Top > JRM > Spontaneous Rhythmic Behavior Generation in Robot Locomotion B ...

single-rb.php

JRM Vol.38 No.2 pp. 619-635
(2026)
doi: 10.20965/jrm.2026.p0619

Paper:

Views over last 60 days: 8

Spontaneous Rhythmic Behavior Generation in Robot Locomotion Based on Mechanical Stabilization

Kai Ito, Keita Sato, and Yusuke Ikemoto ORCID Icon

Department of Mechanical Engineering, Faculty of Science and Technology, Meijo University
1-501 Shiogamaguchi, Tempaku-ku, Nagoya, Aichi 486-8502, Japan

Received:
March 11, 2025
Accepted:
October 23, 2025
Published:
April 20, 2026
Creative Commons License
Keywords:
differential mechanism, leg-equipped robot, hardware experiment, nonlinear dynamical analysis, rhythmic motion
Abstract

Animals exhibit a variety of gait patterns that vary with locomotor speed and energy efficiency. Although a variety of gait patterns have been studied, the mechanism of gait generation has remained vague. In this study, we performed ground reaction force equalization for stable locomotion by developing a one-input, two-output leg-equipped robot with a differential gear. The developed robot can tolerate angular velocity differences and equalize the torque transmitted to the legs. To investigate the possibility of rhythm generation based on ground reaction force equalization, hardware experiments and mathematical analysis were conducted using a nonlinear system. The robot experiments and theoretical analysis show that the robot can spontaneously generate rhythm by equalizing the ground reaction force.

