods for designing nonlinear optimal controllers in a closed-loop form are usually based on indirect methods, but the proposed method is a combination of direct and indirect methods. Optimal control law is given by solving the nonlinear Hamilton–Jacobi–Bellman (HJB) partial differential equation. This equation is complex to solve exactly for complex dynamics, so it is solved numerically using the Galerkin procedure combined with a nonlinear optimization algorithm. To check the performance of the proposed algorithm, the simulation is performed for a fixed manipulator. The results represent the efficiency of the method for tracking the pre-determined path and determining the DLCC. Finally, an experimental test has been done for a two-link manipulator and compare with simulation results.

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Corresponding author
*Corresponding author. E-mail: irani@kashanu.ac.ir
References
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1. Kong, M., Chen, Z., Ji, C. and You, W., “Optimal Point-to-point Motion Planning of Heavy-Duty Industry Robot with Indirect Method,” International Conference on Robotics and Biomimetics (2013) pp. 768–773.
2. Kashiri, N., Ghasemi, M. H. and Dardel, M., “An iterative method for time optimal control of dynamic systems,” Arch. Control Sci. 21 (1), 523 (2011).
3. Korayem, M. H., Irani, M. and Rafee Nekoo, S., “Motion control and dynamic load carrying capacity of mobile robot via nonlinear optimal feedback,” Int. J. Manuf. Mater. Sci. 2 (1), 1621 (2012).
4. Korayem, M. H. and Irani, M., “New optimization method to solve motion planning of dynamic systems: Application on mechanical manipulators,” Multibody Syst. Dyn. 31 (2), 169189 (2014).
5. Kong, M., Chen, Z., Ji, C. and Liu, M., “Optimal Point-to-point Motion Planning of Flexible Parallel Manipulator with Adaptive Gauss Pseudo-Spectral Method,” International Conference on Advanced Intelligent Mechatronics (AIM) (2014) pp. 852–858.
6. Korayem, A. H., Irani Rahagi, M., Babaee, H. and Korayem, M. H., “Maximum load of flexible joint manipulators using nonlinear controllers,” Robotica35 (1), pp. 119142 (2017).
7. Shafei, A. M. and Korayem, M. H., “Theoretical and experimental study of DLCC for flexible robotic arms in point-to-point motion,” Optim. Control Appl. Methods 38 (6), 963972 (2017).
8. Korayem, M. H., Shafei, A. M. and Shafei, H. R., “Dynamic modeling of nonholonomic wheeled mobile manipulators with elastic joints using recursive Gibbs-Appell formulation,” Sci. Iran. 19 (4), 10921104 (2012).
9. Korayem, M. H., Irani Rahagi, M., and Nekoo, S. Rafee, “Load maximization of flexible joint mechanical manipulator using nonlinear optimal controller,” Acta Astronaut 69 (7–8), 458469 (2011).
10. Guo, W., Li, R., Cao, C., Tong, X. and Gao, Y., “A new methodology for solving trajectory planning and dynamic load-carrying capacity of a robot manipulator,” Math. Probl. Eng. (2016) 28 pages.
11. Wu, J., Chen, X., Wang, L. and Liu, X., “Dynamic load-carrying capacity of a novel redundantly actuated parallel conveyor,” Nonlinear Dyn. 78 (1), 241250 (2014).
12. Kong, M., Chen, Z. and Ji, C., “Optimal Point-to-point Motion Planning of Flexible Parallel Manipulator with Multi-Interval Radau Pseudospectral Method,” MATEC Web of Conferences, 42, EDP Science (2016).
13. Fen, L., Jiang-hai, Z., Xiao-bo, S., Pei-ying, Z., Shi-hui, F. and Zhong-jie, L., “Path Planning of 6-DOF Humanoid Manipulator Based on Improved Ant Colony Algorithm,” Control and Decision Conference (ccdc) (2012) pp. 4158–4161.
14. Gallant, A. and Gosselin, C., “Parametric trajectory optimisation for increase payload,” Trans. Canadian Soc. Mech. Eng. 40 (2), 125137 (2016).
15. Korayem, M. H., Azimirad, V. and Irani Rahagi, M., “Maximum allowable load of mobile manipulator in the presence of obstacle using non-linear open and closed loop optimal control,” Arab. J. Sci. Eng. 39 (5), 41034117 (2014).
16. Chen, C. T. and Liao, T. T., “Trajectory planning of parallel kinematic manipulators for the maximum dynamic load-carrying capacity,” Meccanica 51 (8), 16531674 (2016).
17. Kirk, D. E., Optimal Control Theory. (Prentice-Hall Inc, Englewood Cliffs, New Jersey, USA, 1970).
18. Fletcher, C., “Computational Galerkin Methods,” In: Springer Series in Computational Physics (Springer Verlag, New York, 1984).
19. Beeler, S. C., Tran, H. T. and Banks, H. T., “Feedback control methodologies for nonlinear systems,” J. Optim. Theory Appl. 107 (1), 133 (2000).
20. Cizniar, M., Fikar, M. and Latifi, M. A., “Matlab Dynamic Optimisation Code,” Institute of Information Engineering, Automation, and Mathematics, Department of Information Engineering and Process Control, Faculty of Chemical and Food Technology, Slovak University of Technology in Bratislava, Radlinského 9, 812 37 Bratislava, Slovak Rebublic (2009).
21. 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, 10451060 (2008).
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Robotica
  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
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