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Cooperative Movement of Human and Swarm Robot Maintaining

Stability of Swarm

Hiroshi Hashimoto, Shinichi Aso, Sho Yokota, Akinori Sasaki, Yasuhiro Ohyama and Hiroyuki Kobayashi

Abstract—This paper proposes a method that a human and

a swarm robot move cooperatively so as to maintain the swarm

situation that the swarm robot surround the moving human. This

paper is concerned with the control for maintaining the high

stability of the swarm, and proposes a control algorithm for the

robotic swarm in obstacle space. In this paper, the robotic swarm

which includes whole robots is defined as a whole swarm. In

addition, each robot with neighboring robots forms a local swarm

that overlapped the other ones partially, so a robot can belong

to some local swarms. The proposed algorithm for overcoming

above problems is based on the center of gravity of the local

swarm which attracts the robot of it, and is applied to the omni-

directional mobile robots. It is confirmed that the effectiveness

about maintaing the stability of the swarm through simulations

using ODE (Open Dynamics Engine).

I. INTRODUCTION

This paper proposes a method that a human and a swarm

robot move cooperatively so as to maintain the swarm situation

that the swarm robot follow the moving human by surrounding

one.

In various fields, it is desired that human and swarm robot

are able to work cooperativly. Fig.1 shows its conceptual illus-

tration. To do this, it is important to realize the robot function

of cooperative movement such as the swarm robot surround

and follow the human who moves around. There are several

researches on the cooperative movement of swarm robot, but

not cooperative movement of human and swarm robot. First of

all, let us see the previous research of cooperative movement

of swarm robot.

Conventional mobile robots have been controlled for only

task which was given. Therefore, these robots have been used

in limited environment such as a factory. However autonomous

Fig. 1. Illustration of cooperative movement of a human and swarm robot

H.Hashimoto is with Advanced Institute of Industrial Technology, Tokyo,

Japan hashimoto@aiit.ac.jp

S.Aso, S.Yokota, A.Sasaki and Y.Ohyama are with Tokyo University of

Technology, Tokyo, Japan

H.Kobayashi is with Osaka Institute of Technology, Osaka, Japan

mobile robots are developed, because a robot technology

has been advancing. In particular various works have been

researching on a distributed cooperative control for multiple

autonomous mobile robots.

The basic task of the distributed cooperative control is that

multiple autonomous mobile robots advance to the common

place [2]. For this reason, if multiple autonomous mobile

robots behave as a swarm, these robots effectually can ad-

vance to the common place. Recently, a considerable number

of studies have been made on the control for the robotic

swarm [1] - [10]. Makino et al. proposed an algorithm that

controls the robotic swarm by applying simple virtual forces

to individual robots [1]. Shimizu et al. proposed an algorithm

that controls a coherent swarm by the Molecular Dynamics

method and Stokesian Dynamics method [3] [4]. Kurabayashi

et al. proposed a formation transition algorithm based on

Delaunay diagram [2]. However, these studies do not consider

maintaining the stability of the swarm while robots advance

to the goal in obstacle space.

In this case, there are some problems with the swarm

structure and the stability of it. For examples, to pass a narrow

corridor decreases the stability of the swarm, and may remain

the low stability of the swarm after passing. To pass a fork of

the road may tear the swarm. However, there is no algorithm

to overcome these problems.

Therefore, this paper is concerned with the control for

maintaining the high stability of the swarm, and proposes a

control algorithm for the robotic swarm in obstacle space. In

this paper, the robotic swarm which includes whole robots is

defined as a whole swarm. In addition, each robot with neigh-

boring robots forms a local swarm that overlapped the other

ones partially, so a robot can belong to some local swarms. The

proposed algorithm for overcoming above problems is based

on the center of gravity of the local swarm which attracts

the robot of it, and is applied to the omni-directional mobile

robots.

