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Modeling and Effective Foot Force Distribution for the Legs of a Quadruped Robot

Published online by Cambridge University Press:  08 January 2021

Priyaranjan Biswal*
Affiliation:
Department of Mechanical Engineering, National Institute of Technology, Arunachal Pradesh791112, India E-mail: prases@nitap.ac.in
Prases K. Mohanty
Affiliation:
Department of Mechanical Engineering, National Institute of Technology, Arunachal Pradesh791112, India E-mail: prases@nitap.ac.in
*
*Corresponding author. E-mail: priyaranjan.phd@nitap.ac.in

Summary

This paper presents the detailed dynamic modeling of a quadruped robot. The forward and inverse kinematic analysis of each leg of the proposed model is deduced using Denavit-Hartenberg (D-H) parameters. It desires to calculate the optimal feet forces of the quadruped robot’s joint torque, which is essential for its online control. To find out the optimal feet force distribution, two approaches are implemented to fulfill the locomotion objective. The four-legged quadruped robot and torso body’s detailed dynamics are modeled to generate an equation of motion for the robot control system. The Euler–Langrage theory has been used to find out the joint motion. The computer simulation results are presented to verify the effectiveness of the dynamic model.

Type
Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Meng, X., Wang, S., Cao, Z. and Zhang, L., “A Review of Quadruped Robots and Environment Perception,2016 35th Chinese Control Conference (CCC), IEEE (2016) pp. 63506356.CrossRefGoogle Scholar
Zhuang, H., Gao, H., Deng, Z., Ding, L. and Liu, Z., “A review of heavy-duty legged robots,” Sci. China Tech. Sci. 57(2), 298314 (2014).CrossRefGoogle Scholar
Zhong, Y., Wang, R., Feng, H. and Chen, Y., “Analysis and research of quadruped robot’s legs: A comprehensive review,” Int. J. Adv. Robot. Syst. 16(3), 1729881419844148 (2019),CrossRefGoogle Scholar
Kar, D. C., “Design of statically stable walking robot: A review,” J. Robot. Syst. 20(11), 671686 (2003).CrossRefGoogle Scholar
Rubio, F., Valero, F. and Llopis-Albert, C., “A review of mobile robots: Concepts, methods, theoretical framework, and applications,” Int. J. Adv. Robot. Syst. 16(2), 1729881419839596 (2019).CrossRefGoogle Scholar
Todd, D. J., Walking Machines: An Introduction to Legged Robots (Springer Science & Business Media, Springer US, 2013).Google Scholar
Ding, X. and Chen, H., “Dynamicmodeling and locomotion control for quadruped robots based on center of inertia on SE (3),” J. Dyn. Syst. Meas. Control 138(1), 011004 (2016) Paper No: DS-15-1298. doi: 10.1115/1.4031728.CrossRefGoogle Scholar
Gehring, C., Coros, S., Hutter, M., Bloesch, M., Hoepflinger, M. A. and Siegwart, R., “Control of Dynamic Gaits for a Quadrupedal Robot,2013 IEEE International Conference on Robotics and Automation (IEEE, 2013) pp. 32873292.CrossRefGoogle Scholar
Zhang, J., Gao, F., Han, X., Chen, X. and Han, X.. “Trot gait design and CPG method for a quadruped robot,” J. Bionic Eng. 11(1), 1825 (2014).CrossRefGoogle Scholar
Linand, B. S., Song, S. M., “Dynamicmodeling, stability, and energy efficiency of aquadrupedal walking machine,” J. Robot. Syst. 18(11), 657670 (2001).Google Scholar
Mahapatra, A., Royand, S. S. Pratihar, D. K., “Study on feet forces’ distributions, energy consumption and dynamic stability measure of hexapod robot during crab walking,” Appl. Math. Model. 65, 717744 (2019). doi: 10.1016/j.apm.2018.09.015.CrossRefGoogle Scholar
Liu, M., Qu, D., Xu, F., Zou, F., Di, P. and Tang, C., “Quadrupedal robots whole-body motion control based on centroidal momentum dynamics,” Appl. Sci. 9(7), 1335 (2019).CrossRefGoogle Scholar
Li, Z., Ge, S. S. and Liu, S., “Contact-Force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks,” IEEE Trans. Neural Netw. Learn. Syst. 25(8), 14601473 (2013).CrossRefGoogle Scholar
