An analogue recurrent neural networks

Edith Cowan UniversityResearch Online ECU Publications 2005 An analogue recurrent neural networks for trajectory learning and other industrial applications Ganesh Kothapalli Edith Cowan

Edith Cowan University

Research Online

ECU Publications

2005

An analogue recurrent neural networks for

trajectory learning and other industrial applications

Ganesh Kothapalli

Edith Cowan University

This conference paper was originally published as: Kothapalli, G (2005) An analogue recurrent neural networks for trajectory learning and other industrial applications Proceedings of 3rd IEEE International Conference on Industrial Informatics, 2005 INDIN '05 2005 (pp 462 - 467 ) Perth IEEE Original article available here

This Conference Proceeding is posted at Research Online.

http://ro.ecu.edu.au/ecuworks/2889

20053rd IEEE International ConferenceonIndustrialInformatics(INDIN)

An analogue recurrent neural network for trajectory learning and

other industrial applications

Ganesh Kothapalli EdithCowanUniversity,SchoolofEngineering andMathematics,Joondalup, WA 6027, Australia

e-mail:g.kothapalligecu.edu.au

Abstract

Areal-time analoguerecurrentneural network(RNN) can

extractandlearn the unknown dynamics (and features) ofa

typical control system such as a robot manipulator The

task at hand is a tracking problem in the presence of

disturbances With referenceto the tasks assigned to an

industrial robot, one important issue is to determine the

motion of thejointsandtheeffector of the robot Inorder

tomodel robotdynamicswe use aneural network thatcan

beimplemented in hardware

Thesynaptic weightsaremodelledasvariablegain cells

that canbe implemented with afew MOStransistors The

network output signals portray the periodicity and other

characteristics of the input signal in unsupervised mode

For the specific purpose ofdemonstrating the trajectory

learning capabilities, a periodic signal with varying

characteristics is used The developed architecture,

however, allows formoregeneral learning taskstypical in

applications ofidentification and control Theperiodicity

of the input signal ensuresconvergence of theoutput to a

limitcycle On-line versions of thesynaptic updatecanbe

formulated using simple CMOS circuits Because the

architecture depends on the network generating a stable

limit cycle, and consequently a periodic solution which is

robust over an interval of parameter uncertainties, we

currently place the restriction ofaperiodic format for the

input signals The simulated network contains

interconnected recurrent neurons with continuous-time

dynamics The system emulates random-direction descent

of the error as a multidimensional extension to the

stochastic approximation.Toachieveunsupervised learning

in recurrent dynamical systems we propose a synapse

circuit which hasaverysimplestructureandis suitable for

implementationin VLSI

Index Terms-Artificial neural network (ANN), Electronic

Synapse,trajectory tracking,Recurrent Neurons.

I INTRODUCTION

Recently, interest has been increasing in using neural

networks for the identification of dynamic systems

Feedforward neural networksareusedtolearn static

input-outputmaps Thatis, givenaninputset thatismappedinto

a corresponding output set by some unknown map, the feedforwardnet is usedto learn this map The extensive use of these networks is mainly due to their powerful

approximation capabilities Similarly, recurrent neural

networks are natural candidates for leaming dynamically varying input-output For instance, one class ofrecurrent

neural networks which is widely used are the so-called

Hopfield networks In this case, the parameters of the

network have a particular symmetric structure and are

chosen so that the overall dynamics of the network are

asymptotically stable [1] Ifthe parameters do nothavea

symmetric structure the analysis of the network dynamics becomes intractable Despite the complexity of the internal dynamics of recurrent networks, it has been shown

empirically that certain configurations are capable of learningnon-constanttime-varying motions

Thecapability ofRNNsofadapting themselvestoleam certain specified periodic motions is due to their highly nonlinear dynamics So far, certain types of cyclic recurrent neural configurations have been studied These

types of recurrent neural networks are well known,

especially in the neurobiology area, where they have been studied for abouttwenty years The existence ofoscillating

behaviour in certain cellular systems has also been documented [1-3,10] Such cellular systems have the

structureofwhat, inengineering applications, hasbecome known as a recurrent neural network Thus the neural network behaviourdepends not only onthe current input

