Research Papers

A Neuronal Model of Central Pattern Generator to Account for Natural Motion Variation

[+] Author and Article Information
Reza Sharif Razavian

Motion Research Group,
Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: rsharifr@uwaterloo.ca

Naser Mehrabi

Motion Research Group,
Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: nmehrabi@uwaterloo.ca

John McPhee

Fellow ASME
Motion Research Group,
Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: mcphee@uwaterloo.ca

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 23, 2015; final manuscript received July 7, 2015; published online August 26, 2015. Assoc. Editor: Ahmet S. Yigit.

J. Comput. Nonlinear Dynam 11(2), 021007 (Aug 26, 2015) (9 pages) Paper No: CND-15-1019; doi: 10.1115/1.4031086 History: Received January 23, 2015

We have developed a simple mathematical model of the human motor control system, which can generate periodic motions in a musculoskeletal arm. Our motor control model is based on the idea of a central pattern generator (CPG), in which a small population of neurons generates periodic limb motion. The CPG model produces the motion based on a simple descending command—the desired frequency of motion. Furthermore, the CPG model is implemented by a spiking neuron model; as a result of the stochasticity in the neuron activities, the motion exhibits a certain level of variation similar to real human motion. Finally, because of the simple structure of the CPG model, it can generate the sophisticated muscle excitation commands much faster than optimization-based methods.

