Task space path following for planar redundant robots using Pontryagin’s principle in optimal control

Ghaemi Osgouie, Kambiz; Haghighatpars, Assal; Farivar, Faezeh

doi:10.30506/ijmep.2020.90792.1441

Task space path following for planar redundant robots using Pontryagin’s principle in optimal control

Authors

Kambiz Ghaemi Osgouie ¹

Assal Haghighatpars ²

Faezeh Farivar ²

¹ Mechanical Engineering Division, Caspian Faculty of Engineering, College of Engineering, University of Tehran, Rezvanshar, Iran.

² Department of Electronics and Computer, Science and Research Branch, Islamic Azad University, Tehran, Iran.

10.30506/ijmep.2020.90792.1441

Abstract

Several actuation systems in the nature are modelled as redundant robotic arms for which various criteria, such as time, energy, or jerk, might be optimized to generate the most natural motion trajectories. The most suitable yet challenging optimization criterion is manipulator’s consumed energy. In this paper, the joint space kinematic optimization of a redundant planar robot is performed to follow a given task space path. Considering the redundancy of the robot, an initial guess is made for the joint space excessive degrees of freedom of the robot. Then applying the inverse kinematic equations and Pontryagin’s relations, the whole joint space path is calculated. In the implementation of the transversality conditions, according to the error occurred at the other end of the path, the initial guess is updated. Through a try-error process using shooting method, the optimal initial guess is converged and its corresponding joint space trajectory is also obtained. As a numerical evaluation, a sample task space desired path is considered and using the proposed method the proper joint space trajectory is obtained.

Keywords

Redundant Robot

Kinematic optimization

Redundancy

Pontryagin’s Minimum Principle