[一些机器人方面的PDF].Maaref-Sensor-based.navigation.of.a.mobile.robot.in.an.indoor.environment

Robotics and Autonomous Systems 38(2002)1–18

Sensor-based navigation of a mobile robot in

an indoor environment

H.Maaref ?,C.Barret

CEMIF—Complex Systems Group,University of Evry,CE 1455Courcouronnes,40rue du Pelvoux,91020Evry Cedex,France

Received 14December 1998;received in revised form 23May 2001

Communicated by T.C.Henderson

Abstract

The work presented in this paper deals with the problem of the navigation of a mobile robot either in unknown indoor environment or in a partially known one.

A navigation method in an unknown environment based on the combination of elementary behaviors has been developed.Most of these behaviors are achieved by means of fuzzy inference systems.The proposed navigator combines two types of obstacle avoidance behaviors,one for the convex obstacles and one for the concave ones.The use of zero-order Takagi–Sugeno fuzzy inference systems to generate the elementary behaviors such as “reaching the middle of the collision-free space”and “wall-following”is quite simple and natural.However,one can always fear that the rules deduced from a simple human expertise are more or less sub-optimal.This is why we have tried to obtain these rules automatically.A technique based on a back-propagation-like algorithm is used which permits the on-line optimization of the parameters of a fuzzy inference system,through the minimization of a cost function.This last point is particularly important in order to extract a set of rules from the experimental data without having recourse to any empirical approach.

In the case of a partially known environment,a hybrid method is used in order to exploit the advantages of global and local navigation strategies.The coordination of these strategies is based on a fuzzy inference system by an on-line comparison between the real scene and a memorized one.The planning of the itinerary is done by visibility graph and A ?algorithm.Fuzzy controllers are achieved,on the one hand,for the following of the planned path by the virtual robot in the theoretical environment and,on the other hand,for the navigation of the real robot when the real environment is locally identical to the memorized one.Both the methods have been implemented on the miniature mobile robot Khepera ?that is equipped with rough sensors.The good results obtained illustrate the robustness of a fuzzy logic approach with regard to sensor imperfections.?2002Elsevier Science B.V .All rights reserved.

Keywords:Mobile robot;Reactive navigation;Fuzzy inference systems;On-line optimization

1.Introduction

Various methods for controlling mobile robot systems have been developed which are generally

?Corresponding author.Tel.:+33-01-6947-7554;fax:+33-01-6947-7599.

E-mail address:maaref@cemif.univ-evry.fr (H.Maaref).

classi?ed into two categories:global planning and local control.Many works,based on the complete knowledge of the robot and the environment,use a global planning method such as arti?cial potential ?elds [11],connectivity graph,cell decomposition [12],etc.These methods build some paths (set of sub-goals)which are free of obstacles.Their main advantages are to prove the existence of a solution

0921-8890/02/$–see front matter ?2002Elsevier Science B.V .All rights reserved.PII:S 0921-8890(01)00165-8

2H.Maaref,C.Barret/Robotics and Autonomous Systems38(2002)1–18

which permits the robot to reach its destination and to generate collision-free map-making.Thus,in this map,a global optimal solution can be achieved with the assistance of a cost function.The latter is related to either the global route between a start position to a goal position due to the A?algorithm,e.g.,the time path,or the security of the mission[18].However, they have some well-known drawbacks.For example, an exact model of the environment is needed which unfortunately cannot be de?ned in most applications. Then,it is dif?cult to handle correctly a modi?ca-tion of the environment due to some new or dynamic objects.

The local methods are mainly used in an unknown environment.They could be called reactive strategies and are completely based on sensory information. Therefore,an absolute localization is not requisite and only the relative interactions between the robot and the environment have to be assessed.In these cir-cumstances,a structural modeling of the environment is unnecessary,but the robot has to acquire through its sensory inputs a set of stimulus–response mecha-nisms.In this scheme,the robot is generally expected to carry out only simple tasks.Numerous methods have been proposed[4].They do not guarantee a solution for the mission because of the occurrence of deadlock problems.The reason is that the robot does not have a high-level map-reading ability.For more ef?ciency and safety,perception tools have to be increased(several types of sensors including,e.g., cameras)to get more pertinent information about the environment.But then it is not easy to process the data under real time constraints.These constraints often lead to a degradation of the accuracy and the richness of the information.

Some constraints are added to the intrinsic draw-backs of these methods caused by:

?the imprecision or lack of knowledge in understand-ing all the phenomena contributing to the behavior of the system and its environment;

?the dif?culties to represent correctly the environ-ment and to locate the robot,due to errors in the sensors data which are still far from perfect,taking into account the present day technologies.

