{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:24:02Z","timestamp":1754155442420,"version":"3.41.2"},"reference-count":43,"publisher":"Emerald","issue":"3","license":[{"start":{"date-parts":[[2016,5,16]],"date-time":"2016-05-16T00:00:00Z","timestamp":1463356800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IR"],"published-print":{"date-parts":[[2016,5,16]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to explore the possible roles of active tails for steady-state legged locomotion, focusing on a design principle which simplifies control by decoupling different control objectives.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title><jats:p>A series of simple models are proposed which capture the dynamics of an idealized running system with an active tail. These models suggest that the overall control problem can be simplified and effectively decoupled via a proper tail design. This design principle is further explored in simulation using trajectory optimization. The results are then validated in hardware using a one degree-of-freedom active tail mounted on the quadruped robot Cheetah-Cub.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title><jats:p>The results of this paper show that an active tail can greatly improve both forward velocity and reduce body-pitch per stride while adding minimal complexity. Further, the results validate the design principle of using long, light tails compared to shorter heavier ones.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title><jats:p>This paper builds on previous results, with a new focus on steady-state locomotion and in particular deals directly with stance phase dynamics. A novel design principle for tails is proposed and validated.<\/jats:p><\/jats:sec>","DOI":"10.1108\/ir-10-2015-0190","type":"journal-article","created":{"date-parts":[[2016,5,24]],"date-time":"2016-05-24T11:34:06Z","timestamp":1464089646000},"page":"338-346","source":"Crossref","is-referenced-by-count":20,"title":["On designing an active tail for legged robots: simplifying control via decoupling of control objectives"],"prefix":"10.1108","volume":"43","author":[{"given":"Steve W.","family":"Heim","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mostafa","family":"Ajallooeian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Eckert","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Massimo","family":"Vespignani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Auke Jan","family":"Ijspeert","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","reference":[{"first-page":"3390","article-title":"Modular control of limit cycle locomotion over unperceived rough terrain","year":"2013","key":"key2020121604583359900_ref045"},{"issue":"2","key":"key2020121604583359900_ref002","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1111\/j.1469-7998.1975.tb05983.x","article-title":"The mechanics of hopping by kangaroos (Macropodidae)","volume":"177","year":"1975","journal-title":"Journal of Zoology"},{"issue":"3","key":"key2020121604583359900_ref003","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1023\/A:1012426720699","article-title":"Rhex: a biologically inspired hexapod runner","volume":"11","year":"2001","journal-title":"Autonomous Robots"},{"issue":"4","key":"key2020121604583359900_ref004","doi-asserted-by":"crossref","first-page":"046005","DOI":"10.1088\/1748-3182\/7\/4\/046005","article-title":"Towards a bio-inspired leg design for high-speed running","volume":"7","year":"2012","journal-title":"Bioinspiration & Biomimetics"},{"issue":"1","key":"key2020121604583359900_ref005","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1242\/jeb.35.1.109","article-title":"The speed of swimming of fish as related to size and to the frequency and amplitude of the tail beat","volume":"35","year":"1958","journal-title":"Journal of Experimental Biology"},{"issue":"2","key":"key2020121604583359900_ref006","doi-asserted-by":"crossref","first-page":"155","DOI":"10.2307\/1375371","article-title":"Locomotion in kangaroo rats and its adaptive significance","volume":"32","year":"1951","journal-title":"Journal of Mammalogy"},{"first-page":"441","article-title":"Design and control of ranger: an energy-efficient, dynamic walking robot","year":"2012","key":"key2020121604583359900_ref007"},{"issue":"11","key":"key2020121604583359900_ref008","first-page":"1217","article-title":"The spring-mass model for running and hopping","volume":"22","year":"1989","journal-title":"Journal of Biomechanics"},{"first-page":"1889","article-title":"Dynamic torque control of a hydraulic quadruped robot","year":"2012","key":"key2020121604583359900_ref009"},{"first-page":"1473","article-title":"Tails in biomimetic design: analysis, simulation, and experiment","year":"2012","key":"key2020121604583359900_ref010"},{"year":"2015","key":"key2020121604583359900_ref011","article-title":"Parallel composition of templates for tail-energized planar hopping"},{"issue":"23","key":"key2020121604583359900_ref012","doi-asserted-by":"crossref","first-page":"3325","DOI":"10.1242\/jeb.202.23.3325","article-title":"Templates and anchors: neuromechanical hypotheses of legged locomotion on land","volume":"202","year":"1999","journal-title":"Journal of Experimental Biology"},{"issue":"3","key":"key2020121604583359900_ref013","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1109\/TNSRE.2010.2047592","article-title":"A muscle-reflex model that encodes principles of legged mechanics produces human walking dynamics and muscle activities","volume":"18","year":"2010","journal-title":"IEEE Transactions on Neural Systems and Rehabilitation Engineering"},{"volume-title":"Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields","year":"1983","key":"key2020121604583359900_ref014"},{"issue":"5\/6","key":"key2020121604583359900_ref015","first-page":"355","article-title":"Towards a theoretical foundation for morphological computation with compliant bodies","volume":"105","year":"2011","journal-title":"Biological Cybernetics"},{"key":"key2020121604583359900_ref016","unstructured":"Heim, S. 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