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Journal of Intelligent & Robotic Systems

, Volume 82, Issue 1, pp 51–68 | Cite as

Generation and Analyses of the Reinforced Wave Gait for a Mammal-Like Quadruped Robot

  • Dongping Lu
  • Erbao Dong
  • Chunshan Liu
  • Min Xu
  • Jie Yang
Article

Abstract

The statically stable gait control of a mammal-like quadruped robot that provides an adequate or stable manner of traversing over irregular terrain was addressed. The reinforced wave gait which integrates new parameters of the lateral offset and displacements of the center of gravity (COG) based on the profiles of standard wave gait was investigated. The continuous and discontinuous motion trajectory of a robot’s COG in the periodic reinforced wave gait could be realized. The longitudinal and lateral stability margins of a reinforced wave gait were formulated for the gait generation and control of a quadruped robot. Moreover, the effects of the lateral offset on the stability, velocity and the energy efficiency were studied in details. The reinforced wave gait with lateral sway motion adequately improved the stability, and two particular gait patterns that involve the lateral sway motion for a maximal velocity and maximum achievable stability were described. With consideration of a quadruped robot with asymmetric carrying loads on its body, a scheme that relates to the gait parameters of the displacement of a robot’s COG to avoid losing stability was proposed. The simulation and experimental results about the effects of lateral offset added in the reinforced wave gait on the minimum power consumption during a quadruped robot walking on a flat terrain indicated that the reinforced wave gait with a larger lateral offset would generate a better wave gait with a higher velocity and energy efficiency.

Keywords

Quadruped robot Reinforced wave gait Stability margin Energy efficiency Gait parameters optimizations 

