Motion Control of a 2-link Revolute Manipulator in an Obstacle-Ridden Workspace
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50395", author = "Avinesh Prasad and Bibhya Sharma and Jito Vanualailai", title = "Motion Control of a 2-link Revolute Manipulator in an Obstacle-Ridden Workspace", 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.", volume = "6", number = "12", pages = "1629-6", }