In other respects,a set of methodologies,called qualitative or approximate reasoning,have been devel-oped to build a decision making approach in systems where imperfection cannot be completely avoided or corrected.These methodologies attempt to capture some aspects of the human behavior in system control. Their aim is to incorporate implicitly the imperfection in the information gathering and reasoning process, rather than to determine them explicitly through nu-merical calculations or mathematical representations. Some qualitative reasoning theories have been de-veloped over the past few years[10]and currently the most used for application in control systems is the theory of fuzzy sets[30].The control based on this theory[13]provides satisfying results even in cases where classical control failed.As a fuzzy controller is built following the knowledge of experts,a complex or ill-de?ned system can be described without using an exact mathematical model.Therefore,the fuzzy sets theory is a good candidate both to handle impre-cision and to assign built-in guidance control enabling the robot to navigate throughout complex environ-ments.In fact,we know from our own experience of human motion that it is unnecessary either to know our own exact location or to have a comprehensive knowledge of the whole scene.It can be suf?cient, e.g.,to know whether there is enough free space to get around an obstacle and to recognize marks indicat-ing whether the passageway leads to the goal or not. Many application works of fuzzy logic in the mobile robot?eld have given promising results[23,27,28], etc.

The?nality of our work consists of developing low cost navigation strategies in indoor environment,e.g., the aim is to help disabled people[8].In this con-text,the main concern is to build ef?cient navigation techniques giving more priority to safety than to op-timality.Fig.1gives a global scheme of the adopted strategy.It is based on the fact that generally one can dispose of a building’s map in which some main?xed elements of the environment are located:walls,doors, heavy and?xed furniture,etc.But,many un?xed el-ements,whose positions is a priori unknown,can be added to the initial map.In this situation,two extreme cases can happen.If the environment detected by the robot corresponds to the memorized map,then the robot should follow with high speed a planed trajec-tory using a global method.On the contrary,if the environment is not recognized,a displacement at a reduced speed has to be generated by a local method of reactive navigation.Between these two extreme

H.Maaref,C.Barret/Robotics and Autonomous Systems38(2002)1–18

3

Fig.1.Global scheme of the adopted strategy.

situations,a progressive evolution must be done by fusing outputs coming from both modules as a func-tion of a degree of recognition of the memorized scene.

This paper is organized as follows:?rst the used mobile robot is described and some working assump-tions are given in Section2.Section3presents the local method for navigation in an unknown environ-ment.In Section4the global method used in known environment is given and the fusion of both the meth-ods is developed.Finally,a conclusion is given in Section5.2.Physical implementation and working assumptions

The experimentation is mainly done on Khepera?which is a small mobile robot developed at the Ecole Polytechnic Fédérale de Lausanne(EPFL).Our mo-tivations to work with such a miniature robot are the following:

1.Our methodology is based on developing strate-

gies using logical rules independently of a precise model of the robot.So the transfer of control

4H.Maaref,C.Barret/Robotics and Autonomous Systems38(2002)

1–18

Fig.2.The miniature mobile robot Khepera?.

algorithms from one robot to another is not a dif?cult problem.

2.Nevertheless,to work with a real robot is largely

preferable to use simulations as far as,e.g.,dealing with sensor imperfections or real time constraints is concerned.

3.Finally it is clear that the easiness to build and

modify the environment of a mini robot is greatly appreciable.

Khepera?has a circular shape featuring55mm in diameter(2r),30mm in height and70g in weight [20].Two wheels and two small Te?on balls support it. The robot possesses eight infrared sensors,which are composed of an emitter and an independent receiver. These sensors(S0,S1,...,S7)are disposed in a somewhat circular fashion around its body(Fig.2)and allow the measurement of distances in a short range from about1to5cm.Its maximum linear speed is about40mm/s.

The robot’s linear and angular speeds are sent from a host computer via a serial link to an on-board chip, which is based on a Motorola68331micro-controller. The linear speeds of the right and left wheels are then calculated.

In this study,we assume the following conditions:?The robot moves on a?at ground.

?Inertial effects are neglected.

?The used mobile robot has the non-holonomic characteristic but this later is not constraining.?The robot moves without sliding and can be localized when it?nds itself in a locally known scene[22].

Most of the experiments are done on both the real and a simulated mobile robot.The simulator dedicated to Khepera?has been written in C++by Michel [19]and runs on SUN Sparc station.The experimental results deduced from the real and simulated mobile robot are very near.

