Biological Cybernetics

, Volume 101, Issue 1, pp 49–61

Energy efficient walking with central pattern generators: from passive dynamic walking to biologically inspired control

  • B. W. Verdaasdonk
  • H. F. J. M. Koopman
  • F. C. T. van der Helm
Open Access
Original Paper


Like human walking, passive dynamic walking—i.e. walking down a slope with no actuation except gravity—is energy efficient by exploiting the natural dynamics. In the animal world, neural oscillators termed central pattern generators (CPGs) provide the basic rhythm for muscular activity in locomotion. We present a CPG model, which automatically tunes into the resonance frequency of the passive dynamics of a bipedal walker, i.e. the CPG model exhibits resonance tuning behavior. Each leg is coupled to its own CPG, controlling the hip moment of force. Resonance tuning above the endogenous frequency of the CPG—i.e. the CPG’s eigenfrequency—is achieved by feedback of both limb angles to their corresponding CPG, while integration of the limb angles provides resonance tuning at and below the endogenous frequency of the CPG. Feedback of the angular velocity of both limbs to their corresponding CPG compensates for the time delay in the loop coupling each limb to its CPG. The resonance tuning behavior of the CPG model allows the gait velocity to be controlled by a single parameter, while retaining the energy efficiency of passive dynamic walking.


Legged locomotion Central pattern generator Resonance tuning Energy efficiency Passive dynamic walking Route to chaos 


