Exploration of Unknown Map for Safety Purposes using Wheeled

Mobile Robots

Sara Ashry Mohammed

1,3

and Walid Gomaa

1,2

Cyber-Physical Systems Lab (CPS), Computer Science and Engineering Department (CSE),

Egypt-Japan University of Science and Technology (E-JUST), Alexandria, Egypt

Faculty of Engineering, Alexandria University, Alexandria, Egypt

Computers and Systems Department, Electronic Research Institute (ERI), Giza, Egypt

Keywords: Mobile Robots, Explore Unknown Map using Multi-robot, Rectilinear Obstacles, Gas and Fire Detection,

V-REP, Khepera III, Albers Algorithm, Zigzag Algorithm, Heuristic Backtracking SRT Algorithm.

Abstract: Exploring unknown 2-D grid map using multi-robots has a great significance in a vast domain of applications.

One possible application is to search for a gas leakage or a fire source which we address in this paper. We

propose an algorithm called Zigzag Ray for multi-robot exploration. The aim is to reduce the required time to

discover the environment as much as possible to suit the critical applications such as rescue operations.

Experiments are done using two, three, and four Khepera robots for exploring a map. The exploration time

without the boundary scan offset is ranged from 28.4% to 17.2% of the time taken by Albers algorithm and

from 41.2% to 30.7% of the time taken by the Zigzag algorithm for a single robot. Also, the time of four

robots by using a Zigzag algorithm for multi-robots is about 46% of Albers time of four robots. A disparity

in time existing between the algorithms shows the effectiveness of the new proposed algorithm. Additionally,

the Zigzag algorithm of a single robot is compared with the heuristic SRT algorithm. Zigzag time takes about

54.5% to 77.4% from heuristic SRT time. The evaluation is done using the Exploration Index strategy.

1 INTRODUCTION

Historically robots have been limited to industry,

where fixed manipulators were used for welding,

painting, assembly, product inspection, and testing.

Currently, robots are being used more for other

purposes. For instance, mobile robots have become

more present in our daily life; cleaning our flats,

mowing the lawn or searching for gas seepage or fire

in an unknown environment.

Robotic exploration algorithms grow because

they are crucial in many applications in this field.

Recently, looking for olfactory targets using mobile

robots has received a considerable interest because of

its importance in the detection of chemical seepage as

well as rescue and searching operations. Many studies

have been done in this field in (Marjovi et al., 2011),

(Soldan et al., 2014) and (Soares et al., 2016). Hiroshi

used chemical sensors as Noses for mobile robots

(Ishida et al., 2016). Multi- robots for odour source

localisation in an indoor map is presented by Wang

(Wang et al., 2016). A gas leak source detection with

mobile robots is introduced by (Martinez et al. 2014).

The motivation of this work is to give a

prototype of a robotic system that helps saving people

from fires and suffocation resulting from gas seepage.

Using a multi-robot in hard operations instead of

firefighters ensures the safety of their lives. Similarly,

it can also be applied in a smart home. It can be

essential for older whose abilities to move and to

sense gas seep are weak. This is not limited to only

the elderly, but also children who are left alone at

home sometimes. This application will have broader

prospects if it is applied as a protection factor

everywhere. Furthermore, the exploration time and

speed are the most significant factors in critical

applications.

This paper contributes a novel of exploration

algorithm using a multi-robot system. Robots

cooperate through a centralised PC station to explore

a map. The experiments are done on two, three, and

four robots. Also, the results are compared to both

Albers (Albers, 2002) and Zigzag algorithm of single-

robot (Ashry and Gomaa, 2016) to show the

effectiveness of the multi-robot exploration

algorithm, especially, in critical applications.

Mohammed, S. and Gomaa, W.

Exploration of Unknown Map for Safety Purposes using Wheeled Mobile Robots.

DOI: 10.5220/0006430903590367

In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 2, pages 359-367

ISBN: Not Available

359

Additionally, we compare Zigzag single robot with a

Heuristic SRT (Hussieny et al., 2015) algorithm.

Our paper organisation is as following: an

introduction is showed in section 1, after that the

related work is mentioned in Section 2, Section 3 is

discussing the background. Section 4 describes the

zigzag algorithm of multi-robots. Section 5 shows the

experiments in both a real world and simulation.

