INTEGRATING A POTENTIAL FIELD BASED PILOT INTO A

MULTIAGENT NAVIGATION ARCHITECTURE FOR

AUTONOMOUS ROBOTS

Manikanth Mohan

Kanpur Genetic Algorithm Laboratory(KanGAL)

Indian Institute of Technology, Kanpur, India

ıdac Busquets, Ramon L

opez de M

antaras, Carles Sierra

Artiﬁcial Intelligence Research Institute(IIIA-CSIC)

Campus UAB, 08193 Belleterra, Barcelona, Spain

Keywords:

Potential Fields, Obstacle-Avoidance, Autonomous Robot Navigation, Multi-Agent Systems, Bidding Strate-

gies

Abstract:

In this paper we present a new Pilot for a Multi-Agent based control architecture for Autonomous Robots. This

Pilot is based on the use of virtual potential ﬁelds and is easy to implement yet effective. The Pilot functions as

an autonomous agent in a complex Multi-Agent Architecture for the control of an autonomous robot. In this

architecture, various agents are responsible for different tasks, and they might have to compete and cooperate

for the successful completion of a particular navigation mission. The interaction between different agents is

achieved through the use of a bidding mechanism. In this respect, we also present a way to deﬁne the bid for

the new pilot, so that the pilot can be integrated easily into the Multi-Agent Architecture. The pilot has been

tested on navigation experiments involving a real robot and it has given successful and encouraging results.

We also deal with some problems of this pilot and ways to get around them.

1 INTRODUCTION

Robot systems for navigating through unknown en-

vironments has been a focus area of research for

many years now, with many application areas includ-

ing rovers, handling hazardous materials, and search

and rescue missions, to name a few. Real time obsta-

cle avoidance is a major concern in Robotic systems

(Arkin, 1998; Latombe, 1996) for their critical im-

portance to the success in any real life application of

robotics. (Manz et al., 1991) presents a good compar-

ison of some real time obstacle avoidance methods.

The use of virtual potential ﬁelds (PF) was introduced

in (Khatib, 1985) and since it has been explored and

discussed to a great deal (Masoud and Masoud, 2000;

Khosla and Volpe, 1988). A modiﬁed implementation

based on PF can be found in (Koren and Borenstein,

1991). Using this as a base idea we have developed an

agent, the Pilot, which takes care of real time obstacle

avoidance. This agent is a part of the overall Multi-

Agent System where various agents are responsible

for different tasks, and they have to compete and co-

operate for the successful completion of a particular

navigation mission. The interaction between different

agents is achieved through the use of a bidding mech-

anism. See (Busquets et al., 2003) for further details.

2 THE NEW PF BASED PILOT

The Pilot is responsible for safely commanding the

motors that control the robot to move in a given direc-

tion. It implements the requests for motion received

from the Navigation system (if they are safe), and is

responsible for avoiding obstacles and for providing

reﬂex reaction when the robot makes an unexpected

collision. With the information of the known obstacle

locations, it uses a PF based technique, to decide the

turn necessary for avoiding collisions. The Pilot also

generates a bid, indicating the urgency of the action

it is proposing. Since obstacle avoidance is of maxi-

mal importance, the bid, in critical conditions, should

be higher than the bids coming from the Navigation

system. However, it should not be set to the high-

est possible value, 1, so that there is the possibility of

adding a new system that can override the Pilot (e.g.

a manual override). Additionally the Pilot also makes

bids for camera control, to look ahead when required

(e.g. for gathering additional information about ob-

stacles). This bid is based on a function that raises

the bid depending on the distance traveled since the

last time the robot looked forward. Although this is

also an important function of the Pilot, in this paper

we only focus on the obstacle avoidance module.

287

Mohan M., Busquets D., López de Màntaras R. and Sierra C. (2004).

