{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T14:31:40Z","timestamp":1782311500327,"version":"3.54.5"},"reference-count":45,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T00:00:00Z","timestamp":1747353600000},"content-version":"unspecified","delay-in-days":15,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Spherical robots face significant challenges in motion control on non-horizontal terrains, such as slopes, due to their unique spherical structure. This paper systematically investigates the motion stability of spherical robots on inclined surfaces through modeling, control algorithm design, and experimental validation. Precise Equilibrium Modeling: Using the virtual displacement method, the precise equilibrium equation for spherical robots on slopes is derived, addressing the issue of insufficient accuracy in describing the actual center of gravity in existing studies. Control Algorithm Design: For known slope conditions, a Backstepping Control (BSC) algorithm is designed, demonstrating excellent tracking performance. For unknown slope conditions, an Adaptive Backstepping Control (ABSC) algorithm is proposed, which significantly reduces tracking errors and enhances system robustness through parameter adaptation. Simulation and Physical Validation: Simulations confirm the effectiveness of the algorithms: BSC achieves high-precision control under known slopes, while ABSC exhibits strong adaptability under unknown slopes. Physical experiments validate the stability of the algorithms in a <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0263574725000591_inline1.png\"\/><jats:tex-math>\n$5^\\circ$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> slope environment, demonstrating reliable performance across different control angles.<\/jats:p>","DOI":"10.1017\/s0263574725000591","type":"journal-article","created":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T05:47:27Z","timestamp":1747374447000},"page":"1910-1928","source":"Crossref","is-referenced-by-count":1,"title":["Research on motion control of spherical robot in slope environment"],"prefix":"10.1017","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1912-7621","authenticated-orcid":false,"given":"Rui","family":"Lin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tujiu","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4414-1484","authenticated-orcid":false,"given":"Jianwen","family":"Huo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiguan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,5,16]]},"reference":[{"key":"S0263574725000591_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-016-0414-4"},{"key":"S0263574725000591_ref11","doi-asserted-by":"publisher","DOI":"10.3901\/JME.2009.10.008"},{"key":"S0263574725000591_ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2019.2934180"},{"key":"S0263574725000591_ref14","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)AS.1943-5525.0000158"},{"key":"S0263574725000591_ref19","doi-asserted-by":"publisher","DOI":"10.3901\/JME.2011.11.001"},{"key":"S0263574725000591_ref21","doi-asserted-by":"publisher","DOI":"10.1007\/s12206-016-1038-0"},{"key":"S0263574725000591_ref18","doi-asserted-by":"publisher","DOI":"10.1109\/ICCA.2009.5410546"},{"key":"S0263574725000591_ref27","doi-asserted-by":"publisher","DOI":"10.3390\/app10062117"},{"key":"S0263574725000591_ref28","doi-asserted-by":"publisher","DOI":"10.1002\/asjc.2696"},{"key":"S0263574725000591_ref7","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/456727"},{"key":"S0263574725000591_ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3705-9"},{"key":"S0263574725000591_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2024.104657"},{"key":"S0263574725000591_ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2012.2202900"},{"key":"S0263574725000591_ref29","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2022.3203224"},{"key":"S0263574725000591_ref31","doi-asserted-by":"publisher","DOI":"10.1007\/s12206-018-0135-z"},{"key":"S0263574725000591_ref34","doi-asserted-by":"publisher","DOI":"10.5772\/45711"},{"key":"S0263574725000591_ref37","doi-asserted-by":"crossref","unstructured":"[37] Moazami, S. , Palanki, S. and Zargarzadeh, H. . 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