Skip to main content
SpringerLink
Log in

Capturability-based Fuzzy Footstep Planner for a Biped Robot with Centroidal Compliance

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

Abstract

Compliance motion and footstep adjustment are active balance control strategies from learning human subconscious behaviors. The force estimation without direct end-actuator force measurement and the optimal footsteps based on complex analytical calculation are still challenging tasks for elementary and kid-size position-controlled robots. In this paper, an online compliant controller with Gravity Projection Observer (GPO), which can express the external force condition of perturbations by the estimated Projection of Gravity (PoG) with estimation covariance, is proposed for the realization of disturbance absorption, with which the robustness of the humanoid contact with environments can be maintained. The fuzzy footstep planner based on capturability analysis is proposed, and the Model Predictive Control (MPC) is applied to generate the desired steps. The fuzzification rules are well-designed and give the corresponding control output responding to complex and changeable external disturbances. To validate the presented methods, a series of experiments on a real humanoid robot are conducted. The results verify the effectiveness of the proposed balance control framework.

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
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Data Availability

The datasets generated during the current study are available from the corresponding author on reasonable request. The codes can be found in the Github repository, https://github.com/southwestCat/railbot

Notes

  1. https://github.com/southwestCat/railbot

  2. https://www.bilibili.com/video/BV1Qe4y127Et

References

  1. Kheddar, A., Caron, S., Gergondet, P., Comport, A., Tanguy, A., Ott, C., Henze, B., Mesesan, G., Englsberger, J., Roa, M. A., Wieber, P., Chaumette, F., Spindler, F., Oriolo, G., Lanari, L., Escande, A., Chappellet, K., Kanehiro, F., & Rabaté, P. (2019). Humanoid robots in aircraft manufacturing: The airbus use cases. IEEE Robotics & Automation Magazine, 26(4), 30–45. https://doi.org/10.1109/MRA.2019.2943395

    Article  Google Scholar 

  2. Duan, H. L., Dao, J., Green, K., Apgar, T., Fern, A., & Hurst, J. (2021). Learning task space actions for bipedal locomotion. In 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi’an, China, 1276–1282. https://doi.org/10.1109/ICRA48506.2021.9561705

  3. Stephens, B. J., & Atkeson, C. G. (2010). Push recovery by stepping for humanoid robots with force controlled joints. In 2010 10th IEEE-RAS International conference on humanoid robots, Nashville, USA, 52–59. https://doi.org/10.1109/ICHR.2010.5686288

  4. Schuller, R., Mesesan, G., Englsberger, J., Lee, J., & Ott, C. (2021). Online centroidal angular momentum reference generation and motion optimization for humanoid push recovery. IEEE Robotics and Automation Letters, 6(3), 5689–5696. https://doi.org/10.1109/LRA.2021.3082023

    Article  Google Scholar 

  5. Ferigo, D., Camoriano, R., Viceconte, P. M., Calandriello, D., Traversaro, S., Rosasco, L., & Pucci, D. (2021). On the emergence of whole-body strategies from humanoid robot push-recovery learning. IEEE Robotics and Automation Letters, 6(4), 8561–8568. https://doi.org/10.1109/LRA.2021.3076955

    Article  Google Scholar 

  6. Zhu, H. B., Luo, M. Z., Mei, T., Zhao, J. H., Li, T., & Guo, F. Y. (2016). Energy-efficient bio-inspired gait planning and control for biped robot based on human locomotion analysis. Journal of Bionic Engineering, 13(2), 271–282. https://doi.org/10.1016/S1672-6529(16)60300-1

    Article  Google Scholar 

  7. Zhou, C. X., Wang, X., Li, Z. B., & Tsagarakis, N. (2017). Overview of gait synthesis for the humanoid coman. Journal of Bionic Engineering, 14(1), 15–25. https://doi.org/10.1016/S1672-6529(16)60373-6

