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applied sciencesArticleEnergy Optimization of Functionally RedundantRobots through Motion DesignPaolo Boscariol * , Roberto Caracciolo , Dario Richiedei and Alberto TrevisaniDipartimento di Tecnica e Gestione dei sistemi industriali, Università degli Studi di Padova, 36100 Vicenza, Italy;roberto.caracciolo@unipd.it (R.C.); dario.richiedei@unipd.it (D.R.); alberto.trevisani@unipd.it (A.T.)* Correspondence: paolo.boscariol@unipd.itReceived: 26 March 2020; Accepted: 23 April 2020; Published: 26 April 2020????????? ????????Abstract: This work proposes to exploit functional redundancy as a tool to enhance the energyeff i ciency of a robotic system. In a functionally redundant system, i.e., one in which the number ofdegrees of freedom required to complete the task is smaller than the number of available degreesof freedom, the motion of the extra degrees of freedom can be tailored to enhance a performancemetric. This work showcases a method that can be used to effectively enhance the energy eff i ciencythrough motion design, using a detailed dynamic model of the UR5 serial robot arm. The method isbased on an optimization of the motion prof i le, using a parametrized description of the end-effectororientation: the results showcase an increased eff i ciency that allows energy savings up to 20.8%,according to the energy consumption results according to the electro-mechanical dynamic model ofthe robot.Keywords: energy eff i ciency; robot; motion design; functional redundancy; UR51. IntroductionThe optimization of robotic operation is a topic that has drawn a considerable attention and hasbeen the central topic of countless works, also in the light that several metrics can be def i ned to measurethe performance of a robot. Most often the only tool available for optimizing a robotic operation in thetrajectory planning, as most industrial robots are programmed by def i ning their motion as a sequenceof via-points or by composing the motion using a pre-def i ned set of motion primitives.Within this framework, traditionally trajectory optimization has been used to minimizethe execution time of a task [ 1 , 2 ], or the smoothness of the motion prof i le [ 3 , 4 ] for minimummotion-induced vibrations. Later on, the minimization of the actuator effort, usually def i ned as themechanical energy required to drive the robot joint or a quadratic torque norm, has been investigatedin several works, such as [ 5 – 7 ]. Recently, the attention has shifted to the investigation and optimizationof the energy consumption of a robotic system [ 8 ]. Such works are motivated by the energy savingpolicies supported by the European Union, as well as by the clear economic advantage associatedwith increased eff i ciency. The review work [ 8 ] lists several methods to reduce energy consumption,among which are the use of regenerative motor drives and energy sharing on a bus [ 9 , 10 ], the useof mechanical energy storage devices [ 11 – 15 ]. Such methods are listed in the work [ 8 ] as hardwaresolutions, meaning that the energy eff i ciency enhancement is obtained by introducing some physicalmodif i cations to the system. On the other hand, all methods that do not require any physical alterationare listed as software solutions, being based just on the modif i cation of the software that handles therobotic operation. Among them, the most common solution is to def i ne an energy-optimal motionprof i le: within this approach the estimated energy saving can be very signif i cant, since improvementsup to 33% are testif i ed by Park in the work [16].Appl. Sci. 2020, 10, 3022; doi:10.3390/app10093022 www.mdpi.com/journal/applsci