{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T16:36:14Z","timestamp":1772037374117,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2016,11,24]],"date-time":"2016-11-24T00:00:00Z","timestamp":1479945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Reduction of contour error is a very important issue for high precise contour tracking applications, and many control systems were proposed to deal with contour tracking problems for two\/three axial translational motion systems. However, there is no research on cross-coupled contour tracking control for serial multi-DOF robot manipulators. In this paper, the contouring control of multi-DOF serial manipulators is developed for the first time and a new cross-coupled PD (CC-PD) control law is proposed, based on contour errors of the end-effector and tracking errors of the joints. It is a combination of PD control for trajectory tracking at joint level and PD control for contour tracking at the end-effector level. The contour error of the end-effector is transformed to the equivalent tracking errors of the joints using the Jacobian regulation, and the CC-PD control law is implemented in the joint level. Stability analysis of the proposed CC-PD control system is conducted using the Lyapunov method, followed by some simulation studies for linear and nonlinear contour tracking to verify the effectiveness of the proposed CC-PD control system.<\/jats:p>","DOI":"10.3390\/a9040081","type":"journal-article","created":{"date-parts":[[2016,11,24]],"date-time":"2016-11-24T10:19:15Z","timestamp":1479982755000},"page":"81","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Cross-Coupled Contouring Control of Multi-DOF Robotic Manipulator"],"prefix":"10.3390","volume":"9","author":[{"given":"Puren","family":"Ouyang","sequence":"first","affiliation":[{"name":"Department of Aerospace Engineering, Ryerson University, Toronto, ON M5B 2K3, Canada"},{"name":"College of Mechanical and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuqi","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenhui","family":"Yue","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deshun","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,11,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1115\/1.3149612","article-title":"Cross-coupled biaxial computer controls for manufacturing systems","volume":"102","author":"Koren","year":"1980","journal-title":"ASME J. 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