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Push Recovery Control Based on Model Predictive Control of Hydraulic Quadruped Robots

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Abstract

This work is aimed at addressing the balance problem of hydraulic quadruped robots, trotting on even terrain, which is impacted by lateral disturbance. The ability of push recovery means that a robot can restore stability when the roll angle of the body is too large after a strong side impact. To maintain the balance of the impacted robot, three strategies are proposed inspired by the human response to external disturbance, including supporting leg adjustment strategy, one-step motion of swinging legs strategy, and N-step motion of swinging legs strategy. Quadruped robots can be considered as humanoids owing to the nature of their trotting gait. Thus, the contributions of this artile are as follows. A simplified dynamic model of a quadruped robot is established based on linear inverted pendulum (LIP), and the idea of capture point (CP) and zero moment point (ZMP). A push recovery control system based on model predictive controller (MPC) is established according to the requirement of the control strategy. Finally, the effectiveness of the push recovery control system is verified by simulation and experiment.

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Data Availability

No datasets were generated or analyzed during the current study.

References

  1. Di Carlo, J., Wensing, P.M., Katz, B., Bledt, G., Kim, S.: Dynamic locomotion in the MIT cheetah 3 through convex model-predictive control. In: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). pp. 1–9. IEEE, Madrid (2018)

  2. Katz, B., Carlo, J.D., Kim, S.: Mini cheetah: a platform for pushing the limits of dynamic quadruped control. In: 2019 International Conference on Robotics and Automation (ICRA). pp. 6295–6301. IEEE, Montreal, QC, Canada (2019)

  3. Gehring, C., Coros, S., Hutter, M., Bloesch, M., Fankhauser, P., Hoepflinger, M.A., Siegwart, R.: Towards automatic discovery of agile gaits for quadrupedal robots. In: 2014 IEEE International Conference on Robotics and Automation (ICRA). pp. 4243–4248. IEEE, Hong Kong, China (2014)

  4. Gehring, C., Coros, S., Hutter, M., Bloesch, M., Hoepflinger, M.A., Siegwart, R.: Control of dynamic gaits for a quadrupedal robot. In: 2013 IEEE International Conference on Robotics and Automation. pp. 3287–3292. IEEE, Karlsruhe, Germany (2013)

  5. Luo, J., Zhao, Y., Ruan, L., Mao, S., Fu, C.: Estimation of CoM and CoP trajectories during human walking based on a wearable visual odometry device. IEEE Trans. Automat. Sci. Eng. 19, 396–409 (2022). https://doi.org/10.1109/TASE.2020.3036530

    Article  Google Scholar 

  6. Gu, S., Meng, F., Liu, B., Zhang, Z., Sun, N., Wang, M.: Stability control of quadruped robot based on active state adjustment. Biomimetics. 8, 112 (2023). https://doi.org/10.3390/biomimetics8010112

    Article  Google Scholar 

  7. Englsberger, J., Ott, C., Roa, M.A., Albu-Schaffer, A., Hirzinger, G.: Bipedal walking control based on capture point dynamics. In: 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems. pp. 4420–4427. IEEE, San Francisco, CA (2011)

  8. Joe, H.-M., Oh, J.-H.: Balance recovery through model predictive control based on capture point dynamics for biped walking robot. Robot. Auton. Syst. 105, 1–10 (2018). https://doi.org/10.1016/j.robot.2018.03.004

    Article  Google Scholar 

  9. Dini, N., Majd, V.J.: Sliding-mode tracking control of a walking quadruped robot with a push recovery algorithm using a nonlinear disturbance observer as a virtual force sensor. Iran J Sci Technol Trans Electr Eng. 44, 1033–1057 (2020). https://doi.org/10.1007/s40998-019-00283-7

    Article  Google Scholar 

  10. Sutyasadi, P., Parnichkun, M.: Push recovery control of quadruped robot using particle swarm optimization based structure specified mixed sensitivity H 2 / H control. IR. 47, 423–434 (2020). https://doi.org/10.1108/IR-06-2019-0135

    Article  Google Scholar 

  11. Chen, H., Hong, Z., Yang, S., Wensing, P.M., Zhang, W.: Quadruped capturability and push recovery via a switched-systems characterization of dynamic balance

  12. Khorram, M., Moosavian, S.A.A.: Push recovery of a quadruped robot on challenging terrains. Robotica 35, 1670–1689 (2017). https://doi.org/10.1017/S0263574716000394

    Article  Google Scholar 

  13. Shang, W., Wu, Z., Liu, Q., Duan, L., Wang, C.: Foot placement estimator for quadruped push recovery. In: 2019 IEEE 9th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER). pp. 1530–1534. IEEE, Suzhou, China (2019)

  14. Dini, N., Majd, V.J.: An MPC-based two-dimensional push recovery of a quadruped robot in trotting gait using its reduced virtual model. Mech. Mach. Theory 146, 103737 (2020). https://doi.org/10.1016/j.mechmachtheory.2019.103737

    Article  Google Scholar 

  15. Zhu, X., Wan, J., Zhou, C., Xu, W.: A composite robust reactive control strategy for quadruped robot under external push disturbance. Comput. Electr. Eng. 91, 107027 (2021). https://doi.org/10.1016/j.compeleceng.2021.107027

    Article  Google Scholar 

  16. Gold, T., Völz, A., Graichen, K.: Model predictive interaction control for industrial robots. IFAC-PapersOnLine. 53, 9891–9898 (2020). https://doi.org/10.1016/j.ifacol.2020.12.2696

