Optimization of Leg Mechanism and PD Control for Efficient Quadruped Robot Locomotion

Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

Mobin Salehi ¹ , Arash Emami ² , Mojtaba Norozi ³

1 -
2 -
3 -

Received: 2024-10-14 Accepted : 2024-12-30 Published : 2025-03-01

Keywords: Quadruped, Genetic algorithm, Dynamics-independent control, Trotting gait,

Abstract :

This paper presents the design and control of a quadruped robot. One of the primary challenges in building quadruped robots is the need for high torque density actuators and an efficient control algorithm. To address these challenges, this work focuses on optimizing the transmission torque ratio of the 4-bar linkage used in the robot's legs, using a genetic algorithm. The optimization is achieved by deriving the kinematic equations of the robot’s legs and introducing a novel objective function tailored to the robot’s application. To evaluate the impact of the optimization, the full dynamics of the robot are derived and validated through variations in total mechanical energy. A kinematics-based controller, suitable for real-time applications, is proposed, and its performance is tested in various scenarios to assess its effectiveness. The controller is applied to robots with two different linkage lengths, one optimized for maximum and the other for minimum torque requirements. The results show that the optimization reduces the required torque by nearly 42% when comparing the maximum to the minimum case.

References:


[1] Biswal, P., & Mohanty, P. K. (2021). Development of quadruped walking robots: A review. Ain Shams Engineering Journal, 12 (2), 2017–2031. https: //doi.org/https://doi.org/10.1016/j.asej.2020.11.005

[2] Chen, J.-P., San, H.-J., Wu, X., & Xiong, B.-Z. (2022). Structural design and gait research of a new bionic quadruped robot. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 236 (14), 1912–1922. https://doi.org/10.1177/0954405421995663

[3] Zhou, Q., Yang, S., Jiang, X., Zhang, D., Chi, W., Chen, K., Zhang, S., Li, J., Zhang, J., Wang, R., Li, J., Zhang, Y., Wang, H., Wang, S., Xiang, L., Zheng, Y., & Zhang, Z. (2024). Max: A wheeled-legged quadruped robot for multimodal agile locomotion. IEEE Transactions on Automation Science and Engineering, 21 (4), 7562–7582. https://doi.org/10.1109/ TASE.2023.3345876

[4] Hutter, M., Gehring, C., Jud, D., Lauber, A., Bellicoso, C. D., Tsounis, V., Hwangbo, J., Bodie, K., Fankhauser, P., Bloesch, M., Diethelm, R., Bachmann, S., Melzer, A., & Hoepflinger, M. (2016). Anymal - a highly mobile and dynamic quadrupedal robot. 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 38–44. https: //doi.org/10.1109/IROS.2016.7758092

[5] Abrar, M. M., & Islam, R. (2020). Design and development of a biologically inspired robotic cat for research and education. 2020 30th International Conference on Computer Theory and Applications (ICCTA), 82– 87. https://doi.org/10.1109/ICCTA52020.2020.9477678

[6] Sun, Y., Pancheri, F., Rehekampff, C., & Lueth, T. C. (2024). Turbot: A turtleinspired quadruped robot using topology optimized soft-rigid hybrid legs. IEEE/ASME Transactions on Mechatronics, 29 (4), 3193–3202. https://doi.org/10.1109/TMECH.2024.3404667

[7] Seok, S., Wang, A., Chuah, M. Y., Hyun, D. J., Lee, J., Otten, D. M., Lang, J. H., & Kim, S. (2015). Design principles for energy-efficient legged locomotion and implementation on the mit cheetah robot. IEEE/ASME Transactions on Mechatronics, 20 (3), 1117–1129. https://doi.org/10. 1109/TMECH.2014.2339013

[8] Taheri, H., & Mozayani, N. (2023). A study on quadruped mobile robots. Mechanism and Machine Theory, 190, 105448. https://doi.org/https://doi. org/10.1016/j.mechmachtheory.2023.105448

[9] Raibert, M., Blankespoor, K., Nelson, G., & Playter, R. (2008). Bigdog, the rough-terrain quadruped robot [17th IFAC World Congress]. IFAC Proceedings Volumes, 41 (2), 10822–10825. https://doi.org/https://doi. org/10.3182/20080706-5-KR-1001.01833

[10] Zhaoxi, L. (2022). A review of motion control methods and bionic control theory for quadruped robots. 2022 IEEE Conference on Telecommunications, Optics and Computer Science (TOCS), 928–931. https://doi.org/10. 1109/TOCS56154.2022.10016139

[11] https://www.facebook.com/48576411181. (n.d.). Whoa: Boston Dynamics Announces New WildCat Quadruped Robot — spectrum.ieee.org [[Accessed 09-09-2024]].

