1080 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 21, NO. 2, APRIL 2016 Development and Control of a Compliant Asymmetric Antagonistic Actuator for Energy Efﬁcient Mobility Wesley Roozing, Zhibin Li, Gustavo A. Medrano-Cerda, Darwin G. Caldwell, and Nikos G. Tsagarakis Abstract—This paper presents the development and con- trol of a novel asymmetric antagonistic actuation scheme characterized by large energy storage capacity that enables efﬁcient execution of motions. The asymmetric design con- sists of two actuation branches that transfer their power to a single joint through two compliant elements with differ- ent stiffness and storage capacity properties. The guideline for selecting the stiffness of both elements is elaborated, given the design parameters and control requirements. We propose a novel control strategy that distributes the effort required to generate the motion using the two actuation branches of this novel hardware, to drive the prototype joint in an energy efﬁcient manner. As a proof of concept, a sin- gle degree-of-freedom knee-actuated hopping robot is de- signed for experimental validation. The dynamics of the leg and actuators are rigorously modeled and formulated. The data from simulation and experimental studies demonstrate a signiﬁcant improvement in electrical energy efﬁciency and reduction in torque requirements. Index Terms—Antagonistic actuator, compliant actuator, energy efﬁcient actuation, variable stiffness. I. INTRODUCTION O NE of the primary challenges in robotic actuation today is the development of high-performance energy efﬁcient actuation concepts that allow for more efﬁcient machines with larger capabilities and more autonomy. This has led to the devel- opment of actuation systems that include compliant elements, which are used for energy storage and release during different stages of the motion. Similar to biological systems, the use of nonstiff actuation can lead to improved energy efﬁciency [1]–[4] and increased peak output power capacity [5], [6]. Additionally, compliance provides advantages such as increased robustness, interaction safety [7]–[9] as well as protection of the actuator drives from impacts. Compliant elements can also be used to compensate for gravitational effects on a system, e.g., by plac- ing pretensioned compliant elements in parallel with the primary actuation mechanism [10]. This can result in large beneﬁts in terms of energy efﬁciency. Manuscript received February 20, 2015; revised June 4, 2015 and Au- gust 5, 2015; accepted September 23, 2015. Date of publication October 26, 2015; date of current version February 24, 2016. Recommended by Technical Editor Y.-J. Pan. This work was supported by the European Commission project WALK-MAN (FP7-ICT-2013-10). The authors are with the Department of Advanced Robotics, (Fon- dazione) Istituto Italiano di Tecnologia, 16163 Genova, Italy (e-mail: wesley.roozing@iit.it; zhibin.li@iit.it; gustavo.cerda@iit.it; darwin. caldwell@iit.it; nikos.tsagarakis@iit.it). Color versions of one or more of the ﬁgures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identiﬁer 10.1109/TMECH.2015.2493359 It has been shown that by tuning the joint compliance to the natural frequency of a system, the energy consumption can be signiﬁcantly reduced while executing harmonic motions [1], [2]. However, for nonperiodic tasks or multidegree-of-freedom (DoF) systems in which the natural dynamics with respect to the joint are continuously changing, this approach is generally not feasible. Existing concepts of actuators that utilize compli- ant elements range from series-elastic actuators (SEAs) with constant compliance [11] to variable stiffness actuators (VSAs) with variable compliance [3], [5]–[7], [9], [12]–[17]. The SEA concept proposed in [11] ﬁrst demonstrated the beneﬁcial properties of compliant actuation, including energy storage, interaction safety, and improved force control. A me- chanical torsion spring was placed in series with a stiff actuator, resulting in series-elastic actuation with constant intrinsic com- pliance. In that study, the authors suggested that investigations into designs with variable stiffness and those with parallel actu- ation branches could further improve performance. The role of compliant actuation systems in improving energy efﬁciency was studied analytically in [4]. The authors analyti- cally derived the optimal stiffness and pretension of SEA and parallel-elastic actuation (PEA) systems for given desired tra- jectories of multi-DoF systems. In simulation studies, it was shown that the use of compliant actuation can yield very large energy efﬁciency beneﬁts compared to the traditional stiff ac- tuation. A PEA system was used in [10] to provide gravity compensation in humanoid legs. The knee joint was augmented with passive springs that provide gravity compensation during squatting. Many VSA designs have been proposed in the literature. In [12], a lever arm connected to a linear spring was used to provide compliant coupling between two links. By setting the lever arm position and spring pretension independently, the equilibrium position and stiffness could be regulated independently. The de- sign was improved in [13] by using a proﬁled cam instead of a lever arm, allowing to shape the deﬂection–torque proﬁle. A design that uses two superimposed proﬁled cam mechanisms was proposed in [14], which resulted in an integrated design. The cams have a proﬁle that combined with rollers extends an internal spring upon deﬂection. By moving one of the cams, the spring can be pretensioned to increase joint stiffness. The design described in [9] obtained a nonlinear stiffness characteristic by using nonlinear transmissions between the internal DoF and the output link, coupled by elastic elements. The authors also showed the intrinsic safety obtained with variable stiffness ac- tuation by impact experiments. 1083-4435 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.