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Control of a one-link arm by burst signal generators

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Abstract

The focus of this paper is the study of stability and point-to-point movement of a one-link arm. The sagittal arm has two musculotendon actuators, two neural oscillators that generate burst signals as motoneuron inputs, and spindles and Golgi tendon organs for extrinsic reflex feedbacks. It is shown that coactivation leads to intrinsic position and velocity feedback, and that the tendons introduce intrinsic force and rate of force feedback. In addition, the integrating effects of the tendons are studied when the actuator is constructed from a large number of identical fibers that are excited by alpha signals whose arrival times at the fiber are randomly distributed. Each of the musculotendon actuators receives two input signals — a burst signal analogous to alpha inputs and a conventional analogue signal that represents fusimotor input to the spindles. The process of combining burst signals and conventional analogue signals is studied. Simulation results show that the movement of the system with burst signals as inputs has overshoot and speed similar to the system with analogue signals.

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Abbreviations

α:

strength of self-inhibition 0.2

β:

decay constant 0.14

ɛ:

small positive fraction for the spindle feedback signal 0.2

η:

gain constant of the low-pass filter 20

μ:

quadratic nonlinearity parameter 0.4

Δs,Δg :

delay of feedback signal

δx,δy :

threshold values of the burst signal generator 0.4, 0.6

λx,λy :

gain parameters of the burst signal generator 0.05, 0.05

κ:

bandwidth of the low-pass filter 20

v:

small positive fraction for Golgi tendon organ signal 0.1

θe :

target angle π/2

τj :

delay constant

τx,τy :

time constants of excitatory and inhibitory components 0.9, 1

B:

viscous constant of the single contractile element 160

C:

passive elastic constant of the single contractile element 110

F:

actuator force

Fth :

threshold force 0 (N)

I:

external input to the burst signal generator from higher control center

J:

moment of inertia about the base 0.075 (kg · m2)

K:

tendon stiffness 55 000, 43 000 (N/m)

N:

total number of contractile fibers in one actuator 50

P:

gain matrix of spindle feedback signal

Q:

gain matrix of Golgi tendon organ

Ri :

firing rate to the single-fiber actuator

W:

mutual connection of the burst signal generator 1.2,-0.7

T:

synaptic strength parameter in self-component Txx=1.0, Txy=1.9, Tyx = 1.3, Tyy = 1.2

Tb :

period of the burst signal 70 (ms)

Vj :

tension of the fiber

a:

moment arm of the actuator 0.04 (m)

b:

viscous constant of the contractile fiber 3.2

c:

passive elastic constant of the contractile fiber 15.5525

d:

distance of the center of gravity from the base 0.18(m)

e:

small input signal

g:

gravity constant 10 (m/s2)

k:

amplification factor 7.0728

l0 c :

initial length of the contractile fiber 0.3 (m)

l0 t :

initial length of the tendon 0.05 (m)

l0 :

threshold length — 0.0618, 0.0618 (m)

m:

mass of the arm 1.9 (kg)

n:

amplification factor 40

ri :

firing rate to the multifiber actuator

rs :

delayed spindle feedback signal

rg :

delayed Golgi tendon organ feedback

-x, -y:

average values of excitatory and inhibitory activity 0.2, 0.2

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Authors and Affiliations

  1. Department of Electrical Engineering, Ohio State University, 2015 Neil Ave., 43210-1272, Columbus, OH, USA

    Jaywoo Kim & Hooshang Hemami

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  1. Jaywoo Kim
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  2. Hooshang Hemami
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Kim, J., Hemami, H. Control of a one-link arm by burst signal generators. Biol. Cybern. 73, 37–47 (1995). https://doi.org/10.1007/BF00199054

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