{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T13:47:50Z","timestamp":1783604870290,"version":"3.55.0"},"reference-count":26,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T00:00:00Z","timestamp":1766448000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Innovation Academy for Microsatellites of CAS","award":["Y4ZZBSWN01"],"award-info":[{"award-number":["Y4ZZBSWN01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the mission scenario of On-Orbit Assembly (OOA), servicing spacecraft are frequently tasked with towing large-scale, flexible truss structures to designated assembly sites. This process involves complex coupled dynamics between the spacecraft and the flexible payload, which are often unmodeled or unknown, posing significant challenges to control precision. Furthermore, the proximity of other assembled structures in the construction area necessitates strict collision avoidance. To address these challenges, this paper proposes a novel adaptive robust controller for spacecraft thruster-based orbital control that integrates Prescribed Performance Control (PPC) with a Radial Basis Function Neural Network (RBFNN). The PPC framework ensures that the position tracking errors remain within user-predefined, time-varying boundaries, providing an intrinsic mechanism for collision avoidance during the towing of large flexible structures. Concurrently, the RBFNN is employed to approximate the entire unknown nonlinear dynamics of the combined spacecraft-truss system online, effectively compensating for uncertainties arising from the flexibility of the truss and external disturbances. The performance of the proposed controller is validated through both numerical simulations and hardware experiments on a ground-based air-bearing satellite simulator. Simulation results demonstrate the controller\u2019s superior tracking accuracy compared to a conventional PID controller, while strictly adhering to the prescribed error constraints. Experimental results further confirm its effectiveness, showing that the simulator can track a desired trajectory with high precision, with tracking errors converging to approximately 5 mm while consistently remaining within the predefined safety boundaries. The proposed approach provides a robust and safe control solution for complex proximity operations in on-orbit construction, eliminating the need for precise dynamic modeling of flexible payloads.<\/jats:p>","DOI":"10.3390\/s26010108","type":"journal-article","created":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T09:58:34Z","timestamp":1766570314000},"page":"108","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An RBFNN-Based Prescribed Performance Controller for Spacecraft Proximity Operations with Collision Avoidance"],"prefix":"10.3390","volume":"26","author":[{"given":"Xianghua","family":"Xie","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"},{"name":"Innovation Academy for Microsatellites of Chinese Academy of Science, Shanghai 201203, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weidong","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9441-5105","authenticated-orcid":false,"given":"Chengkai","family":"Xia","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites of Chinese Academy of Science, Shanghai 201203, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiajian","family":"Xing","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites of Chinese Academy of Science, Shanghai 201203, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang","family":"Chang","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites of Chinese Academy of Science, Shanghai 201203, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,23]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"A Review of Robotics Technologies for On-Orbit Services","volume":"68","author":"Ma","year":"2013","journal-title":"DTIC Doc. ADA576377"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Papadopoulos, E., Aghili, F., Ma, O., and Lampariello, R. (2021). Robotic Manipulation and Capture in Space: A Survey. Front. Robot. AI, 21.","DOI":"10.3389\/frobt.2021.686723"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5921","DOI":"10.3934\/mbe.2023256","article-title":"Adaptive predefined-time prescribed performance control for spacecraft systems","volume":"20","author":"Su","year":"2023","journal-title":"Math. Biosci. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"51","DOI":"10.5194\/ms-16-51-2025","article-title":"A predefined-time radial basis function (RBF) neural network tracking control method considering actuator faults for a new type of spraying robot","volume":"16","author":"Zhao","year":"2025","journal-title":"Mech. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1868","DOI":"10.1049\/cth2.12736","article-title":"Neuro-Adaptive Prescribed Performance Control for Spacecraft Rendezvous Based on Fully-Actuated System Approach","volume":"18","author":"Li","year":"2024","journal-title":"IET Control Theory Appl."