{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T17:52:32Z","timestamp":1775325152292,"version":"3.50.1"},"reference-count":41,"publisher":"SAGE Publications","issue":"8","license":[{"start":{"date-parts":[[2015,10,6]],"date-time":"2015-10-06T00:00:00Z","timestamp":1444089600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2016,7]]},"abstract":"<jats:p> This paper presents a relaxed definition of hover for multicopters with propellers pointing in a common direction. These solutions are found by requiring that the multicopter remain substantially in one position, and that the solutions be constant when expressed in a coordinate system attached to the vehicle. The vehicle\u2019s angular velocity is then shown to be either zero or parallel to gravity. The controllability of a vehicle\u2019s attitude about these solutions is then investigated. These relaxed hover solutions may be applied as an algorithmic failsafe, allowing, for example, a quadrocopter to fly despite the complete loss of one, two, or three of its propellers. Experimental results validate the quadrocopter failsafe for two types of failure (a single propeller and two opposing propellers failing), and a nonlinear simulation validates the remaining two types of failure (two adjacent and three propellers failing). The relaxed hover solutions are also shown to allow a multicopter to maintain flight in spite of extreme center of mass offsets. Finally, the design and experimental validation of three novel vehicles is presented. <\/jats:p>","DOI":"10.1177\/0278364915596233","type":"journal-article","created":{"date-parts":[[2015,10,8]],"date-time":"2015-10-08T01:27:51Z","timestamp":1444267671000},"page":"873-889","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":108,"title":["Relaxed hover solutions for multicopters: Application to algorithmic           redundancy and novel vehicles"],"prefix":"10.1177","volume":"35","author":[{"given":"Mark W.","family":"Mueller","sequence":"first","affiliation":[{"name":"Institute for Dynamic Systems and Control, ETH Zurich,\r          Switzerland"}]},{"given":"Raffaello","family":"D\u2019Andrea","sequence":"additional","affiliation":[{"name":"Institute for Dynamic Systems and Control, ETH Zurich,\r          Switzerland"}]}],"member":"179","published-online":{"date-parts":[[2015,10,6]]},"reference":[{"key":"bibr1-0278364915596233","doi-asserted-by":"publisher","DOI":"10.2514\/6.2012-4779"},{"key":"bibr2-0278364915596233","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2013.6759988"},{"key":"bibr3-0278364915596233","volume-title":"Optimal Control: Linear Quadratic Methods","author":"Anderson BD","year":"2007"},{"key":"bibr4-0278364915596233","volume-title":"Linear System Theory","author":"Callier F","year":"1994"},{"key":"bibr5-0278364915596233","doi-asserted-by":"publisher","DOI":"10.1109\/TAES.2012.6324664"},{"key":"bibr6-0278364915596233","doi-asserted-by":"publisher","DOI":"10.1109\/TASE.2014.2326952"},{"key":"bibr7-0278364915596233","volume-title":"Modern Control Systems","author":"Dorf R","year":"2008","edition":"11"},{"key":"bibr8-0278364915596233","unstructured":"Dronologista (2014) DJI dropsafe\n            system. 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