Our robot with differential mechanism

Our robot with differential mechanism

Full text
Cite this article as:
K. Ito, K. Sato, and Y. Ikemoto, “Spontaneous Rhythmic Behavior Generation in Robot Locomotion Based on Mechanical Stabilization,” J. Robot. Mechatron., Vol.38 No.2, pp. 619-635, 2026.
Data files:
References
  1. [1] R. M. Alexander, “The gaits of bipedal and quadrupedal animals,” Int. J. Robot. Res., Vol.3, No.2, pp. 49-59, 1984. https://doi.org/10.1177/027836498400300205
  2. [2] R. M. Alexander, “Bipedal animals, and their differences from humans,” J. Anat., Vol.204, No.5, pp. 321-330, 2004. https://doi.org/10.1111/j.0021-8782.2004.00289.x
  3. [3] P. Fihl and T. B. Moeslund, “Classification of gait types based on the duty-factor,” IEEE Conf. on Advanced Video and Signal Based Surveillance, 2007. https://doi.org/10.1109/AVSS.2007.4425330
  4. [4] A. E. Minetti, “The biomechanics of skipping gaits: A third locomotion paradigm?,” Proc. Biol. Sci., Vol.265, No.1402, pp. 1227-1235, 1998. https://doi.org/10.1098/rspb.1998.0424
  5. [5] D. M. Wilson, “Insect walking,” Annu. Rev. Entomol., Vol.11, pp. 103-122, 1966. https://doi.org/10.1146/annurev.en.11.010166.000535
  6. [6] K. Naniwa et al., “Novel Method for Analyzing Flexible Locomotion Patterns of Animals by Using Polar Histogram,” J. Robot. Mechatron., Vol.32, No.4, pp. 812-821, 2020. https://doi.org/10.20965/jrm.2020.p0812
  7. [7] G. Hayes and R. M. Alexander, “The hopping gaits of crows (Corvidae) and other bipeds,” J. Zool., Vol.200, No.2, pp. 205-213, 1983. https://doi.org/10.1111/j.1469-7998.1983.tb05784.x
  8. [8] D. F. Hoyt and C. R. Taylor, “Gait and the energetics of locomotion in horses,” Nature, Vol.292, No.5820, pp. 239-240, 1981. https://doi.org/10.1038/292239a0
  9. [9] T. J. Dawson and C. R. Taylor, “Energetic cost of locomotion in kangaroos,” Nature, Vol.246, No.5431, pp. 313-314, 1973. https://doi.org/10.1038/246313a0
  10. [10] Z. Wang et al., “Optimization design and performance analysis of a bionic knee joint based on the geared five-bar mechanism,” Bioengineering (Basel), Vol.10, No.5, Article No.582, 2023. https://doi.org/10.3390/bioengineering10050582
  11. [11] A. Sayyad, B. Seth, and P. Seshu, “Single-legged hopping robotics research—A review,” Robotica, Vol.25, No.5, pp. 587-613, 2007. https://doi.org/10.1017/S0263574707003487
  12. [12] G. Heppner et al., “LAUROPE – Six legged walking robot for planetary exploration participating in the SPACEBOT cup,” WS Adv. Space Technol. Robot. Autom., Vol.2, No.13, pp. 69-76, 2015.
  13. [13] T. Kinugasa and Y. Sugimoto, “Dynamically and Biologically Inspired Legged Locomotion: A Review,” J. Robot. Mechatron., Vol.29, No.3, pp. 456-470, 2017. https://doi.org/10.20965/jrm.2017.p0456
  14. [14] G. Taga, Y. Yamaguchi, and H. Shimizu, “Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment,” Biol. Cybern., Vol.65, pp. 147-159, 1991. https://doi.org/10.1007/BF00198086
  15. [15] E. Marder and D. Bucher, “Central pattern generators and the control of rhythmic movements,” Curr. Biol., Vol.11, No.23, pp. R986-R996, 2001. https://doi.org/10.1016/s0960-9822(01)00581-4
  16. [16] J. J. Collins and S. A. Richmond, “Hard-wired central pattern generators for quadrupedal locomotion,” Biol. Cybern., Vol.71, pp. 375-385, 1994. https://doi.org/10.1007/BF00198915
  17. [17] Y. Fukuoka, Y. Habu, and T. Fukui, “A simple rule for quadrupedal gait generation determined by leg loading feedback: A modeling study,” Sci. Rep., Vol.5, Article No.8169, 2015. https://doi.org/10.1038/srep08169
  18. [18] A. J. Ijspeert, “Central pattern generators for locomotion control in animals and robots: A review,” Neural Netw., Vol.21, No.4, pp. 642-653, 2008. https://doi.org/10.1016/j.neunet.2008.03.014
  19. [19] D. Owaki and A. Ishiguro, “A quadruped robot exhibiting spontaneous gait transitions from walking to trotting to galloping,” Sci. Rep., Vol.7, No.1, Article No.277, 2017. https://doi.org/10.1038/s41598-017-00348-9
  20. [20] T. Fukui, S. Matsukawa, Y. Habu, and Y. Fukuoka, “Gait transition from pacing by a quadrupedal simulated model and robot with phase modulation by vestibular feedback,” Robotics, Vol.11, No.1, Article No.3, 2022. https://doi.org/10.3390/robotics11010003
  21. [21] J. Humphreys et al., “Bio-inspired gait transitions for quadruped locomotion,” IEEE Robot. Autom. Lett., Vol.8, No.10, pp. 6131-6138, 2023. https://doi.org/10.1109/LRA.2023.3300249
  22. [22] C. P. Santos and V. Matos, “Gait transition and modulation in a quadruped robot: A brainstem-like modulation approach,” Robot. Auton. Syst., Vol.59, No.9, pp. 620-634, 2011. https://doi.org/10.1016/j.robot.2011.05.003
  23. [23] S. Grillner, “Locomotion in vertebrates: Central mechanisms and reflex interaction,” Physiol. Rev., Vol.55, No.2, pp. 247-304, 1975. https://doi.org/10.1152/physrev.1975.55.2.247
  24. [24] T. G. Brown, “The intrinsic factors in the act of progression in the mammal,” Proc. Biol. Sci., Vol.84, No.572, pp. 308-319, 1911. https://doi.org/10.1098/rspb.1911.0077
  25. [25] T. McGeer, “Passive dynamic walking,” Intern. J. Robot. Res., Vol.9, No.2, pp. 62-82, 1990. https://doi.org/10.1177/027836499000900206
  26. [26] T. McGeer, “Passive walking with knees,” IEEE Int. Conf. on Robotics and Automation, pp. 1640-1645, 1990. https://doi.org/10.1109/ROBOT.1990.126245
  27. [27] T. McGeer, “Principles of walking and running,” Adv. Comp. Environ. Physiol., pp. 113-139, 1992.
