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This paper proposes two control strategies for the motion synchronization of the master-slave manipulators based on their ender trajectories. First, the basic equations used by the two control methods for motion synchronization are presented. Such procedures are proved to be stable for negative definite gain matrices, according to the Lyapunov theory. Then, the controlled items of the slave manipulator are determined for the ender trajectory synchronization by the coordinate transformations between the joint variables and the ender trajectory in the form of pseudo-Jacobian matrix. Finally, the two control methods for synchronization are validated by the numerical simulation for a master-slave system consisting of two planar three-degree-of-freedom (3-DOF) manipulators. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a continuous extension of the Ott, Grehogi and Yorke control method [Ott et al., 1990]. This extension allows the control of chaotic behavior in higher-order dynamical systems. To begin with, studying the so-called Poincaré Sections (PS) enables determining fixed points and the effect of small changes in the control Parameter on the system trajectory. Introduction of a stabilizer parameter in the control law keeps the dynamical properties and maintains them on a cyclic trajectory. The effectiveness of the proposed method is tested by numerical examples on the two typical Chen and Chua chaotic systems. [ABSTRACT FROM AUTHOR]