In order to be compatible with maintaining a high stability

of the whole swarm and surrounding the moving human,

virtual forces; local forces and an surrounding force which are

produced by the algorithm, are applied to multiple autonomous

mobile robots. Local forces such as an attraction and a

repulsion, are applied to each robot for increasing the stability

of the local swarm. The attraction is applied to each robot for

forming the local swarm with neighboring robots. Besides,

the repulsion is applied to each robot for avoiding collisions

with neighboring objects which are both other robots and

obstacles. Overlapping each local swarm partially increases the

stability of the whole swarm. The surrounding force is applied

Proceedings of the 17th IEEE International Symposium on Robot and Human Interactive Communication, Technische

Universität München, Munich, Germany, August 1-3, 2008

978-1-4244-2213-5/08/$25.00 ©2008 IEEE249

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to each robot for surrounding the human while maintaining the

stability of the local swarm.

Since obstacles which prevent the robot follow the moving

human are considered as a disturbance from the viewpoint

of the stability of the whole swarm, an effectiveness of the

algorithm in obstacle space is evaluated using ODE (Open

Dynamics Engine) [11] which is dynamics simulations. This

paper defines the stability of the swarm for robots, and

twenty mobile robots, each is omni-directional mobile robot,

surrounding the human is simulated. As a result, it is found

that the algorithm is able to achieve the high stability of the

whole swarm surrounding and follwoing the human moves.

II. CONFIGURATION OF MULTIPLE AUTONOMOUS MOBILE

ROBOTS

Ideal mobile robots are the omni-directional mobile robots,

because the distributed cooperative control requires high mo-

bility to the robot. Therefore, the proposed algorithm is ap-

plied to the omni-directional mobile robot. This paper defines

autonomous mobile robot as follows and shown in Fig. 2.

• Autonomous mobile robots are the omni-directional mo-

bile circular robot with radius R.

• It is possible to measure the position of neighboring

robots and obstacles relative to the robot in its sight S.

• It is possible to measure the direction of the goal relative

to the robot.

• There is no communication between robots.

Autonomous mobile robot with neighboring robots in its

sight S forms local swarms, and avoids neighboring objects

which are both other robots and obstacles within range for

collision avoidance A.

The assumed robot is equipped with three omni-directional

wheels as shown in Fig. 3. Rw, Rrw are wheel radius and

distance to wheel from center of robot, and eiis unit vector

along rotational direction of wheeliin Fig. 3. Such the mobile

robot as robot shown in Fig. 3 has been realized already, and

is used in various environments. Here, the coordinate system

of Fig. 3 is the local coordinate system. This paper proposes

the distributed cooperative control using local information for

these robots.

Fig. 2.Parameters of robots

Fig. 3. Omni-directional mobile robot

(a)The swarm (b)The torn swarm

Swarm structureFig. 4.

III. FORMATION OF SWARM OF ROBOTS

This section defines conditions for forming swarm structure

in order to be compatible with maintaining the high stability

of the whole swarm and surrounding the human.

Each definition is explained below.

A. Conditions for forming swarm structure

Conditions for forming swarm structure are defined as

follows.

1) The center of robot is defined as the vertex.

2) The vertex of robot and vertexes of neighboring robots

in its sight are joined by edge.

3) The simple graph on adjacent edges is defined as G.

4) The vertex set of G is defined as V er(G).

5) The element count of V er(G) is defined as |V er(G)|.

6) The number of robots is defined as N.

7) If |V er(G)| = N, robots are forming the swarm.

Multiple autonomous mobile robots shown in Fig. 4(a)

are forming the whole swarm, because |V er(G)| = N. In

contrast, the whole swarm shown in Fig. 4(b) is torn, because

|V er(G)| < N.

B. Definition of stability of swarm

The stability of the swarm is defined as follows. Multiple

autonomous mobile robots must be forming the whole swarm,

namely robots have to satisfy above mentioned conditions for

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forming the swarm structure. Then, the center of gravity of

the whole swarm g is given by eq. (1).

g

=

1

N

N

∑

i=1

ip

(1)

whereip, N are the position of roboti and the number of

robots. Furthermore, this paper supposes that a trajectory of g

represent a trajectory of the whole swarm.

