Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T07:25:00.092Z Has data issue: false hasContentIssue false

An energy efficiency index for elastic actuators during resonant motion

Published online by Cambridge University Press:  04 October 2021

Andrea Calanca*
Affiliation:
Department of Computer Science, University of Verona - Verona, Italy
Tom Verstraten
Affiliation:
Robotics and Multibody Mechanics Research Group (R&MM), Vrije Universiteit Brussel/Flanders Make - Brussels, Belgium
*
*Corresponding author. E-mail: andrea.calanca@gmail.com

Abstract

The energetic advantages of series and parallel elastic actuators have been characterized in the literature considering different elastic systems and different tasks. These characterizations usually determine the energy consumption of a specific system during a specific task and generalize poorly. This paper proposes an energetic characterization of elastic actuators, following an analytical approach, rather than a data-driven one. In particular, this work analyzes the energy consumption of elastic actuators during resonant motion and introduces a novel efficiency index. This index characterizes energy consumption as a function of inherent actuator parameters only, generalizing over the specific tasks. The proposed analysis is validated using simulations and experiments, demonstrating its coherence with analytical results.

Type
Research Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Kubo, K., Kawakami, Y. and Fukunaga, T., “Influence of elastic properties of tendon structures on jump performance in humans,” J. Appl. Physiol. (Bethesda, Md. : 1985) 87, 20902096 (1999). ISSN 8750-7587.CrossRefGoogle Scholar
Ettema, G. J., “Mechanical efficiency and efficiency of storage and release of series elastic energy in skeletal muscle during stretch-shorten cycles,” J. Exp. Biol. 199, 19831997 (1996). ISSN 0022-0949.CrossRefGoogle ScholarPubMed
Roberts, T. J., “The Integrated Function of Muscles and Tendons During Locomotion,” In: Comparative Biochemistry and Physiology - A Molecular and Integrative Physiology, vol. 133 (2002) pp. 10871099. ISBN 1541737822. doi: 10.1016/S1095-6433(02)00244-1.CrossRefGoogle ScholarPubMed
Pratt, G. A. and Williamson, M., “Series Elastic Actuators,” In: International Conference on Intelligent Robots and Systems, vol. 1 (IEEE, 1995) pp. 399406. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=525827.Google Scholar
Calanca, A., Muradore, R. and Fiorini, P., “A review of algorithms for compliant control of stiff and fixed compliance robots, IEEE Trans. Mechatron. 210(2), 613624 (2016). doi: 10.1109/TMECH.2015.2465849.CrossRefGoogle Scholar
Calanca, A. and Fiorini, P., “Human-adaptive control of series elastic actuators,” Robotica 20(08), 13011316 (2014). doi: 10.1017/S0263574714001519.CrossRefGoogle Scholar
Calanca, A. and Fiorini, P., “On the Role of Compliance in Force Control,” In: Advances in Intelligent Systems and Computing (Menegatti, E., Michael, N., Berns, K., and Yamaguchi, H., eds.), vol. 302, Padova, Italy (Springer International Publishing, 2016) pp. 12431255. doi: 10.1007/978-3-319-08338-4_90.CrossRefGoogle Scholar
Oh, S. and Kong, K., “High precision robust force control of a series elastic actuator,” IEEE/ASME Trans. Mechatron. 220(1), 7180 (2017). ISSN 1083-4435. doi: 10.1109/TMECH.2016.2614503. http://ieeexplore.ieee.org/document/7579567/.CrossRefGoogle Scholar
Park, Y., Paine, N. and Oh, S., “Development of force observer in series elastic actuator for dynamic control,” IEEE Trans. Ind. Electron. 00460(c), 11 (2017). ISSN 0278-0046. doi: 10.1109/TIE.2017.2745457. http://ieeexplore.ieee.org/document/8016638/.Google Scholar
Sariyildiz, E., Mutlu, R. and Yu, H., “A sliding mode force and position controller synthesis for series elastic actuators,” Robotica 380 (1), 1528 (2020). doi: 10.1017/S0263574719000420.CrossRefGoogle Scholar