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Ijspeert, A. J. , 2008, “Central Pattern Generators for Locomotion Control in Animals and Robots: A Review,” Neural Networks, 21(4), pp. 642–653. [CrossRef] [PubMed]
MacKay-Lyons, M. , 2002, “Central Pattern Generation of Locomotion: A Review of the Evidence,” Phys. Ther., 82(1), pp. 69–83. [PubMed]
Brown, T. , 1914, “On the Nature of the Fundamental Activity of the Nervous Centres; Together With an Analysis of the Conditioning of Rhythmic Activity in Progression, and a Theory of the Evolution of Function in the Nervous System,” J. Physiol., 48(1), pp. 18–46. [CrossRef] [PubMed]
Noble, J. W. , 2010, “Development of a Neuromechanical Model for Investigating Sensorimotor Interactions During Locomotion,” Ph.D. thesis, University of Waterloo, ON, Canada.
Rybak, I. A. , Shevtsova, N. A. , Lafreniere-Roula, M. , and McCrea, D. A. , 2006, “Modelling Spinal Circuitry Involved in Locomotor Pattern Generation: Insights From Deletions During Fictive Locomotion,” J. Physiol., 577(Pt. 2), pp. 617–639. [CrossRef] [PubMed]
Rybak, I. A. , Stecina, K. , Shevtsova, N. A. , and McCrea, D. A. , 2006, “Modelling Spinal Circuitry Involved in Locomotor Pattern Generation: Insights From the Effects of Afferent Stimulation,” J. Physiol., 577(Pt. 2), pp. 641–658. [CrossRef] [PubMed]
Ekeberg, O. , 1993, “A Combined Neuronal and Mechanical Model of Fish Swimming,” Biol. Cybern., 69(5–6), pp. 363–374. [CrossRef]
Ekeberg, O. , and Grillner, S. , 1999, “Simulations of Neuromuscular Control in Lamprey Swimming,” Philos. Trans. R. Soc., B, 354(1385), pp. 895–902. [CrossRef]
Kozlov, A. , Huss, M. , Lansner, A. , Kotaleski, J. H. , and Grillner, S. , 2009, “Simple Cellular and Network Control Principles Govern Complex Patterns of Motor Behavior,” Proc. Natl. Acad. Sci. U. S. A., 106(47), pp. 20027–20032. [CrossRef] [PubMed]
Ijspeert, A. J. , 2001, “A Connectionist Central Pattern Generator for the Aquatic and Terrestrial Gaits of a Simulated Salamander,” Biol. Cybern., 84(5), pp. 331–348. [CrossRef] [PubMed]
Ijspeert, A. J. , Crespi, A. , Ryczko, D. , and Cabelguen, J.-M. , 2007, “From Swimming to Walking With a Salamander Robot Driven by a Spinal Cord Model,” Science, 315(5817), pp. 1416–1420. [CrossRef] [PubMed]
Harischandra, N. , Knuesel, J. , Kozlov, A. , Bicanski, A. , Cabelguen, J.-M. , Ijspeert, A. J. , and Ekeberg, O. , 2011, “Sensory Feedback Plays a Significant Role in Generating Walking Gait and in Gait Transition in Salamanders: A Simulation Study,” Front. Neurorobotics, 5, p. 3.
Sharif Shourijeh, M. , and McPhee, J. , 2014, “Forward Dynamic Optimization of Human Gait Simulations: A Global Parameterization Approach,” ASME J. Comput. Nonlinear Dyn., 9(3), p. 031018. [CrossRef]
Eliasmith, C. , Stewart, T. C. , Choo, X. , Bekolay, T. , DeWolf, T. , Tang, Y. , Tang, C. , and Rasmussen, D. , 2012, “A Large-Scale Model of the Functioning Brain,” Science, 338(6111), pp. 1202–1205. [CrossRef] [PubMed]
Eliasmith, C. , 2013, How to Build a Brain: A Neural Architecture for Biological Cognition, Oxford University Press, New York.
DeWolf, T. , and Eliasmith, C. , 2011, “The Neural Optimal Control Hierarchy for Motor Control,” J. Neural Eng., 8(6), p. 065009. [CrossRef] [PubMed]
Sharif Shourijeh, M. , and McPhee, J. , 2013, “Optimal Control and Forward Dynamics of Human Periodic Motions Using Fourier Series for Muscle Excitation Patterns,” ASME J. Comput. Nonlinear Dyn., 9(2), p. 021005. [CrossRef]
Silva, M. P. T. , and Ambrósio, J. A. C. , 2003, “Solution of Redundant Muscle Forces in Human Locomotion With Multibody Dynamics and Optimization Tools,” Mech. Based Des. Struct. Mach., 31(3), pp. 381–411. [CrossRef]
Garner, B. A. , and Pandy, M. G. , 2001, “Musculoskeletal Model of the Upper Limb Based on the Visible Human Male Dataset,” Comput. Methods Biomech. Biomed. Eng., 4(2), pp. 37–41. [CrossRef]
Lebiedowska, M. K. , 2006, “Dynamic Properties of Human Limb Segments,” International Encyclopedia of Ergonomics and Human Factors, 2nd ed., Vol. 3, W. Karwowski , ed., CRC Press, London, p. 137.
Leva, P. D. , 1996, “Adjustments to Zatsiorsky–Seluyanov's Segment Inertia Parameters,” J. Biomech., 29(9), pp. 1223–1230. [CrossRef] [PubMed]
Eliasmith, C. , and Anderson, C. H. , 2003, Neural Engineering Computation, Representation, and Dynamics in Neurobiological Systems, MIT Press, Cambridge, MA.
Tripp, B. , 2014, “Software—Bryan Tripp,” accessed Dec. 4, 2014, http://bptripp.com/node/3
