Skip to main content
SpringerLink
Log in

Kinematic Modeling for Biped Robot Gait Trajectory Using Machine Learning Techniques

  • Research Article
  • Published:
Journal of Bionic Engineering Aims and scope Submit manuscript

Abstract

This paper presents the predictive models for biped robot trajectory generation. Predictive models are parametrizing as a continuous function of joint angle trajectories. In a previous work, the authors had collected the human locomotion dataset at RAMAN Lab, MNIT, Jaipur, India. The MNIT gait dataset consists of walking data on a plane surface of 120 human subjects from different age groups and genders. Thirty-two machine learning models (linear, support vector, k-nearest neighbor, ensemble, probabilistic, and deep learning) trained using the collected dataset. In addition, two types of mapping, (a) one-to-one and (b) many-to-one, are presented for each model. These mapping models act as a reference policy for the control of joints and prediction of state for the next time instant in advance if the onboard sensor fails. Results show that the deep learning and probabilistic learning models perform better for both types of mappings. Also, the probabilistic model outperforms the deep learning-based models in terms of maximum error, because the probabilistic model effectively deals with the prediction uncertainty. In addition, many-to-one outperforms the one-to-one mapping because it captures the correlation between knee, hip, and ankle trajectories. Therefore, this study suggests a many-to-one mapping using the probabilistic model for biped robot trajectory generation.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Conde, M. A., Rodriguez-Sedano, F. J., Fernandez-Llamas, C., Goncalves, J., Lima, J., & Garcia-Penalvo, F. J. (2021). Fostering STEAM through challenge-based learning, robotics, and physical devices: A systematic mapping literature review. Computer Applications in Engineering Education, 29, 46–65.

    Google Scholar 

  2. Singh, B., Kumar, R., & Singh, V. P. (2021). Reinforcement learning in robotic applications: a comprehensive survey. Artificial Intelligence Review. https://doi.org/10.1007/s10462-021-09997-9

    Article  Google Scholar 

  3. Zheng, T. J., Zhu, Y., Zhang, Z., Zhao, S., Chen, J., & Zhao, J. (2018). Parametric gait online generation of a lower-limb exoskeleton for individuals with paraplegia. Journal of Bionic Engineering, 15, 941–949.

    Google Scholar 

  4. Boudon, B., Linares, J. M., Abourachid, A., Vauquelin, A., & Mermoz, E. (2018). Bio-inspired topological skeleton for the analysis of quadruped kinematic gait. Journal of Bionic Engineering, 15, 839–850.

    Google Scholar 

  5. Gong, Z., Cheng, J., Chen, X., Sun, W., Fang, X., Hu, K., Xie, Z., Wang, T., & Wen, L. (2018). A bio-inspired soft robotic arm: Kinematic modeling and hydrodynamic experiments. Journal of Bionic Engineering, 15, 204–219.

    Google Scholar 

  6. Ma, Y., Fan, X., Cai, J., Tao, J., Gao, Y., & Yang, Q. (2021). Application of sensor data information cognitive computing algorithm in adaptive control of wheeled robot. IEEE Sensors Journal. https://doi.org/10.1109/JSEN.2021.3054058

    Article  Google Scholar 

  7. Ficht, G., & Behnke, S. (2021). Bipedal humanoid hardware design: A technology review. Current Robotics Reports. https://doi.org/10.1007/s43154-021-00050-9

    Article  Google Scholar 

  8. Liu, B., Xiao, X., & Stone, P. (2021). A lifelong learning approach to mobile robot navigation. IEEE Robotics and Automation Letters, 6, 1090–1096.

    Google Scholar 

  9. Pratt, J., Chew, C. M., Torres, A., Dilworth, P., & Pratt, G. (2001). Virtual model control: An intuitive approach for bipedal locomotion. The International Journal of Robotics Research, 20, 129–143.

    Google Scholar 

  10. Golliday, C., & Hemami, H. (1977). An approach to analyzing biped locomotion dynamics and designing robot locomotion controls. IEEE Transactions on Automatic Control, 22, 963–972.

    Google Scholar 

  11. Park, J. H., Chung, H. (1999) ZMP compensation by online trajectory generation for biped robots. In IEEE SMC’99 Conference Proceedings IEEE International Conference on Systems, Man, and Cybernetics (Cat. No. 99CH37028), 4, 960–965.

  12. Hasegawa, Y., Arakawa, T., & Fukuda, T. (2000). Trajectory generation for biped locomotion robot. Mechatronics, 10, 67–89.

    Google Scholar 

  13. Arakawa, T., Fukuda, T. (1996) Natural motion trajectory generation of biped locomotion robot using genetic algorithm through energy optimization. In 1996 IEEE International Conference on Systems, Man and Cybernetics, Information Intelligence and Systems (Cat. No. 96CH35929), 2, 1495–1500.

  14. Suzuki, T., Tsuji, T., Shibuya, M., & Ohnishi, K. (2008). ZMP reference trajectory generation for biped robot with inverted pendulum model by using virtual supporting point. IEEE Transactions on Industry Applications, 128, 687–693.

