Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 65028, 23 pages
Research Article

Design of Optimal Hybrid Position/Force Controller for a Robot Manipulator Using Neural Networks

Vikas Panwar1 and N. Sukavanam2

1Department of Mathematics, Chaudhary Devi Lal University, Sirsa, Haryana, India
2Department of Mathematics, Indian Institute of Technology, Roorkee 247667, Uttaranchal, India

Received 21 November 2004; Revised 25 April 2006; Accepted 21 November 2006

Academic Editor: Semyon M. Meerkov

Copyright © 2007 Vikas Panwar and N. Sukavanam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The application of quadratic optimization and sliding-mode approach is considered for hybrid position and force control of a robot manipulator. The dynamic model of the manipulator is transformed into a state-space model to contain two sets of state variables, where one describes the constrained motion and the other describes the unconstrained motion. The optimal feedback control law is derived solving matrix differential Riccati equation, which is obtained using Hamilton Jacobi Bellman optimization. The optimal feedback control law is shown to be globally exponentially stable using Lyapunov function approach. The dynamic model uncertainties are compensated with a feedforward neural network. The neural network requires no preliminary offline training and is trained with online weight tuning algorithms that guarantee small errors and bounded control signals. The application of the derived control law is demonstrated through simulation with a 4-DOF robot manipulator to track an elliptical planar constrained surface while applying the desired force on the surface.