    Article  Google Scholar 

  8. Kim, S., Hirota, K., Nozaki, T., & Murakami, T. (2018). Human motion analysis and its application to walking stabilization with COG and ZMP. IEEE Transactions on Industrial Informatics, 14(11), 5178–5186. https://doi.org/10.1109/TII.2018.2830341

    Article  Google Scholar 

  9. Wang, Z. P., He, B., Zhou, Y. M., Yuan, T. T., Xu, S. L., & Shao, M. Z. (2018). An experimental analysis of stability in human walking. Journal of Bionic Engineering, 15(5), 827–838. https://doi.org/10.1007/s42235-018-0070-4

    Article  Google Scholar 

  10. De Viragh, Y., Bjelonic, M., Bellicoso, C. D., Jenelten, F., & Hutter, M. (2019). Trajectory optimization for wheeled-legged quadrupedal robots using linearized zmp constraints. IEEE Robotics and Automation Letters, 4(2), 1633–1640. https://doi.org/10.1109/LRA.2019.2896721

    Article  Google Scholar 

  11. Caron, S., Escande, A., Lanari, L., & Mallein, B. (2019). Capturability-based pattern generation for walking with variable height. IEEE Transactions on Robotics, 36(2), 517–536. https://doi.org/10.1109/TRO.2019.2923971

    Article  Google Scholar 

  12. Pratt, J., Carff, J., Drakunov, S., & Goswami, A. (2006). Capture point: A step toward humanoid push recovery. In 2006 6th IEEE-RAS International Conference on Humanoid Robots, Genova, Italy, 200–207. https://doi.org/10.1109/ICHR.2006.321385

  13. Englsberger, J., Ott, C., & Albu-Schäffer, A. (2015). Three-dimensional bipedal walking control based on divergent component of motion. IEEE Transactions on Robotics, 31(2), 355–368. https://doi.org/10.1109/TRO.2015.2405592

    Article  Google Scholar 

  14. Nenchev, D. N., & Iizuka, R. (2021). Emergent humanoid robot motion synergies derived from the momentum equilibrium principle and the distribution of momentum. IEEE Transactions on Robotics, 38(1), 536–555. https://doi.org/10.1109/TRO.2021.3083195

    Article  Google Scholar 

  15. Han, Y. H., & Cho, B. K. (2022). Slope walking of humanoid robot without IMU sensor on an unknown slope. Robotics and Autonomous Systems, 155, 104163. https://doi.org/10.1016/j.robot.2022.104163

    Article  Google Scholar 

  16. Kajita, S., Morisawa, M., Miura, K., Nakaoka, S. I., Harada, K., Kaneko, K., Kanehiro, F., & Yokoi, K. (2010) Biped walking stabilization based on linear inverted pendulum tracking. In 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, China, 4489–4496. https://doi.org/10.1109/IROS.2010.5651082

  17. Li, Q. Q., Meng, F., Yu, Z. G., Chen, X. C., & Huang, Q. (2021). Dynamic torso compliance control for standing and walking balance of position-controlled humanoid robots. IEEE/ASME Transactions on Mechatronics, 26(2), 679–688. https://doi.org/10.1109/TMECH.2021.3061825

    Article  Google Scholar 

  18. Jiang, Z. H., Xu, J. F., Li, H., & Huang, Q. (2019). Stable parking control of a robot astronaut in a space station based on human dynamics. IEEE Transactions on Robotics, 36(2), 399–413. https://doi.org/10.1109/TRO.2019.2936302

    Article  Google Scholar 

  19. Benallegue, M., Cisneros, R., Benallegue, A., Tanguy, A., Escande, A., Morisawa, M., & Kanehiro, F. (2021). On compliance and safety with torque-control for robots with high reduction gears and no joint-torque feedback. In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Prague, Czech Republic, 6262–6269. https://doi.org/10.1109/IROS51168.2021.9636081

  20. Huang, Q., Dong, C. C., Yu, Z. G., Chen, X. C., Li, Q. Q., Chen, H. Z., & Liu, H. X. (2022). Resistant compliance control for biped robot inspired by humanlike behavior. IEEE/ASME Transactions on Mechatronics, 27(5), 3463–3473. https://doi.org/10.1109/TMECH.2021.3139332

