P. S´nchez-S´nchez and F. Reyes-Cort´s a a e


Cartesian controller, energy shaping, Jacobian transposed controller, artificial potential energy, DRILL-BOT, Lyapunov function, global asymptotical stability


This paper analyzes the position control problem of robot ma- nipulators on Cartesian space. The main objective of this paper is to propose a new controller family with gravity compensation and formal stability proof using Lyapunov’s theory. We have used the simple PD controller representation on Cartesian coordinates to make a comparison with the proposed controller to verify its performance. By means of the application of the L2 norm, the acting of both controllers is analyzed and their behavior is verified. The main contribution of this paper is to prove that the closed-loop system composed by full nonlinear robot dynamic system, and the proposed controller family is asymptotically stable in a global way of agreement with Lyapunov’s direct method and La Salle’s invariance principle. Besides the theoretical results, a real time experimental comparison is also presented to illustrate the performance of the proposed family with other well-known control algorithms such as PD scheme on three degrees of freedom prototype. In this pa- per, we describe an experimental Cartesian robot for research and development of robot control algorithms. This system allows the development and easy test of Cartesian control strategies on three degrees of freedom. The functionality of this system is explained via real time experimental results of a new position Cartesian con- trol algorithm with global asymptotic stability of the closed-loop system.

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