Abstract
Herein, a control method based on the optimal energy efficiency of a hydraulic quadruped robot was proposed, which not only realizes the optimal energy efficiency of flying trot gait but also ensures the stability of high-speed movement. Concretely, the energy consumption per unit distance was adopted as the energy efficiency evaluation index based on the constant pressure oil supply characteristics of the hydraulic system, and the global optimization algorithm was adopted to solve the optimal parameters. Afterward, the gait parameters that affect the energy efficiency of quadruped were analyzed and the mapping relationship between each parameter and energy efficiency was captured, so as to select the optimum combination of energy efficiency parameters, which is significant to improve endurance capability. Furthermore, to ensure the stability of the high-speed flying trot gait motion of the hydraulic quadruped robot, the active compliance control strategy was employed. Lastly, the proposed method was successfully verified by simulations and experiments. The experimental results reveal that the flying trot gait of the hydraulic quadruped robot can be stably controlled at a speed of 2.2 m/s.
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The datasets generated during and/or analyzed during this study are available from the corresponding author on reasonable request.
References
Raibert, M., Blankespoor, K., Nelson, G., & Playter, R. (2008). Bigdog the rough-terrain quadruped robot. IFAC Proceedings Volumes, 41(2), 10822–10825.
Wooden, D., Malchano, M., Blankespoor, K., Howardy, A., Rizzi, A. A., & Raibert, M. (2010). Autonomous navigation for BigDog. In 2010 IEEE International Conference on Robotics and Automation, Alaska, America, pp. 4736–4741.
Michael, K. (2012). Meet Boston dynamics' LS3-the latest robotic war machine. The Conversation, 03 October.
Semini, C., Tsagarakis, N. G., Guglielmino, E., Focchi, M., Cannella, F., & Caldwell, D. G. (2011). Design of HyQ–a hydraulically and electrically actuated quadruped robot. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 225(6), 831–849.
Hutter, M., Gehring, C., Höpflinger, M. A., Blösch, M., & Siegwart, R. (2014). Toward combining speed, efficiency, versatility, and robustness in an autonomous quadruped. IEEE Transactions on Robotics, 30(6), 1427–1440.
Seok, S., Wang, A., Chuah, M. Y., Otten, D., Lang, J., & Kim, S. (2013). Design principles for highly efficient quadrupeds and implementation on the MIT Cheetah robot. In 2013 IEEE International Conference on Robotics and Automation , Karlsruhe, Germany, pp. 3307–3312.
Li, T., Zhou, L., Li, Y., Chai, H., & Yang, K. (2020). An energy efficient motion controller based on SLCP for the electrically actuated quadruped robot. Journal of Bionic Engineering, 17, 290–302.
Bi, J., Chen, T., Rong, X. W., Zhang, G. T., Lu, G., Cao, J. X., Jiang, H., & Li, Y. B. (2024). Efficient dynamic locomotion of quadruped robot via adaptive diagonal gait. Journal of Bionic Engineering, 21(1), 126–136.
Nabulsi, S., Sarria, J. F., Montes, H., & Armada, M. A. (2009). High-resolution indirect feet–ground interaction measurement for hydraulic-legged robots. IEEE Transactions on Instrumentation & Measurement, 58(10), 3396–3404.
Hirose, S., Fukuda, Y., Yoneda, K., Nagakubo, A., Tsukagoshi, H., Arikawa, K., et al. (2009). Quadruped walking robots at Tokyo Institute of Technology. IEEE Robotics & Automation Magazine, 16(2), 104–114.
Wait, K. W., & Goldfarb, M. (2014). A pneumatically actuated quadrupedal walking robot. IEEE/ASME Transactions on Mechatronics, 19(1), 339–347.
Lee, Y. H., Lee, Y. H., Lee, H., Kang, H., Lee, J. H., Phan, L. T., Jin, S., Kim, Y. B., Seok, D. Y., Lee, S. Y., Moon, H., Koo, J. C., & Choi, H. R. (2020). Development of a quadruped robot system with torque-controllable modular actuator unit. IEEE Transactions on Industrial Electronics, 68(8), 7263–7273.
Boaventura, T., Medrano-Cerda, G. A., Semini, C., Buchli, J., & Caldwell, D. G. (2013). Stability and performance of the compliance controller of the quadruped robot HyQ. In 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, pp. 1458–1464
Semini, C., Barasuol, V., Boaventura, T., Frigerio, M., Focchi, M., Caldwell, D. G., & Buchli, J. (2015). Towards versatile legged robots through active impedance control. The International Journal of Robotics Research, 34(7), 1003–1020.
Gu, S., Meng, F., Liu, B., Gao, J., & Huang, Q. (2023). High dynamic bounding and jumping motion of quadruped robot based on stable optimization control. Journal of Bionic Engineering, 21(1), 101–111.
Spröwitz, A., Tuleu, A., Vespignani, M., Ajallooeian, M., Badri, E., & Ijspeert, A. J. (2013). Towards dynamic trot gait locomotion: Design, control, and experiments with Cheetah-cub, a compliant quadruped robot. The International Journal of Robotics Research, 32(8), 932–950.
