Hybrid CPG–FRI dynamic walking algorithm balancing agility and stability control of biped robot

  • Bin HeEmail author
  • Yuanyuan Si
  • Zhipeng WangEmail author
  • Yanmin ZhouEmail author


Dynamic walking fulfill agility and stability simultaneously is one of the most difficulty for biped robot control. The traditional zero moment point (ZMP) is the most commonly used reference point for biped robot static and quasi dynamic walking control. However, human walking experimental results indicate that during walking process of human beings, the ZMP trajectory is not always conformed to the requirement of stability, such as giant strides, acceleration walking or fast walking. In order to reveal the mechanism of the biped dynamic walking, this paper proposed a novel stability criterion for the biped walking by tuning the conventional fixed support polygon area to an adjustable one. This method includes the tiptoe underactuated phase of the support foot during the biped walking. A new algorithm for the real-time biped walking generation by combining central pattern generation (CPG) with foot rotation indicator (FRI) is presented. The FRI monitor establishes the mapping function between the center of mass of the biped robot with the boundary of the elastic support polygon. By introducing FRI information, the CPG parameters can be adjusted in real time to generate a rhythmic and stable walking pattern. Numerical simulation results show that the proposed algorithm extends the application area of the ZMP criterion and improves the walking velocity of the biped robot. Moreover, the algorithm builds a bridge for the dynamic biped walking from the robot agility to motor parameters. This means that the agility of the biped robot can be quantitative controlled by modulating the motor parameters.


Biped robot Foot rotation indicator Central pattern generator Stability control Elastic support polygon Dynamic walking 



The work was supported by National Natural Science Foundation of China (Grant Nos. 51605334, U1713215, and 51705368), and Shanghai Municipal Science and Technology Commission Project (Grant No. 17DZ1203405). We thank the reviewers and editors for their helpful comments on the manuscript.


