{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T20:51:17Z","timestamp":1779223877260,"version":"3.51.4"},"reference-count":256,"publisher":"Cambridge University Press (CUP)","issue":"12","license":[{"start":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T00:00:00Z","timestamp":1713225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Multibody dynamics methodologies have been fundamental tools utilized to model and simulate robotic systems that experience contact conditions with the surrounding environment, such as in the case of feet and ground interactions. In addressing such problems, it is of paramount importance to accurately and efficiently handle the large body displacement associated with locomotion of robots, as well as the dynamic response related to contact-impact events. Thus, a generic computational approach, based on the Newton\u2013Euler formulation, to represent the gross motion of robotic systems, is revisited in this work. The main kinematic and dynamic features, necessary to obtain the equations of motion, are discussed. A numerical procedure suitable to solve the equations of motion is also presented. The problem of modeling contacts in dynamical systems involves two main tasks, namely, the contact detection and the contact resolution, which take into account for the kinematics and dynamics of the contacting bodies, constituting the general framework for the process of modeling and simulating complex contact scenarios. In order to properly model the contact interactions, the contact kinematic properties are established based on the geometry of contacting bodies, which allow to perform the contact detection task. The contact dynamics is represented by continuous contact force models, both in terms of normal and tangential contact directions. Finally, the presented formulations are demonstrated by the application to several robotics systems that involve contact and impact events with surrounding environment. Special emphasis is put on the systems\u2019 dynamic behavior, in terms of performance and stability.<\/jats:p>","DOI":"10.1017\/s026357472400050x","type":"journal-article","created":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T04:21:50Z","timestamp":1713241310000},"page":"4070-4102","source":"Crossref","is-referenced-by-count":17,"title":["Multibody dynamics in robotics with focus on contact\u00a0events"],"prefix":"10.1017","volume":"42","author":[{"given":"Mariana Rodrigues","family":"da Silva","sequence":"first","affiliation":[{"name":"University of Minho"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5992-975X","authenticated-orcid":false,"given":"Joana","family":"Coelho","sequence":"additional","affiliation":[{"name":"University of Minho"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fernando","family":"Gon\u00e7alves","sequence":"additional","affiliation":[{"name":"University of Minho"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco","family":"Novais","sequence":"additional","affiliation":[{"name":"University of Minho"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7013-4202","authenticated-orcid":false,"given":"Paulo","family":"Flores","sequence":"additional","affiliation":[{"name":"University of Minho"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2024,4,16]]},"reference":[{"key":"S026357472400050X_ref137","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s11044-020-09744-y","article-title":"A general formulation for the contact between superellipsoid surfaces and nodal points","volume":"50","author":"Ambr\u00f3sio","year":"2020","journal-title":"Multibody Syst Dyn"},{"key":"S026357472400050X_ref148","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/0094-114X(91)90039-7","article-title":"Rough collisions in multibody systems","volume":"26","author":"Batlle","year":"1991","journal-title":"Mech Mach Theory"},{"key":"S026357472400050X_ref218","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.biosystemseng.2005.04.005","article-title":"Determination of parameters of a tangential contact force model for viscoelastic spheroids (fruits) using a rheometer device","volume":"91","author":"Dintwa","year":"2005","journal-title":"Biosyst Eng"},{"key":"S026357472400050X_ref28","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.ijmecsci.2018.07.010","article-title":"A review of continuous contact-force models in multibody dynamics","volume":"145","author":"Skrinjar","year":"2018","journal-title":"Int J Mech Sci"},{"key":"S026357472400050X_ref21","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1017\/S0263574707003864","article-title":"Assisted passive snake-like robots: Conception and dynamic modeling using Gibbs-Appell method","volume":"26","author":"Vossoughi","year":"2008","journal-title":"Robotica"},{"key":"S026357472400050X_ref160","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.mechmachtheory.2019.07.009","article-title":"Ball-on-plate motion planning for six-parallel-legged robots walking on irregular terrains using pure haptic information","volume":"141","author":"Chen","year":"2019","journal-title":"Mech Mach Theory"},{"key":"S026357472400050X_ref251","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1109\/9.376053","article-title":"A new model for control of systems with friction","volume":"40","author":"de Wit","year":"1995","journal-title":"IEEE Trans Autom Cont"},{"key":"S026357472400050X_ref166","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/S0022-460X(03)00074-9","article-title":"Development of elastic force model for wheel\/rail contact problems","volume":"269","author":"Shabana","year":"2004","journal-title":"J Sound Vib"},{"key":"S026357472400050X_ref147","unstructured":"[147] Khulief, Y. 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