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One remedy is to add some penalty for switching between controls. This paper explores the implications of this switching cost for optimal trajectories, using kinematic rigid bodies in the plane (which have been studied extensively in the cost-free-switch model) as an example system. Blatt\u2019s Indifference Principle is used to derive necessary conditions on optimal trajectories; Lipschitzian optimization techniques together with an A* search yield an algorithm for finding trajectories that can arbitrarily approximate the optimal trajectories.<\/jats:p>","DOI":"10.1177\/0278364915594243","type":"journal-article","created":{"date-parts":[[2015,8,21]],"date-time":"2015-08-21T21:50:24Z","timestamp":1440193824000},"page":"454-475","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Optimal trajectories for kinematic planar rigid bodies with switching costs"],"prefix":"10.1177","volume":"35","author":[{"given":"Yu-Han","family":"Lyu","sequence":"first","affiliation":[{"name":"Department of Computer Science, Dartmouth College, Hanover, NH, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Devin","family":"Balkcom","sequence":"additional","affiliation":[{"name":"Department 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