Vanderborght, B., Verrelst, B., Van Ham, R., Van Damme, M., Lefeber, D., Duran, B. M. Y. and Beyl, P., “Exploiting natural dynamics to reduce energy consumption by controlling the compliance of soft actuators,” Int. J. Robot. Res. 250 (4), 343358 (2006). ISSN 0278-3649. doi: 10.1177/0278364906064566. http://ijr.sagepub.com/content/25/4/343.abstract.CrossRefGoogle Scholar
Albert, K. B.. Efficient Control of SEA Through Exploitation of Resonant Modes. PhD thesis, MIT, 2007.Google Scholar
Beckerle, P., Wojtusch, J., Rinderknecht, S. and von Stryk, O.. “Analysis of system dynamic influences in robotic actuators with variable stiffness,” Smart Struct. Syst. 130 (4), 711730 (2014). doi: 10.12989/sss.2014.13.4.711.CrossRefGoogle Scholar
Verstraten, T., Beckerle, P., Furnémont, R., Mathijssen, G., Vanderborght, B. and Lefeber, D., “Series and parallel elastic actuation: Impact of natural dynamics on power and energy consumption,” Mech. Mach. Theory 102, 232246 (2016). ISSN 0094114X. doi: 10.1016/j.mechmachtheory.2016.04.004.CrossRefGoogle Scholar
Beckerle, P., Verstraten, T., Mathijssen, G., Furnémont, R., Vanderborght, B. and Lefeber, D., “Series and parallel elastic actuation: Influence of operating positions on design and control,” IEEE/ASME Trans. Mech. 220(1), 521529 (2017). ISSN 1083-4435. doi: 10.1109/TMECH.2016.2621062.CrossRefGoogle Scholar
Paluska, D. and Herr, H., “The effect of series elasticity on actuator power and work output: Implications for robotic and prosthetic joint design,” Robot. Autonom. Syst. 54, 667673 (2006). doi: 10.1016/j.robot.2006.02.013. http://www.sciencedirect.com/science/article/pii/S0921889006000650.CrossRefGoogle Scholar
Hitt, J. K., Sugar, T. G., Holgate, M. and Bellman, R., “An active foot-ankle prosthesis with biomechanical energy regeneration,” J. Med. Dev. 40(1), 011003 (2010). doi: 10.1115/1.4001139.CrossRefGoogle Scholar
Haeufle, D. F. B., Taylor, M. D., Schmitt, S. and Geyer, H., “A Clutched Parallel Elastic Actuator Concept: Towards Energy Efficient Powered Legs in Prosthetics and Robotics,” In: 2012 4th IEEE RAS EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob), (June 2012) pp. 16141619. doi: 10.1109/BioRob.2012.6290722. http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5628015.Google Scholar
Verstraten, T., Flynn, L., Geeroms, J., Vanderborght, B. and Lefeber, D., “On the Electrical Energy Consumption of Active Ankle Prostheses with Series and Parallel Elastic Elements,” In: 2018 7th IEEE International Conference on Biomedical Robotics and Biomechatronics (BioRob) (2018) pp. 720725. doi: 10.1109/BIOROB.2018.8487656.Google Scholar
Blickhan, R., The Spring-Mass Model for Running and Hopping (1989). ISSN 00219290.Google Scholar
McGeer, T., “Passive dynamic walking,” Int. J. Robot. Res. 9, 6282 (1990). ISSN 0278-3649. doi: 10.1177/027836499000900206.CrossRefGoogle Scholar
Sugar, T. G., Hollander, K. W., Boehler, A. and Ward, J., “Comparison and analysis of a robotic tendon and jackspring actuator for wearable robotic systems,” J. Med. Dev. 70(4), 41003 (2013).CrossRefGoogle Scholar
Ward, J. A., Sugar, T. G. and Hollander, K. W., “Using the Translational Potential Energy of Springs for Prosthetic systems,In: 2011 IEEE International Conference on Control Applications (CCA). (IEEE, 2011) pp. 14611467.CrossRefGoogle Scholar
Wang, S., van Dijk, W. and van der Kooij, H., “Spring Uses in Exoskeleton Actuation Design,” In: IEEE International Conference on Rehabilitation Robotics, vol. 2011 (2011). ISBN 9781424498628. doi: 10.1109/ICORR.2011.5975471. http://www.ncbi.nlm.nih.gov/pubmed/22275669.CrossRefGoogle Scholar
Moro, F. L., Tsagarakis, N. G. and Caldwell, D. G., “Walking in the resonance with the COMAN robot with trajectories based on human kinematic motion primitives (kMPs),” Autonom. Robots 360(4), 331347 (2013). ISSN 0929-5593. doi: 10.1007/s10514-013-9357-9. http://link.springer.com/10.1007/s10514-013-9357-9.Google Scholar
Kormushev, P., Ugurlu, B., Calinon, S., Tsagarakis, N. G. and Caldwell, D. G., “Bipedal Walking Energy Minimization by Reinforcement Learning with Evolving Policy Parameterization,” In: 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (2011) pp. 318324. doi: 10.1109/IROS.2011.6094427. http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6094427.CrossRefGoogle Scholar