3.Navigation strategies in unknown environment 3.1.Principle

In a totally unknown environment,the navigation is done completely in a reactive manner.So a classical method such as the arti?cial potential?elds[11]could be used.But it is well known that this method suffers from local minima problems leading to blocking sit-uations.A solution has been proposed in a previous work[14]based on an automatic tuning of attractive and repulsive force coef?cients due to fuzzy rules. Nevertheless some oscillation problems remain in nar-row environments and passageways,which are very constraining for dedicated utilities indoor robotics. The described approach(Fig.1)here is largely based on fuzzy inference systems(FISs)and inspired from human behavior,which consists to reach the free space while seeking the goal(strategy S1).This allows avoiding local minima by reaching the mid-dle of the available free space when the robot passes through a cluttered environment[2].But some failing situations are yet encountered in the case on concave obstacles.That is why coordination of S1and another elementary behavior of wall-following type including the creation of transition sub-goals develop a second strategy S2.As a matter of fact,the idea is to antic-ipate in order to avoid a potential blocking situation rather than to discover it and subsequently react.So, an obstacle will be in fact quali?ed as concave if all the used exteroceptive sensors give simultaneously small measurements of distances,since,even if the obstacle has not really a concave geometric shape,it is preferable to trigger the S2strategy instead of taking the risk to fall in a blocking situation with S1strategy. To skirt the two sides of the wall,the detection of a concave obstacle(Fig.3)provokes the creation of an intermediate sub-goal of transition“SG[i]”at the point of detection and triggers the wall-following be-havior to act,e.g.,on the left side.If the robot goes

H.Maaref,C.Barret /Robotics and Autonomous Systems 38(2002)1–185

Fig.3.Concave obstacle skirting.

away from the target and the distance of displacement is greater than a threshold distance T ;it turns back to the intermediate sub-goal SG[i ]previously memo-rized,due to the strategy S1.Then,it skirts the obsta-cle on the other side,with the same threshold distance T .The wall-following ceases if the two following con-ditions are ?lled:

?The three sensors measure big distances.

?The goal is in the right or in the left (depending on the side of the obstacle followed by the robot)quadrant with respect to the actual direction of the robot.The developed algorithm allows a robot with exte-roceptive sensors to travel from any start point S to any target point G in a cluttered environment without any prior knowledge on the location of the obstacles.3.2.On-line optimization of FISs for reactive strategies

The reactive strategies of navigation (reaching a collision-free space,goal-seeking and wall-following)are completely based on sensory information.Two

Fig.4.Learning architecture.

of them (reaching a collision-free space and wall-following)are built due to self-tunable fuzzy inference systems (STFISs)controlling the angular ωand lin-ear v speeds of the mobile robot.The angular speed is generated ?rst at a given linear speed and,then after convergence of this later structure,the control rules of the linear velocity are deduced.

With respect to the use of a classical,manually tuned FIS to build the reactive behaviors of the robot,the STFIS has the following two main advantages:

?It avoids the manual tuning of the parameters of the FIS that can be in some cases quite long and cumbersome.Moreover,this manual tuning leads inevitably to a sub-optimal behavior.

?It allows to cope exactly with the physical char-acteristics of the robot.If either these characteris-tics evolve with time or the robot is changed (or a change from a simulator robot to a real one is car-ried out),the controller will adapt automatically to the new situation.

The structure of the FIS is as follows.The member-ship function for the input values are triangular and ?xed.A min operator performs the conjunction of the inputs and the conclusions of the rules are numeri-cal values W i (so-called weights).They are optimized through a learning process [1].

The shape of the used membership functions is tri-angular and ?xed in order to extract and represent eas-ily the knowledge from the ?nal results.So the output value y (v or ω)is given by

y = n

i =1W i ×αi

n

i =1αi ,where αi are the truth values of each ?red rule.

The learning architecture is presented in Fig.4.This architecture is a simpli?ed version of the “distal

6H.Maaref,C.Barret/Robotics and Autonomous Systems38(2002)1–18 control”method proposed by Jordan and Rumelhart

[9]for neuro-control.In the original method,two neu-

ral networks are used:one for modeling the plant and

another for the controller.In fact,as pointed by Jordan

and Rumelhart it is not necessary to work with an ac-

curate model of the plant to obtain an ef?cient con-

trol.Saerens[26]and Renders[24]have shown that

the model network can be successfully approximated

by the sign of the terms of the Jacobian matrix of

the plant(in the assumption that these signs are?xed

on the working space,which is valid for a lot of real

systems).These results have been extended by substi-

tuting to the neural controller a fuzzy controller with

adaptive parameters[5],leading to the very simple

architecture as in Fig.4for single input single output

(SISO)systems.

