Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Comparative study of forced oscillators for the adaptive generation of rhythmic movements in robot controllers

  • 100 Accesses


The interest of central pattern generators in robot motor coordination is universally recognized so much so that a lot of possibilities on different scales of modeling are nowadays available. While each method obviously has its advantages and drawbacks, some could be more suitable for human–robot interactions. In this paper, we compare three oscillator models: Matsuoka, Hopf and Rowat–Selverston models. These models are integrated to a control architecture for a robotic arm and evaluated in simulation during a simplified handshaking interaction which involves constrained rhythmic movements. Furthermore, Hebbian plasticity mechanisms are integrated to the Hopf and Rowat–Selverston models which can incorporate such mechanisms, contrary to the Matsuoka. Results show that the Matsuoka oscillator is subpar in all aspects and for the two others, that plasticity improves synchronization and leads to a significant decrease in the power consumption.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12


  1. Al-Busaidi AM, Zaier R, Al-Yahmadi AS (2012) Control of biped robot joints’ angles using coordinated matsuoka oscillators. In: International conference on artificial neural networks, Springer, pp 304–312

  2. Arena P, Fortuna L, Frasca M, Patane L, Pollino M (2006) An autonomous mini-hexapod robot controlled through a cnn-based cpg vlsi chip. In: IEEE 10th international workshop on cellular neural networks and their applications, 2006. CNNA’06, pp 1–6

  3. Arikan KB, Irfanoglu B (2011) A test bench to study bioinspired control for robot walking. J Control Eng Appl Inform 13(2):76–80

  4. Ayers J (2004) Underwater walking. Arthropod Struct Dev 33(3):347–360

  5. Brambilla G, Buchli J, Ijspeert AJ (2006) Adaptive four legged locomotion control based on nonlinear dynamical systems. In: International conference on simulation of adaptive behavior, Springer, pp 138–149

  6. Buchli J, Ijspeert AJ (2008) Self-organized adaptive legged locomotion in a compliant quadruped robot. Auton Robots 25(4):331

  7. Buchli J, Righetti L, Ijspeert AJ (2005) A dynamical systems approach to learning: a frequency-adaptive hopper robot. In: European conference on artificial life, Springer, pp 210–220

  8. Buchli J, Iida F, Ijspeert AJ (2006) Finding resonance: Adaptive frequency oscillators for dynamic legged locomotion. In: 2006 IEEE/RSJ international conference on Intelligent robots and systems, IEEE, pp 3903–3909

  9. Cattaert D, Le Ray D (2001) Adaptive motor control in crayfish. Prog Neurobiol 63(2):199–240

  10. Chung SJ, Dorothy M (2010) Neurobiologically inspired control of engineered flapping flight. J Guid Control Dyn 33(2):440–453

  11. Collins JJ, Richmond SA (1994) Hard-wired central pattern generators for quadrupedal locomotion. Biol Cybern 71(5):375–385

  12. de Rugy A, Wei K, Müller H, Sternad D (2003) Actively tracking passive stability in a ball bouncing task. Brain Res 982(1):64–78

  13. Degallier S, Santos CP, Righetti L, Ijspeert A (2006) Movement generation using dynamical systems: a humanoid robot performing a drumming task. In: 2006 6th IEEE-RAS international conference on humanoid robots, IEEE, pp 512–517

  14. Degallier S, Righetti L, Natale L, Nori F, Metta G, Ijspeert A (2008) A modular bio-inspired architecture for movement generation for the infant-like robot icub. In: 2nd IEEE RAS and EMBS international conference on biomedical robotics and biomechatronics, BioRob 2008, IEEE, pp 795–800

  15. Fang F, Xu WL, Lin K, Alam F, Potgieter J (2013) Matsuoka neuronal oscillator for traffic signal control using agent-based simulation. Proced Comput Sci 19:389–395

  16. Fuente LA, Lones MA, Turner AP, Caves LS, Stepney S, Tyrrell AM (2013) Adaptive robotic gait control using coupled artificial signalling networks, hopf oscillators and inverse kinematics. In: 2013 IEEE congress on evolutionary computation (CEC), IEEE, pp 1435–1442

  17. Grillner S, Wallen P (1985) Central pattern generators for locomotion, with special reference to vertebrates. Ann Rev Neurosci 8(1):233–261

  18. He J, Lu C, Yin S (2006) The design of cpg control module of the bionic mechanical crab. In: IEEE International Conference on Robotics and Biomimetics, 2006. ROBIO’06, pp 280–285

  19. Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544

  20. Hopf E (1942) Abzweigung einer periodischen lösung von einer stationären lösung eines differentialsystems. Ber Math-Phys Kl Sächs Akad Wiss Leipzig 94:1–22