There are some gaps between robots even if robots show

the swarm structure. However, too large gaps, namely a large

swarm, lead to the torn swarm. On the other hand, too small

gaps, namely a narrow swarm, restrict the individual behavior.

This paper supposes that stabilities of these swarms are low.

Therefore, this paper defines the stability of the swarm using

an extent of the whole swarm r which is described by eq. (2).

?

N

r

=

?

?

?1

N

∑

i=1

|ip − g|2

(2)

Since this is the conventional equation of the standard

deviation, the value of r shows the extent of the whole swarm.

It is assumed that the extent of the whole swarm r converges

to the constant extent if robots maintain the high stability

of the whole swarm. The constant extent is defined as r∗.

Accordingly, the stability of the whole swarm becomes the

most high if r converges to r∗.

The stability of the whole swarm is verified in section V-C.

IV. ROBOT CONTROL BY VIRTUAL FORCES

Multiple autonomous mobile robots are controlled using

local information by the proposed algorithm based on the

center of gravity of the local swarm which attracts the robot of

it. In order to be compatible with maintaining the high stability

of the whole swarm and surrounding the human, virtual forces;

local forces and the advancing force which are produced by

the algorithm, are applied to each autonomous mobile robot

by eq. (3).

fi= fRi+ fOi+ fGi

(3)

where fRi, fOi are local forces; the attraction and the re-

pulsion, and fGiis the surrounding force, respectively. Local

forces fRi, fOi are applied to each robot for increasing the

stability of the local swarm. Besides, the surrounding force

fGi is applied to each robot for surrounding to the human

while maintaining the stability of it.

Each force is explained below. Table I shows definition of

variables which use below.

A. Local forces

1) Attraction: The robot with neighboring robots in its sight

S forms local swarms that overlapped the other ones partially,

so a robot can belong to some local swarms. Then, the center

of gravity of the local swarm giin the robotiis given by eq.

(4).

1

Ni+ 1

j∈RTSi

gi=

∑

ipj

(4)

TABLE I

DEFINITION OF VARIABLES

RTSi

RTAi

:

:

The set of neighboring robots in roboti’s sight S.

The set of neighboring robots within the roboti’s

range for collision avoidance A.

The set of obstacles within the roboti’s range for

collision avoidance A.

The union of RTAiand OBSi.

The number of the element of set RTSi.

The proximate position of objectjrelative to the

roboti. (ixj,iyj)T

The position of the goal relative to the roboti.

(ixG,iyG)T

The angle of direction of velocity in the roboti

relative to the roboti.

The angle of the center of gravity of the local

swarm in the robotirelative to the roboti.

The angle of the goal relative to the roboti.

OBSi

:

OBJi

Ni

ipj

:

:

:

ipG

:

iθi

:

iθgi

:

iθG

:

Furthermore, the attraction which is based on the impedance

control is applied to each robot for approaching giby eq. (5).

fRi= Md2gi

dt2+ Bdgi

dt

+ Kgi

(5)

where M, B are a mass and a dumper, and K is a spring.

2) Repulsion: The repulsion is applied to each robot from

neighboring objects which are both other robots and obstacles

within its range for collision avoidance A by eq. (6).

∑

where Q is a constant repulsion, and fOi is in inverse

proportion to the distance of objects relative to each robot.

Therefore, the robot avoids objects by fOiwhich strengthens

as the distance of objects relative to it is more near.

