{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T01:23:55Z","timestamp":1780449835344,"version":"3.54.1"},"reference-count":37,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2015,12,1]],"date-time":"2015-12-01T00:00:00Z","timestamp":1448928000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>Accuracy is one of the most important criteria for the performance evaluation of micro- and nanorobots or systems. Nanopositioning stages are used to achieve the high positioning resolution and accuracy for a wide and growing scope of applications. However, their positioning accuracy and repeatability are not well known and difficult to guarantee, which induces many drawbacks for many applications. For example, in the mechanical characterisation of biological samples, it is difficult to perform several cycles in a repeatable way so as not to induce negative influences on the study. It also prevents one from controlling accurately a tool with respect to a sample without adding additional sensors for closed loop control. This paper aims at quantifying the positioning repeatability and accuracy based on the ISO 9283:1998 standard, and analyzing factors influencing positioning accuracy onto a case study of 1-DoF (Degree-of-Freedom) nanopositioning stage. The influence of thermal drift is notably quantified. Performances improvement of the nanopositioning stage are then investigated through robot calibration (i.e., open-loop approach). Two models (static and adaptive models) are proposed to compensate for both geometric errors and thermal drift. Validation experiments are conducted over a long period (several days) showing that the accuracy of the stage is improved from typical micrometer range to 400 nm using the static model and even down to 100 nm using the adaptive model. In addition, we extend the 1-DoF calibration to multi-DoF with a case study of a 2-DoF nanopositioning robot. Results demonstrate that the model efficiently improved the 2D accuracy from 1400 nm to 200 nm.<\/jats:p>","DOI":"10.3390\/mi6121461","type":"journal-article","created":{"date-parts":[[2015,12,1]],"date-time":"2015-12-01T10:26:58Z","timestamp":1448965618000},"page":"1856-1875","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Calibration of Nanopositioning Stages"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0710-6409","authenticated-orcid":false,"given":"Ning","family":"Tan","sequence":"first","affiliation":[{"name":"FEMTO-ST Institute, UMR CNRS 6174 - UFC \/ ENSMM \/ UTBM, Universit\u00e9 de Franche-Comt\u00e9, 25000 Besan\u00e7on, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C\u00e9dric","family":"Cl\u00e9vy","sequence":"additional","affiliation":[{"name":"FEMTO-ST Institute, UMR CNRS 6174 - UFC \/ ENSMM \/ UTBM, Universit\u00e9 de Franche-Comt\u00e9, 25000 Besan\u00e7on, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicolas","family":"Chaillet","sequence":"additional","affiliation":[{"name":"FEMTO-ST Institute, UMR CNRS 6174 - UFC \/ ENSMM \/ UTBM, Universit\u00e9 de Franche-Comt\u00e9, 25000 Besan\u00e7on, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,12,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"600","DOI":"10.3390\/mi6050600","article-title":"Nano-Workbench: A Combined Hollow AFM Cantilever and Robotic Manipulator","volume":"6","author":"Garza","year":"2015","journal-title":"Micromachines"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1109\/TMECH.2012.2224122","article-title":"Robust Control of a MEMS Probing Device","volume":"19","author":"Zhang","year":"2014","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"648","DOI":"10.3390\/mi6050648","article-title":"On-Chip Transportation and Measurement of Mechanical Characteristics of Oocytes in an Open Environment","volume":"6","author":"Nakahara","year":"2015","journal-title":"Micromachines"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1109\/TMECH.2011.2106136","article-title":"Automatic Hysteresis Modeling of Piezoelectric Micromanipulator in Vision-Guided Micromanipulation Systems","volume":"17","author":"Zhang","year":"2012","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_5","unstructured":"Chaillet, N., and R\u00e9gnier, S. (2010). Microrobotics for Micromanipulation, Wiley-ISTE."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"956","DOI":"10.1109\/TMECH.2014.2337933","article-title":"Mechanical deformation analysis and high-Precision control for ball-screw-driven stages","volume":"20","author":"Zhu","year":"2015","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1109\/TMECH.2012.2235455","article-title":"A Long-Stroke Nanopositioning Control System of the Coplanar Stage","volume":"19","author":"Wang","year":"2014","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1109\/TCST.2007.903345","article-title":"A survey of control issues in nanopositioning","volume":"15","author":"Devasia","year":"2007","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1120","DOI":"10.1109\/TMECH.2011.2160074","article-title":"Design and robust repetitive control of a new parallel kinematic XY piezostage for Micro\/Nanomanipulation","volume":"17","author":"Li","year":"2012","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2128","DOI":"10.1049\/iet-cta.2013.0086","article-title":"Computed force control system using functional link radial basis function network with asymmetric membership function for piezo-flexural nanopositioning stage","volume":"7","author":"Lin","year":"2013","journal-title":"IET Control Theory Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1109\/TASE.2009.2028617","article-title":"Complete open loop control of hysteretic, creeped, and oscillating piezoelectric cantilevers","volume":"7","author":"Rakotondrabe","year":"2009","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/TMECH.2014.2301824","article-title":"Laser-based sensing, measurement, and misalignment control of coupled linear and angular motion for ultrahigh precision movement","volume":"20","author":"Clark","year":"2015","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Cl\u00e9vy, C., Rakotondrabe, M., and Chaillet, N. (2011). Signal Measurement and Estimation Techniques for Micro and Nanotechnology, Springer-Verlag New York.","DOI":"10.1007\/978-1-4419-9946-7"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1109\/TCST.2014.2345098","article-title":"A high-bandwidth MEMS nanopositioner for on-chip AFM: Design, characterization, and control","volume":"23","author":"Maroufi","year":"2015","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.precisioneng.2014.12.006","article-title":"A flexure-based electromagnetic nanopositioning actuator with predictable and re-configurable open-loop positioning resolution","volume":"40","author":"Teo","year":"2015","journal-title":"Precis. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1109\/TCST.2014.2360498","article-title":"Enhanced Tracking for Nanopositioning Systems Using Feedforward\/Feedback Multivariable Control Design","volume":"23","author":"Heath","year":"2015","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Tan, N., Cl\u00e9vy, C., Laurent, G., and Chaillet, N. (2012, January 11\u201314). Calibration and validation of XY\u0398 micropositioners with vision. Proceedings of the IEEE\/ASME International Conference on Advanced Intelligent Mechatronics, Kachsiung, Taiwan.","DOI":"10.1109\/AIM.2012.6266031"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1109\/TMECH.2014.2306231","article-title":"A monolithic self-sensing precision stage: Design, modeling, calibration, and hysteresis compensation","volume":"20","author":"Chen","year":"2015","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1109\/TMECH.2014.2326865","article-title":"A Microactuation and Sensing Platform with Active Lockdown for in Situ Calibration of Scale Factor Drifts in Dual-Axis Gyroscopes","volume":"20","author":"Aktakka","year":"2015","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Tan, N., Cl\u00e9vy, C., and Chaillet, N. (2013, January 6\u201310). Calibration of single-axis nanopositioning cell subjected to thermal disturbance. Proceedings of the IEEE International Conference on Robotics and Automation, Karlsruhe, Germany.","DOI":"10.1109\/ICRA.2013.6631091"},{"key":"ref_21","unstructured":"Lubrano, E., and Clavel, R. (2008, January 18\u201319). Thermal Behavior of an Ultra High-Precision Linear Axis Operating in Industrial Environment. Proceedings of the 9th International Workshop on Research and Education in Mechatronics, Bergamo, Italy."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1007\/BF01239613","article-title":"Thermal Error Modelling for Real-Time Error Compensation","volume":"12","author":"Chen","year":"1996","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1115\/1.2830168","article-title":"Modelling, Identification and Control of Thermal Deformation of Machine Tool Structures, Part 2: Generalized Transfer Functions","volume":"120","author":"Fraser","year":"1998","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/S0957-4158(97)00059-7","article-title":"Temperature Integration Model and Measurement Point Selection for Thermally Induced Machine Tool Errors","volume":"8","author":"Krulewich","year":"1998","journal-title":"Mechatronics"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2119","DOI":"10.1016\/S0890-6955(00)00023-7","article-title":"Nongeometric error identification and compensation for robotic system by inverse calibration","volume":"40","author":"Gong","year":"2000","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1016\/j.ijmachtools.2006.06.018","article-title":"Simulation of Thermal Behavior of a CNC Machine Tool Spindle","volume":"47","author":"Zhao","year":"2007","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_27","unstructured":"Zhu, J. (2008). Robust Thermal Error Modeling and Compensation for CNC Machine Tools. [Ph.D. Thesis, The University of Michigan]."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"046108","DOI":"10.1063\/1.2908162","article-title":"Thermal effect on piezoelectric stick-slip actuator systems","volume":"79","author":"Li","year":"2008","journal-title":"Rev. Sci. Instrum."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s11249-010-9578-4","article-title":"Effects of Temperature on the Microscale Adhesion Behavior of Thermoplastic Polymer Film","volume":"38","author":"Kim","year":"2010","journal-title":"Tribol. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1109\/TASE.2011.2173570","article-title":"A Multiscale Assembly and Packaging System for Manufacturing of Complex Micro-Nano Devices","volume":"9","author":"Das","year":"2012","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Mattos, L., and Caldwell, D. (2009, January 22\u201325). A fast and precise micropipette positioning system based on continuous camera-robot recalibration and visual servoing. Proceedings of the IEEE International Conference on Automation Science and Engineering, Bangalore, India.","DOI":"10.1109\/COASE.2009.5234157"},{"key":"ref_32","unstructured":"Zhang, Y., Han, M., Shee, C., and Ang, W. (2008, January 2\u20135). Calibration of piezoelectric actuator-based vision guided cell microinjection system. Proceedings of the IEEE\/ASME International Conference on Advanced Intelligent Mechatronics, Xi\u2019an, China."},{"key":"ref_33","unstructured":"(1998). ISO 9283:1998 Manipulating Industrial Robots\u2014Performance Criteria and Related Test Methods, International Organization for Standardization."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1049\/el.2014.0926","article-title":"Performance analysis and characterization of micro-nanopositioning systems","volume":"50","author":"Tan","year":"2014","journal-title":"Electron. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1109\/TASE.2008.2010074","article-title":"M3-deterministic, multiscale, multirobot platform for microsystems packaging: Design and quasi-static precision evaluation","volume":"6","author":"Popa","year":"2009","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1016\/j.mechatronics.2013.10.003","article-title":"Measuring and predicting resolution in nanopositioning systems","volume":"24","author":"Fleming","year":"2014","journal-title":"Mechatronics"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.precisioneng.2007.05.001","article-title":"Uncertainty Analysis of a Laser Calibration System for Evaluating the Positioning Accuracy of a Numerically Controlled Axis of Coordinate Measuring Machines and Machine Tools","volume":"32","author":"Castro","year":"2008","journal-title":"Precis. Eng."}],"container-title":["Micromachines"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-666X\/6\/12\/1461\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:53:06Z","timestamp":1760215986000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-666X\/6\/12\/1461"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,1]]},"references-count":37,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2015,12]]}},"alternative-id":["mi6121461"],"URL":"https:\/\/doi.org\/10.3390\/mi6121461","relation":{},"ISSN":["2072-666X"],"issn-type":[{"value":"2072-666X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,12,1]]}}}