INTEGRATING A POTENTIAL FIELD BASED PILOT INTO A MULTIAGENT NAVIGATION ARCHITECTURE FOR AUTONOMOUS ROBOTS.

In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 287-290

DOI: 10.5220/0001129402870290

 SciTePress

2.1 Mathematical Formulation:

Point Obstacles and the Target

For developing the PF-method, we follow the usual

approach where the magnitude of the virtual force is

dependent on the square of the distance between the

robot and the obstacle. The direction of the force is

that of the line joining the obstacle and the robot. If

the body in question is an obstacle, then the force is

repulsive in nature meaning that the robot and obsta-

cles hypothetically have “charges” of the same sign.

The target “charge” is of the opposite nature, thereby

providing an attractive force on the robot. We can ex-

press the virtual force on the robot due to an obstacle

o, F

, by (we denote vectors in boldface):

where K is a constant of propotionality, d is the di-

tance between the robot and the obstacle, and

u is

a unit vector in the direction from o to the robot.

The obstacles are initially represented as points (for

landmarks and simple obstacles) and lines (for linear

obstacles), but are later “grown” to become circles

and rounded rectangles respectively. These areas, re-

ferred to as prohibited areas, represent the obstacles

they contain. In our case, the growing size is kept

slightly larger than the diameter of the robot. The cal-

culation of the forces is made using the centers of the

“grown” circles. We represent the radius of this circle

by R

min

. If the robot is inside this prohibited region,

(a situation we denote by the name IN

DISTRESS)

then the force exerted by this body is of constant

magnitude away from the obstacle, F

max

min

Therefore, the ﬁnal equation expressing the force due

to an obstacle is given as:







u if d > R

min

max

if d ≤ R

min

To take into account the direction of the target, and

the fact that no matter where the robot is our aim is to

reach the target, we take the attractive (i.e. negative)

force of the target to be a constant value. We therefore

deﬁne the target force, F

, by:

= −A

where A

is a constant of proportionality, and

v is a

unit vector in the direction of t.

So far we have deﬁned the forces for the point ob-

stacles and the target, we are yet to deﬁne the force for

linear obstacles, which we treat in the next section.

2.2 Linear Obstacles

The natural extension for calculating repulsive forces

for linear obstacles is by integrating the force (per

Direction

Distance

Linear Obstacle

Figure 1: Calculation of force for a Linear Obstacle

unit length) over the length of the obstacle. But, this

causes a non-uniform distribution of forces, for ex-

ample, it is stronger at points which lie near the per-

pendicular bisector of the line obstacles, compared to

the points on the sides. Due to this, the presence of

another obstacle nearby can cause the robot to collide

into the linear obstacle. So, the magnitude of the re-

pulsive force is calculated by taking the nearest point

from the robot to the linear obstacle, while the direc-

tion is given from its center (see Figure 1). This new

method for dealing with linear obstacles ensures that

the repulsive force is high always whenever the robot

is near the linear obstacle, independent of the orienta-

tion with respect to the robot.

2.3 Diverting Targets

Under the overall architecture of the robot, the Navi-

gation system communicates the current target to the

Pilot. This may differ from the initial target given at

the beginning of the mission because the Navigation

system can set up temporary targets (called diverting

targets), in the form of crossing a virtual line joining

two landmarks to help the robot escaping from a dif-

ﬁcult or blocked position. Here, we would like the

Pilot to lead the robot across the virtual line without

colliding with the landmarks at both ends. Simply

putting an attractive force towards the line can cause

the robot to crash into one of the landmarks at the

end. Another easy way out is by putting an attractive

force towards the middle of the line. But this might

not be optimal, specially if the diverting line is very

long. We therefore approach this problem in a differ-

ent manner. We deﬁne a corridor perpendicular to the

line target, which is at a safe distance from the land-

marks at both ends. If the robot is inside this corridor,

the attractive force is simply perpendicularly towards

the line target; otherwise it is towards the center of

the line. This makes sure that the Pilot leads the robot

across the lines without risking a collision.