  1. Amemiya M, Yamaguchi T (1984) Fictive locomotion of the forelimb evoked by stimulation of the mesencephalic locomotor region in the decerebrate cat. Neurosci Lett 50: 91–96PubMedCrossRefGoogle Scholar
  2. Barbeau H, McCrea DA, O’Donovan MJ, Rossignol S, Grill WM, Lemay MA (1999) Tapping into spinal circuits to restore motor function. Brain Res Brain Res Rev 30: 27–51PubMedCrossRefGoogle Scholar
  3. Borzova E, Hurmuzlu Y (2004) Passively walking five-link robot. Automatica 40: 621–629CrossRefGoogle Scholar
  4. Burke RE (2001) The central pattern generator for locomotion in mammals. Adv Neurol 87: 11–24PubMedGoogle Scholar
  5. Cazalets JR, Borde M, Clarac F (1995) Localization and organization of the central pattern generator for hindlimb locomotion in newborn rat. J Neurosci 15: 4943–4951PubMedGoogle Scholar
  6. Dimitrijevic MR, Gerasimenko Y, Pinter MM (1998) Evidence for a spinal central pattern generator in humans. Ann NY Acad Sci 860: 360–376PubMedCrossRefGoogle Scholar
  7. Donelan JM, Kram R, Kuo AD (2002) Mechanical work for step-to-step transitions is a major determinant of the metabolic cost of human walking. J Exp Biol 205: 3717–3727PubMedGoogle Scholar
  8. Feigenbaum MJ (1978) Quantitative universality for a class of non-linear transformations. J Stat Phys 19: 25–52CrossRefGoogle Scholar
  9. Garcia M, Chatterjee A, Ruina A, Coleman M (1998) The simplest walking model: stability, complexity, and scaling. J Biomech Eng 120: 281–288PubMedCrossRefGoogle Scholar
  10. Goswami A, Espiau B, Keramane A (1997) Limit cycles in a passive compass gait biped and passivity-mimicking control laws. Auton Robots 4: 273–286CrossRefGoogle Scholar
  11. Goswami A, Thuilot B, Espiau B (1998) A study of the passive gait of a compass-like biped robot: Symmetry and chaos. Int J Rob Res 17: 1282–1301CrossRefGoogle Scholar
  12. Grillner S, Ekeberg O, El Manira A, Lansner A, Parker D, Tegner J, Wallen P (1998) Intrinsic function of a neuronal network—a vertebrate central pattern generator. Brain Res Brain Res Rev 26: 184–197PubMedCrossRefGoogle Scholar
  13. Grillner S, McClellan A, Perret C (1981) Entrainment of the spinal pattern generators for swimming by mechano- sensitive elements in the lamprey spinal cord in vitro. Brain Res 217: 380–386PubMedCrossRefGoogle Scholar
  14. Inman V, Ralston H, Todd F (1981) Human Walking. Williams and Wilkins, BaltimoreGoogle Scholar
  15. Koopman HFJM (1989) The three-dimensional analysis and prediction of human walking. Department of Mechanical Engineering. University of Twente, Enschede, The NetherlandsGoogle Scholar
  16. Kuo AD (2002) Energetics of actively powered locomotion using the simplest walking model. J Biomech Eng 124: 113–120PubMedCrossRefGoogle Scholar
  17. MacKay-Lyons M (2002) Central pattern generation of locomotion: a review of the evidence. Phys Ther 82: 69–83PubMedGoogle Scholar
  18. Matsuoka K (1985) Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biol Cybern 52: 367–376PubMedCrossRefGoogle Scholar
  19. Matsuoka K (1987) Mechanisms of frequency and pattern control in the neural rhythm generators. Biol Cybern 56: 345–353PubMedCrossRefGoogle Scholar
  20. McCrea DA (2001) Spinal circuitry of sensorimotor control of locomotion. J Physiol 533: 41–50PubMedCrossRefGoogle Scholar
  21. McGeer T (1990) Passive dynamic walking. Int J Rob Res 9: 62–82CrossRefGoogle Scholar
  22. McMahon TA (1984) Muscles, reflexes, and locomotion. Princeton University Press, Princeton, p 331Google Scholar
  23. Mochon S, McMahon TA (1980) Ballistic walking. J Biomech 13: 49–57PubMedCrossRefGoogle Scholar
  24. Nishimaru H, Kudo N (2000) Formation of the central pattern generator for locomotion in the rat and mouse. Brain Res Bull 53: 661–669PubMedCrossRefGoogle Scholar
  25. Schwab AL, Wisse M (2001) Basin of attraction of the simplest walking model. In: Proceedings of ASME 2001 design engineering technical conferences and computers and information in engineering conference, Pittsburgh, PennsylvaniaGoogle Scholar
  26. Shik ML, Severin FV, Orlovskii GN (1966) Control of walking and running by means of electrical stimulation of the mid-brain. Biophysics 11: 756–765Google Scholar
  27. Sqalli-Houssaini Y, Cazalets JR, Clarac F (1993) Oscillatory properties of the central pattern generator for locomotion in neonatal rats. J Neurophysiol 70: 803–813PubMedGoogle Scholar
  28. Taga G (1995a) A model of the neuro-musculo-skeletal system for human locomotion. I. Emergence of basic gait. Biol Cybern 73: 97–111PubMedCrossRefGoogle Scholar
  29. Taga G (1995b) A model of the neuro-musculo-skeletal system for human locomotion. II Real-time adaptability under various constraints. Biol Cybern 73: 113–121PubMedCrossRefGoogle Scholar
  30. Taga G, Yamaguchi Y, Shimizu H (1991) Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment. Biol Cybern 65: 147–159PubMedCrossRefGoogle Scholar
  31. Van de Crommert HW, Mulder T, Duysens J (1998) Neural control of locomotion: sensory control of the central pattern generator and its relation to treadmill training. Gait Posture 7: 251–263PubMedCrossRefGoogle Scholar
  32. van der Kooij H, Jacobs R, Koopman B, van der Helm F (2003) An alternative approach to synthesizing bipedal walking. Biol Cybern 88: 46–59PubMedCrossRefGoogle Scholar
  33. van der Linde RQ (1999) Passive bipedal walking with phasic muscle contraction. Biol Cybern 81: 227–237PubMedCrossRefGoogle Scholar
  34. Verdaasdonk BW, Koopman HF, Helm FC (2006) Energy efficient and robust rhythmic limb movement by central pattern generators. Neural Netw 19: 388–400PubMedCrossRefGoogle Scholar
  35. Verdaasdonk BW, Koopman HF, Van Der Helm FC (2007a) Achieving energy efficient and robust bipedal gait with a CPG-controlled bipedal walker: Tuning the neural coupling gains. In: Williams TO(eds) Biological Cybernetics Research Trends. Nova Science, HauppaugeGoogle Scholar
  36. Verdaasdonk BW, Koopman HF, Van der Helm FC (2007b) Resonance tuning in a neuro-musculo-skeletal model of the forearm. Biol Cybern 96: 165–180PubMedCrossRefGoogle Scholar
  37. Verdaasdonk BW, Koopman HF, Van Gils SA, Van Der Helm FC (2004a) Bifurcation and stability analysis in musculoskeletal systems: a study in human stance. Biol Cybern 91: 48–62PubMedCrossRefGoogle Scholar
  38. Verdaasdonk BW, Koopman HFJM, Van Gils SA, Van Der Helm FC (2004b) Stable walking with central pattern generators. In: Proceedings of the European Society of Biomechanics Congress, Eindhoven University of Technology, ’s-Hertogenbosch, The NetherlandsGoogle Scholar
  39. Waters RL, Mulroy S (1999) The energy expenditure of normal and pathologic gait. Gait Posture 9: 207–231PubMedCrossRefGoogle Scholar
  40. Whelan PJ (1996) Control of locomotion in the decerebrate cat. Prog Neurobiol 49: 481–515PubMedCrossRefGoogle Scholar
  41. Wisse M, Schwab AL, van der Linde RQ, van der Helm FCT (2005) How to keep from falling forward: elementary swing leg action for passive dynamic walkers. Robotics, IEEE Transactions on [see also Robotics and Automation, IEEE Transactions on] 21: 393–401Google Scholar

Copyright information

© The Author(s) 2009

Authors and Affiliations

  • B. W. Verdaasdonk
    • 1
  • H. F. J. M. Koopman
    • 1
  • F. C. T. van der Helm
    • 2
  1. 1.Department of Bio-mechanical Engineering, Faculty of Engineering TechnologyUniversity of TwenteEnschedeThe Netherlands
  2. 2.Department of BioMechanical Engineering, Faculty of Mechanical EngineeringDelft University of TechnologyDelftThe Netherlands

Personalised recommendations