    Google Scholar 

  15. Kim, J., Ba, D. X., Yeom, H., & Bae, J. (2021). Gait optimization of a quadruped robot using evolutionary computation. Journal of Bionic Engineering, 18, 306–318.

    Google Scholar 

  16. Chen, J., Liu, C., Zhao, H., Zhu, Y., & Zhao, J. (2020). Learning to identify footholds from geometric characteristics for a six-legged robot over rugged terrain. Journal of Bionic Engineering, 17, 512–522.

    Google Scholar 

  17. Juang, C. F., & Yeh, Y. T. (2017). Multi-objective evolution of biped robot gaits using advanced continuous ant-colony optimized recurrent neural networks. IEEE Transactions on Cybernetics, 48, 1910–1922.

    Google Scholar 

  18. Embry, K. R., Villarreal, D. J., Macaluso, R. L., & Gregg, R. D. (2018). Modeling the kinematics of human locomotion over continuously varying speeds and inclines. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 26, 2342–2350.

    Google Scholar 

  19. Clever, D., Hu, Y., & Mombaur, K. (2018). Humanoid gait generation in complex environments based on template models and optimality principles learned from human beings. The International Journal of Robotics Research, 37, 1184–1204.

    Google Scholar 

  20. Riley, M., Ude, A., Wade, K., Atkeson, C. G. (2003) Enabling real-time full-body imitation: A natural way of transferring human movement to humanoids. In 2003 IEEE International Conference on Robotics and Automation (Cat. No. 03CH37422), 2, 2368–2374.

  21. Aithal, C. N., Ishwarya, P., Sneha, S., Yashvardhan, C. N., & Suresh, K. V. (2020). Design of a Bipedal Robot. Advances in VLSI, Signal Processing, Power Electronics, IoT, Communication and Embedded Systems: Select Proceedings of VSPICE, 2021, 752–755.

    Google Scholar 

  22. Prakash, C., Kumar, R., & Mittal, N. (2018). Recent developments in human gait research: Parameters, approaches, applications, machine learning techniques, datasets and challenges. Artificial Intelligence Review, 49, 1–40.

    Google Scholar 

  23. Prakash, C., Gupta, K., Mittal, A., Kumar, R., & Laxmi, V. (2015). Passive marker based optical system for gait kinematics for lower extremity. Procedia Computer Science, 45, 176–185.

    Google Scholar 

  24. Prakash, C., Mittal, A., Kumar, R., Mittal, N. (2015) Identification of spatio-temporal and kinematics parameters for 2-D optical gait analysis system using passive markers. In 2015 International Conference on Advances in Computer Engineering and Applications, 143–149.

  25. Prakash, C., Mittal, A., Tripathi, S., Kumar, R., Mittal, N. (2016) A framework for human recognition using a multimodel gait analysis approach. In 2016 International Conference on Computing, Communication and Automation (ICCCA), 348–353.

  26. Prakash, C., Mittal, A., Kumar, R., Mittal, N. (2015) Identification of gait parameters from silhouette images. In 2015 Eighth International Conference on Contemporary Computing (IC3), 190–195.

  27. Prakash, C., Gupta, K., Kumar, R., Mittal, N. (2016) Fuzzy logic-based gait phase detection using passive markers. In Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Springer, Singapore, 561–572.

  28. Prakash, C., Sujil, A., Kumar, R., Mittal, N. (2019) Linear prediction model for joint movement of lower extremity. In Recent Findings in Intelligent Computing Techniques, Springer, Singapore, 235–243.

  29. Prakash, C., Kumar, R., Mittal, N., & Raj, G. (2018). Vision based identification of joint coordinates for marker-less gait analysis. Procedia Computer Science, 132, 68–75.

    Google Scholar 

  30. Weisberg, S. (2005). Applied linear regression (p. 528). Wiley.

    MATH  Google Scholar 

  31. Hoerl, A. E., Kannard, R. W., & Baldwin, K. F. (1975). Ridge regression: Some simulations. Communications in Statistics-Theory and Methods, 4, 105–123.

    MATH  Google Scholar 

  32. Marquardt, D. W., & Snee, R. D. (1975). Ridge regression in practice. The American Statistician, 29, 3–20.

    MATH  Google Scholar 

  33. Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004). Least angle regression. Annals of Statistics, 32, 407–499.

    MathSciNet  MATH  Google Scholar 

  34. Then, Q. (2020). Conversion modeling: Machine learning for marketing decision support (p. 95). Humboldt University of Berlin.

    Google Scholar 

  35. Sun, Q., Zhou, W. X., & Fan, J. (2020). Adaptive huber regression. Journal of the American Statistical Association, 115, 254–265.

    MathSciNet  MATH  Google Scholar 

  36. Choi, S., Kim, T., & Yu, W. (1997). Performance evaluation of RANSAC family. Journal of Computer Vision, 24, 271–300.

    Google Scholar 

  37. Wilcox, R. (1998). A note on the Theil-Sen regression estimator when the regressor is random and the error term is heteroscedastic. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 40, 261–268.

