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Design and Dynamic Analysis of a Compliant Leg Configuration towards the Biped Robot’s Spring-Like Walking

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Abstract

The spring-loaded inverted pendulum (SLIP) model has been proven successfully applied to implement spring-like walking for biped robots. This work presents a compliant leg configuration that can meet the requirements of the SLIP model. The leg is characterized by the fact that most of the mass is concentrated in the hip, and the leg is spring-like and light in weight. Numerical models were introduced to analyze the stiffness of the leg, and its dynamic characteristics with the mass of the leg being taken into account. Using the proposed model, the analysis on the stiffness showed that the leg could be taken as a variable stiffness spring with respect to the length of the leg, the longer the leg, the greater the stiffness. In addition to this, it suggested that the mass of the leg should be maintained below one-tenth of the mass concentrated in the hip to perform spring-like walking. Experiments regarding the stiffness and dynamic characteristics showed a good agreement with the simulation results, thus verifying the presented leg configuration and the numerical models. Afterwards, experiments were conducted on vertical jumps of the leg, demonstrating the feasibility of the leg to perform the biped’s spring-like walking, regardless of being at a certain speed, or at varying speeds.

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References

  1. Raibert, M.: Legged Robots that Balance. MIT press Cambridge, MA (1986)

    Book  Google Scholar 

  2. Chevallereau, C., Westervelt, E.R., Grizzle, J.W.: Asymptotically stable running for a five-link, four-actuator, planar bipedal robot. Int. J. Rob. Res. 24(6), 431–464 (2005)

    Article  Google Scholar 

  3. Kajita S., Kanehiro F., Kaneko K., Yokoi K., Hirukawa H.: The 3D linear inverted pendulum mode: A simple modeling for a biped walking pattern generation. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium, Maui, pp. 239–246(2001)

  4. Shigemi, S., Goswami, A., & Vadakkepat, P.: ASIMO and humanoid robot research at Honda, Humanoid robotics: A reference. Springer, pp. 55–90(2019)

  5. Tsagarakis, N.G., Caldwell, D.G., Negrello, F., et al.: Walk-man: A high-performance humanoid platform for realistic environments. J. Field. Robot. 34(7), 1225–1259 (2017)

    Article  Google Scholar 

  6. Zhang R., Zhao M., Wang C.L.:Standing push recovery based on LIPM dynamics control for biped humanoid robot In: 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO), Kuala Lumpur, pp. 1732–1737(2018)

  7. Yuan, H., Song, S., Du, R., et al.: A Capturability-based Control Framework for the Underactuated Bipedal Walking. In 2021 IEEE International Conference on Robotics and Automation (ICRA), pp. 6804–6810(2021)

  8. Hereid, A., Hubicki, C.M., Cousineau, E.A., Ames, A.D.: Dynamic humanoid locomotion: A scalable formulation for HZD gait optimization. IEEE T Robot. 34(2), 370–387 (2018)

    Article  Google Scholar 

  9. Kaneko, K., Kaminaga, H., Sakaguchi, T., et al.: Humanoid robot HRP-5P: An electrically actuated humanoid robot with high-power and wide-range joints. IEEE Robot. Autom. Lett. 4(2), 1431–1438 (2019)

    Article  Google Scholar 

  10. Kuindersma S., Permenter F., Tedrake R.: An efficiently solvable quadratic program for stabilizing dynamic locomotion. In: 2014 IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, pp. 2589–2594(2014)

  11. Lohmeier S.: Design and realization of a humanoid robot for fast and autonomous bipedal locomotion. Ph.D. thesis, Technische Universität München, 2010

  12. Park, I.-W., Kim, J.-Y., Lee, J., Oh, J.-H.: Mechanical design of the humanoid robot platform. HUBO. Adv. Robot. 21(11), 1305–1322 (2007)

    Article  Google Scholar 

  13. Wang Z., He B., Shen R., Meng W.: Contact impact inhibition strategy for biped robot walking based on central pattern generator. In: 2015 IEEE International Conference on Robotics and Biomimetics (ROBIO), Zhuhai, pp. 733–738(2015)

  14. Seleem I.A., Assal S. F. M., Mohamed A. M.: Cyclic gait planning and control of underactuated five-link biped robot during single support and impact phases for normal walking. In: 2018 IEEE International Conference on Industrial Technology (ICIT), Lyon, pp. 123–128(2018)