(as in feedforward networks) but also on previous

operationsofthe network[4]

II ANN FORTRAJECTORYTRACKING

In this paper we treat a neural network configuration relatedtocontrol systems Wedescribeaclass of recurrent neural networks which are able to learn and replicate

autonomously a particular class of time varying periodic

signals

Neural networks are used to develop a model-based controlstrategyfor robotpositioncontrol Inthispaperwe

investigatethefeasibility ofapplying single-chipelectronic (CMOSIC) solutionstotrackrobottrajectories

Fig 1 The blockdiagramof the proposed recurrent neural

network

Neuralnetwork withdynamicneurons

The blockdiagramof thetypeof network understudyis

illustrated in theFig. 1 Inthis figure u(t)is the inputand

v,(t) is the output of the network A recurrent network of

thetypedepictedin theFig. 1 isdescribedbythefollowing

systemofdifferentialequations

XI = RIV- RIC,dx

R

va RI

v'iz, =_x _RIv

Ra

= R,v T

Ra RI

=-_xI +yi(x2)

Similarly,

Vr2X2 =-_x2 ±yf/(XI) + U(t)

Finally,fortheoutputofthecircuit,wehave,

=-vx +WIV(XI) + w)2 Y02)

Thetimeconstants v, z-l,and r2govern thedynamicsof the

network, providing first order low-pass filtering in the

evolution of theneuron statevariables Amoreelaborate

model of neural dynamics would incorporate individual

Subcimudshow?

Ma,

R 2"

R'2

FOX

adjustable time constants at the level of the synaptic

contributions [5-7].

AnalternativetypeofRNNthatcanbe describedbythe differentialequations givenbelowcanalsobe built with the electronic neurons discussed in the next section We see

that the above schematic (Fig 1) implements the neural network with only twodynamic neurons (neuron circuit is shown in Fig 2.). The equations of the branch currents (Iml and Im2) discussed in the next section suggest the synapses are suitable to implement both types of RNN

represented byeither(1)or(2).

The simulated network contained six fully

interconnected recurrent neurons with continuous-time

dynamics. Thesimulated neural networkcan be described

byageneralsetofequationssuchastheonesgivenbelow

N

r5',=ýWi-exp(y,) -A Lexp(yj)

N

(2)

withx,(t)theneuronstatevariablesconstitutingtheoutputs

of thenetwork,x,(t) the external inputstothenetwork,and

ặ)asigmnoidalactivation function The value for -riskept

fixed anduniform in thepresentimplementation. Thereare

several free paramneters, to be optimally adjusted by the

learningprocess For example ifwe implementafully in-terconnected RNN, there will be 36 connection strengths Wijand -6thresholds Oj.

The so called triggering nonlinear function of the

neurons associated with this network is taken as tanh(x,) and is shown in the Fig. 1 as VI(xi). However, it is likely

that a larger class of triggering functions with the same

propertiesofođity,boundedness,continuity, monotonicity

and smoothness could be considered Such triggering

functions include arctan(x), (1I+ e-x )1, e x2 etc Inthe

463

next section we will introduce a synaptic circuit that

implements theoiw showninFig 1

III RECURRENT NEURON CHARACTERISTICS

Inthesynaptic circuit, thecurrent ofM5, whichwe

de-note asIM5acts as an excitatorycurrentwhich increases the

membrane potential vc, while the currents ofMl andM2,

whichwedenoteasIMI andIM2,respectively, act as

lateral-and self-inhibitory currents which decrease the membrane

potential Inthis synaptic circuit, the node equationsatthe

nodev,are asfollows:

c" =IM5 /M1 IM2

where IMa stands for the current of transistor Ma of the

synaptic circuit.Itshould be noticed that the left side of the

above equation represents the current of the capacitor,

whilethe right side ofthe equation is given by the linear

combination of saturationcurrents ofMOS transistors

op-erating in the subthreshold (weak inversion) region The

inputtransistorsareoperatedinweakinversion fortwo

rea-sons Inthisconfiguration, (1)theydeliver maximal

trans-conductance for a given current and (2) low vgs and Vds

voltages are needed forlarge swing This implies that the

network caneasily be implemented by the MOS circuit of

Figure-2operating in the subthresholdregion[8]