Section 6 concludes this paper.

2 RELATED WORK

The majority of the multi-robot exploration

algorithms have relied on using the concept of

frontier cells. The frontier-based exploration was

initially introduced by (Yamauchi, 1997) where each

grid cell in a 2-D map has a numeric value that shows

the existence of objects in the map.

Additionally, (Yamauchi, 1998) contended that to

find out the map; each robot moves towards the

nearest free frontier cell, and at least one of its

neighbouring cells is unexplored. The challenge is

how to choose the best frontier cell if more than one

robot is included in the exploration, it is important to

avoid the situation where two robots move to the cell

itself. Nevertheless, He considered that it is probable

that more than one robot move to explore the same

frontier and then more time is required to accomplish

the task. A more advanced technique where the robots

start at a known initial points is suggested by Burgard

(Burgard et al., 2005). The aim is to minimise the

whole time by choosing proper frontier cells for each

robot so that they explore different parts of the map

and the overlap between them is reduced.

(Sheng et al., 2006) considered that a limitation

communication range between the robots is a great

problem. In all of the mentioned research, the robot

senses the neighbouring cells using laser range

sensors. But, what if laser sensors aren’t available or

expensive. So, the proposed algorithm is suitable.

3 BACKGROUND

3.1 Albers Algorithm

Albers supposed that the robot starts at a corner point

and moves along the external border of a rectilinear

map in a clockwise direction until it backs to its origin

again. So, the robot could know the map dimension

and determine the lower segment. Then, it moves up

in a northern ray until hitting the boundary.

The robot then goes south on the same column and

takes one step east and radiate another northern ray in

a recursive operation till hitting the exterior boundary

or an obstacle. If the up ray hits an obstacle, then the

robot follows obstacle exploring process as described

in (Ashry and Gomaa, 2016). Albers algorithm is

shown in figure 1.

Figure 1: Shows Albers algorithm (Ashry, Gomaa, 2016).

3.2 Heuristic SRT Algorithm

Heuristic SRT algorithm is one of the randomised

motion exploring approaches. Robots are directed to

gain information through random steps. Those steps

should validate certain conditions to maximise the

acquired information and cover the entire map. While

random techniques have been used intensively for the

exploration, they are not efficient for the time critical

applications since the robot may visit the place itself

more than once during the backtrack operation like

(SRT) Sensor Random Tree (Oriolo et al., 2004).

(Hussieny et al., 2015) suggested a Heuristic SRT to

solve the backtracking problem to find a new frontier

cell. It reduced the exploration time to 30 % and 28

% respectively from basic SRT as shown in figure 2.

Figure 2: Left figure shows the basic SRT and right figure

shows heuristic backtracking algorithm, where a green line

(shortest path A*) is planned to the most informative node

and then the exploration process starts again. The robot

equipped with 360

laser finder (Hussieny et al., 2015).

3.3 Zigzag Algorithm of Single Robot

The problem of Albers algorithm is that the robot

moves on the same column twice because it goes up

and down on the same line to hit the lower segment.

Hence, this algorithm doubles the time of exploration.

The Zigzag algorithm proposed an enhancement of

this drawback. The robot radiates a ray to the north,

and then move one step in the east and emit a ray in

the southern direction of the next column

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

360

(up/east/down/east) (Ashry and Gomaa, 2016). It

does not reverse again on the same column like

Albers algorithm. If it faces an obstacle, it will follow

obstacle exploring process as in figure 3.

Figure 3: Shows Zigzag Ray lines, lower /upper segments.

4 ZIGZAG MULTI-ROBOTS

Zigzag of multi robots algorithm is proposed to

enhance the performance of zigzag of a single robot.

The experiments at section 5 show the effectiveness

of this algorithm compared to Albers and zigzag

(Ashry and Gomaa, 2016). The following algorithm

steps explain the zigzag of multi-robots on two robots

to illustrate the concept. Sure, the same algorithm can

be applied on multi-robots (3, 4, and so on). The PC

works as a centralised station, and the robots work

through a client to server’s network.

Figure 4: Shows the zigzag algorithm for multi-robots.

Protocol

Figure 5: The protocol between the client and servers.

PC centralised station:

1. Initialize a connection between the PC as a client

and each robot as a server.

