Auction like Task Allocation and Motion Coordination

Strategies for Multi-Robot Transport Tasks

Jos

e Guerrero and Gabriel Oliver

Universitat de les Illes Balears, Mathematics and Computer Science Department

Cra. de Valldemossa, Km. 7,5, 07122 Palma de Mallorca, Spain

Abstract. In this paper we present a task allocation method based on auction

mechanisms that allows to ﬁnd how many robots are needed to execute a task.

This number is unknown and depends on several factors. There are also different

types of tasks that must be executed using different skills of the robots. It is very

difﬁcult to ﬁnd a correct allocation under this conditions and at present it is an

open problem. We also propose two motion coordination methods to reduce the

interference effect between robots. To test our system a modiﬁcation of the well

know foraging task has been used. This task introduces special characteristics,

not directly studied in previous work, that our method try to solve.

1 Introduction

Multi-robot systems can provide several advantages over single-robot systems: robust-

ness, ﬂexibility and efﬁciency among others. To beneﬁt from these potential aspects

several problems have to be solved. Among these problems, our work tries to minimize

the physical interference between robots. Interference is the result of competition for

the shared resources, especially the physical space. It’s well known that interference

has an important impact on the system performance. To reduce this impact, ﬁrst of all,

we have to decide the optimum number of robots to execute each task, using a task al-

location method. Moreover, during the execution of the task the robots must coordinate

their motion.

During this paper we extend our previous task allocation method, proposed in [5,6]

to allow more complex tasks. Now the robots have different skills to carry out the tasks

with different characteristics. Our method is inspired in both swarm systems, and, very

especially auction-like methods. Moreover, it extends the current auction mechanisms

to ﬁnd the number of robots needed to execute a task. This number is unknown a priori

and not ﬁxed. The current auction mechanisms doesn’t take into account this character-

istic. In this paper we also analyze some very simple methods to coordinate the motion

of robots in order to reduce the interference between them. Two coordinate methods has

been proposed: follow the header and stay on the side. These methods try to take into

account the special characteristics of the foraging task used, that will be explained later.

To our knowledge no other work studies the impact of the motion coordination strate-

gies over the interference using the transportation tasks that will be used during this

paper. To test our system we use a foraging like task, where the robots must ﬁnd a set

Guerrero J. and Oliver G. (2005).

Auction like Task Allocation and Motion Coordination Strategies for Multi-Robot Transport Tasks.

In Proceedings of the 1st International Workshop on Multi-Agent Robotic Systems, pages 80-87

DOI: 10.5220/0001195000800087

 SciTePress

of objects and carry them to a delivery point. The robots have different load capacities

(or skills) for each type of object. For exemple, one robot can have a high load capacity

for tasks of type 1 and very low for other kind of tasks. Unlike the classical foraging

task, multiple robots can cooperate to transport the same object. In this case we have to

decide how many robots and which ones do we need to transport each object according

to its priority, weight and type.

The rest of this paper is organized as follows: section 2 presents some relevant pre-

vious work; sections 3 and 4 describe our task allocation and motion coordination meth-

ods; section 5 shows the experiments carried out to validate the different approaches;

ﬁnally, section 6 exposes some conclusions and future work.

2 Related Work

Our task allocation mechanism is inspired in both the auction processes, that use ex-

plicit communication between robots, and response threshold systems. Classical auction

mechanism can only assign a robot to each task [3]. Other authors like L. Chamowicz in

[2] use an auction like system, similar to our method, but the number of robots assigned

to each task is predeﬁned. Swarm systems [1] can use a response threshold mecha-

nisms where multiple robots can be assigned to each task. A disadvantage of this kind

of systems is the absence of knowledge about the other robots. Thus, a robot can de-

cide by itself to execute a task when other option could be better. Our task allocation

mechanism try to solve these two problems. On the other hand, to reduce the interfer-

ence effect we can use motion coordination strategies. Mataric explained in [8] some

potential advantages of ﬂocking in classical foraging tasks, but no experimental results

were given. Finally, reference [4] demonstrated that during a classical foraging if the

number of robots that simultaneously could access to the delivery point is limited the

interference is also reduced.

