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The robot is deployed from the mother satellite by using a long, flexible tether and moving along the target through the desired trajectory. The TSR is modeled as a flexible multibody system consisting of a point mass, a rigid body, and a flexible viscoelastic string. In this regard, the mother spacecraft is modeled as a point mass orbiting in a circular Keplerian orbit. The active robot, which is responsible for docking with the target, is modeled with a three-degree-of-freedom equation of motion that reflects its rigid body and free-floating characteristics. The flexible towing tether, which can experience large displacements and deformations, is modeled using an absolute nodal coordinate formulation (ANCF). The equations of motion of the whole system are derived by using Lagrange\u2019s equation. The overall equations of motion and parameters are described in the natural coordinate frame (NCF). Since the point where the tether is attached to the robot is displaced from its center of mass, there is highly nonlinear coupling between tether deformation\/tension and robot motion. The robot\u2019s position and attitude are controlled actively to sync with the target based on relative pose motion equations, while the tether is dragged behind it. A numerical simulation based on the final approach scenario was conducted, and the results confirm the physical plausibility of the model.<\/jats:p>","DOI":"10.1038\/s41598-026-51564-1","type":"journal-article","created":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T07:04:31Z","timestamp":1778742271000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["ANCF-based dynamic modeling and control of an active tethered space robot in approaching phase"],"prefix":"10.1038","volume":"16","author":[{"given":"Ali","family":"Kasiri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Farhad Fani","family":"Saberi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,14]]},"reference":[{"key":"51564_CR1","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/502973","volume":"2013","author":"Y Chen","year":"2013","unstructured":"Chen, Y., Huang, R., Ren, X., He, L. & He, Y. 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