    MATH  Google Scholar 

  38. Zou, H., & Hastie, T. (2005). Regularization, and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67, 301–320.

    MathSciNet  MATH  Google Scholar 

  39. Pati, Y. C., Rezaiifar, R., Krishnaprasad, P. S. (1993) Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, 40–44.

  40. Vovk, V. (2013). Kernel ridge regression. In E. Inference (Ed.), Springer (pp. 105–116). Germany.

    Google Scholar 

  41. Drucker, H., Burges, C. J., Kaufman, L., Smola, A., & Vapnik, V. (1997). Support vector regression machines. Advances in Neural Information Processing Systems, 9, 155–161.

    Google Scholar 

  42. Smola, A. J., & Schölkopf, B. (2004). A tutorial on support vector regression. Statistics and Computing, 14, 199–222.

    MathSciNet  Google Scholar 

  43. Cheng, D., Zhang, S., Deng, Z., Zhu, Y., Zong, M. (2014) KNN algorithm with data-driven k value. In International Conference on Advanced Data Mining and Applications, Springer, Cham, 499–512.

  44. Chou, P. A. (1991). Optimal partitioning for classification and regression trees. IEEE Computer Architecture Letters, 13, 340–354.

    Google Scholar 

  45. Breiman, L. (2001). Random forests. Machine Learning, 45, 5–32.

    MATH  Google Scholar 

  46. Schapire, R. E. (2010). The convergence rate of AdaBoost. In COLT, 10, 308–309.

    Google Scholar 

  47. Zemel, R. S., Pitassi, T. (2001) A. gradient-based boosting algorithm for regression problems. In: Advances in Neural Information Processing Systems, 696–702.

  48. Raftery, A. E., Madigan, D., & Hoeting, J. A. (1997). Bayesian model averaging for linear regression models. Journal of the American Statistical Association, 92, 179–191.

    MathSciNet  MATH  Google Scholar 

  49. Park, T., & Casella, G. (2008). The Bayesian lasso. Journal of the American Statistical Association, 103, 681–686.

    MathSciNet  MATH  Google Scholar 

  50. Schulz, E., Speekenbrink, M., & Krause, A. (2018). A tutorial on gaussian process regression: Modelling, exploring, and exploiting functions. Journal of Mathematical Psychology, 85, 1–16.

    MathSciNet  MATH  Google Scholar 

  51. Burt, D., Rasmussen, C. E., Van Der Wilk, M. (2019) Rates of convergence for sparse variational Gaussian process regression. In International Conference on Machine Learning, 862–871.

  52. Thimm, G., & Fiesler, E. (1997). High-order and multilayer perceptron initialization. IEEE Transactions on Neural Networks, 8, 349–359.

    Google Scholar 

  53. Murtagh, F. (1991). Multilayer perceptrons for classification and regression. Neurocomputing, 2, 183–197.

    MathSciNet  Google Scholar 

  54. Hinton, G. E., Osindero, S., & Teh, Y. W. (2006). A fast-learning algorithm for deep belief nets. Neural Computation, 18, 1527–1554.

    MathSciNet  MATH  Google Scholar 

  55. Liu, W., Wang, Z., Liu, X., Zeng, N., Liu, Y., & Alsaadi, F. E. (2017). A survey of deep neural network architectures and their applications. Neurocomputing, 234, 11–26.

    Google Scholar 

  56. Gallicchio, C. (2018) Short-term memory of deep rnn. arXiv preprint https://arxiv.org/abs/1802.00748. Accessed 2 Feb 2018.

  57. Greff, K., Srivastava, R. K., Koutník, J., Steunebrink, B. R., & Schmidhuber, J. (2016). LSTM: A search space odyssey. IEEE Transactions on Neural Networks and Learning Systems, 28, 2222–2232.

    MathSciNet  Google Scholar 

  58. Chung, J., Gulcehre, C., Cho, K., Bengio, Y. (2014) Empirical evaluation of gated recurrent neural networks on sequence modeling. arXiv preprint https://arxiv.org/abs/1412.3555. Accessed 11 Dec 2014.

  59. Huang, Z., Xu, W., Yu, K. (2015) Bidirectional LSTM-CRF models for sequence tagging. arXiv preprint https://arxiv.org/abs/1508.01991. Accessed 9 Aug 2015.

  60. Sheng, H., Xiao, J., Cheng, Y., Ni, Q., & Wang, S. (2017). Short-term solar power forecasting based on weighted Gaussian process regression. IEEE Transactions on Industrial Electronics, 65, 300–308.

    Google Scholar 

Download references

Funding

None.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Malaviya National Institute of Technology, Jaipur, 302017, India

    Bharat Singh, Ankit Vijayvargiya & Rajesh Kumar

Authors
  1. Bharat Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ankit Vijayvargiya
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rajesh Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bharat Singh.

Ethics declarations

Conflict of interest

All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

Ethics approval and consent to participate

Not applicable.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, B., Vijayvargiya, A. & Kumar, R. Kinematic Modeling for Biped Robot Gait Trajectory Using Machine Learning Techniques. J Bionic Eng 19, 355–369 (2022). https://doi.org/10.1007/s42235-021-00142-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42235-021-00142-4

Keywords

Search

Navigation