Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Dynamics Modeling and Simulation of a Hexapod Robot with a Focus on Trajectory Prediction

  • Regular paper
  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

Dynamics simulation is an important technique for hexapod robots. However, the realistic locomotion of a robot is comprehensive due to kinematics error, mechanism deformation, sinkage, slippage, and dragging of the feet on the ground. To investigate this phenomenon, this paper presents a kinematics and dynamics model of a hexapod robot to include this effect in dynamics simulation. The compliance of both the robot and terrain are taken into consideration. The total compliance matrix and compatibility equation are established with the consideration of the compliance of the legs, body, and terrain. The body of the robot is modeled to have a coupled compliance to consider the effect of all six legs. The theory of terramechanics is introduced to describe the constraint between the feet of the robot and terrain. The complete dynamics model of hexapodal walking is built on the foundation of the compliant kinematics model and foot-terrain interaction mechanics model. Numerical simulation and experiments are performed based on a bio-inspired hexapod robot. The simulation and experimental results indicate that the model can provide a reliable accuracy with only analytical and a priori data as inputs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data Availability

The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.

Code Availability

The code used during the current study is available from the corresponding author on reasonable request.

References

  1. Tan, H., Zhang, H., Wang Y., Huang, Z., Li, L., Chen, X. Huang, T., Chen, X., Chen S.: Dynamics modeling and gait analysis of transport-oriented hexapod robot. In: Yan, L., Duan, H., Yu, X. (eds) Advances in guidance, navigation and control. Lecture notes in electrical engineering. 644. Springer, Singapore (2022). https://doi.org/10.1007/978-981-15-8155-7_360

  2. Yu, H., Gao, H., Deng, H.: Enhancing adaptability with local reactive behaviors for hexapod walking robot via sensory feedback integrated central pattern generator. Robot .Auton. Syst. 124, (2020). https://doi.org/10.1016/j.robot.2019.103401

  3. Hu, N., Li, S., Zhu, Y., Gao, F.: Constrained model predictive control for a hexapod robot walking on irregular terrain. J. Intell. Robot. Syst. 94, 179–201 (2019). https://doi.org/10.1007/s10846-018-0827-3

    Article  Google Scholar 

  4. Chen, G., Jin, B., Chen, Y.: Accurate position and posture control of a redundant hexapod robot. Arab J Sci Eng. 42, 2031–2042 (2017). https://doi.org/10.1007/s13369-017-2421-6

    Article  Google Scholar 

  5. Yamile, X., Garcia-Murillo, M., Alberto, L., Castillo-Castane, E.: Kinematics of hex-piderix - a six-legged robot - using screw theory. Int. J. Adv. Robot. Syst. 10, (2013). https://doi.org/10.5772/53796

  6. Wang, Z., Ding, X., Rovetta, A., Giusti, A.: Mobility analysis of the typical gait of a radial symmetrical six-legged robot. Mechatronics 21, 1133–1146 (2011). https://doi.org/10.1016/j.mechatronics.2011.05.009

    Article  Google Scholar 

  7. Ding, X., Yang, F.: Study on hexapod robot manipulation using legs. Robotica 34, 468–481 (2016). https://doi.org/10.1017/S0263574714001799

    Article  Google Scholar 

  8. Bombled, Q., Verlinden, O.: Dynamic simulation of six-legged robots with a focus on joint friction. Multibody Sys.Dyn. 28, 395–417 (2012). https://doi.org/10.1007/s11044-012-9305-z

    Article  Google Scholar 

  9. Pretorius, C.J., du Plessis, M.C., Gonsalves, J.W.: Evolutionary robotics applied to hexapod locomotion: a comparative study of simulation techniques. J. Intell. Robot. Syst. 96, 363–385 (2019). https://doi.org/10.1007/s10846-019-00989-0

    Article  Google Scholar 

  10. Shih, L., Frank, A.A., Ravani, B.: Dynamic simulation of legged machines using a compliant joint model. Int. J. Robot. Res. 6, 33–46 (1987). https://doi.org/10.1177/027836498700600403

    Article  Google Scholar 

  11. Zarrouk, D., Fearing, R. S.: Compliance-based dynamic steering for hexapods. IEEE/RSJ International Conference on Intelligent Robots and Systems. 3093–3098 (2012). https://doi.org/10.1109/IROS.2012.6385663

  12. Ganesh, K. K., Pushparaj, M. P.: Dynamic modelling & simulation of a four legged jumping robot with compliant legs.Robot. Auton. Syst. 61, 221–228 (2013). https://doi.org/10.1016/j.robot.2012.09.025

  13. Chen, C., Zha, F., Guo, W., Li, Z., Sun, L., Shi, J.: Trajectory adaptation of biomimetic equilibrium point for stable locomotion of a large-size hexapod robot. Auton. Robot. 45, 155–174 (2021). https://doi.org/10.1007/s10514-020-09955-4

    Article  Google Scholar 

  14. Roy, S.S., Pratihar, D.K.: Kinematics, dynamics and power consumption analyses for turning motion of a six-legged robot. J. Intell. Rob. Syst. 74, 663–688 (2014). https://doi.org/10.1007/s10846-013-9850-6

    Article  Google Scholar 

  15. Waldron K.: Force and motion management in legged locomotion. IEEE J. Robot. Auto. 2, 214–220 (1986) https://doi.org/10.1109/JRA.1986.1087060

  16. Ding, L., Gao, H., Deng, Z., Song, J., Liu, Y., Liu, G., Iagnemma, K.: Foot-terrain interaction mechanics for legged robots: Modeling and experimental validation. Int. J. Robot. Res. 32, 1585–1606 (2013). https://doi.org/10.1177/0278364913498122

    Article  Google Scholar 

  17. Komizunai S., Konno A.,. Abiko S, Uchiyama M.: Development of a static sinkage model for a biped robot on loose soil. In: 2010 IEEE/SICE International Symposium on System Integration. pp. 61–66 (2010) https://doi.org/10.1109/SII.2010.5708302.

