{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:59:53Z","timestamp":1777715993664,"version":"3.51.4"},"reference-count":25,"publisher":"SAGE Publications","issue":"9","license":[{"start":{"date-parts":[[2009,8,20]],"date-time":"2009-08-20T00:00:00Z","timestamp":1250726400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2010,8]]},"abstract":"<jats:p>A lack of sufficient actuation power as well as the presence of passive degrees of freedom are often serious constraints for feasible motions of a robot. Installing passive elastic mechanisms in parallel with the original actuators is one of a few alternatives that allows for large modifications of the range of external forces or torques that can be applied to the mechanical system. If some motions are planned that require a nominal control input above the actuator limitations, then we can search for auxiliary spring-like mechanisms complementing the control scheme in order to overcome the constraints. The intuitive idea of parallel elastic actuation is that spring-like elements generate most of the nominal torque required along a desired trajectory, so the control efforts of the original actuators can be mainly spent in stabilizing the motion. Such attractive arguments are, however, challenging for robots with non-feedback linearizable non-minimum phase dynamics that have one or several passive degrees of freedom. We suggest an approach to resolve the apparent difficulties and illustrate the method with an example of an underactuated planar double pendulum. The results are tested both in simulations and through experimental studies.<\/jats:p>","DOI":"10.1177\/0278364909344002","type":"journal-article","created":{"date-parts":[[2009,8,20]],"date-time":"2009-08-20T21:25:56Z","timestamp":1250803556000},"page":"1186-1198","source":"Crossref","is-referenced-by-count":79,"title":["Parallel Elastic Actuators as a Control Tool for Preplanned Trajectories of Underactuated Mechanical Systems"],"prefix":"10.1177","volume":"29","author":[{"given":"Uwe","family":"Mettin","sequence":"first","affiliation":[{"name":"Department of Applied Physics and Electronics, Ume\u00e5 University, SE-901 87 Ume\u00e5, Sweden,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pedro X.","family":"La Hera","sequence":"additional","affiliation":[{"name":"Department of Applied Physics and Electronics, Ume\u00e5 University, SE-901 87 Ume\u00e5, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leonid B.","family":"Freidovich","sequence":"additional","affiliation":[{"name":"Department of Applied Physics and Electronics, Ume\u00e5 University, SE-901 87 Ume\u00e5, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anton S.","family":"Shiriaev","sequence":"additional","affiliation":[{"name":"Department of Applied Physics and Electronics, Ume\u00e5 University, SE-901 87 Ume\u00e5, Sweden, Department of Engineering Cybernetics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2009,8,20]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1177\/027836499000900205"},{"key":"atypb2","volume-title":"Proceedings of the International Workshop on Robot Motion and Control","author":"Aoustin, Y."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2007.05.002"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2007.07.011"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84800-147-3_2"},{"key":"atypb6","volume-title":"Energy-free Systems: Theory, Conception and Design of Statically Balanced Spring Mechanisms. 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