3 Task Allocation

Our task allocation mechanism has been detailed in [5, 6]. In the following paragraphs it

is brieﬂy presented just to clarify the main concepts that are used in the rest of the paper.

Moreover, this previous work has been extended to accept robots with multiple skills

and different types of tasks. Our mechanism modiﬁes the classical auction methods to

select which robots, and very specially, how many of them are needed to execute a task.

In an initial stage, each robot is looking for a task. When a robot ﬁnds a new task, it will

try to lead it. There is only one leader for each task. If a robot is promoted to leader,

it will create, if necessary, a work group; that is, a set of robots that will cooperate to

execute this speciﬁc task. In that case, the leader must decide which the optimum group

size is and what robots will be part of the group. To take this decision the leader uses an

auction like mechanism. During this process only robots without any assigned task can

be selected and they bid using only their work capacity. This work capacity depends on

the type of the task that will be carried out. The leader selects the robots with the highest

work capacity, until the ratio between the weight of the object and the load capacities

of all the robots in the work group is greater than a ﬁxed threshold. That is, the leader

selects the best robots until this condition is veriﬁed:

T H

priority ∗ taskW orkLoad

1≤i≤N

workCapacity

< T H (1)

Where N is the number of robots of the group and workCapacity

is the individual

work capacity of the ith robot for this kind of task. T H is the group threshold; this

value is a parameter that will be used to compare the efﬁciency of the group formation

policy. taskW orkLoad is the amount of work required to ﬁnish the assigned task that

is calculated by the leader. Finally, priority is the priority of the task. Thus, it limits

the maximum number of robots that will be part of the group. If after this process

equation 1 is not veriﬁed, the exchange of robots between groups is allowed using a

new auction process. It’s important to note that a leader substitution protocol has been

implemented when the leader must change its work group or when it fails. The details

of this processes can be found in our previous work [5,6].

4 Motion Coordination Strategies

This section describes the motion coordination strategies implemented to reduce the

interference effect. These strategies are: follow the header and stay on the side. These

coordination strategies are executed after the task allocation process, described in the

previous section.

4.1 Follow the Header

The ﬁrst motion coordination strategy implemented is called follow the header. In this

strategy the robots of the same group and with the same objective (object or delivery

point) are attracted, instead of avoiding between them. The follow the header is imple-

mented such that, if proper parameters are used, the robots form a line. To implement

the follow the header strategy, a new behavior, called follow the header, has been used.

This behavior creates an attraction force from the robot to the nearest one in the same

group and with the same objective. A robot is only attracted by another one if this one

is nearer to the objective. The objective can be the object to gather or the delivery point.

We suppose that the robots have no sensors to know if the detected object is another

robot or it is an obstacle. Moreover, when a robot detects another one, it needs to know

its group and its objective (object or delivery point). Thus, the robots periodically send

a broadcast message to all the other robots with all this information. If a robot fails it

can’t send any more messages. When a follower doesn’t receive these messages from

its leader, it supposes that the leader is broken and tries to follow another robot. Thus,

our system is robust and it can continue the execution of the task after the failure of

some robots.

As demonstrated in [4], the highest interference during the execution of a classical

foraging task is produced around the delivery point. During our foraging-like task, the

highest interference is produced in points nearby the delivery point and also around

the object to gather. To reduce the interference, the number of robots that can access at

the same time to the neighborhood of the object or delivery point is limited. Thus, the

robots wait to access to the objects or to the delivery point using physical queues.

4.2 Stay on the side

The stay on the side coordination method focuses on reducing the interference produced

when a robot ﬁnds another one in the same group but with the opposite direction. This

situation is produced when a robot, which goes to the object, ﬁnds another one, of the

same group, which goes to the delivery point, or vice versa. The interference degree in

this case is grater than in other cases, like, for example, when one robot ﬁnds another

one but with the same objective or direction. The stay on the side mechanism is inspired

by the behavior of the cars when they drive in a two ways road. In these roads, the cars

which drive in opposite direction also use opposite sides of the road. Thus, in our case,

the robots that have to go to the object will drive by one side of a ’virtual road’, and

the robots that go to the delivery point will use the opposite side of this road. Figure 1

shows an example of this situation. The line in the middle represents the virtual path,

the big circle is the delivery point and the little square is the object to gather.

