{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,28]],"date-time":"2026-08-28T05:17:51Z","timestamp":1787894271150,"version":"build-2784847793"},"reference-count":54,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T00:00:00Z","timestamp":1787702400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science and Technology Plan of Suzhou Municipal","award":["SYG202327"],"award-info":[{"award-number":["SYG202327"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Industrial robots, particularly six-axis serial manipulators, have been widely deployed in manufacturing workflows including assembly, welding, material handling, inspection and precision machining. As the demand for higher end-effector positioning accuracy and trajectory tracking performance grows, end-position errors induced during manipulator operation\u2014stemming from geometric deviations, joint friction, load fluctuations, current surges, as well as variations in velocity and acceleration\u2014have emerged as a critical bottleneck limiting high-precision applications. Conventional error compensation approaches mostly rely on geometric calibration, empirical formulas or fixed regression algorithms, which struggle to adequately characterize error trends featuring strong temporal dependencies, nonlinearity and multi-factor coupling. To address the aforementioned limitations, this paper takes the UR5 industrial manipulator as the research object. Leveraging the NIST-released dataset for manipulator positional accuracy degradation monitoring, this study develops and implements a physics-aware Transformer-based compensation framework that integrates a physics-consistent constraint loss and a nonlinear exponential error amplification strategy with a standard Transformer encoder for end-effector positional accuracy degradation. Multiple variables including target joint position, velocity, acceleration, torque, motor current and control current are selected to construct time-window input vectors, which are used to train the Transformer regression model to capture the correlation between historical motion states and real-time end-effector positional accuracy degradation. Experimental results demonstrate that the proposed Transformer model can fully capture temporal contextual correlations and multi-feature fusion information embedded within manipulator kinematic data, delivering superior error compensation performance for the six-dimensional end-effector pose error prediction task. The self-attention-based time-series modeling framework is well-suited to the nonlinear, coupled and time-varying characteristics of manipulator operational errors. This work provides valuable references for accuracy enhancement of industrial robots and the design of intelligent error compensation schemes. This work provides valuable references for accuracy enhancement of industrial robots and the design of intelligent error compensation schemes, with the proposed physics-aware strategies being model-agnostic and potentially extensible to other regression architectures.<\/jats:p>","DOI":"10.3390\/s26175402","type":"journal-article","created":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T15:04:32Z","timestamp":1787756672000},"page":"5402","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Pose Compensation Method for Robotic Manipulators Based on Transformer"],"prefix":"10.3390","volume":"26","author":[{"given":"Qingqing","family":"Ji","sequence":"first","affiliation":[{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuqian","family":"Li","sequence":"additional","affiliation":[{"name":"School of Cyber Science and Engineering, University of International Relations, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yaxuan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5450-8131","authenticated-orcid":false,"given":"Zhaoxin","family":"Li","sequence":"additional","affiliation":[{"name":"Agricultural Information Institute, Chinese Academy of Agricultural Sciences, Beijing 100081, China"},{"name":"Key Laboratory of Agricultural Big Data, Ministry of Agriculture and Rural Affairs, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Min","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dengming","family":"Zhu","sequence":"additional","affiliation":[{"name":"Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Taicang-ZK Institute of Information and Technology, Taicang 215400, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhaoqi","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,26]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Research Progress on Positioning Error Compensation Technology of Industrial Robot","volume":"59","author":"Liu","year":"2023","journal-title":"J. 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