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An Alternative Approach for Setting the Optimum Coupling Parameters Among the Neural Central Pattern Generators Considering the Amplitude and the Phase Error Calculations

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Abstract

In general, the equivalent amplitude values and the specific phase differences between the oscillators/neurons are desired to obtain the smooth movements in the CPG based robotic applications. However, in the literature, the error minimization functions calculate either the amplitude or the phase errors between the nonlinear dynamics. This study offers an alternative error minimization approach. This approach calculates both the amplitude and the phase errors, simultaneously. The proposed approach, the RMS function and the phase error function have been utilized as the cost functions of the genetic and the ABC algorithms for the performance evaluation of the proposed approach. These functions have been assessed for estimating the coupling parameters of the electrically coupled HR neurons. According to the results, the proposed approach has minimum errors when compared with the other two functions. On the other hand, to utilize these estimated coupling parameters in the real-time applications, to create the CPG networks by using the coupled neurons and to use these emulated neurons in a locomotion control problem offer a particular importance for the developments in this field. Here, the HR neurons, which are coupled with the estimated parameters, have been implemented with FPGA device by using the SGDSP tool. Thus, the applicability to the real-time systems of the proposed approach has been verified with a hardware realization. Then, the trot gait pattern of a quadruped robot has been controlled by using these emulated neuronal responses, so the coupled biological neurons have been used as a controller in a CPG based multi-legged robotic application, successfully.

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References

  1. Delcomyn F (1980) Neural basis for rhythmic behaviors in animals. Science 210:492–498

    Article  Google Scholar 

  2. Selverston AI (2010) Invertebrate central pattern generator circuits. Philos Trans R Soc B 365:2329–2345

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Barron-Zambrano JH, Torres-Huitzil C (2013) FPGA implementation of a configurable neuromorphic CPG-based locomotion controller. Neural Netw 45:50–61

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Wang Q, Duan Z, Perc M, Chen G (2008) Synchronization transitions on small-world neuronal networks: effects of information transmission delay and rewiring probability. EPL (Europhys Lett) 83(5):50008

    Article  Google Scholar 

  7. Wang Q, Perc M, Duan Z, Chen G (2009) Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. Phys Rev E 80(2):026206

    Article  Google Scholar 

  8. Wang Q, Chen G, Perc M (2011) Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling. PLoS ONE 6(1):e15851

    Article  Google Scholar 

  9. Sun X, Lei J, Perc M, Kurths J, Chen G (2011) Burst synchronization transitions in a neuronal network of subnetworks. Chaos Interdiscip J Nonlinear Sci 21(1):016110

    Article  Google Scholar 

  10. Dtchetgnia Djeundam SR, Yamapi R, Filatrella G, Kofane TC (2015) Stability of the synchronized network of Hindmarsh–Rose neuronal models with nearest and global couplings. Commun Nonlinear Sci Numer Simul 22:545–563

    Article  MathSciNet  MATH  Google Scholar 

  11. Nguyen LH, Hong KS (2013) Adaptive synchronization of two coupled chaotic Hindmarsh–Rose neurons by controlling the membrane potential of a slave neuron. Appl Math Model 37:2460–2468

    Article  MathSciNet  MATH  Google Scholar 

  12. Deng B, Wang J, Fei X (2006) Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control. Chaos Solitons Fract 29:182–189

    Article  Google Scholar 

  13. Wang J, Chen LS, Deng B (2009) Synchronization of Ghostburster neuron in external electrical stimulation via H-infinity variable universe fuzzy adaptive control. Chaos Solitons Fract 39:2076–2085

    Article  Google Scholar 

  14. Chen M (2007) Synchronization in time-varying networks: a matrix measure approach. Phys Rev E 76:016104

    Article  MathSciNet  Google Scholar 

  15. Li Z (2008) Exponential stability of synchronization in asymmetrically coupled dynamical networks. Chaos Interdiscip J Nonlinear Sci 18(2):023124

    Article  MathSciNet  MATH  Google Scholar 

  16. Li Z, Lee J (2007) New eigenvalue based approach to synchronization in asymmetrically coupled networks. Chaos Interdiscip J Nonlinear Sci 17(4):043117

    Article  MathSciNet  MATH  Google Scholar 

  17. Ge ZM, Chen C-C (2004) Phase synchronization of coupled chaotic multiple time scales systems. Chaos Solitons Fract 20(3):639–647

    Article  MATH  Google Scholar 

  18. Pikovsky Arkady S, Michael Rosenblum G, Grigory Osipov V, Kurths J (1997) Phase synchronization of chaotic oscillators by external driving. Phys D Nonlinear Phenom 104(3–4):219–238

