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In this approach, we simultaneously shape and exploit the robot's natural dynamics by finding a set of compliant elements and task frequency that result in minimization of an energy-based cost function. The cost function is the integral of a weighted squared norm of the generalized forces. We prove that the generalized force needed for tracking the reference trajectory is a linear function of compliance coefficients and a quadratic function of task frequency. Therefore, the cost function is quadratic with respect to stiffness coefficients and quartic with respect to the task frequency. These properties lead to a well-posed optimization problem with a closed-form solution. Using three case studies, we elucidate the properties of our method.<\/jats:p>","DOI":"10.1017\/s0263574717000030","type":"journal-article","created":{"date-parts":[[2017,2,10]],"date-time":"2017-02-10T04:15:07Z","timestamp":1486700107000},"page":"2363-2380","source":"Crossref","is-referenced-by-count":13,"title":["Compliance and frequency optimization for energy efficiency in cyclic tasks"],"prefix":"10.1017","volume":"35","author":[{"given":"Mohammad","family":"Shushtari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rezvan","family":"Nasiri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Javad","family":"Yazdanpanah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Majid Nili","family":"Ahmadabadi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2017,2,10]]},"reference":[{"key":"S0263574717000030_ref31","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2013.2283927"},{"key":"S0263574717000030_ref11","doi-asserted-by":"publisher","DOI":"10.1080\/01969722.2012.659977"},{"key":"S0263574717000030_ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2007.03.001"},{"key":"S0263574717000030_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2006.02.009"},{"key":"S0263574717000030_ref6","doi-asserted-by":"crossref","unstructured":"M. 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