    Article  Google Scholar 

  21. Tsagarakis, N. G., Morfey, S., Cerda, G. M., Li, Z. B., & Caldwell, D. G. (2013). Compliant humanoid coman: Optimal joint stiffness tuning for modal frequency control. In 2013 IEEE International Conference on Robotics and Automation, Karlsruhe, Germany, 673–678. https://doi.org/10.1109/ICRA.2013.6630645

  22. Jin, M. L., Lee, J., & Tsagarakis, N. G. (2017). Model-free robust adaptive control of humanoid robots with flexible joints. IEEE Transactions on Industrial Electronics, 64(2), 1706–1715. https://doi.org/10.1109/TIE.2016.2588461

    Article  Google Scholar 

  23. Spyrakos-Papastavridis, E., Caldwell, D. G., & Tsagarakis, N. G. (2016). Balance and impedance optimization control for compliant humanoid stepping. In 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, Korea (South), 1349–1355. https://doi.org/10.1109/IROS.2016.7759222

  24. Hirayama, K., Hirosawa, N., & Hyon, S. H. (2018, November). Passivity-based compliant walking on torque-controlled hydraulic biped robot. In: 2018 IEEE-RAS 18th International Conference on Humanoid Robots (Humanoids), Beijing, China, 1–6. https://doi.org/10.1109/HUMANOIDS.2018.8624964

  25. Makrini, I. E., Rodriguez-Guerrero, C., Lefeber, D., & Vanderborght, B. (2017). The variable boundary layer sliding mode control: A safe and performant control for compliant joint manipulators. IEEE Robotics and Automation Letters, 2(1), 187–192. https://doi.org/10.1109/LRA.2016.2587059

    Article  Google Scholar 

  26. Kim, M., Kim, J. H., Kim, S., Sim, J., & Park, J. (2018). Disturbance observer based linear feedback controller for compliant motion of humanoid robot. In: 2018 IEEE International Conference on Robotics and Automation (ICRA), Brisbane, Australia, 403–410. https://doi.org/10.1109/ICRA.2018.8460618

  27. Kim, M., Lim, D., & Park, J. (2019). Online walking pattern generation for humanoid robot with compliant motion control. In: 2019 International Conference on Robotics and Automation (ICRA), Montreal, Canada, 1417–1422. https://doi.org/10.1109/ICRA.2019.8794174

  28. Abi-Farraj, F., Henze, B., Ott, C., Giordano, P. R., & Roa, M. A. (2019). Torque-based balancing for a humanoid robot performing high-force interaction tasks. IEEE Robotics and Automation Letters, 4(2), 2023–2030. https://doi.org/10.1109/LRA.2019.2898041

    Article  Google Scholar 

  29. Yu, W., & Perrusquía, A. (2020). Simplified stable admittance control using end-effector orientations. International Journal of Social Robotics, 12(5), 1061–1073. https://doi.org/10.1007/s12369-019-00579-y

    Article  Google Scholar 

  30. Caron, S., Kheddar, A., & Tempier, O. (2019). Stair climbing stabilization of the HRP-4 humanoid robot using whole-body admittance control. In 2019 International Conference on Robotics and Automation (ICRA), Montreal, Canada, 277–283. https://doi.org/10.1109/ICRA.2019.8794348

  31. Li, Z. J., Huang, B., Ye, Z. F., Deng, M. D., & Yang, C. G. (2018). Physical human-robot interaction of a robotic exoskeleton by admittance control. IEEE Transactions on Industrial Electronics, 65(12), 9614–9624. https://doi.org/10.1109/TIE.2018.2821649

    Article  Google Scholar 

  32. Khan, M. S., & Mandava, R. K. (2023). A review on gait generation of the biped robot on various terrains. Robotica, 41(6), 1888–1930. https://doi.org/10.1017/S0263574723000097

