Redundancy facilitates some of the most remarkable capabilities of humans, and is therefore omni-present in our physiology. The relationship between redundancy in robotics and biology is investigated in detail on the Series Elastic Dual-Motor Actuator (SEDMA), an actuator inspired by the kinematic redundancy exhibited by myofibrils. The actuator consists of two motors coupled to a single spring at the output. Such a system has a redundant degree of freedom, which can be exploited to optimize aspects such as accuracy, impedance, fault-tolerance and energy efficiency. To test its potential for human-like motions, the SEDMA actuator is implemented in a hopping robot. Experiments on a physical demonstrator show that the robot’s movement patterns resemble human squat jumps. We conclude that robots with bio-inspired actuator designs facilitate human-like movement, although current technical limitations may prevent them from reaching the same dynamic and energetic performance.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Raibert M H. Legged Robots That Balance, MIT press, Cambridge, MA, USA, 1986.
Sayyad A, Seth B, Seshu P. Single-legged hopping robotics research — A review. Robotica, 2007, 25, 587–613.
Zhang Z Q, Zhao J, Chen H L, Chen D S. A survey of bioinspired jumping robot: Takeoff, air posture adjustment, and landing buffer. Applied Bionics and Biomechanics, 2017, 2017, 22.
Full R J, Koditschek D E. Templates and anchors: Neuromechanical hypotheses of legged locomotion on land. The Journal of Experimental Biology, 1999, 202, 3325–3332.
Blickhan R. The spring-mass model for running and hopping. Journal of Biomechanics, 1989, 22, 1217–1227.
Sharbafi M A, Seyfarth A, Zhao G. Locomotor sub-functions for control of assistive wearable robots. Frontiers in Neurorobotics, 2017, 11, 44.
Haldane D W, Plecnik M M, Yim J K, Fearing R S. Robotic vertical jumping agility via series-elastic power modulation. Science Robotics, 2016, 1, eaag2048.
Sato A, Buehler M. A planar hopping robot with one actuator: Design, simulation, and experimental results. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Sendai, Japan, 2004, 3540–3545.
Batts Z, Kim J, Yamane K. Design of a hopping mechanism using a voice coil actuator: Linear elastic actuator in parallel (LEAP). Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, 2016, 655–660.
Liu X, Poulakakis I. On the energetics of a switchable parallel elastic actuator design for monopedal running. Proceedings of the IEEE International Conference on Robotics and Biomimetics (ROBIO), Zhuhai, China, 2015, 769–774.
Alexander R McN. Three uses for springs in legged locomotion. The International Journal of Robotics Research, 1990, 9, 53–61.
Lichtwark G A, Wilson A M. In vivo mechanical properties of the human Achilles tendon during one-legged hopping. The Journal of Experimental Biology, 2005, 208, 4715–4725.
Biewener A A, Konieczynski D D, Baudinette R V. In vivo muscle force-length behavior during steady-speed hopping in tammar wallabies. The Journal of Experimental Biology, 1998, 201, 1681–1694.
Anderson F C, Pandy M G. Storage and utilization of elastic strain energy during jumping. Journal of Biomechanics, 1993, 26, 1413–1427.
Bobbert M F, Huijing P A, van Ingen Schenau G J. An estimation of power output and work done by the human triceps surae musle — Tendon complex in jumping. Journal of Biomechanics, 1986, 19, 899–906.
Ontañón-Ruiz J, Daniel R W, McǍree P R. On the use of differential drives for overcoming transmission nonlinearities. Journal of Robotic Systems, 1998, 15, 641–660.
Lee H, Choi Y. A new actuator system using dual-motors and a planetary gear. IEEE/ASME Transactions on Mechatronics, 2012, 17, 192–197.
Girard A, Asada H H. Leveraging natural load dynamics with variable gear-ratio actuators. IEEE Robotics and Automation Letters, 2017, 2, 741–748.
Siciliano B, Khatib O. Springer Handbook of Robotics, 1st ed, Springer-Verlag, Berlin Heidelberg, Germany, 2008.
Field G, Stepanenko Y. Iterative dynamic programming: an approach to minimum energy trajectory planning for robotic manipulators. Proceedings of the IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA, 1996, 2755–2760.
von Stryk O, Schlemmer M. Optimal control of the industrial robot manutec r3. In: Computational Optimal Control, Bulirsch R and Kraft D eds., Birkhäuser Basel, Basel, Switzerland, 1994, 367–382.