The learning is entirely done on-line on the

actual robot.The table of rules(weights W i)is initially

empty.The robot acquires by its sensors the distances

to the environment,calculates the error to be back

propagated,updates the triggered rules in real time,

begins to move and so on,etc.The weights of the

table of decision are then adjusted locally and pro-

gressively.As the learning progresses,the mobile is

more and more able to cope with new situations.

The back-propagation training technique[25]

updates weights according to:

W(k+1)=W(k)+η

??J ?W

,

where k is the training iteration,J is the cost function used in the learning algorithm,ηis the learning rate and W(k)=W(k)?W(k?1).

If the classical quadratic error is used as a cost

function,J=1

2ε2whereεdepends on the task;the

back-propagation minimizes effectively the value of J,leaning rapidly to a good reactive navigation.But, if the learning is prolonged,the weights increase con-tinuously with time and,progressively,the quality of the control decreases.To overcome this dif?culty,a technique known as“weight decay”in classi?cation methods[6]and having a strong relation with ridge regression and regularization theory[3]is used.So a second term is included in the cost function that becomes

J=1

2ε2+λ

W2i,

whereλis a coef?cient proportional toαi/

αi.It

is chosen so that the output value does not exceed

the maximum angular speed of each wheel of the

robot(1.58rad/s).By applying this method,a satura-

tion of the growth of the weights is obtained without

any degradation of the residual quadratic error and

the quality of the control is maintained even under

prolonged learning.

3.3.Avoidance of convex obstacles

This navigator is built by fusing two elementary

behaviors:a self-tunable fuzzy controller to reach the

middle of the free space and a crisp one to track the

current sub-goal.

3.3.1.Reaching the middle of the collision-free

space behavior

When the vehicle is moving towards the target and

the sensors detect an obstacle,an avoiding strategy is

necessary.The method consists of reaching the middle

of a collision-free space.This behavior is obtained by

means of an STFIS.

The input variables are respectively the normalized

measured distance on the right(R),on the left(L)and

in front(F)such as

R n=

R

R+L

,L n=

L

R+L

,F n=

F

σ

,

where front data F=min(S0,S7);right data R=

min(S6,S7);left data L=min(S1,S2)andσis a

distance beyond which the obstacles are not taken into

account.Due to this normalization,the universes of

discourse evolved automatically with the sensor data

(Fig.5).

The shape of the membership function is triangular

and the sum of the membership degrees for each vari-

able is always equal to1.The universes of discourse

are normalized between0and1.

For this behavior and to generate?rst the control

rules for the angular speedωa,the error used in the

cost function is given byεω=Y?12(Y+F n)where

Y is either R n or L n.After a few rounds at a constant

linear speed on a learning track,the navigation of the

robot is satisfying.

The weights of the controller converge to the values

given in Table1,where the linguistic labels for the in-

puts are de?ned as:Z(zero),S(small),M(medium),

H.Maaref,C.Barret /Robotics and Autonomous Systems 38(2002)1–18

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Fig.5.Evolution of the universe of discourse with the width of the environment.

B (big)and VB (very big).These numerical values could be eventually translated in symbolic values to verify the logical meaning of the rules.We can assign to them a linguistic interpretation by substituting the symbolic concept PB (positive big)for the values greater than 0.7,PS (positive small)for the values between 0.2and 0.7,Z (approximately zero)for the values between ?0.2and 0.2,NS (negative small)for the values between ?0.2and ?0.7,and NB (negative big)for the values lesser than ?0.7.We obtain the linguistic table for the angular speed from Table 2.It is interesting to compare this later with a table written

Table 1

Angular speed coef?cient

rules

Table 2

Linguistic table for the angular

speed

empirically from experience of a human driver,and following the very usual diagonal structure known as McVicar–Whelan’s [17]controller (Table 3).We can observe that the two linguistic sets of rules are very near.Only three cases (noted with ?)are different and they differ from only one linguistic concept (PS instead of PB and Z instead of PS and NS).So,we can claim that the extracted rules are quite logical and coherent.Moreover,the use of STFISs allows the op-timization of the controller with respect to the actual characteristics of the robot.This means that the rough and manual tuning of the parameters of the fuzzy con-troller is replaced by a ?ne local automatic tuning and

Table 3

Linguistic table deduced by human

expertise

8H.Maaref,C.Barret /Robotics and Autonomous Systems 38(2002)1–18

this can improve very signi?cantly the performances,e.g.,a given way is traveled more quickly with the STFIS controller than with the classical controller by taking into account the actual maximum speed of the robot’s wheels.