    Article  Google Scholar 

  33. Taherkhorsandi, M., Mahmoodabadi, M. J., Talebipour, M., & Castillo-Villar, K. K. (2015). Pareto design of an adaptive robust hybrid of PID and sliding control for a biped robot via genetic algorithm optimization. Nonlinear dynamics, 79, 251–263. https://doi.org/10.1007/s11071-014-1661-1

    Article  Google Scholar 

  34. Shamna, P., Priya, N., & Ahamed, K. S. (2017, April). Walking stability control of biped robot based on three mass with angular momentum model using predictive PID control. In 2017 International conference of Electronics, Communication and Aerospace Technology (ICECA), Coimbatore, India, 584–588. https://doi.org/10.1109/ICECA.2017.8212732

  35. Mandava, R. K., & Vundavilli, P. R. (2019). An optimal PID controller for a biped robot walking on flat terrain using MCIWO algorithms. Evolutionary Intelligence, 12, 33–48. https://doi.org/10.1007/s12065-018-0184-y

    Article  Google Scholar 

  36. Juang, J. G. (2000). Fuzzy neural network approaches for robotic gait synthesis. IEEE Transactions on Systems, Man, and Cybernetics, Part B Cybernetics, 30(4), 594–601. https://doi.org/10.1109/3477.865178

    Article  CAS  Google Scholar 

  37. Li, T. H. S., Su, Y. T., Lai, S. W., & Hu, J. J. (2010). Walking motion generation, synthesis, and control for biped robot by using PGRL, LPI, and fuzzy logic. IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics), 41(3), 736–748. https://doi.org/10.1109/TSMCB.2010.2089978

    Article  Google Scholar 

  38. Wang, Y., Xue, X., & Chen, B. (2018). Matsuoka’s CPG with desired rhythmic signals for adaptive walking of humanoid robots. IEEE Transactions on Cybernetics, 50(2), 613–626. https://doi.org/10.1109/TCYB.2018.2870145

    Article  PubMed  Google Scholar 

  39. Yao, C., Liu, C., Xia, L., Liu, M., & Chen, Q. (2022). Humanoid adaptive locomotion control through a bioinspired CPG-based controller. Robotica, 40(3), 762–779. https://doi.org/10.1017/S0263574721000795

    Article  Google Scholar 

  40. Xie, Z. M., Clary, P., Dao, J., Morais, P., Hurst, J., & Panne, M. (2020, May). Learning locomotion skills for cassie: Iterative design and sim-to-real. In: Conference on Robot Learning (CoRL), Osaka, Japan, 317–329.

  41. García, J., & Shafie, D. (2020). Teaching a humanoid robot to walk faster through Safe Reinforcement Learning. Engineering Applications of Artificial Intelligence, 88, 103360. https://doi.org/10.1016/j.engappai.2019.103360

    Article  Google Scholar 

  42. Siekmann, J., Godse, Y., Fern, A., & Hurst, J. (2021, May). Sim-to-real learning of all common bipedal gaits via periodic reward composition. In 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi’an, China, 7309–7315. https://doi.org/10.1109/ICRA48506.2021.9561814

  43. Wieber, P. B. (2006, December). Trajectory free linear model predictive control for stable walking in the presence of strong perturbations. In: 2006 6th IEEE-RAS International Conference on Humanoid Robots, Genova, Italy, 137–142. https://doi.org/10.1109/ICHR.2006.321375

  44. Dimitrov, D., Wieber, P. B., Ferreau, H. J., & Diehl, M. (2008, May). On the implementation of model predictive control for on-line walking pattern generation. In: 2008 IEEE International Conference on Robotics and Automation, Pasadena, USA, 2685–2690. https://doi.org/10.1109/ROBOT.2008.4543617

  45. Diedam, H., Dimitrov, D., Wieber, P. B., Mombaur, K., & Diehl, M. (2008, September). Online walking gait generation with adaptive foot positioning through linear model predictive control. In: 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, Nice, France, 1121–1126. https://doi.org/10.1109/IROS.2008.4651055