    Article  MathSciNet  MATH  Google Scholar 

  19. Ma J, Mi L, Zhou P, Xu Y, Hayat T (2017) Phase synchronization between two neurons induced by coupling of electromagnetic field. Appl Math Comput 307:321–328

    MathSciNet  MATH  Google Scholar 

  20. Shuai JW, Durand DM (1999) Phase synchronization in two coupled chaotic neurons. Phys Lett A 264(4):289–297

    Article  MathSciNet  MATH  Google Scholar 

  21. Jalili M (2011) Phase synchronizing in Hindmarsh–Rose neural networks with delayed chemical coupling. Neurocomputing 74(10):1551–1556

    Article  Google Scholar 

  22. Chen Q, Wang J, Yang S, Qin Y, Deng B, Wei X (2017) A real-time FPGA implementation of a biologically inspired central pattern generator network. Neurocomputing 244:63–80

    Article  Google Scholar 

  23. Soleimani H, Ahmadi A, Bavandpour M (2012) Biologically inspired spiking neurons: piecewise linear models and digital implementation. IEEE Trans Circuits Syst I Reg Pap 59:2991–3004

    Article  MathSciNet  Google Scholar 

  24. Geit WV, Schutter ED, Achard P (2008) Automated neuron model optimization techniques: a review. Biol Cybern 99:241–251

    Article  MathSciNet  MATH  Google Scholar 

  25. Lu W, Chen T (2006) New approach to synchronization analysis of linearly coupled ordinary differential systems. Phys D Nonlinear Phenom 213:214–230

    Article  MathSciNet  MATH  Google Scholar 

  26. Chen W, Ren G, Zhang J, Wang J (2012) Smooth transition between different gaits of a hexapod robot via a central pattern generators algorithm. J Intell Robot Syst 67:255–270

    Article  MATH  Google Scholar 

  27. Inagaki S, Yuasa H, Suzuki T, Arai T (2006) Wave CPG model for autonomous decentralized multi-legged robot: gait generation and walking speed control. Robot Auton Syst 54:118–126

    Article  Google Scholar 

  28. Ijspeert AJ, Crespi A, Ryczko D, Cabelguen JM (2007) From swimming to walking with a salamander robot driven by a spinal cord model. Science 315(5817):1416–1420

    Article  Google Scholar 

  29. Carla Pinto MA, Tenreiro Machado JA (2010) Fractional central pattern generators for bipedal locomotion. Nonlinear Dyn 62:27–37

    Article  MathSciNet  MATH  Google Scholar 

  30. Ortega-Zamorano F, Jerez JM, Juárez GE, Franco L (2017) FPGA implementation of neurocomputational models: comparison between standard back-propagation and C-Mantec constructive algorithm. Neural Process Lett 46(3):899–914

    Article  Google Scholar 

  31. Arena P, Fortuna L, Frasca M, Sicurella G (2004) An adaptive, self-organizing dynamical system for hierarchical control of bio-inspired locomotion. IEEE Trans Syst Man Cybern B 34(4):1823–1837

    Article  Google Scholar 

  32. Guerra-Hernandez EI, Espinal A, Batres-Mendoza P, Garcia-Capulin CH, Romero-Troncoso RDJ, Rostro-Gonzalez H (2017) A FPGA-based neuromorphic locomotion system for multi-legged robots. IEEE Access 5:8301–8312

    Article  Google Scholar 

  33. Espinal A, Rostro-Gonzalez H, Carpio M, Guerra-Hernandez EI, Ornelas-Rodriguez M, Sotelo-Figueroa M (2016) Design of spiking central pattern generators for multiple locomotion gaits in hexapod robots by christiansen grammar evolution. Front Neurorobot 10:6

    Article  Google Scholar 

  34. Filho AC, Dutra MS, Raptopoulos LS (2005) Modeling of a bipedal robot using mutually coupled Rayleigh oscillators. Biol Cybern 92(1):1–7

    Article  MathSciNet  MATH  Google Scholar 

  35. Zhang D, Zhang Q, Zhu X (2015) Exploring a type of central pattern generator based on Hindmarsh–Rose model: from theory to application. Int J Neural Syst 25(01):1450028

    Article  Google Scholar 

  36. Rostro-Gonzalez H, Cerna-Garcia PA, Trejo-Caballero G, Garcia-Capulin CH, Ibarra-Manzano MA, Avina-Cervantes JG, Torres-Huitzil C (2015) A CPG system based on spiking neurons for hexapod robot locomotion. Neurocomputing 170:47–54

    Article  Google Scholar 

  37. Lee YJ, Lee J, Kim K, Kim YB, Ayers J (2007) Low power CMOS electronic central pattern generator design for a biomimetic underwater robot. Neurocomputing 71(1):284–296