  15. Hubicki, C., Abate, A., Clary, P., et al.: Walking and running with passive compliance: Lessons from engineering: A live demonstration of the ATRIAS biped. IEEE Robot. Autom. Lett. 25(3), 23–39 (2018)

    Article  Google Scholar 

  16. Seyfarth, A., Geyer, H., Günther, M., et al.: A movement criterion for running. J. Biomech. 35(5), 649–655 (2002)

    Article  Google Scholar 

  17. Daley, M.A.: Understanding the agility of running birds: sensorimotor and mechanical factors in avian bipedal locomotion. Integr. Comp. Biol. 58(5), 884–893 (2018)

    Google Scholar 

  18. Geyer, H., Seyfarth, A., Blickhan, R.: Compliant leg behaviour explains basic dynamics of walking and running. Proc. R. Soc. B. 273, 2861–2867(2006) (1603)

    Article  Google Scholar 

  19. Geyer, H., Seyfarth, A., Blickhan, R.: Spring-mass running: simple approximate solution and application to gait stability. J. Theor. Biol. 232(3), 315–328 (2005)

    Article  MathSciNet  Google Scholar 

  20. Liu Y., Wensing P. M., Schmiedeler J. P., et al.: Terrain-blind humanoid walking based on a 3-D actuated dual-SLIP model. IEEE Robot. Autom. Lett. 1(2), 1073–1080(2016)

  21. Fan Y., Li X., Feng H., et al.: Compliance Control of the Hydraulic-Driven Single Legged Robot. In: 2019 IEEE International Conference on Robotics and Biomimetics (ROBIO), Dali, pp. 2117–2122(2019)

  22. Lee, H.J., Kim, J.Y.: Balance control strategy of biped walking robot SUBO-1 based on force-position hybrid control. Int. J. Precis. Eng. 22(1), 161–175 (2021)

    Article  Google Scholar 

  23. Reher J., Cousineau E.A., Hereid A., et al.: Realizing dynamic and efficient bipedal locomotion on the humanoid robot DURUS. In: 2016 IEEE International Conference on Robotics and Automation (ICRA), Stockholm, pp. 1794–1801(2016)

  24. Hubicki, C., Grimes, J., Jones, M., et al.: Atrias: Design and validation of a tether-free 3d-capable spring-mass bipedal robot. Int. J. Rob. Res. 35(12), 1497–1521 (2016)

    Article  Google Scholar 

  25. Joe, H.M., Oh, J.H.: A robust balance-control framework for the terrain-blind bipedal walking of a humanoid robot on unknown and uneven terrain. Sensors. 19(19), 4194 (2019)

    Article  Google Scholar 

  26. Bledt, G., Powell, M. J., Katz, B., Di Carlo, J., Wensing, P. M., & Kim, S.: MIT Cheetah 3: Design and control of a robust, dynamic quadruped robot. In 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2245–2252 (2018)

  27. Gao, H., Liu, Y., Ding, L., et al.: Low impact force and energy consumption motion planning for hexapod robot with passive compliant ankles. J. Intell. Robot. Syst. 94(2), 349–370 (2019)

    Article  Google Scholar 

  28. Manara, S., GianMaria, G., Garabini, M., Caporale, D., Gabiccini, M., Bicchi, A.: Analysis of series elasticity in locomotion of a planar bipedal robot. Int. J. Mech. Control. 20(11), 1–9 (2019)

    Google Scholar 

  29. Maiorino, A., Muscolo, G.G.: Biped robots with compliant joints for walking and running performance growing. Front. Mech. Eng. 6(11), 1–11 (2020)

    Google Scholar 

  30. Sarkar, A., Dutta, A.: Optimal trajectory generation and design of an 8-dof compliant biped robot for walk on inclined ground. J. Intell. Robot. Syst. 94(3), 583–602 (2019)

    Article  Google Scholar 

  31. Lee, C., Oh, S.: Development, analysis, and control of series elastic actuator-driven robot leg. Front. Neurorobot. 13(17), 1–31 (2019)

    Google Scholar 

  32. Luo, J., Wang, S., Zhao, Y., Fu, Y.: Variable stiffness control of series elastic actuated biped locomotion. Intell. Serv. Robot. 11(3), 225–235 (2018)

    Article  Google Scholar 

  33. Smit-Anseeuw, N., Gleason, R., Vasudevan, R., Remy, C.D.: The energetic benefit of robotic gait selection—a case study on the robot RAMone. IEEE Robot. Autom. Lett. 2(2), 1124–1131 (2017)