2.4 Putting it all together

Once we have deﬁned the virtual forces exerted by

obstacles and targets, we are ready to deﬁne how the

total force is computed. The total virtual force on the

robot is found by vector addition of all obstacle and

ICINCO 2004 - ROBOTICS AND AUTOMATION

288

target forces. So, if O = {All known obstacles}, then

the net force on the robot, F

net

, is given by:

net

∀o∈O

+ F

We can express this in terms of its x and y compo-

nents as: F

net

= F

i + F

j and the turn angle θ

by θ = tan

−1

. The direction of motion of the

robot is in the direction of the net force, and thus, θ is

the turn angle returned by the Pilot. Along with this,

the Pilot also returns a bid (see Section 3) which in

some sense indicates the urgency of taking this turn.

In our implementation the values of the parameters

are: K = 18, A

= 50 and R

min

= 0.40m. These

values were arrived at after considerable experimen-

tation using the simulator and the real robot. These

values can also be derived analytically. The follow-

ing equation sets the relation between A

and d

min

0.76·K

min

, where d

min

is half of the minimum

distance between two obstacles the robot would go

through. We do not include the whole analysis due to

space limitations. With the parameters found exper-

imentally, d

min

= 0.52m, thus, the Pilot is able to

drive the robot between two obstacles 1 meter apart.

3 INTEGRATION INTO THE MAS

As mentioned earlier, the Pilot receives requests from

the Navigation system to move the robot towards the

target and it also proposes its own actions for real-

time obstacle avoidance. Thus, it has to compete with

the Navigation system in order to have its proposed

actions executed. For this competition, the Pilot sends

a bid along with its turn angle.

The Pilot executes the turn of the winning bid (the

higher bid wins). This competition ensures that if the

robot is near an obstacle, the Pilot’s action is executed

because its bid will be higher than that of the Naviga-

tion system. Similarly, if the robot is in a safe region,

then the Pilot’s bid is low. This helps us in achiev-

ing what we want, i.e. that the Pilot should come into

play only when the robot might get into trouble and

not interfere with the navigation otherwise. Usual PF

based methods suffer from this problem, that they in-

terfere with the normal movement of the robot even

when it is unnecessary. But, by treating the new Pilot

as an agent in a Multi-Agent System, where agents

compete and cooperate for the resources of the robot,

we are able to work around this problem.

Now we need to come up with a good way to de-

ﬁne the bid of the robot, so that it meets the needed

requirements (i.e. the bid be high, if the robot is

near or heading towards an obstacle and is low oth-

erwise). But achieving this is not difﬁcult and is in-

Robot

Obstacle

Linear Obstacle

Figure 2: More than one obstacle in same direction

fact very intuitive. We ﬁrst ﬁnd the maximum re-

pulsive force generated by any individual obstacle,

max

= max {|F

| : ∀o ∈ O} We then deﬁne the

bid of the Pilot, bid

as:

bid

= γ

max

The multiplication factor of γ

is to scale the bid

within the interval [0, γ

], so that if necessary, we can

incorporate another agent in the future which has the

ability to overrule the bid of the Pilot. In the current

implementation, the value of γ

is set to 0.9.

The reason why we use the maximum repulsive

force instead of the net force or the total repulsive

force is because the presence of obstacles nearby can

hamper the magnitude of the force. By considering

the maximum repulsive force, it becomes very un-

likely that the bid of an agent from the Navigation

System will win, if the robot is very near to any ob-

stacle. We see that by limiting the maximum force

due to an individual obstacle to G

max

, the generation

and deﬁnition of the Pilot’s bid is easy.

4 SOME PROBLEMS AND

SOLUTIONS

The Pilot at this stage was able to perform the ba-

sic duties of avoiding the obstacles and also lead the

robot to the target. Over some runs of the robot,

some problems were noticed. The two most important

are described below, along with the changes made to

counter them.