    Article  Google Scholar 

  38. Ambroise M, Levi T, Joucla S, Yvert B, Saighi S (2013) Real-time biomimetic central pattern generators in an FPGA for hybrid experiments. Front Neurosci 7:215

    Article  Google Scholar 

  39. Heidarpur M, Ahmadi A, Kandalaft N (2017) A digital implementation of 2D Hindmarsh-Rose neuron. Nonlinear Dyn 89:2259–2272

    Article  Google Scholar 

  40. Zhang J, Huang S, Pang S, Wang M, Gao S (2016) Optimizing calculations of coupling matrix in Hindmarsh–Rose neural network. Nonlinear Dyn 84:1303–1310

    Article  MathSciNet  Google Scholar 

  41. Barron-Zambrano JH, Torres-Huitzil C (2011) Two-phase GA parameter tunning method of CPGs for quadruped gaits. In: International joint conference on neural networks, San Jose, California, USA, pp 1767–1774

  42. Dahasert N, Öztürk İ, Kiliç R (2012) Experimental realizations of the HR neuron model with programmable hardware and synchronization applications. Nonlinear Dyn 70(4):2343–2358

    Article  MathSciNet  Google Scholar 

  43. Korkmaz N, Öztürk İ, Kılıç R (2016) The investigation of chemical coupling in a HR neuron model with reconfigurable implementations. Nonlinear Dyn 86(3):1841–1854

    Article  Google Scholar 

  44. Elson RC, Selverston AI, Huerta R, Rulkov NF, Rabinovich AI, Abarbanel HDI (1998) Synchronous behavior of two coupled biological neurons. Phys Rev Lett 81(25):5692–5695

    Article  Google Scholar 

  45. Hindmarsh JL, Rose RM (1984) A model of neural bursting using three couple first order differential equations. Proc R Soc Lond Biol Sci 221(1222):87–102

    Article  Google Scholar 

  46. Zhang JQ, Huang SF, Pang ST, Wang MS, Gao S (2015) Synchronization in the uncoupled neuron system. Chin Phys Lett 32(12):9–13

    Google Scholar 

  47. Wu K, Wang T, Wang C, Du T, Lu H (2016) Study on electrical synapse coupling synchronization of Hindmarsh–Rose neurons under Gaussian white noise. Neural Comput Appl 30(2):551–561

    Article  Google Scholar 

  48. Chen Y, Li L, Peng H, Xiao J, Yang Y, Shi Y (2017) Particle swarm optimizer with two differential mutation. Appl Soft Comput 61:314–330

    Article  Google Scholar 

  49. Awad NH, Ali MZ, Suganthan PN, Reynolds RG (2017) CADE: a hybridization of cultural algorithm and differential evolution for numerical optimization. Inf Sci 378:215–241

    Article  Google Scholar 

  50. Sharma TK, Pant M (2017) Shuffled artificial bee colony algorithm. Soft Comput 21(20):6085–6104

    Article  Google Scholar 

  51. Hu R, Wen S, Zeng Z, Huang T (2017) A short-term power load forecasting model based on the generalized regression neural network with decreasing step fruit fly optimization algorithm. Neurocomputing 221:24–31

    Article  Google Scholar 

  52. Li L, Yang Y, Peng H, Wang X (2006) Parameters identification of chaotic systems via chaotic ant swarm. Chaos Solitons Fract 28(5):1204–1211

    Article  MATH  Google Scholar 

  53. Haupt RL, Haupt SE (2004) Practical genetic algorithms, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  54. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical Report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department

  55. Dang TL, Hoshino Y (2018) Hardware/software co-design for a neural network trained by particle swarm optimization algorithm. Neural Process Lett 49:1–25

    Google Scholar 

  56. Huang HC, Chiang CH (2016) An evolutionary radial basis function neural network with robust genetic-based immunecomputing for online tracking control of autonomous robots. Neural Process Lett 44(1):19–35

    Article  Google Scholar 

  57. www.xilinix.com

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Acknowledgements

This research is supported by FDK-2016-6719 code project of Scientific Research Projects Coordination Unit of Erciyes University.

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  1. Department of Electrical and Electronics Engineering, Erciyes University, 38039, Kayseri, Turkey

    Nimet Korkmaz & Recai Kılıç

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  1. Nimet Korkmaz
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Correspondence to Nimet Korkmaz.

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Korkmaz, N., Kılıç, R. An Alternative Approach for Setting the Optimum Coupling Parameters Among the Neural Central Pattern Generators Considering the Amplitude and the Phase Error Calculations. Neural Process Lett 50, 645–667 (2019). https://doi.org/10.1007/s11063-019-10070-4

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