    Article  Google Scholar 

  34. Ma, W. L., Kolathaya, S., Ambrose, E. R., et al.: Bipedal robotic running with DURUS-2D: Bridging the gap between theory and experiment. In Proceedings of the 20th international conference on hybrid systems: computation and control, pp. 265–274(2017)

  35. Grimes, J. A., and Hurst J. W.: The design of ATRIAS 1.0 a unique monopod, hopping robot. Adaptive Mobile Robotics. 548–554(2012)

  36. Abate, A.M.: Mechanical design for robot locomotion. Ph.D. thesis, School of Mechanical, Industrial, and Manufacturing Engineering. Oregon State University, USA (2018)

    Google Scholar 

  37. “Cassie - Next Generation Robot”, https://www.youtube.com/watch?v=Is4JZqhAy-M

  38. Gong Y., Grizzle J.: One-step ahead prediction of angular momentum about the contact point for control of bipedal locomotion: Validation in a lip-inspired controller. In: 2021 IEEE International Conference on Robotics and Automation (ICRA), 2021

  39. Green K., Hatton R.L, Hurst J. W.: Planning for the unexpected: Explicitly optimizing motions for ground uncertainty in running. In: 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, pp. 1445–1451(2020)

  40. Apgar, T., Clary, P., Green, K., Fern, A., & Hurst, J. W.: Fast Online Trajectory Optimization for the Bipedal Robot Cassie. In Robotics: Science and Systems, Pittsburgh, 101(14) (2018)

  41. Xiong X., Ames A. D.: Bipedal hopping: Reduced-order model embedding via optimization-based control. In: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, pp. 3821–3828(2018)

  42. Xiong X., Ames A.D.: Coupling reduced order models via feedback control for 3d underactuated bipedal robotic walking. In: 2018 IEEE-RAS 18th International Conference on Humanoid Robots (Humanoids), Beijing, pp. 67–74(2018)

  43. Karssen, J.G.D., Haberland, M., Wisse, M., et al.: The effects of swing-leg retraction on running performance: analysis, simulation, and experiment. Robotica. 33(10), 2137–2155 (2015)

    Article  Google Scholar 

  44. Karssen J. G. D., Haberland M., Wisse M., et al.: The optimal swing-leg retraction rate for running. In: 2011 IEEE International Conference on Robotics and Automation, Shanghai, pp. 4000–4006(2011)

Download references

Funding

This work was supported by NSFC Project (No. 51905495, No.51821093, No.51890885), the China Postdoctoral Project (No. 2020 M671821), NSF Project of Zhejiang Province (No. LQ20E050009, No. LQ21F030003), and the National Key Research and Development Project (2018YFB2001203).

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Author notes

  1. Guifu Luo and Ruilong Du contributed equally to this work.

Authors and Affiliations

  1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 310027, China

    Guifu Luo & Hua Zhou

  2. Intelligent Robot Research Center, Zhejiang Lab, Hangzhou, China

    Ruilong Du, Shiqiang Zhu, Sumian Song & Haihui Yuan

  3. Department of Automation, Tsinghua University, Beijing, China

    Ruilong Du, Haihui Yuan & Mingguo Zhao

  4. Department of Electrical Engineering, Dalhousie University, Halifax, Nova Scotia, Canada

    Jason Gu

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  1. Guifu Luo
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Contributions

Guifu Luo and Ruilong Du designed the study, performed the research, analyzed data, and wrote the paper. They contributed equally to this work.

Shiqiang Zhu contributed to the design of the test rig, helped performed the analysis with constructive discussions.

Sumian Song and Haihui Yuan wrote and debugged the code, helped conduct the experiment and analyze data.

Hua Zhou contributed to the manuscript preparation, helped perform the analysis with constructive discussions.

Mingguo Zhao and Jason Gu contributed to the improvement of the manuscript quality, helped perform the analysis with constructive discussions.

Corresponding authors

Correspondence to Ruilong Du, Sumian Song, Haihui Yuan or Hua Zhou.

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Research supported by NSFC Project (No. 51905495, No.51821093, No.51890885), the China Postdoctoral Project (No. 2020M671821), NSF Project of Zhejiang Province (No. LQ20E050009, No. LQ21F030003), and the National Key Research and Development Project (2018YFB2001203).

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Luo, G., Du, R., Zhu, S. et al. Design and Dynamic Analysis of a Compliant Leg Configuration towards the Biped Robot’s Spring-Like Walking. J Intell Robot Syst 104, 64 (2022). https://doi.org/10.1007/s10846-022-01614-3

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