Gehring, C., Coros, S., Hutter, M., Bellicoso, C. D., Heijnen, H., Diethelm, R., Bloech, M., Rankhauser, T., Hwangbo, J., Hoepflinger, M., & Siegwart, R. (2016). Practice makes perfect: An optimization-based approach to controlling agile motions for a quadruped robot. IEEE Robotics & Automation Magazine, 23(1), 34–43.
Chen, T., Rong, X., Li, Y., Ding, C., Chai, H., & Zhou, L. (2018). A compliant control method for robust trot motion of hydraulic actuated quadruped robot. International Journal of Advanced Robotic Systems, 15(6), 1729881418813235.
Boaventura, T., Buchli, J., Semini, C., & Caldwell, D. G. (2015). Model-based hydraulic impedance control for dynamic robots. IEEE Transactions on Robotics, 31(6), 1324–1336.
Zhu, R., Yang, Q., Song, J., Yang, S., Liu, Y., & Mao, Q. (2021). Research and improvement on active compliance control of hydraulic quadruped robot. International Journal of Control, Automation and Systems, 19(5), 1931–1943.
Shi, Y., Wang, P., Wang, X., Zha, F., Jiang, Z., Guo, W., & Li, M. (2018). Bio-inspired equilibrium point control scheme for quadrupedal locomotion. IEEE Transactions on Cognitive and Developmental Systems, 11(2), 200–209.
Hua, Z., Rong, X., Li, Y., Chai, H., & Zhang, S. (2019). Active compliance control on the hydraulic quadruped robot with passive compliant servo actuator. IEEE Access, 7, 163449–163460.
Zhu, R., Yang, Q., Liu, Y., Dong, R., Jiang, C., & Song, J. (2022). Sliding mode robust control of hydraulic drive unit of hydraulic quadruped robot. International Journal of Control, Automation and Systems, 20(4), 1336–1350.
Nanua, P., & Waldron, K. J. (1995). Energy comparison between trot, bound, and gallop using a simple model. Journal of Biomechanical Engineering, 117(4), 466–473.
Bhounsule, P. A., Cortell, J., & Ruina, A. (2012). Design and control of Ranger: an energy-efficient, dynamic walking robot. Adaptive Mobile Robotics (pp. 441–448).
Yang, K., Zhou, L., Rong, X., & Li, Y. (2018). Onboard hydraulic system controller design for quadruped robot driven by gasoline engine. Mechatronics, 52, 36–48.
Yang, K., Zhou, L., Rong, X., & Li, Y. (2018). An energy optimal foot trajectory for the hydraulic actuated quadruped robot. In 2018 IEEE 8th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER), Tianjin, China, 2018, 329–333.
Yang, K., Li, Y., Zhou, L., & Rong, X. (2019). Energy efficient foot trajectory of trot motion for hydraulic quadruped robot. Energies, 12(13), 2514.
Bellicoso, C. D., Jenelten, F., Gehring, C., & Hutter, M. (2018). Dynamic locomotion through online nonlinear motion optimization for quadrupedal robots. IEEE Robotics and Automation Letters, 3(3), 2261–2268.
Hwangbo, J., Lee, J., Dosovitskiy, A., Bellicoso, D., Tsounis, V., Koltun, V., & Hutter, M. (2019). Learning agile and dynamic motor skills for legged robots. Science Robotics, 4(26), eaau5872.
Chen, T., Sun, X., Xu, Z., Li, Y., Rong, X., & Zhou, L. (2019). A trot and flying trot control method for quadruped robot based on optimal foot force distribution. Journal of Bionic Engineering, 16(4), 621–632.
Shi, Y., Li, M., Zha, F., Sun, L., Guo, W., Ma, C., & Li, Z. (2020). Force-controlled compensation scheme for PQ valve-controlled asymmetric cylinder used on hydraulic quadruped robots. Journal of Bionic Engineering, 17(6), 1139–1151.
Neunert, M., Farshidian, F., Winkler, A. W., & Buchli, J. (2017). Trajectory optimization through contacts and automatic gait discovery for quadrupeds. IEEE Robotics and Automation Letters, 2(3), 1502–1509.
Mistry, M., Buchli, J., & Schaal, S. (2010). Inverse dynamics control of floating base systems using orthogonal decomposition. In 2010 IEEE International Conference on Robotics and Automation, Taipei, China, pp. 3406–3412.
Buchli, J., Kalakrishnan, M., Mistry, M., Pastor, P., & Schaal, S. (2009). Compliant quadruped locomotion over rough terrain. In 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, Munich, Germany, pp. 814–820.
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Yang, Q., Zhang, Z., Zhu, R. et al. Optimal Energy Efficiency Based High-speed Flying Control Method for Hydraulic Quadruped Robot. J Bionic Eng (2024). https://doi.org/10.1007/s42235-024-00509-3
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DOI: https://doi.org/10.1007/s42235-024-00509-3