[12] Chignoli, M., & Wensing, P. M. (2020). Variational-based optimal control of underactuated balancing for dynamic quadrupeds. IEEE Access, 8, 49785– 49797. https://doi.org/10.1109/ACCESS.2020.2980446

[13] Hattori, A. (2020, May). Design of a high torque density modular actuator for dynamic robots [Master’s thesis]. ]. Massachusetts Institute of Technology, Department of Mechanical Engineering.

[14] Wait, K. W., & Goldfarb, M. (2014). A pneumatically actuated quadrupedal walking robot. IEEE/ASME Transactions on Mechatronics, 19 (1), 339– 347. https://doi.org/10.1109/TMECH.2012.2235078

[15] Majithia, A., Shah, D., Dave, J., Kumar, A., Rathee, S., Dogra, N., H. M, V., Chiniwar, D., & Hiremath, S. (2024). Design, motions, capabilities, and applications of quadruped robots: A comprehensive review [Publisher Copyright: Copyright © 2024 Majithia, Shah, Dave, Kumar, Rathee, Dogra, H. M., Chiniwar and Hiremath.]. Frontiers in Mechanical Engineering, 10. https://doi.org/10.3389/fmech.2024.1448681

[16] Tedeschi, F., & Carbone, G. (2014). Design issues for hexapod walking robots. Robotics, 3 (2), 181–206. https://doi.org/10.3390/robotics3020181

[17] Tsitsimpelis, I., Taylor, C. J., Lennox, B., & Joyce, M. J. (2019). A review of ground-based robotic systems for the characterization of nuclear environments. Progress in Nuclear Energy, 111, 109–124. https://doi.org/ https://doi.org/10.1016/j.pnucene.2018.10.023

[18] Wang, H., Fang, D., Sang, L., Wang, Y. J., Wen, Y., & Chen, N. (2013). Gait planning of the quadruped walking chair robot with parallel leg mechanism. 2013 IEEE International Conference on Mechatronics and Automation, 13–18. https://api.semanticscholar.org/CorpusID:18019

[19] Hongjun, M., Shupeng, Z., Wei, Z., & Yuke, R. (2024). Design and control of a new pneumatic quadruped soft robot based on honeycomb structure. IEEE Access, PP, 1–1. https://doi.org/10.1109/ACCESS.2024.3427844

[20] Lee, J., Coutinho, A., Oh, N., Jang, J. H., Park, Y. J., Namgung, H., Oh, D. G., & Rodrigue, H. (2024). Vacuum-driven class-2 tensegrity-based mechanism for quadrupedal robot motion. IEEE Robotics and Automation Letters, 9 (7), 6520–6527. https://doi.org/10.1109/LRA.2024.3407410

[21] Yang, J.-M. (2008). Two-phase discontinuous gaits for quadruped walking machines with a failed leg. Robotics and Autonomous Systems, 56 (9), 728– 737. https://doi.org/https://doi.org/10.1016/j.robot.2008.01.002

[22] Ju, Z., Wei, K., Jin, L., & Xu, Y. (2024). Investigating stability outcomes across diverse gait patterns in quadruped robots: A comparative analysis. IEEE Robotics and Automation Letters, 9 (1), 795–802. https:// doi.org/10.1109/LRA.2023.3338064

[23] Khoramshahi, M., Spr¨owitz, A., Tuleu, A., Ahmadabadi, M. N., & Ijspeert, A. J. (2013). Benefits of an active spine supported bounding locomotion with a small compliant quadruped robot. 2013 IEEE International Conference on Robotics and Automation, 3329–3334. https://doi.org/ 10.1109/ICRA.2013.6631041

[24] Wang, C., Fan, C., Yang, Y., Zhan, M., Shao, H., & Ma, B. (2020). Realization of a bio-inspired cheetah robot with a flexible spine. 2020 IEEE International Conference on Mechatronics and Automation (ICMA), 1185– 1190. https://doi.org/10.1109/ICMA49215.2020.9233690