Nenchev D N. Redundancy resolution through local optimization: A review. Journal of Robotic Systems, 1989, 6, 769–798.
Mathijssen G, Furnémont R, Verstraten T, Brackx V, Premec J, Jiménez R, Lefeber D, Vanderborght B. +SPEA introduction: Drastic actuator energy requirement reduction by symbiosis of parallel motors, springs and locking mechanisms. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, 2016, 676–681.
Verstraten T, Furnémont R, Lopez-Garcia P, Rodriguez-Cianca D, Cao H L, Vanderborght B, Lefeber D. Modeling and design of an energy-efficient dual-motor actuation unit with a planetary differential and holding brakes. Mechatronics, 2018, 49, 134–148.
Rabindran D, Tesar D. Parametric design and power-flow analysis of parallel force/velocity actuators. Journal of Mechanisms and Robotics, 2009, 1, 011007.
Rabindran D, Tesar D. Study of the dynamic coupling term (p.) in parallel force/velocity actuated systems. Proceedings of the IEEE International Conference on Automation Science and Engineering, Scottsdale, AZ, USA, 2007, 418–423.
Kim B S, Park J J, Song J B. Improved manipulation efficiency using a serial-type dual actuator unit. Proceedings of the International Conference on Control, Automation and Systems (ICCAS), Seoul, Korea, 2007, 30–35.
Verstraten T, Furnémont R, López-García P, Rodriguez-Cianca D, Vanderborght B, Lefeber D. Kinematically redundant actuators, a solution for conflicting torque-speed requirements. The International Journal of Robotics Research, 2019, 38, 612–629.
Rabindran D, Tesar D. A differential-based dual actuator for a safe robot joint: Theory and experiments. Proceedings of the World Automation Congress (WAC), Waikoloa, HI, USA, 2014, 142–147.
Verstraten T, Furnémont R, López-García P, Crispel S, Vanderborght B, Lefeber D. A series elastic dual-motor actuator concept for wearable robotics. Proceedings of the 4th International Symposium on Wearable Robotics (WeRob2018), Pisa, Italy, 2018, 165–169.
Pratt J, Chew C M, Torres A, Dilworth P, Pratt G. Virtual model control: An intuitive approach for bipedal locomotion. The International Journal of Robotics Research, 2001, 20, 129–143.
Verstraten T, Furnémont R, Beckerle P, Vanderborght B, Lefeber D. A hopping robot driven by a series elastic dual-motor actuator. IEEE Robotics and Automation Letters, 2019, 4, 2310–2316.
Hoffmann M, Simanek J. The merits of passive compliant joints in legged locomotion: Fast learning, superior energy efficiency and versatile sensing in a quadruped robot. Journal of Bionic Engineering, 2017, 14, 1–14.
Kajita S, Nagasaki T, Kaneko K, Yokoi K, Tanie K. A running controller of humanoid biped HRP-2LR. Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain, 2005, 616–622.
Oehlke J, Sharbafi M A, Beckerle P, Seyfarth A. Template-based hopping control of a bio-inspired segmented robotic leg. Proceedings of the 6th IEEE International Conference on Biomedical Robotics and Biomechatronics (BioRob), Singapore, Singapore, 2016, 35–40.
Winter D A. Biomechanics and Motor Control of Human Movement, 4th ed, John Wiley & Sons, Hoboken, NJ, USA, 2009.
Oehlke J, Beckerle P, Seyfarth A, Sharbafi M A. Human-like hopping in machines. Biological Cybernetics, 2019, 113, 227–238.
Guo W, Cai C R, Li M T, Zha F S, Wang P F, Wang K N. A parallel actuated pantograph leg for high-speed locomotion. Journal of Bionic Engineering, 2017, 14, 202–217.
Seyfarth A, Blickhan R, Van Leeuwen J L. Optimum take-off techniques and muscle design for long jump. Journal of Experimental Biology, 2000, 203, 741–750.
Seyfarth A, Friedrichs A, Wank V, Blickhan R. Dynamics of the long jump. Journal of Biomechanics, 1999, 32, 1259–1267.
Finni T, Komi P V, Lepola V. In vivo human triceps surae and quadriceps femoris muscle function in a squat jump and counter movement jump. European Journal of Applied Physiology, 2000, 83, 416–426.