  1. Aoi, S., & Tsuchiya, K. (2011). Generation of bipedal walking through interactions among the robot dynamics, the oscillator dynamics, and the environment: Stability characteristics of a five-link planar biped robot. Autonomous Robots, 30(2), 123–141.CrossRefGoogle Scholar
  2. Farzaneh, Y., Akbarzadeh, A., & Akbari, A. A. (2014). Online bio-inspired trajectory generation of seven-link biped robot based on t–s fuzzy system. Applied Soft Computing, 14, 167–180.CrossRefGoogle Scholar
  3. Ferreira, J. P., Crisostomo, M., & Coimbra, A. P. (2012). SVR controller for a biped robot in the sagittal plane with human-based ZMP trajectory reference and gait. International Journal of Humanoid Robotics, 9(03), 1250018.CrossRefGoogle Scholar
  4. Fu, C., & Chen, K. (2006). Research progress on stability and control strategy for biped robots. Chinese High Technology Letters, 16(3), 319–324.Google Scholar
  5. Goswami, A. (1999). Postural stability of biped robots and the foot-rotation indicator (FRI) point. The International Journal of Robotics Research, 18(6), 523–533.CrossRefGoogle Scholar
  6. He, B., Wang, Z., Shen, R., & Hu, S. (2014). Real-time walking pattern generation for a biped robot with hybrid CPG–ZMP algorithm. International Journal of Advanced Robotic Systems, 11(10), 160.CrossRefGoogle Scholar
  7. Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences, 79(8), 2554–2558.MathSciNetCrossRefzbMATHGoogle Scholar
  8. Huang, Q., & Nakamura, Y. (2005). Sensory reflex control for humanoid walking. IEEE Transactions on Robotics, 21(5), 977–984.CrossRefGoogle Scholar
  9. Huang, Q., Yokoi, K., Kajita, S., Kaneko, K., Arai, H., Koyachi, N., et al. (2001). Planning walking patterns for a biped robot. IEEE Transactions on Robotics and Automation, 17(3), 280–289.CrossRefGoogle Scholar
  10. Kajita, S., Hirukawa, H., Harada, K., & Yokoi, K. (2014). Introduction to humanoid robotics. Berlin: Springer.CrossRefGoogle Scholar
  11. Li, Z., Zhou, C., Zhu, Q., & Xiong, R. (2017). Humanoid balancing behavior featured by underactuated foot motion. IEEE Transactions on Robotics, 33(2), 298–312.CrossRefGoogle Scholar
  12. Matsuoka, K. (1985). Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biological Cybernetics, 52(6), 367–376.MathSciNetCrossRefzbMATHGoogle Scholar
  13. Miyake, Y. (2009). Interpersonal synchronization of body motion and the Walk-Mate walking support robot. IEEE Transactions on Robotics, 25(3), 638–644.CrossRefGoogle Scholar
  14. Nakamura, Y., Mori, T., Sato, M.-A., & Ishii, S. (2007). Reinforcement learning for a biped robot based on a CPG—Actor—Critic method. Neural Networks, 20(6), 723–735.CrossRefzbMATHGoogle Scholar
  15. Nassour, J., Hénaff, P., Ouezdou, F. B., Cheng, G. (2010). A study of adaptive locomotive behaviors of a biped robot: Patterns generation and classification. In International conference on simulation of adaptive behavior, pp. 313–324.Google Scholar
  16. Or, J. (2010). A hybrid CPG–ZMP control system for stable walking of a simulated flexible spine humanoid robot. Neural Networks, 23(3), 452–460.CrossRefGoogle Scholar
  17. Or, J., & Takanishi, A. (2004). A biologically inspired CPG–ZMP control system for the real-time balance of a single-legged belly dancing robot. IEEE/RSJ International Conference on Intelligent Robots and Systems, 1, 931–936.Google Scholar
  18. Park, H.-W., Ramezani, A., & Grizzle, J. (2013). A finite-state machine for accommodating unexpected large ground-height variations in bipedal robot walking. IEEE Transactions on Robotics, 29(2), 331–345.CrossRefGoogle Scholar
  19. Perrin, N., Stasse, O., Baudouin, L., Lamiraux, F., & Yoshida, E. (2012). Fast humanoid robot collision-free footstep planning using swept volume approximations. IEEE Transactions on Robotics, 28(2), 427–439.CrossRefGoogle Scholar
  20. 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.CrossRefGoogle Scholar
  21. Taga, G. (1995a). A model of the neuro-musculo-skeletal system for human locomotion. I. Emergence of basic gait. Biological Cybernetics, 73(2), 97–111.CrossRefzbMATHGoogle Scholar
  22. Taga, G. (1995b). A model of the neuro-musculo-skeletal system for human locomotion II. Real-time adaptability under various constraints. Biological Cybernetics, 2(73), 113–121.CrossRefzbMATHGoogle Scholar
  23. Vukobratović, M., & Borovac, B. (2004). Zero-moment point thirty five years of its life. International Journal of Humanoid Robotics, 1(01), 157–173.CrossRefGoogle Scholar
  24. Vukobratovic, M., Frank, A., & Juricic, D. (1970). On the stability of biped locomotion. IEEE Transactions on Biomedical Engineering, 1, 25–36.CrossRefGoogle Scholar
  25. Wang, L., Liu, Z., Chen, C. P., Zhang, Y., Lee, S., & Chen, X. (2013). Fuzzy SVM learning control system considering time properties of biped walking samples. Engineering Applications of Artificial Intelligence, 26(2), 757–765.CrossRefGoogle Scholar
  26. Wang, T., Guo, W., Li, M., Zha, F., & Sun, L. (2012). CPG control for biped hopping robot in unpredictable environment. Journal of Bionic Engineering, 9(1), 29–38.CrossRefGoogle Scholar
  27. Wang, Z., He, B., Zhou, Y., Yuan, T., Xu, S., & Shao, M. (2018). An experimental analysis of stability in human walking. Journal of Bionic Engineering, 15(5), 827–838.CrossRefGoogle Scholar
  28. Westervelt, E. R., Chevallereau, C., Choi, J. H., Morris, B., & Grizzle, J. W. (2007). Feedback control of dynamic bipedal robot locomotion. Boca Raton: CRC Press.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Control Science and EngineeringTongji UniversityShanghaiChina

Personalised recommendations