Abstract
Nanotechnology applications demand high accuracy positioning systems. Therefore, in order to achieve sub-micrometer accuracy, positioning uncertainty contributions must be minimized by implementing precision positioning control strategies. The positioning control system accuracy must be analyzed and optimized, especially when the system is required to follow a predefined trajectory. In this line of research, this work studies the contribution of the trajectory definition errors to the final positioning uncertainty of a large-range 2D nanopositioning stage. The curve trajectory is defined by curve fitting using two methods: traditional CAD/CAM systems and novel algorithms for accurate curve fitting. This novel method has an interest in computer-aided geometric design and approximation theory, and allows high relative accuracy (HRA) in the computation of the representations of parametric curves while minimizing the numerical errors. It is verified that the HRA method offers better positioning accuracy than commonly used CAD/CAM methods when defining a trajectory by curve fitting: When fitting a curve by interpolation with the HRA method, fewer data points are required to achieve the precision requirements. Similarly, when fitting a curve by a least-squares approximation, for the same set of given data points, the HRA method is capable of obtaining an accurate approximation curve with fewer control points.
Highlights
Current trends in precision engineering demand high accuracy positioning systems that can be used for measuring and manufacturing applications [1]
The previous section showed that the high relative accuracy (HRA) method is capable of performing accurate curve fitting requiring fewer data points in the interpolation operation and with a minimum number of control points in a least-squares approximation, in comparison with CAD/CAM systems
This section experimentally analyzes the relevance of the trajectory definition errors in the final positioning error of the nanopositioning platform (NanoPla) when the trajectory is defined by fitting a certain set of data points
Summary
Current trends in precision engineering demand high accuracy positioning systems that can be used for measuring and manufacturing applications [1]. The meteorological challenge is an obstacle to the achievement of high accuracy, repeatability, and stability at sub-micrometer and nanometre scales over long travel ranges [2]. In these systems, the positioning error is minimized by implementing precision engineering design principles. The control system performance must be optimized to reduce the positioning uncertainty. In this line of research, at the University of Zaragoza, a novel nanopositioning platform (NanoPla) has been designed, built, and implemented [3]. The NanoPla requirements imply sub-micrometer accuracy in a large working range of 50 mm × 50 mm
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