Schumacher C, Seyfarth A. Sensor-motor maps for describing linear reflex composition in hopping. Frontiers in Computational Neuroscience, 2017, 11, 108.
Verstraten T, Beckerle P, Furnémont R, Mathijssen G, Vanderborght B, Lefeber D. Series and parallel elastic actuation: Impact of natural dynamics on power and energy consumption. Mechanism and Machine Theory, 2016, 102, 232–246.
Vu H Q, Yu X X, Iida F, Pfeifer R. Improving energy efficiency of hopping locomotion by using a variable stiffness actuator. IEEE/ASME Transactions on Mechatronics, 2016, 21, 472–486.
Verstraten T, Furnémont R, Mathijssen G, Vanderborght B, Lefeber D. Energy consumption of geared DC motors in dynamic applications: Comparing modeling approaches. IEEE Robotics and Automation Letters, 2016, 1, 524–530.
Verstraten T, Mathijssen G, Furnémont R, Vanderborght B, Lefeber D. Modeling and design of geared DC motors for energy efficiency: Comparison between theory and experiments. Mechatronics, 2015, 30, 198–213.
Cavagna G A. Storage and utilization of elastic energy in skeletal muscle. Exercise and Sport Sciences Reviews, 1977, 5, 89–130.
Bobbert M F, Gerritsen K G M, Litjens M C A, Van Soest A J. Why is countermovement jump height greater than squat jump height? Medicine & Science in Sports & Exercise, 1996, 28, 1402–1412.
Bobbert M F, Mackay M, Schinkelshoek D, Huijing P A, van Ingen Schenau G J. Biomechanical analysis of drop and countermovement jumps. European Journal of Applied Physiology and Occupational Physiology, 1986, 54, 566–573.
Farley C T, Blickhan R, Saito J, Taylor C R. Hopping frequency in humans: A test of how springs set stride frequency in bouncing gaits. Journal of Applied Physiology, 1991, 71, 2127–2132.
Kawakami Y, Muraoka T, Ito S, Kanehisa H, Fukunaga T. In vivo muscle fibre behaviour during counter-movement exercise in humans reveals a significant role for tendon elasticity. The Journal of Physiology, 2002, 540, 635–646.
Farley C T, Morgenroth D C. Leg stiffness primarily depends on ankle stiffness during human hopping. Journal of Biomechanics, 1999, 32, 267–273.
Hobara H, Inoue K, Omuro K, Muraoka T, Kanosue K. Determinant of leg stiffness during hopping is frequency-dependent. European Journal of Applied Physiology, 2011, 111, 2195–2201.
Prilutsky B I, Zatsiorsky V M. Tendon action of two-joint muscles: Transfer of mechanical energy between joints during jumping, landing, and running. Journal of Biomechanics, 1994, 27, 25–34.
Junius K, Moltedo M, Cherelle P, Rodriguez-Guerrero C, Vanderborght B, Lefeber D. Biarticular elements as a contributor to energy efficiency: Biomechanical review and application in bio-inspired robotics. Bioinspiration & Biomimetics, 2017, 12, 061001.
Bobbert M F, Richard Casius L J. Spring-like leg behaviour, musculoskeletal mechanics and control in maximum and submaximum height human hopping. Philosophical Transactions of the Royal Society B: Biological Sciences, 2011, 366, 1516–1529.
Seyfarth A, Günther M, Blickhan R. Stable operation of an elastic three-segment leg. Biological Cybernetics, 2001, 84, 365–382.
Tom Verstraten is a postdoctoral fellow of the Research Foundation Flanders — Fonds voor Wetenschappelijk Onderzoek (FWO). Part of this work was funded by the European Commission starting grant SPEAR (no. 337596) and the DFG grants BE 5729/2 and BE 5729/1. We would like to thank Rustam Galljamov and Philipp Overath for their assistance with the demonstrator and the experiments.
Electronic supplementary material
About this article
Cite this article
Verstraten, T., Schumacher, C., Furnémont, R. et al. Redundancy in Biology and Robotics: Potential of Kinematic Redundancy and its Interplay with Elasticity. J Bionic Eng (2020). https://doi.org/10.1007/s42235-020-0062-z
- redundant actuation
- series elastic actuation
- hopping robots
- energy efficiency
- human physiology