[25] Liu, H., & Yuan, Q. (2024). Safe and robust motion planning for autonomous navigation of quadruped robots in cluttered environments. IEEE Access, 12, 69728–69737.https://doi.org/10.1109/ACCESS.2024.3401827

[26] Fan, Y., Pei, Z., Wang, C., Li, M., Tang, Z., & Liu, Q. (2024). A review of quadruped robots: Structure, control, and autonomous motion. Advanced Intelligent Systems, 6 (6), 2300783. https: / /doi.org /https: / / doi.org/10.1002/aisy.202300783

[27] Hu, C., Mei, T., Sun, S., Liu, Y., Wu, X., & Zhang, Y. (2013). Cpg-based control system for foot locomotion of gecko-inspired robot. 2013 Fifth International Conference on Measuring Technology and Mechatronics Automation, 409–414. https://doi.org/10.1109/ICMTMA.2013.103

[28] Wasista, S., Tjandrasa, H., & Wibisono, W. (2020). Quadruped robot control base on adaptive neuro-fuzzy inference system with v-rep simulator. 2020 3rd International Conference on Information and Communications Technology (ICOIACT), 280–285. https : / / doi . org / 10 . 1109 / ICOIACT50329.2020.9332008

[29] Yu, H., Gao, H., & Deng, Z. (2021). Toward a unified approximate analytical representation for spatially running spring-loaded inverted pendulum model. IEEE Transactions on Robotics, 37 (2), 691–698. https://doi. org/10.1109/TRO.2020.2976304

[30] Zhang, Z., Chang, X., Ma, H., An, H., & Lang, L. (2023). Model predictive control of quadruped robot based on reinforcement learning. Applied Sciences, 13 (1). https://doi.org/10.3390/app13010154

[31] Di Carlo, J., Wensing, P. M., Katz, B., Bledt, G., & Kim, S. (2018). Dynamic locomotion in the mit cheetah 3 through convex model-predictive control. 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 1–9. https://doi.org/10.1109/IROS.2018.8594448

[32] Kim, D., Lee, J., Ahn, J., Campbell, O., Hwang, H., & Sentis, L. (2018). Computationally-robust and efficient prioritized whole-body controller with contact constraints. 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 1–8. https://doi.org/10.1109/ IROS.2018.8593767

[33] Xing, B., Liu, Y., Zhirui, W., Liang, Z., Zhao, J., Su, B., & Jiang, L. (2021). Design of the anti-disturbance virtual model controller for quadruped robot, 4359–4365. https://doi.org/10.1109/CCDC52312.2021.9602160

[34] Tanikawa, T., Masuda, Y., & Ishikawa, M. (2021). A reciprocal excitatory reflex between extensors reproduces the prolongation of stance phase in walking cats: Analysis on a robotic platform. Frontiers in Neurorobotics, 15. https://doi.org/10.3389/fnbot.2021.636864

[35] McKenzie, J. E. (2012). Design of robotic quadruped legs [Master’s thesis]. Massachusetts Institute of Technology, Department of Mechanical Engineering.

[36] Freudenstein, F. (July 1, 2022). "An Analytical Approach to the Design of Four-Link Mechanisms." ASME. Trans. ASME. April 1954; 76(3): 483–489.
[37] Zeng, X., Zhang, S., Zhang, H., Li, X., Zhou, H., & Fu, Y. (2019). Leg trajectory planning for quadruped robots with high-speed trot gait. Applied Sciences, 9 (7). https://doi.org/10.3390/app9071508

[38] Hildebrand, M. (1989). The Quadrupedal Gaits of Vertebrates: The timing of leg movements relates to balance, body shape, agility, speed, and energy expenditure. BioScience, 39 (11), 766–775. https://doi.org/10.2307/ 1311182

[39] Ginsberg, J. H. (1995). Further Concepts in Analytical Mechanics. In Advanced Engineering Dynamics (pp. 309–388). chapter, Cambridge: Cambridge University Press.

[40] Popovic, M. B., Goswami, A., & Herr, H. (2005). Ground reference points in legged locomotion: Definitions, biological trajectories and control implications. The International Journal of Robotics Research, 24 (12), 1013– 1032. https://doi.org/10.1177/0278364905058363