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

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.

A NEW REALIZATION OF THE GLOBAL LUNAR REFERENCE FRAME BASED ON CO-REGISTERED LOLA TRACKS

We present a method that aligns lunar south and north pole LOLA DTMs using selected LOLA tracks and co-registration techniques. The selected LOLA tracks were then co-registered to the aligned polar DTMs with the aim to create a new LOLA frame of high relative accuracy. At the poles the relative accuracy of the resulting LOLA frame improved in comparison with the original LOLA frame, especially at the north pole. At lower latitudes on the lunar near side we could show that we achieve smaller residuals between our LOLA frame and a photogrammetrically derived reference DTM than with the original LOLA frame. On the far side we could not achieve better results which we believe is stemming from the generally less accurate orbit knowledge there. From the aligned polar DTMs we were able to derive a polar radius of 1738,049 km.