Flynn, L., Geeroms, J., Jimenez-Fabian, R., Vanderborght, B., Vitiello, N. and Lefeber, D., “Ankle-knee prosthesis with active ankle and energy transfer: Development of the CYBERLEGs Alpha-Prosthesis,” Robot. Autonom. Syst. (2014). ISSN 09218890. doi: 10.1016/j.robot.2014.12.013. http://www.sciencedirect.com/science/article/pii/S0921889014003108.Google Scholar
Uemura, M. and Kawamura, S., “Resonance-Based Motion Control Method for Multi-Joint Robot Through Combining Stiffness Adaptation and Iterative Learning Control,” In: 2009 IEEE International Conference on Robotics and Automation (2009) pp. 15431548. doi: 10.1109/ROBOT.2009.5152717. http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5152717.CrossRefGoogle Scholar
Goya, H., Matsusaka, K., Uemura, M., Nishioka, Y. and Kawamura, S., “Realization of High-Energy Efficient Pick-and-Place Tasks of SCARA Robots by Resonance,” In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (2012) pp. 27302735. doi: 10.1109/IROS.2012.6386084. http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6386084.CrossRefGoogle Scholar
Vanderborght, B., Albu-Schaeffer, A., Bicchi, A., Burdet, E., Caldwell, D., Carloni, R., Catalano, M., Eiberger, O., Friedl, W., Ganesh, G., Garabini, M., Grebenstein, M., Grioli, G., Haddadin, S., Hoppner, H., Jafari, A., Laffranchi, M., Lefeber, D., Petit, F., Stramigioli, S., Tsagarakis, N., Van Damme, M., Van Ham, R., Visser, L. and Wolf, S., “Variable impedance actuators: A review,” Robot. Autonom. Syst. (2013). ISSN 09218890. doi: 10.1016/j.robot.2013.06.009. http://linkinghub.elsevier.com/retrieve/pii/S0921889013001188.CrossRefGoogle Scholar
Hitt, J., Sugar, T., Holgate, M., Bellman, R. and Hollander, K., “Robotic transtibial prosthesis with biomechanical energy regeneration,” Ind. Robot Int. J. 360(5), 441447 (2009). ISSN 0143-991X. doi: 10.1108/01439910910980169. https://doi.org/10.1108/01439910910980169.CrossRefGoogle Scholar
van den Bogert, A., “Exotendons for assistance of human locomotion,” Biomed. Eng. Online 20(1), 1724 (2003). http://www.biomedcentral.com/content/pdf/1475-925X-2-17.pdf.CrossRefGoogle Scholar
Ortiz, J., Poliero, T., Cairoli, G., Graf, E. and Caldwell, D. G., “Energy efficiency analysis and design optimization of an actuation system in a soft modular lower limb exoskeleton,” IEEE Robot. Automat. Lett. 30(1), 484491 (2018). ISSN 2377-3766. doi: 10.1109/LRA.2017.2768119.CrossRefGoogle Scholar
Bacek, T., Moltedo, M., Rodriguez-Guerrero, C., Geeroms, J., Vanderborght, B. and Lefeber, D., “Design and evaluation of a torque-controllable knee joint actuator with adjustable series compliance and parallel elasticity,” Mech. Mach. Theory 130, 7185 (2018). ISSN 0094-114X. doi: https://doi.org/10.1016/j.mechmachtheory.2018.08.014. https://www.sciencedirect.com/science/article/pii/S0094114X18307559.CrossRefGoogle Scholar
Grimmer, M., Eslamy, M. and Seyfarth, A., “Energetic and peak power advantages of series elastic actuators in an actuated prosthetic leg for walking and running,” Actuators 30(1), 119 (2014). ISSN 2076-0825. doi: 10.3390/act3010001. http://www.mdpi.com/2076-0825/3/1/1/.CrossRefGoogle Scholar
Eslamy, M., Grimmer, M. and Seyfarth, A., “Adding Passive Biarticular Spring to Active Mono-articular Foot Prosthesis: Effects on Power and Energy Requirement,” In: IEEE-RAS International Conference on Humanoid Robots (Humanoids), Madrid, Spain (2014) pp. 677684. ISBN 9781479971732.Google Scholar
Bolívar, E., Rezazadeh, S., Summers, T. and Gregg, R. D., “Robust Optimal Design of Energy Efficient Series Elastic Actuators: Application to a Powered Prosthetic Ankle,” In: 2019 IEEE 16th International Conference on Rehabilitation Robotics (ICORR) (2019) pp. 740747. doi: 10.1109/ICORR.2019.8779446.Google Scholar
Kamadan, A., Kiziltas, G. and Patoglu, V., A systematic design selection methodology for system-optimal compliant actuation,” Robotica 370(4), 656674 (2019). doi: 10.1017/S0263574718001248.CrossRefGoogle Scholar
