Sensorimotor Feedback in a Closed-Loop Model of Biological Rhythmic Movement Control

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Sensorimotor Feedback in a Closed-Loop Model of Biological Rhythmic Movement Control

1

M.F. Simoni

1

,

2

and S.P. DeWeerth

1

1

Laboratory for Neuroengineering, Georgia Institute of Technology, GA, USA

Abstract

— We have developed and analyzed a physi-

cal model of biological rhythmic-movement control. This

closed-loop system consists of: 1) a central pattern genera-

tor (CPG) with biologically relevant dynamics, 2) a linear

mechanical system, and 3) position feedback. We show how

the behavior of rhythmic movements can be controlled by

the mechanical properties and sensory feedback without al-

tering the intrinsic neural activity.

Keywords

— CPG, sensory feedback, movement control

I. Introduction

Rhythmic movements are an essential component to an-

imal locomotion (i.e. walking, crawling, swimming, etc.).

In many animals, oscillatory neural networks called central

pattern generators (CPGs) have been found to underlie

such rhythmic movements[1]. The dynamics of CPGs are

based upon the complex nonlinear dynamics of the individ-

ual neurons and the connectivity of the network[2]. It is

clear that for animals to move in a stable fashion through

a complex and changing environment, the CPGs must re-

ceive some form of sensory information. In this paper we

demonstrate a possible role of proprioceptive feedback in

the form of position information using a physical model of a

closed-loop biological rhythmic-movement control system.

II. Physical Model of the Closed-Loop System

The closed-loop system consists of three major compo-

nents: 1) a CPG, 2) a mechanical system, and 3) sensory

feedback. The CPG drives the mechanical system with its

rhythmic electrical pattern. The sensors detect the posi-

tion of the mechanical system and provide this information

to the CPG via synaptic input.

Our CPG is a half-center oscillator, which consists of

two neurons with reciprocal inhibition. The neurons are

implemented with an analog integrated circuit architec-

ture that we developed, and which we refer to as the sil-

icon neuron[3]. The silicon neuron is essentially a single-

compartment conductance-based model. Each silicon neu-

ron is implemented with six voltage-dependent conduc-

tances. The dynamics of the silicon neuron are sufficiently

matched to the Hodgkin-Huxley formalism to elicit com-

plex bursting behavior as shown in Figure 1.

The mechanical system represents an antagonistic pair

of muscles driving a mass that is restricted to movements

along a single axis. Because our focus was on the neu-

ral dynamics, which are nonlinear and complex, we used

principally linear mechanical components to simplify the

analysis. As such, the motor neurons were represented

with a linear gain and the active force generated by the

muscles was determined by low-pass filtering the spikes of

the half-center oscillator neurons. We assumed the muscles

were active such that their length and velocity dependent

nonlinearities were minimal. The resulting linear mechan-

ical system can be described by the transfer function of a

second order system in the Laplace domain, for which the

input is the active force created by the CPG and the output

is the position of the mass.

H

(

s

) =

1

/m

s

2

+

ω

0

Q

s

+

ω

2

0

(1)

The feedback represents two proprioceptive organs that

sense unidirectional position. Again we simplified the sen-

sors and assumed the output of each sensor is equivalent

to the absolute value of a half-wave rectified version of the

position. The feedback synaptic current is described with

the following equations

I

fb

= ̄

g

fb

tanh(

S

fb

x

s

)(

E

fb

−

V

SN

) (2)

where

I

fb

is the feedback synaptic current, ̄

g

fb

is the max-

imal conductance,

S

fb

determines the value of at which

the conductance saturates,

x

s

is the output of the sensor,

E

fb

is the synaptic reversal potential, and

V

SN

is the mem-

brane potential. The feedback configuration is ipsilateral

inhibition, such that as a neuron of the half-center oscilla-

tor causes the mass to move in a particular direction, that

neuron is inhibited by the feedback. Thus, the feedback is

negative.