Atransistorcanbebiased indifferentwaysbychoosing

the dependent variableas current orvoltage Forvoltage

biasing, thegate-source voltage of the device is the same

and currentis thedependentvariable Forcurrentbiasing,

the current in the devicesisthesamebutthevoltageis the

dependent variable Current-mode circuits should be

bi-ased deep in saturation for best accuracy Inthe case of

voltage-mode circuits, best accuracy is obtained in

weak-inversion

In the subtrhresholdregion ofoperation,'M2 isideally

given by

JM2 =10 exp(v, /VT)

V tanh(x1) ,

ofa voltage, VT= kT/q (k is the Boltzmann's constant, T

the temperature, and q the charge of an electron), q measuresthe effectivenessof the gate potential, v1, is an extemal input voltage, C represents a capacitance, IX, is a

MOStransistor parameter, and/ represents a gainconstant

Wehave conformedto the standard notation in writing the CMOS equations above to represent the dynamics of the

circuit [9]

The current mirror consisting ofM2and M3 impliesthat the output current of the synaptic circuit IM3 is equal to

IM2 ThecurrentIMSwhichdependsontheinput vrn actsas

IM5 =I0 exp(vrn /I 17V). Thevoltage v,isamplified by

the common source amplifier consisting oftransistor M3

and its loadM4

VDD

Fig.2 Thecircuitdiagramoftheproposedrecurrent neuron.

Vc

Figure 3 Small-signal equivalentofthesynapticcircuit

Similarly, Im, isgivenas

IMI =10 exp(vx / 77VT)

interms of the gate-sourcevoltage vtofMI, as long as it

operates in the saturation region (vtr > 4 VT). where v,

represents atransformed variablepossessingthedimension

Analysis of the synapse circuit

The synaptic circuit can be realized in two different formats The format shown in Fig.2 implements the

synapseas againcontrolledvoltage amplifier Analtemate format ofthe synapse (shown in Fig 4) is based on a

transimpedance gain function The main difference between thesetwocircuits is thepresence ofanadditional

., in

feedback transistor placed between v, and output v0

(CompareFigs.2 and4.) Inbothcasesthegateterminal

of transistor Ml can be used to control the gain of the

synapse In this case the small-signal equivalent circuit

shown inFig.3canbeusedtoshow thatthevoltage gainis

givenby:

VI(S) gm2 +gdl +SCc

In thiscase, the outputof the synapse, co *yV(xI) goes

through the output stage integrator and the voltage vx is

usedto control the gate of transistor Ml of the synapse

Hence the synapse behaves like a variable gain amplifier

controlledby the variable conductancegdl Inotherwords,

w,isafunction ofthestatevx

Ms.1

vv

Vin

Fig.4 Thecircuitdiagram oftheproposed synapsethat

im-plementsatransimpedance gainfunctionZ7(s).

IV A NEURALNETWORK BASED

CONTROLLER FOR ROBOT POSITION

CONTROL

Wetrainaneural networktolearnand mimicmovementof

arobotmanipulator A block diagram of such a setup is

depictedinFig.5 Theneural network leams the behaviour

of the robot manipulator over certain time horizon The

neural network alsooptimizes the control action such that

the error between theoutput of the robotmanipulator and

the reference(desired) trajectoryis minimized

Effector Trajectory Referencetrajectory

Fig 5 Block diagram of a neural network based robot controlsystem

Neural network withsigmoidalneurons

In theproposedrecurrentneuralnetwork(Fig 1)weneeda

sigmoidal yI(xi) function This sigmoidal circuit shoule be suitable forimplementation in CMOS Wewillintroducea

simple circuit that can implement the sigmoidal function Fig.6 CircuitdiagramtoimplementtheVI(xi)finction