Stabilities of local swarms increase by local forces. Ac-

cordingly, overlapping each local swarm partially increases the

stability of the whole swarm.

fOi=

j∈OBJi

(

Q

|ipj|2·

ipj

|ipj|)

(6)

B. Surrounding force

The surrounding force to surround a humna is applied to

each robot for surrounding the human while maintaining the

stability of the local swarm by eq. (7).

fGi= FG

ipG

|ipG|ci

(7)

where FG is an adjustable constant parameter. Eq. (7) uses

the relative position of the humanl to center of roboti

However note thatipGis used for expressing the direction of

the humanl relative to the robot.

fGichanges based on ciwhich is shown in eq. (8).

ci=(1 + cosiθG−gi)(1 + cosiθi−gi)

4

whereiθG−gi,iθi−giare calculated in eq. (9) and eq. (10).

iθG−gi

iθi−gi

ipG.

(8)

=

=

iθG−iθgi

iθi−iθgi

(9)

(10)

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Fig. 5. Simulated robot and wheel

where ci increases as angles ofiθi andiθG relative toiθgi

decreases.

fGi weakens as the robot heads the whole swarm, and

strengthens as the robot follows in the rear using eq. (8).

Specifically, robots which follow in the rear push robots which

head the whole swarm until surrounding the human. On the

other hand, robots which head the whole swarm maintain the

stability of the local swarm until advancing to the goal.

For this reason, the proposed algorithm is able to maintain

the high stability of the whole swarm advancing to the goal

in obstacle space as human moving.

V. EXPERIMENTS

Since obstacles which prevent the robot surrounding and

following the human are considered as the disturbance from

the viewpoint of the stability of the whole swarm, the effective-

ness of the proposed algorithm in obstacle space is evaluated

using ODE as a dynamic simulation [11] which is dynamics

simulations. Dynamics simulations are for simulating rigid

body dynamics. Moreover, these are useful for simulating

vehicles and objects in virtual reality environments, because

collision detection functions are incorporated.

A. Configuration of simulated robot

This simulation is evaluated using omni-directional robots

as shown in Fig. 3. Mechanical features of robot are described

as follows.

• The mobile robot has three omni-directional wheels.

• Wheels are omni wheel with small discs which are

perpendicular to the rolling direction.

• The mobile robot moves when wheels rotate.

The simulated robot and the wheel are shown in Fig. 5.

The hemisphere of head shows front in the simulated robot.

Therefore, the forward direction of Xraxis of the coordinate

system is front of robot.

As mentioned above, the simulated robot is controlled by the

proposed algorithm in simulation environment as if that in real

environment. In addition, this paper evaluates the effectiveness

of the algorithm by dynamics simulation.

B. Conditions for simulation

Twenty autonomous mobile robots are controlled by dynam-

ics simulation in obstacle space which have rectangular and

circular obstacles. The sampling period ∆t is 0.02 sec, and

the setting of the mobile robot is that radius R is 0.1 m, sight

S is 1.0 m and range for collision avoidance A is 0.5 m.

Each robot is placed on lattice-like arrangement over the

center of gravity of the whole swarm. These placements are

defined as initial placement.

The proposed algorithm is evaluated by the following sim-

ulations based on these settings.

• The verification of the stability of the swarm.

• Simulations in passing the narrow corridor.

• Simulations in avoiding cylindrical obstacle.

Simulations above are executed twice by changing intervals

of the initial placement. Intervals of the initial placement are

80 % and 20 % of sight S, namely 0.8 m and 0.2 m. The

effectiveness of the proposed algorithm is evaluated by the

stability of the swarm in dynamics simulation.

C. Verification of stability of swarm

The stability of the whole swarm increases by the local

forces. This paper assumes that the whole swarm has moderate

extent, when the stability of it is the most high. In other

words, when the extent of the whole swarm r converges to

the constant extent r∗, the stability of it is the most high.

Thus, this section evaluates the stability of the swarm by r.