A structure of the same type is used to generate the

control rules for the linear speed v a as a function of the angular speed ωαand the front distance F .The cost function is realized with

εv =40?max (|v a +rωα|,|v a ?rωα|)

?(1?15F )·40.

This allows to attain the maximum speed (40mm/s)and to decrease the speed as a function of F .

The linguistic labels for ωare de?ned as N (nega-tive),Z (approximately zero)and P (positive)and for F they are Z (approximately zero),S (medium)and B (big).The output weights of the controller after learn-ing are given in Table 4.

It is easy to verify that these weights correspond rules expressing that the more the robot has to turn and the closer a frontal obstacle is,the greater is the reduction of the linear speed.Fig.6presents an ex-ample of navigation in a real cluttered environment.The self-tunable fuzzy controller shows its ef?ciency to realize the task.But in order to reach its goal the robot has to be provided with a goal-seeking behavior.3.3.2.Goal-seeking behavior

The basic scheme is given in Fig.7.The goal G produces an attractive force F a that guides the robot to its destination.The actions (C ωg and C v g )generated by this force are modulated by the inverse of the distance

Table 4

Linear speed coef?cient rules

Fig.6.“Reaching the middle of the collision-free space”behavior:experimentation with the simulator.

PG between the center of the robot and the goal.θg is the angular deviation needed to reach the goal.D is the distance of in?uence of the goal.It is supposed that no obstacle exists in the circle of diameter D .When the robot is far enough from the sub-goal (PG >D)the angular speed coef?cient is given by C ωg =

C g PG D

θg .The coef?cient C g is chosen in such a way that the robot reaches a maximum angular speed for θg <π.So it does not deviate too much from the PG direc-tion.As soon as the robot reaches the in?uence zone of the goal (PG

Fig.7.Goal-seeking scheme.

H.Maaref,C.Barret /Robotics and Autonomous Systems 38(2002)1–189

becomes C ωg =

C g

π

θg .In both the cases C ωg is normalized so that |C ωg |can-not exceed 1.Moreover,the goal-seeking linear speed coef?cient is determined in relation to C ωg by the equation C v g =1?|C ωg |.

This expresses the following rule:the more the robot is pointed towards the goal direction or the further the robot is from the goal,the faster it can move (knowing that the speed is bounded by a maximal value either by the user or by the hardware).

3.3.3.Fusion of “reaching of the middle”and “goal-seeking”behaviors

In reactive navigation,the safety of the robot is essential.For this reason,we distinguish two cases:?If an obstacle is detected very close to the robot,on only one side or in the front,then the obstacle avoidance has priority and the attraction is cancelled (C ωg =0).

?Else,the angular speed set-point ωr applied to the robot results from a linear combination between the obstacle avoidance and the sub-goal attraction:ωr =αωa +βC ωg ωmax ,

where αand βare coef?cients adjusted by experi-mentation to get the best trajectory generation and ωmax is the maximum chosen angular speed.The linear speed V r set-point is given by V r =min (V a ,C v g V max ),

if the robot is outside the zone of D radius.Else,it is reduced so that V r =min (V a ,C v g V min ),

where V max and V min are the maximum and mini-mum chosen linear speed,respectively.

An example of implementation of this fusion rule on the robot Khepera ?is shown in Fig.8.The task consists in getting through a doorway in an environ-ment like a ?at.For more visual clarity,the obstacle is drawn on the screen in accordance with the sensor

Fig.8.Avoidance of convex obstacles:experimentation with Khepera ?.

impacts.The robot avoids the obstacle while seeking the goals (G1,then G2).

3.4.Avoidance of concave obstacles

In an environment composed with concave obsta-cles and in order to avoid blocking situations,we use an additional behavior,inspired of the myopic method,which consists of following the contour of the obsta-cle in order to skirt round it.This behavior is built by means of an STFIS.The goal is to follow the walls surrounding the robot at a “d setpoint”distance,with regard to the sensor measurements:F (front)and L (left)or F and R (right)(Fig.9).