  46. Scianca, N., De Simone, D., Lanari, L., & Oriolo, G. (2020). MPC for humanoid gait generation: Stability and feasibility. IEEE Transactions on Robotics, 36(4), 1171–1188. https://doi.org/10.1109/TRO.2019.2958483

    Article  Google Scholar 

  47. Kamioka, T., Kaneko, H., Takenaka, T., & Yoshiike, T. (2018, May). Simultaneous optimization of ZMP and footsteps based on the analytical solution of divergent component of motion. In: 2018 IEEE International Conference on Robotics and Automation (ICRA), Brisbane, Australia, 1763–1770. https://doi.org/10.1109/ICRA.2018.8460572

  48. Liu, C. J., Zhang, T., Liu, M., & Chen, Q. J. (2020). Active balance control of humanoid locomotion based on foot position compensation. Journal of Bionic Engineering, 17(1), 134–147. https://doi.org/10.1007/s42235-020-0011-x

    Article  Google Scholar 

  49. Yang, S. P., Chen, H., Fu, Z., & Zhang, W. (2021, September). Force-feedback based whole-body stabilizer for position-controlled humanoid robots. In: 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Prague, Czech Republic, 7432–7439. https://doi.org/10.1109/IROS51168.2021.9636634

  50. Caron, S. (2020, May). Biped stabilization by linear feedback of the variable-height inverted pendulum model. In: 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, France, 9782–9788. https://doi.org/10.1109/ICRA40945.2020.9196715

  51. Pan, Y. N., Du, P. H., Xue, H., & Lam, H. K. (2020). Singularity-free fixed-time fuzzy control for robotic systems with user-defined performance. IEEE Transactions on Fuzzy Systems, 29(8), 2388–2398. https://doi.org/10.1109/TFUZZ.2020.2999746

    Article  Google Scholar 

  52. Hengst, B. (2014). Runswift walk2014 report robocup standard platform league. Technical report. The University of New South Wales. https://cgi.cse.unsw.edu.au/~robocup/2014ChampionTeamPaperReports/20140930-Bernhard.Hengst-Walk2014Report.pdf

  53. Diehl, M., Ferreau, H. J., & Haverbeke, N. (2009). Efficient numerical methods for nonlinear MPC and moving horizon estimation. Nonlinear model predictive control: towards new challenging applications. https://doi.org/10.1007/978-3-642-01094-1_32

    Article  Google Scholar 

  54. Camacho, E. F., & Alba, C. B. (2013). Model predictive control. Springer science & business media.

Download references

Funding

This paper is supported by the National Natural Science Foundation of China under Grants 62173248, 62073245.

Author information

Authors and Affiliations

  1. Robot and Artificial Intelligence Lab (RAIL), College of Electronic and Information Engineering, Tongji University, Shanghai, 201804, China

    Zihan Xu, Qin Fang & Chengju Liu

  2. Applied Technology College, Soochow University, Suzhou, 215000, China

    Yong Ren

Authors
  1. Zihan Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qin Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chengju Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The authors confirm contributions to the paper as follows: study conception and design: Zihan Xu, Chengju Liu; constructive discussion: Zihan Xu, Yong Ren; experiments and data analysis: Zihan Xu, Qin Fang; draft manuscript preparation: Zihan Xu, Qin Fang; All authors reviewed the results and approved the final version of the manuscript.

Corresponding author

Correspondence to Chengju Liu.

Ethics declarations

Conflict of Interest

The authors have no relevant financial or non-financial interests to disclose.

Ethical approval

This study does not involve humans and animals. The experiments are conducted on a humanoid robot.

Consent to Participate

No participate in this study.

Consent to Publish

No participate in this study.

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

Xu, Z., Fang, Q., Ren, Y. et al. Capturability-based Fuzzy Footstep Planner for a Biped Robot with Centroidal Compliance. J Bionic Eng 21, 84–100 (2024). https://doi.org/10.1007/s42235-023-00434-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42235-023-00434-x

Keywords

Search

Navigation