2. The PC asks each robot in the initial state to adjust

its direction till the left sensor is occupied and it will

receive the position and direction of robots during the

boundary scan process.

3. After the PC has the exterior boundary, it will apply

the divide map process which divides the whole map

into small areas equals to the robots number. Then, it

sends small maps to each robot.

4. The PC receives information from each robot about

visited cells and obstacles and update the map.

5. If the PC receives information from any robot that

there is a common obstacle, the “Common Obstacle

process” will apply.

6. During exploring, each robot applies Collision

Avoidance technique at each node.

Robots as servers:

1. At the initial state, if we have two robots, the first

robot will be put at any corner with any direction

(north or east or west or south), and the second robot

will be placed at any point on the exterior boundary

of the map at any direction.

2. Each robot starts to adjust its direction till the left

sensor becomes occupied.

Exploration of Unknown Map for Safety Purposes using Wheeled Mobile Robots

361

3. The first robot starts to apply the Boundary scan

process. It moves on the exterior boundary in a

clockwise direction until it faces the second robot.

Then, it will stop and send the position and

orientation of the second robot to the station.

4. The second robot will continue exploring the

exterior boundary till it finishes it. So, the map

dimension is known. The boundary scan process

occurs at the first execution of the algorithm in the

map, but after that, it is executed without this step.

5. After the PC divided the map, each robot receives

information of a small map that should be explored,

and it starts exploring from the first column in its area.

6. If a small map does not contain any obstacles, then

each robot will apply the same concept of a zigzag ray

of the single robot (Ashry and Gomaa, 2016). But, if

there is any common obstacle between two regions,

the robot will use common obstacle method.

7. After each robot completes exploring its area, it

will park at any corner on its map boundary.

Divide Map process:

This pattern for the robots number (N = 2 or 3 or 4).

If N = 2, then split the large length (LL) by two as

shown in figure 6. If N= 3, then divide LL by 3. If N

= 4, then divide LL by 2 and cutting the large width

by 2.There are general algorithms for dividing a map

into small equal maps (Shermer, 1992).

(a)Divide map to 2 small areas. (b) Divide map to 3 small areas

Figure 6: The pattern of dividing map to 2, 3, and 4 areas.

Common Obstacle:

This method is applied when there is a common

obstacle between the areas. There are two cases:

Collision Avoidance Technique:

Each robot checks if any robot exists in its circle using

ultrasonic sensors as shown in figure 7. The circle

radius equalises to the edge length. If a robot detects

any other robot in its circle, then the robots will stop

and send to the station for taking the decision about

which one should move and which one has to stop and

wait until no other robot is detected on its circle. The

PC chooses any robot randomly to move and ask the

others to wait. Then, all robots will check ultrasonic

again at each node.

Figure 7: Shows the divided small maps virtually and the

circle area indicates the collision avoidance technique.

5 EXPERIMENTS

5.1 V-Rep Simulation

V-REP is used for developing algorithms and check

verification (Rohmer et al., 2013).

5.1.1 Comparing the Results of Zigzag

Algorithms towards Albers for Single

Robot

Experiments are done on V-REP to prove the

efficiency of the new Zigzag multi-robot vs. Albers

algorithm and the zigzag of a single robot. The

environments consist of M obstacles, N robots.

Figure 8: Left figure shows 4 robots on a map with one

obstacle. Middle figure shows them on map with two

obstacles. But, left shows them on a map with 3 obstacles.

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

362

(a)Test1, 1obstacle in

map7*7.

(b) Test2, 2obstacle in

map8*8.

(d) Test4, 3obstacle in map

9*9.

(e) Test5, 5 obstacles in map 19*39.

Figure 9: Charts of v-rep experiments shows the efficiency

of exploration time of the proposed algorithm.

Figure 10: It shows the exploration time at V-REP without

a boundary scan time, so, the speedup by 4 robots ranged

from 71% to 85%.

5.1.2 Comparing the Results of Zigzag

Multi-robots versus Albers

Multi-robots

We applied the same concept of a Zigzag algorithm

for multi robots, as explained in section 4, to Albers

algorithm to make a fair comparison. So, Albers is

tested on 2 robots and 4 robots. They are tested on the

same maps at test 1, 2, 3 and 4. Figure 11 shows the

result of this comparison.