Anderson, F. C. , and Pandy, M. G. , 2001, “Dynamic Optimization of Human Walking,” ASME J. Biomech. Eng., 123(5), pp. 381–390. [CrossRef]
Anderson, F. C. , and Pandy, M. G. , 2001, “Static and Dynamic Optimization Solutions for Gait Are Practically Equivalent,” J. Biomech., 34(2), pp. 153–161. [CrossRef] [PubMed]
An, K.-N. , Kwak, B. M. , Chao, E. Y. , and Morrey, B. F. , 1984, “Determination of Muscle and Joint Forces: A New Technique to Solve the Indeterminate Problem,” ASME J. Biomech. Eng., 106(4), pp. 364–367. [CrossRef]
Happee, R. , and Van der Helm, F. C. T. , 1995, “The Control of Shoulder Muscles During Goal Directed Movements, an Inverse Dynamic Analysis,” J. Biomech., 28(10), pp. 1179–1191. [CrossRef] [PubMed]
Prilutsky, B. I. , and Zatsiorsky, V. M. , 2002, “Optimization-Based Models of Muscle Coordination,” Exercise Sport Sci. Rev., 30(1), pp. 32–38. [CrossRef]
Thelen, D. G. , and Anderson, F. C. , 2006, “Using Computed Muscle Control to Generate Forward Dynamic Simulations of Human Walking From Experimental Data,” J. Biomech., 39(6), pp. 1107–1115. [CrossRef] [PubMed]
Ackermann, M. , and van den Bogert, A. J. , 2010, “Optimality Principles for Model-Based Prediction of Human Gait,” J. Biomech., 43(6), pp. 1055–1060. [CrossRef] [PubMed]
Erdemir, A. , McLean, S. , Herzog, W. , and van den Bogert, A. J. , 2007, “Model-Based Estimation of Muscle Forces Exerted During Movements,” Clin. Biomech., 22(2), pp. 131–154. [CrossRef]
Mehrabi, N. , Sharif Razavian, R. , and McPhee, J. , 2015, “A Physics-Based Musculoskeletal Driver Model to Study Steering Tasks,” ASME J. Comput. Nonlinear Dyn., 10(2), pp. 1–8.
Churchland, M. M. , Cunningham, J. P. , Kaufman, M. T. , Foster, J. D. , Nuyujukian, P. , Ryu, S. I. , and Shenoy, K. V. , 2012, “Neural Population Dynamics During Reaching,” Nature, 487(7405), pp. 51–56. [PubMed]
Thrasher, T. A. , Zivanovic, V. , McIlroy, W. , and Popovic, M. R. , 2008, “Rehabilitation of Reaching and Grasping Function in Severe Hemiplegic Patients Using Functional Electrical Stimulation Therapy,” Neurorehabilitation Neural Repair, 22(6), pp. 706–714. [CrossRef] [PubMed]
Kapadia, N. M. , Nagai, M. K. , Zivanovic, V. , Bernstein, J. , Woodhouse, J. , Rumney, P. , and Popovic, M. R. , 2013, “Functional Electrical Stimulation Therapy for Recovery of Reaching and Grasping in Severe Chronic Pediatric Stroke Patients,” J. Child Neurol., 29(4), pp. 1–7.
Thelen, D. G. , 2003, “Adjustment of Muscle Mechanics Model Parameters to Simulate Dynamic Contractions in Older Adults,” ASME J. Biomech. Eng., 125(1), pp. 70–77. [CrossRef]
Winters, J. M. , and Stark, L. , 1988, “Estimated Mechanical Properties of Synergistic Muscles Involved in Movements of a Variety of Human Joints,” J. Biomech., 21(12), pp. 1027–1041. [CrossRef] [PubMed]


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Fig. 1

Schematic of the musculoskeletal forearm model

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Fig. 2

The layered structure of the CPG controller

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Fig. 3

(a) An example for the average firing rate of 100 neurons to a changing stimulus. (b) The synaptic weight between the 100 neurons is optimally calculated, so that the weighted sum of the neurons' firing rate represents the square of the input stimulus.

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Fig. 4

Schematic of CPG controller implementation with spiking neurons

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Fig. 5

The reference elbow angle, θdes; three periods of motion are shown

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Fig. 6

The optimization framework to find the Fourier series parameters, which will be used in the online generation of muscle excitation signals

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Fig. 7

Optimal Fourier series coefficients for BRD muscle at different periods of motion

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Fig. 8

Comparison of the experimental data with the CPG model response. Left column compares the muscle excitation patterns in one cycle with the average experimental EMGs. Right column compares the resulting motion between the model and experiments. The results are shown for two speeds of motion: (a) fast motion, T = 1.5 s and (b) slow motion, T = 3 s.



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