The shape of the membership functions is triangu-lar and the universes of discourse are de?ned between 0and σ(5cm for Khepera ?)for the inputs.For this behavior,the error used in the cost function for the an-gular speed is given by εω=min (Y,F )?d setpoint,where Y is either R (wall-following on the right side)or L (wall-following on the left side)and d setpoint is a given set-point distance.On the beginning of the learning the robot is near a wall in an unknown

Fig.9.Wall-following strategy.

10H.Maaref,C.Barret /Robotics and Autonomous Systems 38(2002)

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Fig.10.Wall-following learning track:experimentation with the simulator.

environment.After a few rounds at a constant linear speed on the learning track (Fig.10),the robot is able to follow all the walls of the track at the given distance.At this time,the output weights of the controller have converged to the values given in Table 5where the linguistic labels for the inputs are de?ned as:Z (zero),S (small),M (medium),B (big)and VB (very big).For the linear speed,the structure is the same one as for the “reaching the middle of the collision-free space”behavior.After convergence,the obtained nu-merical values are given in decision Table 6.The logical meaning of the rules is obvious since they ver-ify that the more the angular speed increases and the closer a frontal obstacle is,the greater the reduction of the linear speed is.The blocks marked with the sym-

Table 5

Decision table for angular speed

(rad/s)

Table 6

Decision table for linear

speed

bol X are never triggered because,if the robot turns on the right,that’s means there is no wall in front.The robot is now able to follow correctly over the walls of the any shape at the given set-point distance with a smooth and continuous trajectory (Fig.11).The whole algorithm for concave obstacle avoidance has been tested on the robot Khepera ?.In Fig.12(a),only one sub-goal is created,because the value of the threshold of displacement T is quite big (T =1m ).In Fig.12(b),the threshold T is smaller (T =0.5m ):three intermediate sub-goals are created now before the robot converges towards the ?nal goal.Besides,T is chosen depending on the environment size and constraints of the mission.As a general rule,too low

a

Fig.11.Wall-following generalization track.

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Fig.12.Experiments of concave obstacles skirting with Khepera ?.

value of T provokes many direction changes,increas-ing the imprecision of the localization.In the opposite case,too high a value mainly leads to sub-optimal trajectories.

3.5.Coordination of behaviors

Now the whole strategy of reactive navigation (as described in Fig.1and Section 3.1)in a complex environment,using all the developed reactive agents,can be applied.An example of result is shown in Fig.13where the robot avoids and skirts

success-

Fig.13.Coordination of behaviors.

fully obstacles of various shapes before to attain its goal.In fact,the S2strategy is activated in “Z1”and “Z3”zones by coordination of the S1strategy and the wall-following behavior due to the creation of an in-termediate sub-goal.In “Z2”and “Z4”zones only the S1strategy is triggered.

4.Navigation in a partially known environment In the case of indoor robotics ?eld,one has to ex-ploit the a priori knowledge of the environment that takes the form of the map containing the main charac-teristic features (walls,doors,?xed furniture,etc).So it obvious that an ef?cient control of the mobile robot needs:

?a local level based completely on the information of different sensors covering the close circle of the vehicle;

?a high-level for path planning using a global des-cription of the world with possibly incomplete and/or imperfect knowledge.

The original idea is to keep in memory this pre-acquired knowledge contrary of most works done in this ?eld [12],where the a priori knowledge is used only to generate sub-goals.This allows having a safe navigation,to modulate continuously the speed and eventually to update the map.

The approach exploits that the a priori knowledge on the environment (scene called “memorized”in which a virtual robot moves)which is susceptible to local variations by modi?cation and/or by addition of obstacles (scene called “real”)(Fig.14).4.1.Planned path following in a real known environment

For the planning of a path,the visibility graph and the A ?algorithm are used.The visibility graph [12]is a set of straight lines connecting the source,the goal and obstacle vertices.Each point is connected to all viewed points without intersecting obstacles (Fig.15).Then,an optimal path is searched with an A ?algorithm in the generated graph,using the Euclidean distance as a cost function.This path is a polygonal line connecting the source to the goal;it is the shortest collision-free path from source to goal.

12H.Maaref,C.Barret /Robotics and Autonomous Systems 38(2002)

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https://www.sodocs.net/doc/4e9845622.html,parison between real and memorized scenes.

This method is well adapted to generate a path (set of sub-goals)for a robot represented by a point.In order to consider the whole ground space occupied by the robot,we need to extend the area of the obstacles.In our case the used robots have circular shape.Then,the obstacles are dilated by a distance equal to the diameter of the robot with a revolution symmetry such as the arcs of the circle are approximated by some segments.

