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Adaptive Control for Robot Manipulators

Budi Rachmanto

Scho ol of Information Science,

Japan Advanced Institute of Science and Technology

February 14, 1997

Keywords: simple adaptivecontrol, multi-variablemodel reference adaptivesystem,

high-speed control,nonlinear compensator,multi-joint rob ot .

Abstract

Nowadays, the use of multi-joint/multi-linkedrobots in industrial world has became

widely spread. Various usage of these robots leads to the necessity of high-precision and

high-speed motion controllers,and for this reason many researchsare being p erformed.

Once we plan to build a controller for a robot, usually we use conventional feedback

control techniques. First, we estimate the robot model, adjust its parameters, and then

calculate the feedback coecients. However, with these rules, the control accuracy and

reliability is very much aected by the numerical expression of the object (rob ot itself),

or inuencedby friction, measurement errors,noises, and other disturbances.

To solve these problems, adaptive control methods had been intro duced. Two typ-

ical examples of this control method are MRACS (Mo del Reference Adaptive Control

System) and STR (Self-Tuning Adaptive Regulator). However, the structures of these

controllersare verycomplicated. Forinstance, forasingle-inputsingle-outputplantwith

n-dimensions, MRACS needs as manyas 4n integrators.

Forthese reasons, weintroduce Simple Adaptive Control(SAC), a control technique

that has a relativelysmall quantity of calculation inits controller,compared with other

methods of adaptivecontrol.

SAC is a new typ e of model-reference adaptive control technique. Compared with

other adaptive control methods like model-reference adaptive control system (MRACS),

SACismore generousand easytouse. ThemaindierencebetweenMRACSandSACis

that,whileMRACScanb eappliedonlytosystemthatsatisesSPRcondition,SAConly

Copyrightc 1997byBudiRachmanto

Compensator (PFC)F(s) isusable, suchthat the augmented plant

G

a

(s)=G

p

(s)+F(s)

becomes ASPR.

WefoundthatSAChassomecapabilitiestogivebetterperformancethanPIDcontrol

methods. Thus, we considered this control technique ismore suitablefor robotic control

experiments. For a multi-linked rob ot, multi-link synchronous control will become a

necessity. SACisexp ectedtoreduceinterferencesb etweenlinks,anditwillbeveryuseful

for such this multi-linksynchronouscontrolsystem. We haveevaluatedthe use of Multi

VariableSAC(also called MIMO-SAC, Multi-Input Multi-OutputSAC). The result was

that, MIMO-SAC is veryuseful for small systems with small numb er of inputs/outputs.

However,unfortunatelyitisstillnotsuitableforlargescaledsystemswithlargenumb erof

inputs/outputs. Thebiggerthesystem,thenumb erofcontrollercells(integrators,adders,

multipliers, etc.) increasesinaquadraticorder,andthusthecalculationafcontrolsignals

becomes verycomplex.

Asdescribedabove,SAChas arobustnessintermsofplantstabilitycondition. More-

over,the assignment ofplant transfercharacteristicsisgivenina feedforward loop(from

this point SAC takes the form of a 2-DOF 1

control structure). We found that the pat-

tern of the inverse of transfer functions matrix is identicwith the connection formation

between subsystems.

The feedforward controllertakesthe form of

G

c

(s)=G

p (s)

01

G

m (s)

andthus,ifwecho oseasimplereferencemo deltobetracked,theshapeoftransferfunction

matrix of the controller only depends on the inverse of transfer functions matrix of the

plant. Using these sp ecial characteristics, we can progressively remove the unnecessary

controller cells.

Theotherproblemthatneedstob esolvedisthatSAC(likeMRACSorothermethods

of adaptive controller)wasdevelop ed tosolvethe control problems inlinearsystems. On

the contrary, robot is a typical example of nonlinear system. SAC will not match this

condition if it isused without any improvements.

One solution we found is that, ifrobot dynamics can be describedin a quasi-formula

_

x(t)=Ax(t)+Bu(t)+h(t;x(t))

that split the dynamics into linear and nonlinear parts, then we can build a nonlinear

compensatortocompensatetherobotnonlinearityaggresively. Althoughthis mechanism

is mainly expected to compensate the linearity of the robot, it can also b e expected to

compensatethe interferencesbetween links.

To alleviate chattering (furious vibration of input signals) that may be occured dur-

ing the control process, it is also recommended to use PI algorithm in the parameters

adjustment mechanism.

1

degree-of-freedom

other methods of (very complex) adaptive systems. SAC is easy to use in practical

experiments, because it only needs the plant satises ASPR condition or (even) non-

ASPRplant that ASPR-able,comparing with the conventionalmodel reference adaptive

systems that require SPR plants.

However,foralarge scaledsystem, the useof MIMO-SACcomesupagainstacontrol

complexity problem.

In this thesis we intro duced how to solve this complexity, and also how to deal with

systems with nonlinear characteristics.