Gonzalez-Rodriguez, A. G., Gonzalez-Rodriguez, A. and Castillo-Garcia, F., “Improving the energy efficiency and speed of walking robots,” Mechatronics 240(5), 476488 (2014). ISSN 0957-4158. doi: https://doi.org/10.1016/j.mechatronics.2014.05.004.CrossRefGoogle Scholar
Mazumdar, A., Spencer, S. J., Hobart, C., Salton, J., Quigley, M., Wu, T., Bertrand, S., Pratt, J. and Buerger, S. P., Parallel elastic elements improve energy efficiency on the STEPPR bipedal walking robot, IEEE/ASME Trans. Mechatron. 220(2), 898908 (2017). ISSN 1941-014X. doi: 10.1109/TMECH.2016.2631170.CrossRefGoogle Scholar
Reher, J., Cousineau, E. A., Hereid, A., Hubicki, C. M. and Ames, A. D., “Realizing Dynamic and Efficient Bipedal Locomotion on the Humanoid Robot Durus,” In: 2016 IEEE International Conference on Robotics and Automation (ICRA) (2016) pp. 17941801. doi: 10.1109/ICRA.2016.7487325.CrossRefGoogle Scholar
Vu, H. Q., Yu, X., Iida, F. and Pfeifer, R., “Improving energy efficiency of hopping locomotion by using a variable stiffness actuator,” IEEE/ASME Trans. Mechatron. 210(1), 472486 (2016). ISSN 1083-4435. doi: 10.1109/TMECH.2015.2428274.Google Scholar
Yesilevskiy, Y., Gan, Z. and Remy, C. D., Optimal configuration of series and parallel elasticity in a 2D monoped (2016).CrossRefGoogle Scholar
Liu, X., Rossi, A. and Poulakakis, I., “A switchable parallel elastic actuator and its application to leg design for running robots,” IEEE/ASME Trans. Mechatron. 230(6), 26812692 (2018). doi: 10.1109/TMECH.2018.2871670.CrossRefGoogle Scholar
Scheint, M., Sobotka, M. and Buss, M., “Optimized Parallel Joint Springs in Dynamic Motion: Comparison of Simulation and Experiment,” In: 2010 3rd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics (2010) pp. 485490. doi: 10.1109/BIOROB.2010.5628015.CrossRefGoogle Scholar
Schmit, N. and Okada, M., “Optimal design of nonlinear springs in robot mechanism: simultaneous design of trajectory and spring force profiles,” Adv. Robot. 270(1), 3346 (2013). doi: 10.1080/01691864.2013.751162. https://doi.org/10.1080/01691864.2013.751162.CrossRefGoogle Scholar
Nasiri, R., Khoramshahi, M., Shushtari, M. and Ahmadabadi, M. N., “Adaptation in variable parallel compliance: Towards energy efficiency in cyclic tasks,” IEEE/ASME Trans. Mechatron. 220(2), 10591070 (2017). ISSN 1083-4435. doi: 10.1109/TMECH.2016.2637826.CrossRefGoogle Scholar
Shushtari, M., Nasiri, R., Yazdanpanah, M. J. and Ahmadabadi, M. N., Compliance and frequency optimization for energy efficiency in cyclic tasks, Robotica 350(12), 23632380 (2017). doi: 10.1017/S0263574717000030.CrossRefGoogle Scholar
Valero, F., Rubio, F. and Llopis-Albert, C., “Assessment of the effect of energy consumption on trajectory improvement for a car-like robot,” Robotica 370(11), 19982009 (2019). ISSN 14698668. doi: 10.1017/S0263574719000407.CrossRefGoogle Scholar
Vanderborght, B., VanHam, R., Lefeber, D., Sugar, T. G. and Hollander, K. W., “Comparison of mechanical design and energy consumption of adaptable, passive-compliant actuators,” Int. J. Robot. Res. 280(1), 90103 (2009). ISSN 0278-3649. doi: 10.1177/0278364908095333. http://ijr.sagepub.com/cgi/doi/10.1177/0278364908095333.CrossRefGoogle Scholar
Teitler, S. and Proodian, R., “What price speed”, revisited (1980). ISSN 0146-0412.CrossRefGoogle Scholar
Shi, W., Stapersma, D. and Grimmelius, H. T., “Comparison study on moving and transportation performance of transportation modes,” Int. J. Energy Environ. 20(4), 179190 (2008).Google Scholar
Calanca, A., Capisani, L. M., Ferrara, A. and Magnani, L., “MIMO closed loop identification of an industrial robot,” IEEE Trans. Cont. Syst. Technol. 190(5), 12141224 (2011). ISSN 1063-6536. doi: 10.1109/TCST.2010.2077294. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5634145http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5634145.CrossRefGoogle Scholar
Spong, M. and Bhatia, G., “Further Results on Control of the Compass Gait Biped,” In: Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453), vol. 2 (IEEE, 2003) pp. 19331938. ISBN 0-7803-7860-1. doi: 10.1109/IROS.2003.1248927.CrossRefGoogle Scholar