  28. [28] L. Li et al., “High-Frequency Vibration of Leg Masses for Improving Gait Stability of Compass Walking on Slippery Downhill,” J. Robot. Mechatron., Vol.31, No.4, pp. 621-628, 2019. https://doi.org/10.20965/jrm.2019.p0621
  29. [29] S. Collins et al., “Efficient bipedal robots based on passive-dynamic walkers,” Science, Vol.307, No.5712, pp. 1082-1085, 2005. https://doi.org/10.1126/science.1107799
  30. [30] M. W. Spong and F. Bullo, “Controlled symmetries and passive walking,” IEEE Trans. Autom. Control, Vol.50, No.7, pp. 1025-1031, 2005. https://doi.org/10.1109/TAC.2005.851449
  31. [31] O. Makarenkov, “Existence and stability of limit cycles in the model of a planar passive biped walking down a slope,” Proc. Math. Phys. Eng. Sci., Vol.476, No.2233, Article No.20190450, 2020. https://doi.org/10.1098/rspa.2019.0450
  32. [32] M. Garcia et al., “The simplest walking model: Stability, complexity, and scaling,” J. Biomech. Eng., Vol.120, No.2, pp. 281-288, 1998. https://doi.org/10.1115/1.2798313
  33. [33] S. Iqbal et al., “Bifurcations and chaos in passive dynamic walking: A review,” Robot. Auton. Syst., Vol.62, No.6, pp. 889-909, 2014. https://doi.org/10.1016/j.robot.2014.01.006
  34. [34] S. Aoi et al., “A stability-based mechanism for hysteresis in the walk–trot transition in quadruped locomotion,” J. R. Soc. Interface, Vol.10, No.81, Article No.20120908, 2013. https://doi.org/10.1098/rsif.2012.0908
  35. [35] S. H. Strogatz, “Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering,” pp. 44-79, CRC Press, 2000.
  36. [36] A. Goswami, B. Thuilot, and B. Espiau, “A study of the Passive Gait of a Compass-Like Biped Robot: Symmetry and Chaos,” Int. J. Robot. Res., Vol.17, No.12, pp. 1282-1301, 1998. https://doi.org/10.1177/027836499801701202
  37. [37] K. Osuka and K. Kirihara, “Motion analysis and experiment of passive walking robot QUARTET II,” J. of the Robotics Society of Japan, Vol.18, No.5, pp. 737-742, 2000 (in Japanese). https://doi.org/10.7210/jrsj.18.737
  38. [38] S. Aoi et al., “Advanced turning maneuver of a many-legged robot using pitchfork bifurcation,” IEEE Trans. Robot., Vol.38, No.5, pp. 3015-3026, 2022. https://doi.org/10.1109/TRO.2022.3158194
  39. [39] M. Okada and K. Iwano, “Human interface design for semi-autonomous control of leader-follower excavator based on variable admittance and stagnation/trajectory bifurcation of nonlinear dynamics,” Mech. Eng. J., Vol.8, No.6, Article No.21-00127, 2021. https://doi.org/10.1299/mej.21-00127
  40. [40] X. Chen et al., “Foot Shape-Dependent Resistive Force Model for Bipedal Walkers on Granular Terrains,” Int. Conf. on Robotics and Automation, pp. 13093-13099, 2024. https://doi.org/10.1109/ICRA57147.2024.10610190
  41. [41] N. Scianca et al., “MPC for Humanoid Gait Generation: Stability and Feasibility,” Trans. on Robotics, Vol.36, No.4, pp. 1171-1188, 2020. https://doi.org/10.1109/TRO.2019.2958483
  42. [42] C. Chevallereau et al., “Self-synchronization and Self-stabilization of 3D Bipedal Walking Gaits,” Robotics and Autonomous Systems, Vol.100, pp. 43-60, 2018. https://doi.org/10.1016/j.robot.2017.10.018
  43. [43] K. Isomura et al., “Full time two-leg drive bipedal robot: Analysis of gait pattern generations under constraints of reaction forces equality,” Int. Conf. on Advanced Mechatronics, pp. 86-87, 2021. https://doi.org/10.1299/jsmeicam.2021.7.GS6-4
  44. [44] C. Singh et al., “A Study on Vehicle Differential system,” Int. J. Sci. Res. Manag., Vol.2, No.11, pp. 1680-1683, 2014.
  45. [45] S. Shinde et al., “Review paper on design of types of mechanical differentials used in automobiles,” Int. Res. J. Modernization Eng. Technol. Sci., Vol.3, No.1, pp. 1023-1031, 2021.
  46. [46] D. R. Hartree, “The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part II. Some Results and Discussion,” Math. Proc. Camb. Phil. Soc., Vol.24, No.1, pp. 111-132, 1928. https://doi.org/10.1017/S0305004100011920
  47. [47] H. Li et al., “Elastic-viscoplastic self-consistent modeling for finite deformation of polycrystalline materials,” Mater. Sci. Eng. A, Vol.799, No.2, Article No.140325, 2021. https://doi.org/10.1016/j.msea.2020.140325
  48. [48] K. Masani, M. Kouzaki, and T. Fukunaga, “Variability of ground reaction forces during treadmill walking,” J. App. Physiol., Vol.92, No.5, pp. 1885-1890, 2002. https://doi.org/10.1152/japplphysiol.00969.2000
  49. [49] T. Kobayashi et al., “Ground reaction forces during double limb stances while walking in individuals with unilateral transfemoral amputation,” Front. Bioeng. Biotechnol., Vol.10, Article No.1041060, 2022. https://doi.org/10.3389/fbioe.2022.1041060
  50. [50] A. Karatsidis et al., “Estimation of Ground Reaction Forces and Moments during Gait Using Only Inertial Motion Capture,” Sensors, Vol.17, No.1, Article No.75, 2017. https://doi.org/10.3390/s17010075
  51. [51] G. Gabrielli and T. von Karman, “What price speed?,” Vol.63, No.1, pp. 188-200, 1951. https://doi.org/10.1111/j.1559-3584.1951.tb02891.x
  52. [52] V. A. Tucker, “The Energetic Cost of Moving About,” Am. Sci., Vol.63, No.4, pp. 413-419, 1975.
  53. [53] A. Badri-Spröwitz et al., “BirdBot achieves energy-efficient gait with minimal control using avian-inspired leg clutching,” Sci. Robot., Vol.7, No.64, Article No.eabg4055, 2022. https://doi.org/10.1126/scirobotics.abg4055
  54. [54] A. Comoretto et al., “Physical synchronization of soft self-oscillating limbs for fast and autonomous locomotion,” Science, Vol.388, No.6747, pp. 610-615, 2025. https://doi.org/10.1126/science.adr3661

Creative Commons License  This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Apr. 19, 2026