Figure 11: It shows the exploration time of Albers vs.

Zigzag multi-robot at the V-REP without boundary offset

when each robot knows its start position and orientation.

The speed up percentage ranged from 33% to 50.5%.

5.1.3 Albers and Zigzag on a Rectilinear

Map

The experiments are also done on a rectilinear map

to show another environments type.

Figure 12: It shows experiments on a rectilinear map.

Albers with 2 robots on the left figure while Zigzag with 4

robots on the right figure.

Figure 13: It shows the exploration time of Albers vs.

Zigzag on a rectilinear map without boundary offset. The

speed-up percentage for 1, 2, and 4 robots ranged from 37%

to 42.5%. Additionally, using the Zigzag on 4 robots save

82.76% of the Albert time of single robot.

5.2 Controlled Real World

Experiments

The Experiments are done in a controlled

environment with 6*6 nodes and surrounded by a

wooden and cartoon panels as walls. Figure 14 shows

a snapshot from the experiments. Also, figure 15

shows the time of Albert, Zigzag on a single robot,

Exploration of Unknown Map for Safety Purposes using Wheeled Mobile Robots

363

and Zigzag for multi-robot at 2, 3, and 4 robots on a

map with zero, one and two obstacles.

Figure 14: A snapshot from the controlled environment on

the real world of map consist of 6*6 nodes.

Figure 15: It shows the real world experiments without the

boundary time offset. So, the speed-up percentage by using

the Zigzag to Albers approach, for 4 robots ranged from

85% to 89%.

5.3 Searching for Gas or Fire using

Multi-robots

We extended the application of searching for gas

source using one master robot (Ashry, 2016). The

extension includes searching for gas or a fire source

using multi-robots for saving people from gas

suffocations and fires. The master robots apply the

proposed exploration algorithm of Zigzag multi-

robots. Experiments are done on two master robots

equipped with high sensitive gas and flame sensors as

and two slave robots equipped with a gripper to

capture the potential victim by taking the Dijkstra’s

algorithm as shown in figure 16. The candle is used

as a fire source. The sensor module name is MQ-6. It

is sensitive to butane, propane, and natural gas.

After the exploration process and detecting the

target, the map and the target point (object found

beside gas/fire node) are sent to the two slave robots

(R2, R3) by a centralised station. Slaves receive the

map information, and they take the Dijkstra’s shortest

path algorithm to the target point. They equipped with

grippers to capture the object. R3 took the same route

of R2 as it is the shortest one, but its path was

increased with last steps to face R2. To avoid the

collision between robots, R2 precedes R3 with an

edge. R2 checks are arriving of R3 with front

ultrasound sensors. Then, the robots catch the object

as shown in figure 17. The following algorithm

illustrates the approach for safety purposes.

(a)Khepera III robots.

(b) Experiment in the real

world.

Figure 16: Gas or fire source detection in the system.

Figure 17: The slaves with the gripper on face to face.

5.4 Comparing the Results of Zigzag

Algorithm towards Heuristic SRT

for Single Robot

Haitham proposed a heuristic SRT backtracking as an

enhancement of the basic SRT exploration algorithm

while the robot reaches valuable nodes instead of

backtracking all the previous as in the basic sensor-

based techniques (Hussieny et al., 2015).

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

364

The contribution of this approach is the selection

of a valuable node. It is done with the help of the ray-

casting algorithm that estimates the number of cells

to be explored. The robot is equipped with 360

laser

range finder. It starts by choosing any node to explore

randomly depending on a sensor reading such that not

to choose an obstacle node or a node visited before. If

the robot reaches a close area, it chooses the nearest

node by calculating a heuristic function, and it will

take the A* path to it.

We compare the result of the heuristic SRT

backtracking with a zigzag algorithm for a single

robot. Considering the limitation of Khepera III robot

capabilities, we use infrared sensors instead of laser

range sensor. The robot can move in 4 directions (N,

S, E, and W) directions. The experiments are done on

a 2-D grid map on V-REP simulation as shown in

Figures 18, 19 and 20.

(a) Heuristic SRT.

(b) Zigzag on the map with

1 obstacle.

