mmse.96.22.132

Authors: Hadi Asadi, Milad Pouya, Pooyan Vahidi Pashaki

ABSTRACT. This paper is concerned with the optimal path planning for reduction in residual vibration of two- flexible manipulator. Therefore, after presenting the model of a two-link flexible manipulator, the dynamic equations of motion were derived using the assumed modes method. Assuming a desired path for the end effector, the robot was then optimized by considering multiple objective functions. The objective functions should be defined such that in addition to guaranteeing the end effector to travel on the desired path, they can prevent the undesirable extra vibrations of the flexible components. Moreover, in order to assure a complete stop of the robot at the end of the path, the velocity of the end effector at the final point in the path should also reach zero. Securing these two objectives, a time-optimal control may then be applied in order for the robot to travel the path in the minimum duration possible. In all the scenarios, the input motor torques applied to the Two-Link are determined as the optimization variables in a given range. The optimization procedures were carried out based on the Genetic algorithm and Broyden–Fletcher–Goldfarb–Shanno algorithms, and the results are then compared. It is observe that the BFGS algorithm was able to achieve better results compared to GA running a lower number of iterations. Then the final value of the objective function after optimization indicates the decrease in the vibrations of the end effector at the tip of the flexible link.

Keywords: optimization, two-link flexible manipulator, path planning, vibration, genetic algorithm (GA), Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm

DOI 10.2412/mmse.96.22.132

References

[1] Kojima H, Kibe T. Residual Vibration Reduction Control of a Two-Link Flexible Robot Arm Using Optimal Trajectory Planning based on Genetic Algorithm. Journal of the Robotics Society of Japan. 2001, No. 19, 905-912, DOI 10.7210/jrsj.19.905

[2] Kojima H, Kibe T. Optimal trajectory planning of a two-link flexible robot arm based on genetic algorithm for residual vibration reduction. Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems Expanding the Societal Role of Robotics in the Next Millennium (Cat No01CH37180)2001. p. 2276-2281 vol.4, DOI 10.1109/IROS.2001.976409

[3] Andersson J. Sensitivity analysis in Pareto optimal design. [https://www.semanticscholar.org/paper/Sensitivity-Analysis-in-Pareto-Optimal-Design-Andersson/4e11cc0a5beac33d6ab50623ce512b71e709de28]

[4] Li H, Yang Z, Huang T. Dynamics and elasto-dynamics optimization of a 2-DOF planar parallel pick-and-place robot with flexible links. Structural and Multidisciplinary Optimization. 2009, Vol.38, 195-204, DOI 10.1007/s00158-008-0276-x

[5] Caro S, Chablat D, Ur-Rehman R, Wenger P. Multiobjective Design Optimization of 3–PRR Planar Parallel Manipulators. In: Bernard A, editor. Global Product Development: Proceedings of the 20th CIRP Design Conference, Ecole Centrale de Nantes, Nantes, France, 19th-21st April 2010. Springer Berlin Heidelberg, Berlin, Heidelberg, 2011. p. 373-83.

[6] Hegde GS, Vinod MS, Shankar A. Optimum dynamic design of flexible robotic manipulator. International Journal of Mechanics and Materials in Design. 2009, 5, 315-25.

[7] Neto MA, Ambrósio JAC, Leal RP. Sensitivity analysis of flexible multibody systems using composite materials components. International Journal for Numerical Methods in Engineering. 2009, 77, 386-413.

[8] Zhang X, Xu W, Nair SS. Comparison of some modeling and control issues for a flexible two link manipulator. ISA Transactions. 2004, 43, 509-25.

[9] Dubay R, Hassan M, Li C, Charest M. Finite element based model predictive control for active vibration suppression of a one-link flexible manipulator. ISA Transactions. 2014, 53, 1609-19.

[10] Arora JS. Chapter 1 – Introduction to Design Optimization. Introduction to Optimum Design (Third Edition). Academic Press, Boston, 2012. p. 1-15.

[11] Gennert MA, Yuille AL. Determining the optimal weights in multiple objective function optimization. ICCV1988. p. 87-9.

[12] Pashaki, Pooyan Vahidi, and Milad Pouya. “Volumetric error compensation in five-axis CNC machining center through kinematics modeling of geometric error.” Advances in Science and Technology Research Journal 10.30 (2016).

[13] Pashaki, Pouyan Vahidi, and Milad Pouya. “Investigation of High-Speed Cryogenic Machining Based on Finite Element Approach.” Latin American Journal of Solids and Structures 14.4 (2017): 629-642.

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