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Open AccessArticle

Trajectory Definition with High Relative Accuracy (HRA) by Parametric Representation of Curves in Nano-Positioning Systems

Aragon Institute of Engineering Research (I3A), University of Zaragoza, C/María de Luna 3, 50018 Zaragoza, Spain
Department of Applied Mathematics, University Research Institute of Mathematics and its Applications(IUMA), University of Zaragoza, C/María de Luna, 3, 50018 Zaragoza, Spain
Centro Universitario de la Defensa, Ctra. Huesca s/n, 50090 Zaragoza, Spain
Author to whom correspondence should be addressed.
Micromachines 2019, 10(9), 597;
Received: 8 July 2019 / Revised: 4 September 2019 / Accepted: 7 September 2019 / Published: 10 September 2019
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. View Full-Text
Keywords: nano-positioning; CAD/CAM systems; high relative accuracy (HRA) nano-positioning; CAD/CAM systems; high relative accuracy (HRA)
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Díaz Pérez, L.; Rubio Serrano, B.; Albajez García, J.A.; Yagüe Fabra, J.A.; Mainar Maza, E.; Torralba Gracia, M. Trajectory Definition with High Relative Accuracy (HRA) by Parametric Representation of Curves in Nano-Positioning Systems. Micromachines 2019, 10, 597.

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