Figure 18: Shows the result of heuristic backtracking SRT

and zigzag algorithm on 9*9 map with one obstacle.

Figure 19: It shows the result of simulation on a rectilinear

map with 4 obstacles between heuristic SRT on the left

figure and zigzag on the right figure using a single robot.

Figure 20: The result of comparison between heuristic SRT

and zigzag algorithm of a single robot.

6 EVALUATION

There is a trade-off between the metrics evaluating

the exploration approach performance like distance,

time and area completeness percentage which

comesover the exploration cost. A single

“ExplorationIndex” is used to judge the performance

of differentexploration strategies (Hussieny et al.,

2015).

EI is directly proportional to the completeness C,

and is inversely proportional to the exploration

time(ET) and the travelled distance (TD), and the

normalised number of nodes (F). The larger the

values of this index, the better the performance of a

strategy. The index is defined by equation 1.

 





∗







∗



∗







∗





∗



∗





(1)

Where F = N-

tot

/ N

actual visited

and Wc, W

, W

and W

are the proportional weights added to measure the

contribution of each factor to a metric. Different

environments were tested to show a high Exploration

index (EI) as shown in figure 21. Assume W

= W

= W in equation 1.

Table 1: Shows the EI of Zigzag and heuristic SRT.

Test C ET(min) TD(m) F EI

T1:Zigzag 1 10.33 42 1 2.3*10

-3

T1: SRT 1 13.25 56 1 1.3*10

-3

T2:Zigzag 1 8 40 1 3.1*10

-3

T2: SRT 1 14.3 58 1 1.2*10

-3

T3:Zigzag 1 22 70.5 1 6.5*10

-4

T4: SRT 0.97 32 83 1.03 3.5*10

-4

Figure 21: Chart the EI of Zigzag and heuristic SRT.

We evaluate the Zigzag Algorithms vs. Albers by

measuring the exploration time on different case

studies on an experimental work and calculating the

tight bound time complexity for each algorithm as

shown in Table 2 where ϴ is the tight bound function,

n is number of nodes in a column, Obstacles (n) is

function determines total complexity for all obstacles

and C is a constant which include nodes hidden inside

obstacles to remove them from the calculation.

Exploration of Unknown Map for Safety Purposes using Wheeled Mobile Robots

365

Table 2: Shows the tight bound complexity of Albers VS.

Zigzag algorithm for single and multi-robots.

Algorithm Tight bound time complexity

Albers single robot ϴ ((2 n

+ 5n) + Obstacles (n) - C)

Zigzag single robot ϴ ((n

– n -2) + Obstacles (n) - C)

Albers multi-robots

ϴ ((4n +(







) +n ) + Obstacles(n) - C)

Zigzag multi-robots

ϴ ((







) + (n-2)+ Obstacles(n) - C)

7 CONCLUSION

The paper proposes an algorithm for exploring

unknown grid map using a centralised multi-robot

system called Zigzag Multi-robots for safety

purposes. If the map is large, and the common

obstacles are minimum, the exploration time of 4

robots on a rectilinear map is equal to 0.172 of Albers

time. Nevertheless, in the worst case, when there are

common obstacles, the time of 4 robots in the map is

equal to 0.284 of Albers time. Also, we used this

algorithm as a part of the combined approach for the

gas/ fire searching using two robots as masters and

two robots as slaves to hold the potential victim.

Additionally, we compare Zigzag with heuristic SRT,

and we measure the evaluation index where the

higher the EI, the better performance of the algorithm.

In future work, we will apply Zigzag multi-robots

algorithm on a decentralised system in bigger maps

with 8 and 16 robots and compare the results with an

extension for heuristic SRT multi-robots approach.

ACKNOWLEDGMENTS

The author would like to thank Dr. Mohammed

Hamdy from Fayoum University, Dr. Reda El-

Bssuieny, Dr. Haitham El-Hussieny from Banha

University and Dr.Alaa sheta from ERI. The first

author is supported by a scholarship from the Egypt

Scientific Research which is gratefully thankful.

REFERENCES

A. Marjovi and L. Marques. (2011). "Multi-robot olfactory

search in structured environments”. Robotics and

Autonomous Systems, (pp. 867–881, no. 11.).

