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The article presents information on the use of neural networks for geometrical error modeling and compensation in accurate motion systems. To measure the geometrical error, a laser interferometer was used. As neural networks are nonlinear in nature, they help reduce the memory requirements to accomplish the error compensation for a particular motion system.

Task-space regulation of robot manipulators can be classified into two fundamental approaches, namely, transpose Jacobian regulation and inverse Jacobian regulation. In this paper, two inverse Jacobian regulators with gravity compensations are presented, and the stability problems are formulated and solved. It is shown that the inverse Jacobian systems can be stabilized, and there exists a region of attraction such that the system remains stable. Our results show that the two fundamental approaches are two dual controllers, in the sense that the transpose Jacobian matrix can be replaced by the inverse Jacobian matrix and vice versa. The theoretical results are verified experimentally by implementing the inverse Jacobian regulators on an industrial robot, PUMA560. [ABSTRACT FROM AUTHOR]