Some Aspects of Modeling and Robust Control of a Robotic Manipulator EUGEN BOBAU, DAN POPESCU, MONICA ROMAN Department of Automatic Control University of Craiova A.I. Cuza Str. No. 13, RO-200585 Craiova ROMANIA ebobasu@a http://www.ace.ucv.ro Abstract: - The problem of exact linearization via feedback consists in transforming a nonlinear system into a linear one using a state feedback. In the multivariable case, the nonlinear control law achieves also decoupling. The use of feedback linearization requires the complete knowledge of the nonlinear system. In practice, there are many processes whose dynamics is very complex, highly nonlinear and usually incompletely known. It is possible that the controlled system become unstable in the presence of significant model uncertainties. To improve robustness, it may be necessary to modify the exact linearization controller. In this paper, some robustification techniques for the exact linearization method are presented and applied for some multivariable models of a robotic manipulator. Numerical simulations are included to demonstrate the behavior and the performances of these controllers. Key-Words: - Robotic arm, Modelling, Nonlinear control, Linearizing control, Robust control 1 Introduction In this paper, by using the feedback linearizing techniques, a multivariable nonlinear control law is obtained for a robotic manipulator [1]. The model of a robot is obtained from the basic physical laws governing its movement. There are many methods to obtain the dynamical model (see [4], [7], [11]): Lagrange method, Euler method, d'Alembert method, Kane method etc. Here is used the Lagrange method to obtain the dynamical model for a robot, which works in cylindrical coordinates. If we consider some approximations on the robot dynamical model we can do a linear analysis of the manipulator control problem. Without these approximations we have a nonlinear model. In the last years, significant advances have been made in the development of ideas such as feedback linearizing and input-output decoupling techniques ([2], [3], [5]). The problem of exact linearization via feedback and diffeomorphism consists in transforming a nonlinear system into a linear one using a state feedback and a coordinate transformation of the state. Practical implementation of such controllers requires consideration of various sources of uncertainties such as: modelling errors, computation errors, unknown payloads, measurement noise, etc. It is possible that the controlled system become unstable in the presence of significant model uncertainties. To improve robustness, it may be necessary to modify the exact linearization controller to guarantee its robustness. Several techniques from linear and nonlinear control theory have been applied to the problem of robust feedback linearization: Lyapunov redesign method, sliding modes, the ∞ H approach, etc. Here we present two techniques that can be applied to obtain a robust controller for the feedback linearization. First, Glover-McFarlane ∞ H design is presented with the goal of increasing robustness of existing controllers without significantly compromising performance. The second approach is the two-degree of freedom controller design. In these methodologies, it is possible to separate the designing task of meeting performance specifications and robustness into two modular steps. The paper is organized as follows: in Section 2, some basics of the exact linearization theory are presented. In Section 3, the Glover-McFarlane and the two-degree of freedom controller design methods are presented. The mathematical models of a robotic manipulator are analyzed in Section 4. A working example using both nonlinear control laws and the Clover-McFarlane method for robustification of exact linearization design is presented in Section 5 including some computer simulation. Finally, Section 6 collects the conclusions. Proceedings of the 7th WSEAS International Conference on Systems Theory and Scientific Computation, Athens, Greece, August 24-26, 2007 33