Abstract
This paper presents the development of the planar bipedal robot ERNIE as well as numerical and experimental studies of the influence of parallel knee joint compliance on the energetic efficiency of walking in ERNIE. ERNIE has 5 links—a torso, two femurs and two tibias—and is configured to walk on a treadmill so that it can walk indefinitely in a confined space. Springs can be attached across the knee joints in parallel with the knee actuators. The hybrid zero dynamics framework serves as the basis for control of ERNIE’s walking. In the investigation of the effects of compliance on the energetic efficiency of walking, four cases were studied: one without springs and three with springs of different stiffnesses and preloads. It was found that for low-speed walking, the addition of soft springs may be used to increase energetic efficiency, while stiffer springs decrease the energetic efficiency. For high-speed walking, the addition of either soft or stiff springs increases the energetic efficiency of walking, while stiffer springs improve the energetic efficiency more than do softer springs.
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References
Ahmadi, M., & Buehler, M. (1999). ARL monopod II running robot: control and energetics, In Proc. of the 1999 IEEE International Conference on Robotics and Automation, Detroit, MI (vol. 3, pp. 1689–1694).
Alexander, R. M. (1999). Three uses for springs in legged locomotion. International Journal of Robotics Research, 9(2), 53–61.
Anderson, S. O., Wisse, M., Atkeson, C. G., Hodgins, J. K., Zeglin, G. J., & Moyer, B. (2005). Powered bipeds based on passive dynamic principles. In Humanoid Robots, 2005 5th IEEE-RAS International Conference (pp. 110–116).
Bastien, G. J., Willems, P. A., Schepens, B., & Heglund, N. C. (2005). Effect of load and speed on the energetic cost of human walking. European Journal of Applied Physiology, 94(1–2), 76–83.
Browning, R. C., & Kram, R. (2005). Energetic cost and preferred speed of walking in obese vs. normal weight women. Obesity Research, 13(5), 891–899.
Capi, G., Nasu, Y., Barolli, L., & Mitobe, K. (2003). Real time gait generation for autonomous humanoid robots: a case study for walking. Robotics and Autonomous Systems, 42(2), 107–116.
Channon, P. H., Hopkins, S. H., & Pham, D. T. (1992). Derivation of optimal walking motions for a bipedal walking robot. Robotica, 10, 165–172.
Chevallereau, C., Abba, G., Aoustin, Y., Plestan, F., Westervelt, E. R., Canudas, C., & Grizzle, J. W. (2003). RABBIT: a testbed for advanced control theory. IEEE Control Systems Magazine, 23(5), 57–79.
Chevallereau, C., & Aoustin, Y. (2001). Optimal reference trajectories for walking and running of a biped robot. Robotica, 19(5), 557–569.
Chow, C. K., & Jacobson, D. H. (1971). Studies of human locomotion via optimal programming. Mathematical Biosciences, 10, 239–306.
Coleman, M. J., & Ruina, A. (1998). An uncontrolled walking toy that cannot stand still. Physical Review Letters, 80(16), 3658–3661.
Collins, S. H., & Ruina, A. (2005). A bipedal walking robot with efficient and human-like gait. In Proc. of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain (pp. 1983–1988).
Collins, S. H., Ruina, A., Tedrake, R., & Wisse, M. (2005). Efficient bipedal robots based on passive-dynamic walkers. Science, 307, 1082–1085.
Collins, S. H., Wisse, M., & Ruina, A. (2001). A three-dimensional passive-dynamic walking robot with two legs and knees. International Journal of Robotics Research, 20(7), 607–615.
Farrell, K. D., Chevallereau, C., & Westervelt, E. R. (2007). Energetic effects of adding springs at the passive ankles of a walking biped robot. In Proc. of the 2007 IEEE International Conference on Robotics and Automation, Rome, Italy (pp. 3591–3596).
Garcia, M., Chatterjee, A., & Ruina, A. (2000). Efficiency, speed, and scaling of two-dimensional passive-dynamic walking. Dynamics and Stability of Systems, 15(2), 75–99.
Gunther, M., & Ruder, H. (2003). Synthesis of two-dimensional human walking: a test of the lambda-model. Biological Cybernetics, 89(2), 89–106.
Hurst, J. W., Chestnutt, J. E., & Rizzi, A. A. (2007). Design and philosophy of the BiMASC, a highly dynamic biped. In Proc. of the 2007 IEEE International Conference on Robotics and Automation, Rome, Italy (pp. 1863–1868).