The advancing force is not applied to each robot, and the

local forces are applied to it for verifying the stability of the

swarm. Accordingly, the robot is given by eq. (11).

fi= fRi+ fOi

(11)

Results of the simulation from initial placements of robots

at intervals of 0.8 m is shown in Fig. 6, and the extent of

the whole swarm r is shown in Fig. 7. First, robots behave as

increase the stability of the whole swarm. Then, robots behave

as maintain the high stability of the whole swarm in Fig. 6(b),

and r converges to 0.65 in Fig. 7. Similarly, robots behave

as mentioned above and r converges to same value in case

of 0.2 m intervals. As a result, r∗becomes 0.65 if twenty

mobile robots whose radius R is 0.1 m behave as increase the

stability of the whole swarm. Therefore, the stability of the

whole swarm becomes the most high when r converges to r∗.

The following simulations evaluate the stability of the swarm

in the case of robots that advance to the goal in obstacle space.

D. Experimental results in passing narrow corridor

The simulation is examined to investigate the behavior of the

swarm robot surrounding the human when the human passes

a narrow corridor with 1.2 m width. Initial conditionss are

that the placements of robots is at intervals of 0.8 m and the

location of human is at center of the swarm robots as shown

in Fig.8(a). The speed of human increases gradually from 0

m/s to the maximum speed 1m/s.

Simulation results Fig.8 (b)-(e) show that the swarm robots

surrounding and following the human who moves from the

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0

4

8

12

-8 -4 0 4 8

[m]

Time 0.00 sec

1.35

r

X

[m]

Y

(a)

0

4

8

12

-8 -4 0

[m]

X

(b)

4 8

Time 6.00 sec

0.65

r

[m]

Y

Fig. 6.

placements of robots at intervals of 0.8 m

Results in maintaining the stability of the whole swarm from initial

0

0.5

1

1.5

0 1 2 3 4 5 6

r

time [sec]

(a)

(b)

Intervals of 0.8 m

Intervals of 0.2 m

r*

Fig. 7. Extent of whole swarm in maintaining the stability of it

initial location to the exit of the narrow corridor, while

maintaining the stability of the swarm. Finally, the swarm of

the human and the robots were always stable and succeeded

in the passing the narrow corridor without colliding each other

and also obstacles.

To pass the narrow corridor decreases the stability of the

swarm, and may remain the low stability of the swarm after

passing. However, the stability of the whole swarm returns

to the high stability after passing the narrow corridor by the

proposed algorithm.

First, robots behave as increase the stability of the whole

swarm from initial placements of robots at intervals of 0.8 m

in Fig. 8(a) to Fig. 8(b). Similarly, robots behave as mentioned

above in case of 0.2 m intervals. Secondly, robots which head

the whole swarm are pushed from robots which follow in the

whole swarm, and robots pass into the narrow corridor little

by little in Fig. 8(c). Thirdly, all robots pass into the narrow

corridor in Fig. 8(d), but the stability of it decreases because

r diverges from r∗. Finally, after all robots passed the narrow

corridor in Fig. 8(e), the stability of it returns to the high

stability in Fig. 8(f) because r converges to r∗.

E. Experimental results in avoiding obstacle

The simulation is examined to investigate the behavior of

the swarm robot surrounding the human when the human

avoids cylindrical obstacle of radius 1.0 m. Initial conditionss

are same in the case of the previous experiments. Simulation

results Fig.9 (b)-(f) show that the swarm robots surrounding

and following the human who moves from the initial location

to the opposite side of the obstacle while maintaining the

stability of the swarm, without colliding each other and also

obstacles.

VI. CONCLUSION

This paper proposes a method that a human and a swarm

robot move cooperatively so as to maintain the swarm situ-

ation that twenty swarm robot with omni-directional mobile

structure follow the moving human by surrounding him.

By defining the stability of the swarm using the extent of

the whole swarm for evaluating the algorithm, it is confirmed

that the swarm of human and swarm robot are able to maintain

the stability in two cases that are the narrow corridor and the

cylindrical obstacles.

Future works include evaluating the proposed algorithm in

various environment. For example, the algorithm is applied

to multiple autonomous mobile robots in environment which

have slopes.

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