# Modeling and analysis of a new locomotion control neural networks

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## Abstract

Experimental data have shown that inherent bursting of the neuron plays an important role in the generation of rhythmic movements in spinal networks. Based on the mechanism that the spinal neurons of a lamprey generate this inherent bursting, this paper builds a simplified inherent bursting neuron model. A new locomotion control neural network is built that takes advantage of this neuron model and its performance is analyzed mathematically and by numerical simulation. From these analyses, it is found that the new control networks have no restriction on their topological structure for generating the oscillatory outputs. If a network is used to control the motion of bionic robots or build the model of the vertebrate spinal circuitry, its topological structure can be constructed using the unit burst generator model proposed by Grillner. The networks can also be easily switched between oscillatory and non-oscillatory output. Additionally, inactivity and saturation properties of the new networks can also be developed, which will be helpful to increase the motor flexibility and environmental adaptability of bionic robots.

## Keywords

Locomotion control neural networks Central pattern generator (CPG) Oscillatory output Non-oscillatory output Bionic robot control## Notes

### Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 61105110, the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant 14KJB510004 and the Lianyungang “521” Project and the six talent peaks project in Jiangsu Province, and the Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-aged Teachers and President.

## Supplementary material

## References

- Bicanski A, Ryczko D, Cabelguen J-M et al (2013) From lamprey to salamander: an exploratory modeling study on the architecture of the spinal locomotion networks in the salamander. Biol Cybern 107:565–587CrossRefPubMedGoogle Scholar
- Buchanan JT (1992) Neural network simulations of coupled locomotor oscillators in the lamprey spinal cord. Biol Cybern 66:367–374CrossRefPubMedGoogle Scholar
- Cohen AH, Holmes PJ, Rand RH (1982) The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model. J Math Biol 13:345–369CrossRefPubMedGoogle Scholar
- Collins J, Richmond S (1994) Hard-wired central pattern generators for quadrupedal locomotion. Biol Cybern 71:375–385CrossRefGoogle Scholar
- Ekeberg Ö (1993) A combined neuronal and mechanical model of fish swimming. Biol Cybern 69:363–374CrossRefGoogle Scholar
- Ermentrout GB (1992) Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators. SIAM J Appl Math 52:1665–1687CrossRefGoogle Scholar
- Grillner S, Jessell TM (2009) Measured motion: searching for simplicity in spinal locomotor networks. Curr Opin Neurobiol 19:572–586CrossRefPubMedPubMedCentralGoogle Scholar
- Guertin PA (2009) The mammalian central pattern generator for locomotion. Brain Res Rev 62:45–56CrossRefPubMedGoogle Scholar
- Hellgren J, Grillner S, Lansner A (1992) Computer simulation of the segmental neural network generating locomotion in lamprey by using populations of network interneurons. Biol Cybern 68:1–13CrossRefPubMedGoogle Scholar
- Huss M, Wang D, Trané C et al (2008) An experimentally constrained computational model of NMDA oscillations in lamprey CPG neurons. J Comput Neurosci 25:108–121CrossRefPubMedGoogle Scholar
- Ijspeert AJ (2008) Central pattern generators for locomotion control in animals and robots: a review. Neural Netw 21:642–653CrossRefPubMedGoogle Scholar
- Ijspeert AJ, Crespi A, Ryczko D et al (2007) From swimming to walking with a salamander robot driven by a spinal cord model. Science 315:1416–1420CrossRefPubMedGoogle Scholar
- Kopell N, Ermentrout GB (1988) Coupled oscillators and the design of central pattern generators. Math Biosci 90:87–109CrossRefGoogle Scholar
- Kopell N, Ermentrout GB (1991) On chains of oscillators forced at one end. SIAM J Appl Math 51:1397–1417CrossRefGoogle Scholar
- Kozlov A, Huss M, Lansner A et al (2009) Simple cellular and network control principles govern complex patterns of motor behavior. Proc Nati Acad Sci 106:20027–20032CrossRefGoogle Scholar
- Marder E, Calabrese RL (1996) Principles of rhythmic motor pattern generation. Physiol Rev 76:687–717CrossRefPubMedGoogle Scholar
- Massarelli N, Clapp G, Hoffman K et al (2016) Entrainment ranges for chains of forced neural and phase oscillators. J Math Neurosci 6:1–21CrossRefGoogle Scholar
- Matsuoka K (1985) Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biol Cybern 52:367–376CrossRefPubMedGoogle Scholar
- Matsuoka K (1987) Mechanisms of frequency and pattern control in the neural rhythm generators. Biol Cybern 56:345–353CrossRefPubMedGoogle Scholar
- McLean DL, Fan JY, Higashijima S-I et al (2007) A topographic map of recruitment in spinal cord. Nature 446:71–75CrossRefPubMedGoogle Scholar
- Previte JP, Sheils N, Hoffman KA et al (2011) Entrainment ranges of forced oscillators. J Math Biol 62:589–603CrossRefPubMedGoogle Scholar
- Righetti L, Buchli J, Ijspeert AJ (2006) Dynamic Hebbian learning in adaptive frequency oscillators. Phys D 216:269–281CrossRefGoogle Scholar
- Rybak IA, Shevtsova NA, Ptak K et al (2004) Intrinsic bursting activity in the pre-Bötzinger complex: role of persistent sodium and potassium currents. Biol Cybern 90:59–74CrossRefPubMedGoogle Scholar
- Tangorra JL, Mignano AP, Carryon GN et al. (2011) Biologically derived models of the sunfish for experimental investigations of multi-fin swimming. In: IEEE/RSJ international conference on intelligent robots and systems (IROS), pp 580–587Google Scholar
- Wadden T, Hellgren J, Lansner A et al (1997) Intersegmental coordination in the lamprey: simulations using a network model without segmental boundaries. Biol Cybern 76:1–9CrossRefGoogle Scholar
- Wallén P, Williams TL (1984) Fictive locomotion in the lamprey spinal cord in vitro compared with swimming in the intact and spinal animal. J Physiol 347:225–239CrossRefPubMedPubMedCentralGoogle Scholar
- Wallén P, Grillner S (1987) N-Methyl-D-aspartate receptor-induced, inherent oscillatory activity in neurons active during fictive locomotion in the lamprey. J Neurosci 7(9):2745–2755CrossRefPubMedGoogle Scholar
- Williams TL (1992) Phase coupling by synaptic spread in chains of coupled neuronal oscillators. Science 258:662–665CrossRefPubMedGoogle Scholar
- Williams TL, Sigvard KA, Kopell N et al (1990) Forcing of coupled nonlinear oscillators: studies of intersegmental coordination in the lamprey locomotor central pattern generator. J Neurophysiol 64:862–871CrossRefPubMedGoogle Scholar
- Yang GZ, Ma SG, Li B et al (2013) A hierarchical connectionist central pattern generator model for control three-dimensional gaits of snake-like robots. ACTA AUTOMATICA SINICA 39:1611–1622CrossRefGoogle Scholar
- Yu JZ, Tan M, Chen J et al (2014) A survey on cpg-inspired control models and system implementation. IEEE Trans Neural Netw 25:441–456CrossRefGoogle Scholar
- Yuste R, MacLean JN, Smith J et al (2005) The cortex as a central pattern generator. Nat Rev Neurosci 6:477–483CrossRefPubMedGoogle Scholar