In Fig.16we show an example of environment for the mini robot Khepera ?.The obstacles are the shaded polygons.They are surrounded by a

dotted

Fig.15.Optimal path.line representing the dilatation.The optimal path obtained by the A ?algorithm is the dashed line join-ing the source point to the goal point through some sub-goals indicated by the black points.

The path to follow is the segments joining the successive sub-goals.In order to assure the

control

Fig.16.Path planning in a real environment.

H.Maaref,C.Barret /Robotics and Autonomous Systems 38(2002)1–18

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Fig.17.Control architecture for the path tracking.

of the robot between these sub-goals,various meth-ods can be used.These methods can use classical [7,29],etc.or fuzzy control [21,31],etc.The mod-ule of control developed here to generate the path between

the sub-goals is based on a classical fuzzy control (Fig.17).It provides the angular speed (ωp )of

the robot which is supposed to evolve at a given linear speed (v p ).The angular speed of the robot is determined from its current position with regard to the path and is achieved by the relative variation of angular speeds of driving wheels.Since the robot is an indeformable solid,the knowledge of the distance E (between the center point M of the robot and the segment joining the sub-goals D and A (Fig.18))and of the variation of this distance is suf?cient to achieve the task.

The co-ordinates (X M ,Y M ,θM )of the robot are given by odometry.The signed distance E

is given by MH =E =DM sin (

ADM )=P DA

,with

P =(X M ?X D )(Y A ?Y D )?(X A ?X D )(Y M ?Y D ).The controller is constituted of a set of fuzzy rules is given in Table 7.The signi?cation of the used linguis-tics terms is the same as in Section 3.3.

Fig.18.Position of the robot with regard to the path.Table 7

Rules of the path tracking fuzzy controller

The membership functions are of triangular shape,on a normalized universe of discourse between ?1and 1.The operators used in the FIS are similar to those appearing in a Mamdani controller [16]:min for the composition of the input variables and for the fuzzy implication and max for the aggregation of the rules.The center of gravity method is used for the defuzzi?cation,in order to determine the crisp output actions.

Fig.19represents an example of experimental result with the whole previously described method (path planning by visibility graph and A ?algorithm and path tracking by the fuzzy controller)when the real scene is identical to the memorized one.

Fig.19.Displacement of the robot in a known scene.

14H.Maaref,C.Barret /Robotics and Autonomous Systems 38(2002)

1–18

https://www.sodocs.net/doc/4e9845622.html,parison of sensors data.

4.2.Fusion of reactive and planed navigation The aim of this procedure is to navigate the robot from the initial point till the target point by follow-ing as nearly as possible the optimal way without tak-ing into account the missing obstacles and avoiding the unexpected obstacles.For this,a virtual robot dis-placing in the memorized scene and equipped with two lateral virtual sensors is used.An index of prefer-ence,indicating which command is the best to apply,strategies fusion index (SFI),is generated by a fuzzy decision making module,the inputs of which are the difference between (Fig.20):

1.Each sensor data in the memorized scene (modeled as perfect sensor)and the corresponding one in the real scene (data with error)( L , R ).One can note that the comparison of the two lateral sensor data is suf?cient to accomplish the task.

2.Absolute positions of the mobile robot in the mem-orized and the real environments ( p ),knowing that the virtual robot moves along with the orthog-onal projection on the planned path of the center point M of the real

robot.

Fig.21.Fuzzy subsets for the variables R , L , p and SFI.

The SFI value re?ects the situation of the robot with respect to the known environment.By exploiting it,the two strategies (global and local)are fused,by weighting of the orders such as ω=ωp ×SFI +ωr ×(1?SFI ),v =v p ×SFI +v r ×(1?SFI ),

where ωand v are the orders to apply to the robot.Thus,if the sensor data in the two scenes are very close,the navigation in the real scene will be made by tracking the planned path.If they are completely

Table 8

Rules table for

SFI

H.Maaref,C.Barret/Robotics and Autonomous Systems38(2002)1–1815

Fig.22.Examples of experimental results:(a)memorized environment;(b)real environment(identical to the memorized one);(c)real environment(a known obstacle is removed);(d)real environment(added obstacle).

16H.Maaref,C.Barret/Robotics and Autonomous Systems38(2002)1–18

different a strategy of local navigation is triggered.The variable SFI is the output of a fuzzy module and is shared in two fuzzy subsets labeled Sp for releasing the planned path following and Sr for starting the reactive navigation.The universes of discourse of the input variables R, L and p are composed of three fuzzy subsets(Fig.21).The used labels are N(negative),Z (zero),P(positive),M(medium)and B(big).