Ashry, S., & Gomaa, W. (2016). "Exploration Of Unknown

Map For Gas Searching And Picking Up Objects Using

Khepera Mobile Robots". the 13th International

Conference on Informatics in Control, Automation and

Robotics (pp. 294 – 302. (Vol 2)). In Portugal,July 29-

31: ICINCO.

B.Yamauchi. ( 1998). “Frontier-based exploration using

multiple robots”. in Proceedings of the 2th

international conference on Autonomous agents. ACM,,

(pp. 47–53).

B.Yamauchi. (1997). “A frontier-based approach for

autonomous exploration”. In Computational

Intelligence in Robotics and Automation (pp. 146–151).

IEEE, 1997.

D. Martinez, T. Pallej`a, J. Moreno, M. Tresanchez, M.

Teixid´o, D. Font, A. Pardo, S. Marco, and J. Palac´ın.

(2014). “A mobile robot agent for gas leak source

detection”. In Trends in Practical Applications of

Heterogeneous Multi-Agent Systems (pp. 19–25). The

PAAMS Collection. Springer, 2014.

E.W.Dijkstra. (1959). " A note on two problems in

connexion with graphs. Numerische mathematik". 269–

271, vol 1.

G. Oriolo, M. Vendittelli, L. Freda, and G. Troso. (2004).

“The srt method: Randomized strategies for

exploration”. In Proceeding of IEEE International

Conference on Robotics and Automation (pp. 4688–

4694, vol. 5). ICRA.

H. Ishida, A. J. Lilienthal, H. Matsukura, V. H. Bennetts,

and E. Schaffernicht. (2016). “Using chemical sensors

as noses for mobile robots”. Essentials of Machine

Olfaction and Taste, (pp. 219–245).

Haitham El-Hussieny, Samy Assal, and Mohamed

Abdellatif. (2015, Apr 1). "Robotic exploration: new

heuristic backtracking algorithm, performance

evaluation and complexity metric". International

Journal of Advanced Robotic Systems, 12(4), p.33.

J. M. Soares, A. Marjovi, J. Giezendanner, A. Kodiyan, A.

P. Aguiar, A. M. Pascoal, and A. Martinoli. (2016).

“Towards 3-d distributed odour source localisation: an

extended graph-based formation control algorithm for

plume tracking”. In Intelligent Robots and Systems

(IROS) (pp. 1729–1736). IEEE/RSJ International

Conference.

M. Turduev, G. Cabrita, M. Kırtay, V. Gazi, and L.

Marques. (2014). “Experimental studies on chemical

concentration map building by a multi-robot system

using bio-inspired algorithms”. Autonomous agents and

multi-agent systems, (pp. 72–100, vol. 28, no. 1).

S. Albers, K. Kursawe, and S. Schuierer. (2002).

“Exploring unknown environments with obstacles”.

Algorithmica, vol. 32, pp. 123–143.

S. Soldan, J. Welle, T. Barz, A. Kroll, and D. Schulz.

(2014). “Towards autonomous robotic systems for

remote gas leak detection and localization in industrial

environments”. In Field and Service Robotics (pp. 233–

247). Springer, 2014.

Shermer, T. C. (1992). “A linear algorithm for bisecting a

polygon”. Information processing letters, (pp. 135–

140, vol. 41, no. 3.).

W. Wang, M. Cao, S. Ma, C. Ren, X. Zhu, and H. Lu.

(2016). “Multi-robot odor source search based on

cuckoo search algorithm in ventilated indoor

environment”. n Intelligent Control and Automation

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

366

(WCICA), 12th World Congress (pp. 1496–1501).

IEEE, 2016.

W.Burgard, M.Moors, C.Stachniss, and F.E.Schneider.

(2005). “Coordinated multi-robot exploration”.

Robotics, (pp. 376–386, vol. 21, no. 3).

W.Sheng, Q.Yang, J.Tan, and N.Xi. (2006). “Distributed

multi-robot coordination in area exploration”. Robotics

and Autonomous Systems, (pp. 945–955, vol. 54, no.

12).

Rohmer, E., Singh, S. P., and Freese, M. (2013). V-rep: A

versatile and scalable robot simulation framework. pp.

1321–1326.

Exploration of Unknown Map for Safety Purposes using Wheeled Mobile Robots

367