  21. Hu Y, Tian W, Liang J, Wang T (2011) 2011 IEEE/RSJ international conference on learning fish-like swimming with a CPG-based locomotion controller. In: Intelligent Robots and Systems (IROS), IEEE pp 1863–1868

  22. Hu Y, Liang J, Wang T (2014) Parameter synthesis of coupled nonlinear oscillators for cpg-based robotic locomotion. IEEE Trans Ind Electron 61(11):6183–6191

  23. Ijspeert AJ (2008) Central pattern generators for locomotion control in animals and robots: a review. Neural Netw 21(4):642–653

  24. Ijspeert J (2004) A simple adaptive locomotion toy-system. In: From animals to animats 8: Proceedings of the seventh [ie eighth] international conference on simulation of adaptive behavior, MIT Press, vol 8, p 153

  25. Jouaiti M, Henaff P (2018) Cpg-based controllers can generate both discrete and rhythmic movements. In: 2018 IEEE/RSJ international conference on intelligent robots and systems (IROS)

  26. Jouaiti M, Caron L, Hénaff P (2018) Hebbian plasticity in cpg controllers facilitates self-synchronization for human–robot handshaking. Front Neurorobot 12:29

  27. Kamimura A, Kurokawa H, Yoshida E, Murata S, Tomita K, Kokaji S (2005) Automatic locomotion design and experiments for a modular robotic system. IEEE/ASME Trans Mechatron 10(3):314–325

  28. Kasuga T, Hashimoto M (2005) Human-robot handshaking using neural oscillators. In: Proceedings of the 2005 IEEE international conference on robotics and automation, 2005. ICRA 2005 IEEE, pp 3802–3807

  29. Lachaux JP, Rodriguez E, Martinerie J, Varela FJ et al (1999) Measuring phase synchrony in brain signals. Human Brain Mapp 8(4):194–208

  30. Li C, Lowe R, Ziemke T (2013) Humanoids learning to walk: a natural cpg-actor-critic architecture. Front Neurorobot 7:5

  31. Liu C, Chen Q, Wang D (2011) Cpg-inspired workspace trajectory generation and adaptive locomotion control for quadruped robots. IEEE Trans Syst Man Cybern Part B (Cybern) 41(3):867–880

  32. Liu C, Fan Z, Seo K, Tan X, Goodman E (2012) Synthesis of matsuoka-based neuron oscillator models in locomotion control of robots. In: 2012 Third global congress on intelligent systems (GCIS), IEEE, pp 342–347

  33. Liu GL, Watanabe K, Izumi K (2006) The parameter design of central pattern generators composed of some matsuoka oscillators for the leg movements of human-like robots. In: SCIS and ISIS SCIS and ISIS 2006, Japan Society for Fuzzy Theory and Intelligent Informatics, pp 24–29

  34. Liu GL, Habib MK, Watanabe K, Izumi K (2007) The design of central pattern generators based on the matsuoka oscillator to generate rhythmic human-like movement for biped robots. J Adv Comput Intell Intell Inform 11(8):946–955

  35. Liu GL, Habib MK, Watanabe K, Izumi K (2008) Central pattern generators based on matsuoka oscillators for the locomotion of biped robots. Artif Life Robot 12(1–2):264–269

  36. Manoonpong P, Pasemann F, Wörgötter F (2008) Sensor-driven neural control for omnidirectional locomotion and versatile reactive behaviors of walking machines. Roboti Auton Syst 56(3):265–288

  37. Matos V, Santos C (2010) Omnidirectional locomotion in a quadruped robot: A cpg-based approach. In: The 2010 IEEE/RSJ International conference on intelligent robots and systems, IROS 2010, pp 3392–3397

  38. Matsuoka K (1985) Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biol Cybern 52(6):367–376

  39. Matsuoka K (2011) Analysis of a neural oscillator. Biol Cybern 104(4):297–304

  40. Mori T, Nakamura Y, Sato MA, Ishii S (2004) Reinforcement learning for cpg-driven biped robot. AAAI 4:623–630

  41. Nassour J, Hénaff P, Benouezdou F, Cheng G (2014) Multi-layered multi-pattern cpg for adaptive locomotion of humanoid robots, biological cybernetics. Biol Cybern 108(3):291–303

  42. Nassour J, Hoa TD, Atoofi P, Hamker F (2019) Concrete action representation model: from neuroscience to robotics. IEEE Trans Cognit Dev Syst. https://doi.org/10.1109/TCDS.2019.2896300

  43. Panwart V, Kumar R (2012) Stable biped locomotion using central pattern generators based on matsuoka neural oscillators. In: IET international conference on information science and control engineering 2012 (ICISCE 2012). IEEE, Shenzhen, pp 1–5. https://doi.org/10.1049/cp.2012.2453