Fig.1. Example of stay on the side strategy execution.

First of all, if the robots execute the stay on the side strategy, the leader of the work

group decides which will be the path (’virtual road’) that the robots of its group will use.

During our experiment, this path will be a strength line from the object to the delivery

point. It is under study the use of more complex paths. To implement the stay on the side

strategy we use a new behavior. This behavior generates a force that moves the robots to

its correct side of the path. When the robot is in its correct side, this force will continue

affecting its movements until the distance to the path is grater than a ﬁxed value. This

value is a security distance between the two ways of the path. The magnitude of this

force, |V

|, is calculated using the following equation:

| =







1 if C or d ≤ D

min

max

−d)

max

−D

min

)

if D

min

< d ≤ D

max

0 otherwise

(2)

Where D

max

and D

min

are two distance, such that, D

max

> D

min

. C is a prepo-

sition which indicates if the robot is in its correct side, and d is the distance between

the robot position and the line which indicates the path. As during the follow the header

strategy, the number of robot that can access to the object or to the delivery point at the

same time can be limited.

5 Experiments and validation

This section explains the experiments carried out to evaluate both our task allocation

method when diferent types of task are used and the coordination methods explained

above. All the experiments has been tested using a multi-robot simulator called Robo-

CoT (Robot Colonies Tool). RobotCoT is a software tool developed by the authors at

the University of Balearic Islands [7].

5.1 Task Allocation Experiments

Our previous works [6,5] show the correctness of our task allocation mechanism. Now

we will focus the experiments on showing the performance of the system when we use

diferent type of tasks. The task to be carried out by the robots is described as follows:

some randomly placed robots must locate objects, randomly placed too, and carry them

to a common delivery point. To maintain the initial conditions, when an object is trans-

ported to the delivery point immediately appears, randomly placed, another one. Figure

2 shows a typical situation, where the squares represent the objects to collect and the

delivery point is the big circle in the middle of the image. Each object belongs to a type

that deﬁnes the robot’s characteristics needed to execute the task. During the experi-

ments 5 different kind of tasks has been used. The object to gather has also a weight

and each robot has a set of load capacities. The robot load capacity is the amount of

weight that it can carry at once. This load capacity depends on the task type and a robot

can have diferents load capacities, one for each type of task. If a robot cannot carry the

entire object at once, it takes a part of it, goes to the delivery point and comes back

to the object for more bits. The taskW orkLoad value is the object weight and the

workCapacity of a robot is its load capacity.

Fig.2. Example of initial situation of the experiments

During the experiments we have used 10 objects to gather and 5 robots. Three dif-

ferent conﬁgurations of robots has been tested. In conﬁguration 1 all robots have the

same load capacity (3) for any task. The load capacities of conﬁguration 2 and 3 can

be seen in tables 1 (a) and 1 (b). As it can be seen in these tables the robots can have

different load capacities for each type of task. During these experiments all objects have

the same weight (45 units) and we use two objects of each type, that is, two objects with

type 1, two objects with type 2, etc. For each conﬁguration, we have used group thresh-

old values (TH): 0, 2, 4, 6 and 8. In the case TH=0, equation (1) has not been used, and

therefore the number of robots per group is not limited. Also if TH=0 the robots use a

method very similar to a greedy algorithm to select the task to execute. Using a greedy

algorithm the robots select in each moment the best task for itself. Figure 3 shows the

percentage of increment in transported weight using different values of threshold and

robot conﬁgurations compared to a system with a null threshold. As it can be seen, in

most cases when the threshold is not null, and, therefore when our task allocation mech-

anism is used, the total transported weight is increased. In all cases seems that there are

an optimum threshold value, that during the experiments is about 4 or 2. In other words,

it exists a optimal number of robots to execute a task. The use of learning algorithms to

ﬁnd the optimum TH value is under study.