The fuzzy rules have the following form:

?If R, L and p are zero then the planned path following strategy is activated(Sp).

?If R and L are negative and p is big then the local navigation is triggered(Sr).

A rules table(Table8)is then de?ned.This table shows the set of possible combination between R, L and p.Fig.22shows some experimental re-sults by using this method implemented on the robot Khepera?.

When the actual environment is either the same as the memorized one(Fig.22(b))or not constraining (Fig.22(c)),the robot navigation is done at high speed by following the planned path.If not(Fig.22(d)), reactive modules are triggered(from P1point).The speed is strongly reduced when an obstacle is detected. Then,it increases gradually until the vehicle reaches the sub-goal P2where the memorized scene is again recognized.

It is possible to verify that the trajectory followed in presence of unknown obstacles(Fig.22(d))is very close to the one obtained after including the unknown obstacle in the data base and starting again the plan-ning[15].In fact the main penalization due to un-known obstacles is the decreasing of the linear speed of the robot.

5.Conclusion

We are interested in the navigation of a mobile robot in partially known environment such as inside an of-?ce or a?at.In such cases,a plan of the evolution zone of the robot containing most of its?xed features can be drawn,but numerous undrawn or displaced lo-cal obstacles can also been encountered by the robot. So a natural way to obtain an ef?cient and safe nav-igation in such an environment is to integrate global planning and local reactive control.The solution we propose here is basically founded on human behavior and mainly implemented through FISs.

The navigation method in an unknown environment is based on the combination of two types of obstacle avoidance behaviors,one for the convex obstacles and one for the concave ones.In the case of convex obsta-cles,a behavioral agent fusing a“reaching the mid-dle of the collision-free space”behavior achieved by means of STFISs and a goal-seeking behavior,is suf-?cient.However,the navigation using these strategies can fail if a concave obstacle separates the robot from its goal.In order to solve this problem,a third elemen-tary behavior,of wall-following type,has been devel-oped using another STFIS.Associated to the creation of sub-goals of transition,it permits the robot to skirt round the concave obstacles,before heading again for its goal.The use of FISs to generate elementary be-haviors deduced from human being is quite simple and natural.However,one can always fear that the rules deduced from a simple human expertise are more or less sub-optimal.That is why we have tried to obtain these rules automatically.A gradient technique is used which permits the optimization of the output parame-ters of an FIS through the minimization of a cost func-tion.However,the use of a classical quadratic error as a cost function leads to weight drifting and progres-sive deterioration of the performances.This problem is solved by a method of weight decay that limits the growing of the weights and allows an ef?cient on-line learning.Due to the proposed technique,the tedious manual tuning of parameters of an FIS is avoided and the control law is optimized with respect to the actual physical characteristics of the robot.

The a priori knowledge on the environment is memorized and compared to the real scene detected by the robot sensors.If the sensors data in both scenes (memorized and real)are nearly the same,the nav-igation is done following the planned path at high velocity.If not,it is done under the control of reactive methods.A module,based on fuzzy logic and inte-grating sensor data,allows going progressively from one of these strategies to the other.

We have used here as a test-bed a real mini robot to prove the effectiveness of the proposed navigation method in spite of very limited calculation resources and a low cost and quite inaccurate sensor system.The implementation of this method on various robots of realistic size for inside works is now in progress and

H.Maaref,C.Barret/Robotics and Autonomous Systems38(2002)1–1817

should be quite easy due to the fact that no explicit model of the robot is needed.

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18H.Maaref,C.Barret/Robotics and Autonomous Systems38(2002)

1–18

H.Maaref received his Ph.D.in1990.

Since1990,he is Assistant Professor at the

University of Evry.In2000,he received

the HabilitationàDiriger des Recherches

diploma.He is the Head of the Electrical

Engineering Department of the Institute

of Technology since1999.His research

interests within the Complex Systems

Laboratory of CEMIF concern methods

of processing inaccurate and uncertain data with application to autonomous mobile robot and sensorial

fusion.

C.Barret was born in Marseille,France,

in1946.He obtained the Aggregation

degree in Applied Physics at the Ecole

Normale Supérieure de Cachan in1970

and the Doctorat d’Etat in Electronics at

the University of Paris XI,Orsay in1981.

Since1986,he is Professor at the Uni-

versity of Evry and he was the Head of

Electrical Engineering Department of the

Institute of Technology from1986to1992. His research interests concern mainly fuzzy control,inaccurate and uncertain data treatment and modeling by learning.

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