  44. Pelc EH, Daley MA, Ferris DP (2008) Resonant hopping of a robot controlled by an artificial neural oscillator. Bioinspir Biomime 3(2):026001

  45. Pinto CM, Rocha D, Santos CP (2012) Hexapod robots: new cpg model for generation of trajectories. J Numer Anal Ind Appl Math 7(1–2):15–26

  46. Righetti L, Ijspeert AJ (2006) Programmable central pattern generators: an application to biped locomotion control. In: Proceedings 2006 IEEE international conference on robotics and automation, 2006. ICRA 2006. IEEE, pp 1585–1590

  47. Righetti L, Ijspeert AJ (2008) Pattern generators with sensory feedback for the control of quadruped locomotion. In: IEEE international conference on robotics and automation, 2008. ICRA 2008. IEEE, pp 819–824

  48. Righetti L, Buchli J, Ijspeert AJ (2006) Dynamic hebbian learning in adaptive frequency oscillators. Phys D Nonlinear Phenom 216(2):269–281

  49. Rowat PF, Selverston AI (1993) Modeling the gastric mill central pattern generator of the lobster with a relaxation-oscillator network. J Neurophysiol 70(3):1030–1053

  50. Rybak IA, Shevtsova NA, Lafreniere-Roula M, McCrea DA (2006) Modelling spinal circuitry involved in locomotor pattern generation: insights from deletions during fictive locomotion. J Physiol 577(2):617–639

  51. Schaal S (2006) Dynamic movement primitives-a framework for motor control in humans and humanoid robotics. In: Adaptive motion of animals and machines, Springer, pp 261–280

  52. Seo K, Chung SJ, Slotine JJE (2010) Cpg-based control of a turtle-like underwater vehicle. Autonom Robots 28(3):247–269

  53. Shan J, Nagashima F (2002) Neural locomotion controller design and implementation for humanoid robot hoap-1. In: 20th annual conference of the robotics society of Japan

  54. Sprowitz A, Pouya S, Bonardi S, Van Den Kieboom J, Mockel R, Billard A, Dillenbourg P, Ijspeert AJ (2010) Roombots: reconfigurable robots for adaptive furniture. IEEE Comput Intell Mag 5(3):20–32

  55. Taga G (1995) A model of the neuro-musculo-skeletal system for human locomotion. Biol Cybern 73(2):97–111

  56. Taga G, Yamaguchi Y, Shimizu H (1991) Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment. Biol Cybern 65(3):147–159

  57. Tagne G, Hénaff P, Gregori N (2016) Measurement and analysis of physical parameters of the handshake between two persons according to simple social contexts. In: 2016 IEEE/RSJ international conference on intelligent robots and systems (IROS), pp 674–679

  58. Wang T, Hu Y, Liang J (2013) Learning to swim: a dynamical systems approach to mimicking fish swimming with cpg. Robotica 31(3):361–369

  59. Williamson MM (1998) Rhythmic robot arm control using oscillators. In: 1998 IEEE/RSJ international conference on intelligent robots and systems, 1998. Proceedings, IEEE, vol 1, pp 77–83

  60. Wu X, Ma S (2010) Adaptive creeping locomotion of a cpg-controlled snake-like robot to environment change. Autonom Robots 28(3):283–294

  61. Xu W, Fang FC, Bronlund J, Potgieter J (2009) Generation of rhythmic and voluntary patterns of mastication using matsuoka oscillator for a humanoid chewing robot. Mechatronics 19(2):205–217

  62. Yang W, Bae JH, Oh Y, Chong NY, You BJ, Oh SR (2010) Cpg based self-adapting multi-dof robotic arm control. In: IEEE/RSJ international conference on intelligent robots and systems (IROS), 2010, IEEE, pp 4236–4243

  63. Yu J, Tan M, Chen J, Zhang J (2014) A survey on cpg-inspired control models and system implementation. IEEE Trans Neural Netw Learn Syst 25(3):441–456

  64. Zehr EP, Carroll TJ, Chua R, Collins DF, Frigon A, Haridas C, Hundza SR, Thompson AK (2004) Possible contributions of cpg activity to the control of rhythmic human arm movement. Can J Physiol Pharmacol 82(8–9):556–568

  65. Zhou C, Low K (2012) Design and locomotion control of a biomimetic underwater vehicle with fin propulsion. IEEE/ASME Trans Mechatron 17(1):25–35

Download references

Author information

Correspondence to Melanie Jouaiti.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by Shai Revzen.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jouaiti, M., Hénaff, P. Comparative study of forced oscillators for the adaptive generation of rhythmic movements in robot controllers. Biol Cybern 113, 547–560 (2019). https://doi.org/10.1007/s00422-019-00807-8

Download citation


  • Oscillator
  • Synchronization
  • Rhythmic movements
  • Robot controller