VDD

The circuit shown in Fig 6 is a linearized transconductorwhoseoutput currention, is proportional to

tanh(vj,). In this circuit, the G. is derived from a cross

coupled pair of matched transistors (M7 and M8) operating

in the triode region In this configuration, the Gm is controlledwith gatevoltagesVc1 and

Vc2-The possibility ofbuilding the entire electronicsystem

discussedinthispaperusing CMOS technology is currently explored Inthe absence ofsuchahardwaresystem, we are

465

2

studying the performance by simulating an operational

amplifier based conceptual circuit model

V SIMULATIONOF THEPROPOSED SYSTEM

The novel concepts formulated in this paper can be

experimentally verified by the manufacture ofaprototype

electronic system The circuits needed for such

implementation are presently simulated using CAD

packages For example the circuits ofsigmoidal transfer

function (Fig 6) and synaptic networks (Figs 2 and4.) were

designed using 0.18 micron CMOS technology These

simulations confirmed the scalability of the modularized

architectureofthelearning algorithm We areverifying the

robustness of the architecture under technology parameter

perturbations These simulation results will be discussed

during the presentationattheconference

As an alternative to the experimental verification, we

have simulated the system of differential equations that

representtheproposedrecurrent neural network The task

set for this verification is to apply a variety of input

waveforms to the simulator and observe the output

waveforms Theinputstothesimulatorexplored comprise

a variety of waveforms such as triangular, saw-tooth,

square and sinusoids All these input waveform

characteristics such as frequency, amplitude and phase

werevaried and theabilityoftheneurons tosettletoalimit

cyclewereobserved

VI INDUSTRIALAPPLICATIONS

The architectureof ananalogrecurrentnetwork that can

learn a continuous-time trajectory is presented The

presentation shows that the RNN does not distinguish parameters based on a presumed model ofthe signal or system for identification Simulation of such an autonomoustracking ofatrajectory is shown in Fig.7 The

vertical (y-axis) shows the robot joint position in radians

and thehorizontal (x-axis) shows time inmsec

In many decision making processes such as

manufacturing, aircraft control, robotics etc, we come acrossproblems of controlsystemsthatarehighlycomplex,

noisy, and unstable A tracking system or agent must be

built that observes thestateof the environment andoutputs

a signal that affects the overall system in some desirable way The RNN presented here is suitable for such tasks

because it is general and robust enough to respond

effectively to conditions not explicitly considered or

completely modelled by the designer

The architecture of the analog RNN discussed here is

easiertoimplementin CMOSVLSItechnology TheRNN

presented is a very small network consisting only of two

synaptic weights However, itwasabletolearnperiodicity from the appliedsignals in unsupervised mode Itshould

be noted that this network is scalable AlargeRNNof this

structure canbe built withrelativelylittle hardware andcan

be used for a variety of applications in control,

instrumentation and signal processing applications

Fig 7 The reference trajectory (red) compared with tracking

RNNoutput

Fig.8 Output of the RNN for anapplied varying input

VII CONCLUSIONS The complexity of real world systems often defy

mathematicalanalysis, and, most interestingtasks in these environments are too hard for designing a controller

strategyby hand Both of theseproblemscanbe avoided

by learning from direct interaction given two essential

components:asimulator that behaves like theenvironment,

andalearningmechanism that ispowerful enoughtosolve

thetask

1

0.8

0.6 -.

0.4

0.2-I

In this paper we discussed the application of;

analogue recurrent neural network to learn and track ti

dynamics of an industrial robot The observations ma(

from this study suggestthatRNNs(similartothose inFi

1) can be applied to the control of real systems th

manifest complex properties - specifically, hig

dimensionality, non-linearity and requiring continuoi

action Examples of these real systems include aircri

control, satellite stabilization, and robot manipulat

control

We conclude that robust controllers of partial

observable (non-Markov) systems require real-tin

electronic systems that can be designed as single-ch

IntegratedCircuits (CMOS IC) This paperexploredsu

techniques andidentified suitable circuits

an

he de

g

I at

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