Table 1. Robot’s load capacity for each type of tasks. R1..R5 represent the robots and T1..T5

represent the type of the task. (a) Conﬁguration 2. (b) Conﬁguration 3

- R1 R2 R3 R4 R5

T1 10 1 1 1 1

T2 1 10 1 1 1

T3 1 1 10 1 1

T4 1 1 1 10 1

T5 1 1 1 1 10

- R1 R2 R3 R4 R5

T1 2 4 5 6 10

T2 2 12 15 1 9

T3 5 5 5 3 4

T4 8 13 14 2 3

T5 7 6 10 6 5

(a) (b)

TH=2 TH=4 TH=6 TH=8

−6

Profit (%)

Conf. 1

Conf. 2

Conf. 3

Fig.3. Percentage of increment in transported weight when threshold (TH) is not null.

5.2 Motion Coordination Experiments

This section will analyze the results of the proposed motion coordination methods:

follow the header and stay on the side. During the ﬁrst set of experiments robots must

transport a single object and total weight transported by the robots after 40000 time

units is calculated. Four different distances from the object to the delivery point has

been tested: D

= 278 units, D

= 370 units, D

= 493 and D

= 600 units. The

number of robots vary from 1 to 8 and all of them have the same load capacity (2

units). Figure 4 (a) shows the percentage of increment in transported weight using the

stay on the side strategy compared to not using it. During these experiments, the robots

cannot stop and wait to access to the shared resources. As it can be seen, the beneﬁt

of the stay on the side increases as the distance from the object to the delivery point

is greater. Figure 4 (b) shows the percentage of increment between transported weight

using follow the header strategy compared with a system without any strategy. As it can

be seen, unlike the stay on the side strategy, follow the header in most cases reduces

the total transported weight. Therefore, unlike it seems in principle, and unlike exposed

by other authors in other foraging tasks [8], a ﬂocking behavior, like follow the header,

produces a counterproductive effect in this kind of tasks. That is more evident as the

distance between gather and delivery point is reduced.

2 3 4 5 6 7 8

−2

−1

Profit (%)

Robots

2 3 4 5 6 7 8

−25

−20

−15

−10

−5

Profit (%)

Robots

(a) (b)

Fig.4. (a) Percentage of increment in transported weight using stay on the side compared to a sys-

tem without this strategy. The wait process is not used. (b) Percentage of increment in transported

weight using the follow the header strategy.

During a second set of experiments we tested the stay on the side behavior using

several objects with a ﬁnite weight. The task to do is the same than during the task

allocation experiments, but now all tasks belong to the same type and the same weight

(80 units). All robots have also the same load capacity (3 units). As it has been said

during the last paragraph, the stay on the side can produce good results only when the

distance between the object and the delivery point is large and there are a minimum

number of robots. Thus, during these experiments the robots only use the stay on the

side if the distance is grater than 160 and there are more than 3 robots in the group.

Figure 5 shows the total transported weight, after 42000 time units, using and not using

stay on the side method for different values of TH. As it can be seen, the stay on the

side strategy increases the transported weight in all cases.

6 Conclusion and future work

First of all, this paper presents a simple method of task allocation that extends the

current auction mechanisms to ﬁnd the number of robots needed to execute a task. This

number is unknown and depends on the task, the number of robots, the environment, etc.

In this methods the robots have diferents skills (load capacities) that depends on the type

TH=4 TH=6 TH=8

2400

2500

2600

2700

Transported Weight

Stay on the side

Without stay on the side

Fig.5. Results using multiple objects and stay on the side strategy

of the task. Thus, our system can ﬁnd a good task allocation. Then the paper explain two

new motion coordination strategies: follow the header and stay on the side. The follow

the header is a ﬂocking-like method, but unlike happens with other foraging tasks, this

strategy decrease the performance. It’s important to note that to our knowledge this is

the ﬁrst work that study how motion strategies can decrease the interference effect in

this kind of tasks. On the other hand, stay on the side can increase the total transported

weight.

The work presented is in progress and has some challenging aspects to add. For the

time being we are focused on a deep analysis of the data available. Another aspect of

the systems that should be improved is the use of a non ﬁxed threshold. We are also

developing a learning method, based on reinforcement, to know when the robots must

apply the stay on the side strategy.

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