Ma, W. L., Hamed, K. A. and Ames, A. D., “First steps towards full model-based motion planning and control of quadrupeds: A hybrid zero dynamics approach,” arXiv preprint https://arxiv.org/abs/1909.08124arXiv:1909.08124 (2019).CrossRefGoogle Scholar
Howard, D., Zhang, S. J. and Sanger, D. J., “Kinematic analysis of a walking machine,” Math. Comput. Simul. 41(5–6), 525538 (1996).CrossRefGoogle Scholar
Gorinevsky, D. M. and Shneider, A. Y., “Force control in locomotion of legged vehicles over rigid and soft surfaces,” Int. J. Robot. Res. 9(2), 423 (1990).CrossRefGoogle Scholar
Barreto, J. P., Trigo, A., Menezes, P., Dias, J. and De Almeida, A. T., “FED-the Free Body Diagram Method. Kinematic and Dynamic Modeling of a Six-Leg Robot,AMC’98-Coimbra. 1998 5th International Workshop on Advanced Motion Control. Proceedings (Cat. No. 98TH8354) (IEEE, 1998) pp. 423428.CrossRefGoogle Scholar
Li, Z., Ge, S. S. and Liu, S., “Contact-Force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks,” IEEE Trans. Neural Netw. Learn. Syst. 25(8), 14601473 (2013).CrossRefGoogle Scholar
Chen, X., Watanabe, K., Kiguchi, K. and Izumi, K., “Optimal force distribution for the legs of a quadruped robot,” Mach. Intell. Robot. Control 1(2), 8793 (1999).Google Scholar
Zhou, D., Low, K. H. and Zielinska, T., “An efficient foot-force distribution algorithm for quadruped walking robots,” Robotica 18(4), 403413 (2000).CrossRefGoogle Scholar
Jiang, W. Y., Liu, A. M. and Howard, D., “Foot-Force Distribution in Legged Robots,” Proceedings of Fourth International Conference on Climbing and Walking Robots, Karlsruhe, Germany (2001) pp. 331338.Google Scholar
Marhefka, D. W. and Orin, D. E., “Quadratic Optimization of Force Distribution in Walking Machines,” Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No. 98CH36146), vol.1 (1998) pp. 477483.CrossRefGoogle Scholar
Zheng, Y., Chew, C. M. and Adiwahono, A. H., “A GJK-based approach to contact force feasibility and distribution for multi-contact robots,” Robot. Auto. Syst. 59(3–4), 194207 (2011).CrossRefGoogle Scholar
Kar, D. C., KurienIssac, K. and Jayarajan, K., “Minimum energy force distribution for a walking robot,” J. Robot. Syst. 18(2), 4754 (2001).3.0.CO;2-S>CrossRefGoogle Scholar
Roy, S. S. and Pratihar, D. K., “Effects of turning gait parameters on energy consumption and stability of a six-legged walking robot,” Robot. Auto. Syst. 60(1), 7282 (2012).CrossRefGoogle Scholar
Tan, L., A Generalized Framework of Linear Multivariable Control (Butterworth-Heinemann, Newton, MA, 2017).Google Scholar
Buss, S. R., “Introduction to inverse kinematics with jacobian transpose, pseudoinverse and damped least squares methods,” IEEE J. Robot. Autom. 17(1–19), 16 (2004).Google Scholar
Hoffman, J. D. and Frankel, S., Numerical Methods for Engineers and Scientists (CRC Press, Boca Raton, FL, 2018).CrossRefGoogle Scholar
Rigelsford, J., “Robotics: Control, sensing, vision and intelligence,” Ind. Robot Int. J. 26(2) (1999). doi: 10.1108/ir.1999.04926bae.002.CrossRefGoogle Scholar
Jin, B., Chen, C. and Li, W., “Power consumption optimization for a hexapod walking robot,” J. Intell. Robot. Syst. 71(2), 195209 (2013).CrossRefGoogle Scholar
Hua, Z., Rong, X., Li, Y., Chai, H., Li, B. and Zhang, S., “Analysis and verification on energy consumption of the quadruped robot with passive compliant hydraulic servo actuator,” Appl. Sci. 10(1), 340 (2020).CrossRefGoogle Scholar
Yang, K., Rong, X., Zhou, L. and Li, Y., “Modeling and analysis on energy consumption of hydraulic quadruped robot for optimal trot motion control,” Appl. Sci. 9(9), 1771 (2019).CrossRefGoogle Scholar
Erden, M. S. and Leblebicioglu, K., “Torque distribution in a six-legged robot,” IEEE Trans. Robot 23(1), 179186 (2007).CrossRefGoogle Scholar