Linear Rail Kinematic Calibration using a Legendre Polynomial Model

Published

November 4, 2026

Author(s)

Benjamin Moser, Joshua Gordon, Andrew J. Petruska

Abstract

Linear motion components are widely used in antenna metrology positioning systems, but long motion ranges can reduce positioning accuracy due to the difficulty of eliminating rail component non-linearity. Further, offset device-under-test (DUT) mounting can magnify rotation errors arising from slight variations of rail parallelism not captured by a strictly linear motion model. We present methods to reduce position and rotation inaccuracy through kinematic calibration using a Legendre polynomial model. The motion range of the rail system is conditioned for use over an appropriate evaluation range. The calculation of calibrated coefficients is detailed for an individual rail calibration and is further integrated in a pose-error minimization calibration framework for general robotic implementation. This approach is validated using experimental 6 degree-of-freedom (DoF) measurements collected using Large Antenna Positioning System robotic antenna range. Compared to a strictly linear rail model, the Legendre polynomial model reduced the RMS position error by 67.7% to 27.90 um and RMS rotation error by 29.9% to 84.92 urad.

Proceedings Title

The Proceedings of the 48th​ ​Annual​ ​Meeting​ ​and​ ​Symposium​ ​of​ ​the Antenna​ ​Measurement​ ​Techniques Association

Citation

<i>The Proceedings of the 48th​ ​Annual​ ​Meeting​ ​and​ ​Symposium​ ​of​ ​the Antenna​ ​Measurement​ ​Techniques Association</i> (48th​ ​Annual​ ​Meeting​ ​and​ ​Symposium​ ​of​ ​the Antenna​ ​Measurement​ ​Techniques Association, Tucson, AZ, US, 01-NOV-26 to 06-NOV-26)

Conference Dates

2026-11-01T00:00:00

Conference Location

Tucson, AZ, US

Conference Title

48th​ ​Annual​ ​Meeting​ ​and​ ​Symposium​ ​of​ ​the Antenna​ ​Measurement​ ​Techniques Association

Pub Type

Conferences

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Keywords

Kinematic Calibration, Antenna Range Design, Linear Rail

Citation

Moser, B. , Gordon, J. and Petruska, A. (2026), Linear Rail Kinematic Calibration using a Legendre Polynomial Model, The Proceedings of the 48th​ ​Annual​ ​Meeting​ ​and​ ​Symposium​ ​of​ ​the Antenna​ ​Measurement​ ​Techniques Association, Tucson, AZ, US, [online], https://nps-ext.nist.gov/nps/nps_public_api/api/Publication/file/960238 (Accessed November 10, 2026)

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