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References

  1. 1.
    Raibert, M., Blankespoor, K., Nelson, G., Playter, R.: Bigdog, the rough-terrain quadruped robot. In: Proceedings of the 17th World Congress, pp 10823–10825 (2008)Google Scholar
  2. 2.
    Hutter, M., Gehring, C., Bloesch, M., Hoepflinger, M., Remy, C.D., Siegwart, R.: StarlETH: A compliant quadrupedal robot for fast, efficient, and versatile locomotion. In: 15th International Conference on Climbing and Walking Robot-CLAWAR 2012 (2012)Google Scholar
  3. 3.
    Bazeille, S., Barasuol, V., Focchi, M., Havoutis, I., Frigerio, M., Buchli, J., Caldwell, D.G., Semini, C.: Quadruped robot trotting over irregular terrain assisted by stereo-vision. Intel. Serv. Robotics 7(2), 67–77 (2014)CrossRefGoogle Scholar
  4. 4.
    Ijspeert, A.J.: Central pattern generators for locomotion control in animals and robots: a review. Neural Netw. 21(4), 642–653 (2008)CrossRefGoogle Scholar
  5. 5.
    Roy, S.S., Pratihar, D.K.: Effects of turning gait parameters on energy consumption and stability of a six-legged walking robot. Robot. Auton. Syst. 60(1), 72–82 (2012)CrossRefGoogle Scholar
  6. 6.
    Kar, D., Kurien Issac, K., Jayarajan, K.: Minimum energy force distribution for a walking robot. J. Robot. Syst. 18(2), 47–54 (2001)CrossRefzbMATHGoogle Scholar
  7. 7.
    McGhee, R.B., Frank, A.A.: On the stability properties of quadruped creeping gaits. Math. Biosci. 3, 331–351 (1968)CrossRefzbMATHGoogle Scholar
  8. 8.
    Song, S.-M., Waldron, K.J.: An analytical approach for gait study and its applications on wave gaits. Int. J. Robot. Res. 6(2), 60–71 (1987)CrossRefGoogle Scholar
  9. 9.
    Song, S.-M., Choi, B.S.: The optimally stable ranges of 2 < e1 > n < /e1 > -legged wave gaits. IEEE Trans. Syst. Man Cybern. 20(4), 888–902 (1990)CrossRefzbMATHGoogle Scholar
  10. 10.
    Jeong, K.-M., Oh, J.-H.: An aperiodic z type spinning gait planning method for a quadruped walking robot. Auton. Robot. 2(2), 163–173 (1995)CrossRefGoogle Scholar
  11. 11.
    Zhang, C.-D., Song, S.-M.: Turning gaits of a quadrupedal walking machine. Adv. Robot. 7(2), 121–157 (1992)CrossRefGoogle Scholar
  12. 12.
    Hirose, S., Kikuchi, H., Umetani, Y.: The standard circular gait of a quadruped walking vehicle. Adv. Robot. 1(2), 143–164 (1986)CrossRefGoogle Scholar
  13. 13.
    Jiménez, M.A, de Santos, P.G., Tabera, J.: An omnidirectional control algorithm for walking machines based on a wave-crab gait. In: Advances in Intelligent Autonomous Systems, pp 355–380. Springer (1999)Google Scholar
  14. 14.
    Song, S.-M., Soo Choi, B.: A study on continuous follow-the-leader (FTL) gaits: an effective walking algorithm over rough terrain. Math. Biosci. 97(2), 199–233 (1989)CrossRefzbMATHGoogle Scholar
  15. 15.
    Hirose, S.: A study of design and control of a quadruped walking vehicle. Int. J. Robot. Res. 3(2), 113–133 (1984)CrossRefGoogle Scholar
  16. 16.
    Bai, S., Low, K.H., Zielinska, T.: Quadruped free gait generation based on the primary/secondary gait. Robotica 17(04), 405–412 (1999)CrossRefGoogle Scholar
  17. 17.
    Estremera, J: de Santos, P.G.: Generating continuous free crab gaits for quadruped robots on irregular terrain. IEEE Trans. Robot. 21(6), 1067–1076 (2005)CrossRefGoogle Scholar
  18. 18.
    Erden, M.S., Leblebicioğlu, K.: Analysis of wave gaits for energy efficiency. Auton. Robot. 23 (3), 213–230 (2007)CrossRefGoogle Scholar
  19. 19.
    Inagaki, S., Yuasa, H., Suzuki, T., Arai, T.: Wave CPG model for autonomous decentralized multi-legged robot: Gait generation and walking speed control. Robot. Auton. Syst. 54(2), 118–126 (2006)CrossRefGoogle Scholar
  20. 20.
    Hung, M.H., Cheng, F.T., Lee, H.L., Orin, D.E.: Increasing the stability margin of multilegged vehicles through body sway. J. Chin. Inst. Eng. 28(1), 39–54 (2005)CrossRefGoogle Scholar
  21. 21.
    Tsukagoshi, H., Hirose, S., Yoneda, K.: Maneuvering operations of a quadruped walking robot on a slope. Adv. Robot. 11(4), 359–375 (1996)CrossRefGoogle Scholar
  22. 22.
    Hirose, S., Kunieda, O.: Generalized standard foot trajectory for a quadruped walking vehicle. Int. J. Robot. Res. 10(1), 3–12 (1991)CrossRefGoogle Scholar
  23. 23.
    Santos, P.G.D., Jimenez, M.A.: Generation of discontinuous gaits for quadruped walking vehicles. J. Robot. Syst. 12(9), 599–611 (1995)CrossRefzbMATHGoogle Scholar
  24. 24.
    Lu, D., Dong, E., Liu, C., Xu, M., Yang, J.: Design and development of a leg-wheel hybrid robot “HyTRo-I”. In: 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp 6031–6036. IEEE (2013)Google Scholar
  25. 25.
    Lu, D., Dong, E., Liu, C., Wang, Z., Zhang, X., Xu, M., Yang, J.: Mechanical system and stable gait transformation of a leg-wheel hybrid transformable robot. In: 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), pp 530–535. IEEE (2013)Google Scholar
  26. 26.
    Alexander, R.M.: Principles of animal locomotion. Princeton University Press (2003)Google Scholar
  27. 27.
    Dickinson, M.H., Farley, C.T., Full, R.J., Koehl, M., Kram, R., Lehman, S.: How animals move: an integrative view. Science 288(5463), 100–106 (2000)CrossRefGoogle Scholar
  28. 28.
    Bottaro, A., Casadio, M., Morasso, P.G., Sanguineti, V.: Body sway during quiet standing: is it the residual chattering of an intermittent stabilization process Hum. Mov. Sci. 24(4), 588–615 (2005)CrossRefGoogle Scholar
  29. 29.
    Donelan, J.M., Shipman, D.W., Kram, R., Kuo, A.D.: Mechanical and metabolic requirements for active lateral stabilization in human walking. J. Biomech. 37(6), 827–835 (2004)CrossRefGoogle Scholar
  30. 30.
    Zhang, C.-D., Song, S.-M.: Stability analysis of wave-crab gaits of a quadruped. J. Robot. Syst. 7(2), 243–276 (1990)CrossRefzbMATHGoogle Scholar
  31. 31.
    Zhang, C.-D., Song, S.-M.: A study of the stability of generalized wave gaits. Math. Biosci. 115 (1), 1–32 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Zhang, C.D., Song, S.M.: Stability analysis of wavecrab gaits of a quadruped. J. Robot. Syst. 7 (2), 243–276 (1990)CrossRefzbMATHGoogle Scholar
  33. 33.
    de Santos, P.G., Garcia, E., Ponticelli, R., Armada, M.: Minimizing energy consumption in hexapod robots. Adv. Robot. 23(6), 681–704 (2009)CrossRefGoogle Scholar
  34. 34.
    Garcia, E., Galvez, J.A., De Santos, P.G.: On finding the relevant dynamics for model-based controlling walking robots. J. Intell. Robot. Syst. 37(4), 375–398 (2003)CrossRefGoogle Scholar
  35. 35.
    Roy, S.S., Pratihar, D.K.: Kinematics, dynamics and power consumption analyses for turning motion of a six-legged robot. J. Intell. Robot. Syst. 74(3-4), 663–688 (2014)CrossRefGoogle Scholar
  36. 36.
    Jin, B., Chen, C., Li, W.: Power Consumption Optimization for a Hexapod Walking Robot. J. Intell. Robot. Syst. 71(2), 195–209 (2013)CrossRefGoogle Scholar
  37. 37.
    Roy, S.S., Singh, A.K., Pratihar, D.K.: Estimation of optimal feet forces and joint torques for on-line control of six-legged robot. Robot. Comput. Integr. Manuf. 27(5), 910–917 (2011)CrossRefGoogle Scholar
  38. 38.
    Roy, S.S., Pratihar, D.K.: Dynamic modeling, stability and energy consumption analysis of a realistic six-legged walking robot. Robot. Comput. Integr. Manuf. 29(2), 400–416 (2013)CrossRefGoogle Scholar
  39. 39.
    Lin, B.S., Song, S.M.: Dynamic modeling, stability, and energy efficiency of a quadrupedal walking machine. J. Robot. Syst. 18(11), 657–670 (2001)CrossRefzbMATHGoogle Scholar
  40. 40.
    Gregorio, P., Ahmadi, M., Buehler, M.: Design, control, and energetics of an electrically actuated legged robot. IEEE Trans. Syst. Man Cybern. B Cybern. 27(4), 626–634 (1997)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Dongping Lu
    • 1
  • Erbao Dong
    • 1
  • Chunshan Liu
    • 1
  • Min Xu
    • 1
  • Jie Yang
    • 1
  1. 1.Department of Precision Machinery and Precision InstrumentationUniversity of Science and Technology of ChinaHefeiChina

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