Motion Control of a 2-link Revolute Manipulator in an Obstacle-Ridden Workspace

Authors: Avinesh Prasad, Bibhya Sharma, Jito Vanualailai

Abstract:

In this paper, we propose a solution to the motion control problem of a 2-link revolute manipulator arm. We require the end-effector of the arm to move safely to its designated target in a priori known workspace cluttered with fixed circular obstacles of arbitrary position and sizes. Firstly a unique velocity algorithm is used to move the end-effector to its target. Secondly, for obstacle avoidance a turning angle is designed, which when incorporated into the control laws ensures that the entire robot arm avoids any number of fixed obstacles along its path enroute the target. The control laws proposed in this paper also ensure that the equilibrium point of the system is asymptotically stable. Computer simulations of the proposed technique are presented.

Keywords: 2-link revolute manipulator, motion control, obstacle avoidance, asymptotic stability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1054857

References:

[1] S. Tejomurtula and S. Kak, "Inverse kinematics in robotics using neural networks," Information Science, vol. 116, no. 2-4, pp. 147-164, January 1999.
[2] J. Vanualailai, S. Nakagiri, and J. Ha, "A solution to twodimension findpath problem," Dynamics and Stability of Systems, vol. 13, pp. 373- 401, 1998.
[3] W. Meyer, "Moving a planar robot arm," MAA Notes: The Mathematical Association of America, vol. , no. 29, pp. 180-192, 1993.
[4] E. Sacks, "Path planning for planar articulated robots using configuration spaces and compliant motion," IEEE Transactions on Robotics and Automation, vol. 19, no. 3, pp. 381-390, 2003.
[5] J. Vanualailai and B. Sharma, "Moving a robot arm: an interesting application of the Direct Method of Lyapunov," CUBO: A Mathematical Journal, vol. 6, no. 3, pp. 131-144, 2004.
[6] J. Vanualailai, B. Sharma, and A. Ali, "Lyapunov-based kinematic path planning for a 3-link planar robot arm in a structured environment," Global Journal of Pure and Applied Mathematics, vol. 3, no. 2, pp. 175- 190, 2007.
[7] B. Sharma, A. Prasad, and J. Vanualailai, "A collision-free algorithm of a point-mass robot using neural networks," Journal of Artificial Intelligence, vol. 3, no. 1, pp. 49-55, 2012.
[8] T.M. Martinetz, H.J. Ritter, and K.J. Schulten, "Threedimensional neural net for learning visomotor coordination of a robot arm," EEE Trans. on Neural Networks, vol. 1, no. 1, 1990.
[9] G. Josin, D. Charney, and D. White, "A neural-representation of an unknown inverse kinematic transformation," in First European Conference on Neural Networks, Paris, Paris, France, June 988.
[10] A. Guez and Z. Ahmad, "Solution to the inverse kinematics problem in robotics by neural networks," in Proc. IEEE International Conference on Neural Networks, BSan Diego, USA, 1988, pp. 617-624.
[11] H. Jack, D.M.A. Lee, R.O. Buchal, and W.H. ElMaraghy, "Neural networks and the inverse kinematics problem," The Journal of Intelligent Manufacturing, vol. 4, pp. 43-46, 1993.
[12] B. Sharma. New Directions in the Applications of the Lyapunov-based Control Scheme to the Findpath Problem. PhD thesis, University of the South Pacific, Suva, Fiji Islands, July 2008. PhD Dissertation.