    Article  Google Scholar 

  17. Rezaee, A, Graichen, Knut.: Model predictive controller for mobile robot. Trans. Environ. Electr. Eng. (2017)

  18. Bhatia, V., Ganesh Ram, R.K., Kalaichelvi, V., Karthikeyan, R.: Application of model predictive controller for 2-DOF robot manipulator. In: 2015 10th International Symposium on Mechatronics and its Applications (ISMA). pp. 1–5. IEEE, Sharjah, United Arab Emirates (2015)

  19. Scianca, N., De Simone, D., Lanari, L., Oriolo, G.: MPC for Humanoid Gait Generation: Stability and Feasibility. IEEE Trans. Robot. 36, 1171–1188 (2020). https://doi.org/10.1109/TRO.2019.2958483

    Article  Google Scholar 

  20. Siciliano, B., Sciavicco, L., Villani, L., Oriolo, G.: Robotics. Springer, London, London (2009)

    Book  Google Scholar 

  21. Vukobratović, M., Borovac, B., Potkonjak, V.: ZMP: A REVIEW OF SOME BASIC MISUNDERSTANDINGS. Int. J. Humanoid Rob. (2011). https://doi.org/10.1142/S0219843606000710

    Article  Google Scholar 

  22. Pratt, J., Cardiff, J., Drakunov, S., Goswami, A.: Capture point: a step toward humanoid push recovery. In: 2006 6th IEEE-RAS International Conference on Humanoid Robots. pp. 200–207. IEEE, University of Genova, Genova, Italy (2006)

  23. Hof, A.L.: The ‘extrapolated center of mass’ concept suggests a simple control of balance in walking. Hum. Mov. Sci. 27, 112–125 (2008). https://doi.org/10.1016/j.humov.2007.08.003

    Article  Google Scholar 

  24. Morisawa, M., Kajita, S., Kanehiro, F., Kaneko, K., Miura, K., Yokoi, K.: Balance control based on Capture Point error compensation for biped walking on uneven terrain. In: 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012). pp. 734–740. IEEE, Osaka, Japan (2012)

  25. Koolen, T., De Boer, T., Rebula, J., Goswami, A., Pratt, J.: Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models. Int. J. Robot. Res. 31, 1094–1113 (2012). https://doi.org/10.1177/0278364912452673

    Article  Google Scholar 

  26. Pratt, J., Koolen, T., De Boer, T., Rebula, J., Cotton, S., Carff, J., Johnson, M., Neuhaus, P.: Capturability-based analysis and control of legged locomotion, Part 2: Application to M2V2, a lower-body humanoid. Int. J. Robot. Res. 31, 1117–1133 (2012). https://doi.org/10.1177/0278364912452762

    Article  Google Scholar 

  27. Husty, M., Hofbaur, M. (eds.): New Trends in Medical and service robots: design. analysis and control. Springer International Publishing, Cham (2018)

    Google Scholar 

  28. Johannes, Englsberger.: Combining reduced dynamics models and whole-body control for agile humanoid locomotion. Germany: Technische Universität München (2012)

  29. Shafiee-Ashtiani, M., Yousefi-Koma, A., Shariat-Panahi, M.: Robust bipedal locomotion control based on model predictive control and divergent component of motion. In: 2017 IEEE International Conference on Robotics and Automation (ICRA). pp. 3505–3510. IEEE, Singapore, Singapore (2017)

  30. Aftab, Z., Robert, T., Wieber, P.-B.: Ankle, hip and stepping strategies for humanoid balance recovery with a single Model Predictive Control scheme. In: 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012). pp. 159–164. IEEE, Osaka, Japan (2012)

  31. Stephens, B.: Humanoid push recovery. In: 2007 7th IEEE-RAS International Conference on Humanoid Robots. pp. 589–595. IEEE, Pittsburgh, PA, USA (2007)

  32. Aslan, E., Arserim, M.A., Uçar, A.: Development of push-recovery control system for humanoid robots using deep reinforcement learning. Ain Shams Eng. J. 14, 102167 (2023). https://doi.org/10.1016/j.asej.2023.102167

    Article  Google Scholar 

  33. 陈虹.模型预测控制.北京: 科学出版社 (2013)

  34. Shafiee-Ashtiani, M., Yousefi-Koma, A., Shariat-Panahi, M., Khadiv, M.: Push recovery of a humanoid robot based on model predictive control and capture point. In: 2016 4th International Conference on Robotics and Mechatronics (ICROM). pp. 433–438. IEEE, Tehran, Iran (2016)

  35. Zhu, R., Yang, Q., Song, J., Yang, S., Liu, Y., Mao, Q.: Research and improvement on active compliance control of hydraulic quadruped robot. Int. J. Control. Autom. Syst. 19, 1931–1943 (2021). https://doi.org/10.1007/s12555-020-0221-3

    Article  Google Scholar 

  36. Zhu, R., Yang, Q., Liu, Y., Dong, R., Jiang, C., Song, J.: Sliding mode robust control of hydraulic drive unit of hydraulic quadruped robot. Int. J. Control. Autom. Syst. 20, 1336–1350 (2022). https://doi.org/10.1007/s12555-021-0235-5

    Article  Google Scholar 

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Qingjun Yang, Congfei Li and Rui Zhu. The first draft of the manuscript was written by Congfei Li, Yulong Li, Dianxin Wang and Xuan Wang, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Congfei Li.

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This is an observational study. The XYZ Research Ethics Committee has confirmed that no ethical approval is required.

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Yang, Q., Li, C., Zhu, R. et al. Push Recovery Control Based on Model Predictive Control of Hydraulic Quadruped Robots. J Intell Robot Syst 109, 41 (2023). https://doi.org/10.1007/s10846-023-01972-6

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