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Jia, Q., Shu, R., Yu, D., Zhang, C., and Tan, L. (2023). Neural Network-based Prescribed Performance Fault-Tolerant Control for Spacecraft Formation Reconfiguration with Collision Avoidance. Res. Sq.","DOI":"10.21203\/rs.3.rs-3804664\/v1"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Alizadeh, M., and Zhu, Z.H. (2024). A Comprehensive Survey of Space Robotic Manipulators for On-Orbit Servicing. Front. Robot. AI, 11.","DOI":"10.3389\/frobt.2024.1470950"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Shi, J.F., Ulrich, S., and Allen, A. (2015, January 5\u20139). Spacecraft Adaptive Attitude Control with Application to Space Station Free-Flyer Robotic Capture. Proceedings of the AIAA Guidance, Navigation & Control Conference, Kissimmee, FL, USA.","DOI":"10.2514\/6.2015-1780"},{"key":"ref_9","first-page":"388","article-title":"A Survey on Policy Search for Robotics","volume":"2","author":"Deisenroth","year":"2013","journal-title":"Found. Trends\u00ae Robot."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"100552","DOI":"10.1016\/j.paerosci.2019.100552","article-title":"Historical survey of kinematic and dynamic spacecraft simulators for laboratory experimentation of on-orbit proximity maneuvers","volume":"110","author":"Wilde","year":"2019","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5248","DOI":"10.1109\/TFUZZ.2024.3418577","article-title":"Optimized backstepping attitude containment control for multiple spacecrafts","volume":"32","author":"Fan","year":"2024","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1278","DOI":"10.1109\/TSMC.2019.2896614","article-title":"Command filtered backstepping-based attitude containment control for spacecraft formation","volume":"51","author":"Zhao","year":"2021","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"60776","DOI":"10.1109\/ACCESS.2018.2875971","article-title":"Adaptive backstepping control design for uncertain rigid spacecraft with both input and output constraints","volume":"6","author":"Chen","year":"2018","journal-title":"IEEE Access"},{"key":"ref_14","first-page":"1581","article-title":"A collision-avoidance control algorithm for spacecraft proximity operations based on improved artificial potential function","volume":"52","author":"Xu","year":"2020","journal-title":"Chin. J. Theor. Appl. Mech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2598","DOI":"10.1109\/TCST.2018.2866963","article-title":"Real-time autonomous spacecraft proximity maneuvers and docking using an adaptive artificial potential field approach","volume":"27","author":"Zappulla","year":"2018","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"587","DOI":"10.2514\/1.G000101","article-title":"Asymptotic tracking control for spacecraft formation flying with decentralized collision avoidance","volume":"38","author":"Lee","year":"2015","journal-title":"J. Guid. Control. Dyn."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Fabris, M., Cenedese, A., and Hauser, J. (2019, January 25\u201328). Optimal time-invariant formation tracking for a second-order multi-agent system. Proceedings of the 2019 18th European Control Conference, Naples, Italy.","DOI":"10.23919\/ECC.2019.8796245"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2090","DOI":"10.1109\/TAC.2008.929402","article-title":"Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance","volume":"53","author":"Bechlioulis","year":"2008","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1016\/j.automatica.2008.08.012","article-title":"Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems","volume":"45","author":"Bechlioulis","year":"2009","journal-title":"Automatica"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"111463","DOI":"10.1016\/j.automatica.2023.111412","article-title":"Prescribed performance formation control for second-order multi-agent systems with connectivity and collision constraints","volume":"160","author":"Huang","year":"2024","journal-title":"Automatica"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Shi, Z., Han, W., Zhang, C., and Zhang, G. (2025). A Modular Prescribed Performance Formation Control Scheme of a High-Order Multi-Agent System with a Finite-Time Extended State Observer. Electronics, 14.","DOI":"10.3390\/electronics14091783"},{"key":"ref_22","first-page":"1804","article-title":"Adaptive Pose Control for Spacecraft Proximity Operations with Prescribed Performance Under Spatial Motion Constraints","volume":"29","author":"Sahoo","year":"2020","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5438","DOI":"10.1109\/TIE.2011.2164773","article-title":"Advantages of Radial Basis Function Networks for Dynamic System Design","volume":"58","author":"Yu","year":"2011","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_24","first-page":"321","article-title":"Radial basis functions, multi-variable functional interpolation and adaptive networks","volume":"2","author":"Broomhead","year":"1988","journal-title":"Complex Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"521","DOI":"10.12928\/telkomnika.v11i3.1131","article-title":"Adaptive Control for Robotic Manipulators base on RBF Neural Network","volume":"11","author":"Ma","year":"2013","journal-title":"TELKOMNIKA"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1109\/TCYB.2020.2969281","article-title":"Fully Adaptive-Gain-Based Intelligent Failure-Tolerant Control for Spacecraft Attitude Stabilization Under Actuator Saturation","volume":"52","author":"Zhou","year":"2020","journal-title":"IEEE Trans. Cybern."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/1\/108\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T10:01:37Z","timestamp":1766570497000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/1\/108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,23]]},"references-count":26,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["s26010108"],"URL":"https:\/\/doi.org\/10.3390\/s26010108","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,23]]}}}