Iida, F., Minekawa, Y., Rummel, J., & Seyfarth, A. (2005). Toward a humanlike biped robot with compliant legs. Intelligent Autonomous Systems, 9, 820–827.
Kato, I., & Tsuiki, H. (1972). The hydraulically powered biped walking machine with a high carrying capacity. In Proc. of the Fourth International Symposium on External Control of Human Extremities, Dubrovnik, Yugoslavia (pp. 410–421).
Kuo, A. D. (2007). Choosing your steps carefully. Robotics & Automation Magazine, IEEE, 14(2), 18–29.
Loffler, K., Gienger, M., Pfeiffer, F., & Ulbrich, H. (2004). Sensors and control concept of a biped robot. IEEE Transactions on Industrial Electronics, 51(5), 972–980.
McGeer, T. (1990). Passive dynamic walking. Internarional Journal of Robotics Research, 9(2), 62–82.
Pratt, J. E., Chee, M. C., Torres, A., Dilworth, P., & Pratt, G. A. (2001). Virtual model control: an intuitive approach for bipedal locomotion. International Journal of Robotics Research, 20(2), 129–143.
Pratt, J. E., & Pratt, G. A. (1998). Intuitive control of a planar bipedal walking robot. In Proc. of the 1998 IEEE International Conference on Robotics and Automation, Leuven, Belgium (pp. 2014–2021).
Raibert, M. H. (1986). Legged robots that balance. Cambridge: MIT.
Ralston, H. J. (1958). Energy-speed relation and optimal speed during level walking. European Journal of Applied Physiology, 17(4), x–x.
Rostami, M., & Bessonnet, G. (1998). Impactless sagittal gait of a biped robot during the single support phase. In Proc. of the 1998 IEEE International Conference on Robotics and Automation, Leuven, Belgium (pp. 1385–1391).
Rostami, M., & Bessonnet, G. (2001). Sagittal gait of a biped robot during the single support phase. Part 2: optimal motion. Robotica, 19, 241–253.
Saidouni, T., & Bessonnett, G. (2003). Generating globally optimised sagittal gait cycles of a biped robot. Robotica, 21, 199–210.
Sakagami, Y., Watanabe, R., Aoyama, C., Matsunaga, S., Higaki, N., & Fujimura, K. (2002). The intelligent ASIMO: system overview and integration. In Proc. of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland (pp. 2478–2483).
Tedrake, R. (2004). Applied optimal control for dynamically stable legged locomotion. PhD thesis, Massachusetts Institute of Technology.
Vanderborght, B., Verrelst, B., Van Ham, R., Van Damme, M., Lefeber, D., Meira Y Duran, B., & Beyl, P. (2006). Exploiting natural dynamics to reduce energy consumption by controlling the compliance of soft actuators. International Journal of Robotics Research, 25, 343–358.
Westervelt, E. R., Buche, G., & Grizzle, J. W. (2004). Experimental validation of a framework for the design of controllers that induce stable walking in planar bipeds. International Journal of Robotics Research, 23(6), 559–582.
Westervelt, E. R., Grizzle, J. W., Chevallereau, C., Choi, J. H., & Morris, B. (2007). Feedback control of dynamic bipedal robot locomotion. Taylor & Francis/CRC.
Westervelt, E. R., Grizzle, J. W., & Koditschek, D. E. (2003). Hybrid zero dynamics of planar biped walkers. IEEE Transactions on Automatic Control, 48(1), 42–56.
Wisse, M., Schwab, A. L., van der Linde, R. Q., & van der Helm, F. C. T. (2005). How to keep from falling forward: Elementary swing leg action for passive dynamic walkers. IEEE Transactions on Robotics, 21(3), 393–401.
Wisse, M., Schwab, A. L., & van der Linde, R. Q. (2001). A 3D passive dynamic biped with yaw and roll compensation. Robotica, 19(3), 275–284.
Yang, T., Westervelt, E. R., & Serrani, A. (2007). A framework for the control of stable aperiodic walking in underactuated planar bipeds. In Proc. of the 2007 IEEE International Conference on Robotics and Automation, Rome, Italy (pp. 4661–4666).
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Yang, T., Westervelt, E.R., Schmiedeler, J.P. et al. Design and control of a planar bipedal robot ERNIE with parallel knee compliance. Auton Robot 25, 317–330 (2008). https://doi.org/10.1007/s10514-008-9096-5
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DOI: https://doi.org/10.1007/s10514-008-9096-5