  18. Comin, F. J., Saaj, C. M.: Models for slip estimation and soft terrain characterization with multilegged wheel–legs. IEEE Trans. Robot. 33, 1438–1452 (2017) https://doi.org/10.1109/TRO.2017.2723904

  19. Mahapatra, A., Roy, 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, 717–744 (2019). https://doi.org/10.1016/j.apm.2018.09.015

    Article  MathSciNet  MATH  Google Scholar 

  20. Yang, C., Ding, L., Tang, D., Gao, H., Niu, L., Lan, Q., Li, C., Deng, Z.: Improved Terzaghi-theory-based interaction modeling of rotary robotic locomotors with granular substrates. Mech. Mach. Theory. 152 (2020). https://doi.org/10.1016/j.mechmachtheory.2020.103901

  21. Deblaise, D., Hernot, X., Maurine, P.: A systematic analytical method for PKM stiffness matrix calculation. in: Proceedings 2006 IEEE International Conference on Robotics and Automation, pp. 4213–4219 (2006). https://doi.org/10.1109/ROBOT.2006.1642350

  22. Ding, X., Dai, J.: Compliance analysis of mechanisms with spatial continuous compliance in the context of screw theory and Lie groups. In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. Pp. 2493–2504 (2010). https://doi.org/10.1243/09544062JMES2095

  23. Qi, P., Qiu, C., Liu, H., Dai, J., Seneviratne, L.D., Althoefer, K.: A novel continuum manipulator design using serially connected double-layer planar springs. IEEE/ASME Trans. Mechatron. 21, 1281–1292 (2016). https://doi.org/10.1109/TMECH.2015.2498738

    Article  Google Scholar 

  24. Klimchik, A., Chablat, D., Pashkevich, A.: Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings. Mech. Mach. Theory 79, 1–28 (2014). https://doi.org/10.1016/j.mechmachtheory.2014.04.002

    Article  Google Scholar 

  25. Grizzle, J.W., Abba, G., Plestan, F.: Asymptotically stable walking for biped robots: analysis via systems with impulse effects. IEEE Trans. Autom. Control 46, 51–64 (2001). https://doi.org/10.1109/9.898695

    Article  MathSciNet  MATH  Google Scholar 

  26. Liang, S., Frank, A.A., Ravani, B.: Dynamic simulation of legged machines using a compliant joint model. Int. J. Robot. Res. 6, 33–36 (1987). https://doi.org/10.1177/027836498700600404

    Article  Google Scholar 

  27. Hunt, K.H., Crossley, F.R.E.: Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. 42, 440–445 (1975). https://doi.org/10.1115/1.3423596

    Article  Google Scholar 

  28. Gao, H., Jin, M., Ding, L., Liu, Y., Li, W., Yu, X., Deng, Z., Liu, Z.: A real-time, high fidelity dynamic simulation platform for hexapod robots on soft terrain. Simul. Model. Pract. Theory 68, 125–145 (2016). https://doi.org/10.1016/j.simpat.2016.08.004

    Article  Google Scholar 

  29. Kane, T. R.: Dynamics, theory and applications, McGraw-Hill (1985)

Download references

Acknowledgements

This study was supported in part by the National Key Research and Development Program of China (No. 2019YFB1309500, 2018YFB1306104), the National Natural Science Foundation of China (Grant No. 51822502, 91948202), Science and Technology Major Project of Anhui Province (202003a05020015), and the “111 Project” (Grant No. B07018).

Funding

This study was supported in part by the National Key Research and Development Program of China (No. 2019YFB1309500, 2018YFB1306104), the National Natural Science Foundation of China (Grant No. 51822502, 91948202), Science and Technology Major Project of Anhui Province (202003a05020015), and the “111 Project” (Grant No. B07018).

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Tsinghua University, Beijing, 100089, China

    Ma Jin & Pinjia Zhang

  2. State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, 150001, China

    Liang Ding, Haibo Gao & Yang Su

Authors
  1. Ma Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liang Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haibo Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yang Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pinjia Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Ma Jin, Liang Ding, Haibo Gao and Pinjia Zhang. Experiments were conducted by Ma Jin and Yang Su. The first draft of the manuscript was written by Ma Jin and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Pinjia Zhang.

Ethics declarations

Ethics Approval

Not applicable.

Consent to Participate

Not applicable.

Consent for Publication

Not applicable.

Conflicts of Interest/Competing Interests

The authors have no conflicts of interest to declare that are relevant to the content of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jin, M., Ding, L., Gao, H. et al. Dynamics Modeling and Simulation of a Hexapod Robot with a Focus on Trajectory Prediction. J Intell Robot Syst 108, 8 (2023). https://doi.org/10.1007/s10846-023-01839-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-023-01839-w

Keywords

Search

Navigation