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Vibration optimization of a two-link flexible manipulator with optimal input torques

Pouya M., Vahidi Pashaki P.

Mechanics and Mechanical Engineering

2017

Vol. 21, nr 2

253--265

This paper is concerned with the optimal path planning for reduction in residual vibration of two-flexible manipulator. So 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 GA (Genetic Algorithm) and BFGS (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.