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using Articial Potential Field Technique

Hirokazu Tanaka

Scho ol of Information Science,

Japan Advanced Institute of Science and Technology

February 15, 1999

Keywords: Conguration Space, Delaunay Graph,Potential Field,Motion Planning,

Redundancy.

In recent years, Robotics is studied, not only in the industrial domain but also non-

industrial, for the usageas manipulating robotsworking inassemblylines and as remote

agents working in dangerous places. It takes a long time to teach robots in order to

manufacturegoo dson anassemblyline, and motionsare planned by computers inmany

cases, for ecientcalculation for generating simulatedrobotmotion. Italso takes along

timetogeneratesimulatedmotionforrobotswithmanydegreesoffreedom(DOF).Inthis

paperweproposea new approachin positioning control forarticulated robots operating

in known static environments.

We shall start with dening a certain preprocessing of the conguration space (C-

space), after which many dicult path planning problems can be solved in time of the

order ofa fractionof a second. Andthe preprocessingitselfdoesnot takevery long, too.

During the preprocessingstage randomcongurationsof the robot(no des) aregenerated

inthe freeC-space. The generated congurationis testedfor collisionwithobstacles and

self-collision. Andkeep itonly if it passes these tests. Then interconnect it into a graph

usingDelaunaygraphtechnique;ithasanadvantageofrequiringlesstimetogeneratethe

graph. This step is repeated untila prespecied numb erN of nodes has been computed.

Also the initial conguration isgiven in this prepro cessing.

The problem of path planning for articulatedrobotscan bedenedas that of nding

a continuous motion that will take a manipulator from a given initial conguration to

a desired nal conguration, subject tothe constraint that during the motion the robot

doesnotcollidewithanyobstacleinitsworkspace. Inordinarymethods,thereare several

more constraints todetermine nal conguration, such as tocompute allangles from an

appointed trajectory, to move the elb ow to an appointed point or to keep the elbow

Copyright c

1999byHirokazuTanaka

pose. According to existing C-space methods, the problem of planning a path from a

giveninitialno de toa desiredgoal nodeissolved by searching the graphconsistof edges

connecting thosenodes. But,having onlyone goal conguration may not be agoodidea

for exibility and eciency. An articulated robot is called (kinematically) \redundant"

if it p ossesses more degrees of freedom than are necessary for p erforming the specied

tasks. Redundancy of an articulated rob ot is, therefore, determined according to the

particular task to be performed. For example, in the two-dimensional space, a planar

revoluterob ot withthree jointsis redundantfor achievingany end-eector position. For

anotherexpression,inthe two-dimensionalspace,aplanarrevoluterobotwith fourjoints

and the tasks involving both position and orientation of the end-eector, if we consider

the last revolute joint of the robot as the end-eector p osition, then these tasks can be

replaced by aplanarrevolute rob otwith threejointsonlyachievingend-eectorposition,

which means there is no constraints to determine nal conguration except end-eector

position. This suggests that more goal congurations should b e availablefor performing

specied end-eector position.

After the preprocessing, wend allpossible combinations of angles which satisfy the

desired end-eector position. Then we interconnect them into a graph using Delaunay

graph technique. In the previous procedure the connected comp onents of the resulting

grapharecomputedbyastraightforwardbreadth-rstsearchalgorithm. Butinthisstudy

the idea of articial potential eld technique is used.

Anarticial potentialisamathematicaldescriptionofthe potentialenergywithinthe

C-spaceof amanipulator. Regionsinthe C-spacethatare tobe avoidedare modelledby

repulsive potentials (energy peaks), and the region to which the end eector is to move

is modelled by an attractive potential (energy valley). The addition of repulsive and

attractivepotentials provides the desired C-space energy top ology. Thus, for eachp oint

in the C-space of the manipulator there is a modelled value of potential energy and an

associatedgradientorforce. Thisforcecausestheend-eectorofthemanipulatortomove

throughitsenvironmentinamannerwhichisdirectlyresponsivetothemodelledpotential

energyfunctionofthatenvironment. Previoususeofarticialp otentialshasdemonstrated

theneedforanobstacleavoidancep otentialthatcloselymodels theobstacle,yetdo esnot

generate local minima inthe C-space of the manipulator. But inthis study, the problem

is solved by using agraph and strategy of wavefront.

The path planning algorithm connects any conguration nodes to the goal congura-

tion whosepath isthus the shortestinthe numb er ofnodes. This algorithm behaveslike

aparallel breadth-rstsearchof the graph, and constructs trees rooted ateachgoal con-

guration. Whenthe initialcongurationisonce connected,the algorithmwillterminate

and exhibit allnodes included in the path to the goal conguration. The algorithm fails

if itcannot connecttothe initialconguration inthegraph, orifthe initialconguration

andanyofthegoalcongurations lieintwodierentconnectedcomponentsofthe graph.

The resulting path can also be improvedusing anystandard smoothing algorithm.

We present a new methodology for exacting robot motion planning and control. It

guarantees collision-freemotionand convergencetothedestinationfromalmostallinitial

free congurations. Simulation results of three links of an arm are given to illustrate

program written inC language and implemented it ona workstation. Andexp erimental

results are presented and discussed.