More than one obstacle in the same direction: Con-

sider the situation shown in Figure 2. There are three

repulsive forces on the robot, one from each of the ob-

stacles, producing a strong repulsive force away from

the region. However, a force from A is sufﬁcient, be-

cause obstacles B and C are shielded by A. In this case

it is better not to compute the force for all the obsta-

cles that are hidden behind the linear obstacle. To do

this, we consider only those obstacles which are di-

rectly facing the robot. If the line segment from the

obstacle (or center of linear obstacles) to the robot in-

tersects any other obstacle, it does not contribute any

INTEGRATING A POTENTIAL FIELD BASED PILOT INTO A MULTIAGENT NAVIGATION ARCHITECTURE

FOR AUTONOMOUS ROBOTS

289

Table 1: Results of the performance of the two pilots.

Time Taken (in sec) Path Length (in cm)

Avg Std Dev Avg Std Dev

GP 297.33

81.91

1532.04

429.33

PFP 243.37

99.05

1194.92

198.23

repulsive force. So in the above case , only the force

from the line segment A would be considered. The

line segment joining the center of B to the robot and

from C to the robot intersect A, hence these two ob-

stacles provide no repulsive force.

Effect of obstacles even after they have been

passed: The obstacles continue to affect the motion

of the robot even after the robot has passed by them.

Even though this problem is expected from PF based

approaches, we try to reduce this by setting the re-

pulsive force to be zero if the angle between the net

repulsion and the net attraction is less than 90

. Even

though this does not completely solve the problem, it

helps turning towards the target easier than without

this modiﬁcation. Other ways that could be used to

overcome this is by taking into account the orienta-

tion of the robot and its direction of motion.

5 EXPERIMENTAL RESULTS

This Pilot was implemented and tested on a real Pio-

neer 2 AT robot and was found to give satisfactory re-

sults. To make a comparative study, the performance

of the new Pilot was tested against the Pilot that was

used in the architecture till then. The earlier Pilot,

called the Geometric Pilot (GP) was simple and used

a nearest obstacle avoidance (using geometric princi-

ples) algorithm. We measure the performance of the

Pilot in terms of the time taken to reach the target and

the length of the path taken. Table 1 shows the av-

erages and the standard deviations of these measures

for 45 reruns on an environment of size 8 by 8 me-

ters. The table clearly shows that the performance

of the PF based Pilot is much better than the Geo-

metric Pilot in both measures. The PF-Pilot improves

the time taken by an average of 18.14%, while it im-

proves the path length by around 22%. Therefore the

new PF-Pilot is able to signiﬁcantly improve both the

time and the path taken by the robot.

6 CONCLUSION AND SCOPE

In this paper, we have presented the development of a

new Pilot which uses a virtual potential ﬁeld strategy

for obstacles avoidance. By using the PF method to

build an agent, as part of a Multi-Agent system, we

are able to work around some problems that are in-

herent to PF methods. The way of deﬁning the bid

ensures that the Pilot intervenes only when necessary.

The maximum bid of the Pilot is kept higher than the

other systems to ensure that the Pilot gets higher pri-

ority in critical conditions. As shown by the results

of the experiments, the new Pilot provides much bet-

ter performance and is able to considerably improve

the performance of the robot, by saving both time and

path-length. We have also found ways to deal with

some problems faced by the new Pilot. A simpliﬁ-

cation that we have assumed here is that obstacles are

either linear in shape or are points. This assumption is

usually not valid in actual outdoor environments, but

most indoor environments can be approximated with

such lines and points. The extension of PF methods

to deal with arbitrary shapes can be very complex and

an approximation to lines and points might be easier

and effective rather than an exact method.

ACKNOWLEDGEMENTS

This work has been partially supported by the

MCyT’s project QualNavEx DPI2003-05193-C02-02

and CIRIT’s project CeRTAP.

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