Copyright: 978-1-4799-2722-7/13/$31.00 ©2013 IEEE

An Enhancement in Conventional Potential Field Using a Fuzzy System for Navigation of a Sumo

Robot Carlos Erlan Olival Lima

LABoratory of Intelligent Robotics, Automation and Systems - LABIRAS

CAPES Foundation, Ministry of Education of Brazil Brasilia – DF, ZIP CODE 70.040-020

Instituto Federal do Piauí - IFPI Teresina, Brazil

Tianjin University E-mail: erlanolival@gmail.com

Francisco Marcelino Almeida de Araújo, Mário Bibiano da Silva Júnior, Antônio Edson Rocha Filho

LABoratory of Intelligent Robotics, Automation and Systems - LABIRAS

Instituto Federal do Piauí - IFPI Teresina, Brazil

E-mail: franciscomarcelinoalmeida@gmail.com, mario_bibiano@hotmail.com, edson_engmec@gmail.com.br

Ricardo de Andrade Lira Rabêlo, Thiago Allisson Ribeiro da Silva, Antonio Jose de Oliveira Alves

Computing Department Universidade Federal do Piaui - UFPI

Teresina, Brazil E-mail: ricardor_usp@ieee.org,

allissonribeiro02@gmail.com, aj.alves@zerokol.com

Abstract: An enhancement in conventional potential field is presented in this paper for autonomous sumo robot class navigation with dynamic environments including moving target and static obstacle. This method determines the velocity and the path taken by the robot in order to reach your target in the shortest time possible. This improvement on the conventional potential field is used to determine the velocity and position of an autonomous sumo robot class, which is intended to push the opponent out of the arena. This hybrid method is composed of potential field approach with fuzzy logic, and in this study the Mamdani model is used to obtain the necessary variables to determine the velocity and direction of the robot. Two fuzzy systems are used, both with three inputs and one output. The only difference between the two fuzzy systems is the number of linguistics terms. One simulation has been done in the MATLAB to verify the enhancement of the hybrid method in relation to the conventional potential field. The simulation represents the trajectory of the robot until find the target. Accordingly with the simulation done, the hybrid method was 14% more effective.

Keywords— Potential field, velocity planning, direction planning, mobile robot, fuzzy system.

I. INTRODUCTION Robots have been used for specialized tasks, mainly which

are too dangerous for human beings. The robots can be remote-controlled, semiautonomous or autonomous. Autonomous robots act completely on their own in performing tasks, using microcontrollers or computers for control the movements of the robot and many different sensors to get the environment data [1]. The design of an autonomous robot is a complex task and the criteria of success are evaluated in terms of its

capabilities to make decisions and to act by itself in a reliable and satisfactory manner [2]. When autonomous robots have to deal with unknown environments and imprecise information, the navigational problem becomes extremely complex; therefore different approaches for navigation have been studied. The main approaches are: visibility graph or roadmap, probabilistic road map, path planning and velocity planning methods and potential field approaches [3-5].

The potential field approach is the only method that deals with dynamic environment where the obstacles and the targets are in movement [6]. The potential field has been widely used in robotic for generating paths and for mobile robots navigation. This method creates a field that directs the robot to the goal position. This approach treats the robot as a point under the influence of an artificial potential field. The robot moves by following the field and the goal acts as an attractive force on the robot, and the obstacle acts as repulsive force [7]. Several drawbacks are reported for this approach such as: convergence to local minimum, heavy calculation requirement, and goal non reachable with obstacles nearby [8].

Therefore a modified model of the potential field, which was proposed by [9] has been used in this paper. This model overcomes the convergence to local minimum and goal non reachable with obstacles nearby problems. The model proposed by [9] has the disadvantage with respect to the navigation properly when the target is very close and the velocity of the robot is much greater than the velocity of the target. In this case the robot maintains the higher speed, which is not desirable,

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therefore the robot have difficulty to find situation.

The disadvantages of the model proposedovercome by using a fuzzy system. This developed using a fuzzy system to establishfollowed by the robot, regardless of the distthe robot relative to the target. Therefore, tshowed in this paper does not have the disadvtarget when it is very close and the velocimuch greater than the velocity of the target.

Another disadvantage of the potential fcalculation. This problem has been oversystems, which reduce the high dimensionaliteight inputs (the relative position of the rovelocity of the target, angle of the target in rabscissas, the relative position of the robovelocity of the obstacle, angle of the obstaaxis of abscissas, the angle of the relative pto the obstacle and the angle related to thefrom robot to the target) required by the poteto only four inputs (the relative position otarget, velocity of the target, the angle relaposition from robot to the target and the anposition from robot to the obstacle). computing power required with the reducnumbers will be less than that used in mathe[5].

The approach used in this work has planning the velocity and direction of an arobot class. In this work the opponent robot wmovement and the boundary of the arena wiThe arena is the environment where the robarena is a ring with black surface and whiwhite boundary corresponds to the obstacsurface is the region of the arena where the romove. In this work is considered that thmovement stationary. Although this articlefuzzy-potential field method to the sumo robcan be extended to other types of robots, suchline and soccer class. It also can be deployunstructured environments or semi structuinformation regarding the provision of sobjects.

In this paper a simulation of the environmthe sumo robot class is presented to show this method. The simulation tracks the trajeand of the target of the initial position until throbot finds the target. From this simulation graphics of the velocity of the robot and of trobot in relation to target. The simulation shhas been done in the software MATLAB.

II. MODELING AND CONTROL AR

A. Modeling System Fig. 1 shows the trajectory of the robo

vectors of the velocity and the relative posirobot and the target and between the robotFig. 1 also shows the angles that the vectors o

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the target in this

d by [9] have been new approach is

h guidelines to be tance and speed of the hybrid method vantage to find the ity of the robot is

field is the heavy come with fuzzy ty of the system of obot to the target, relation the axis of ot to the obstacle, cle in relation the osition from robot e relative position ential field method f the robot to the

ated to the relative ngle of the relative

Furthermore, the ction of the input ematical modeling

the objective of autonomous sumo will be the target in ill be the obstacle.

bot is moving. The ite boundary. The cle and the black obot and the target he obstacle is in e uses the hybrid

bots class, their use h as the follower’s yed in industry in ured with limited static or dynamic

ment of combat of the advantages of

ectory of the robot he position that the were generate the the distance of the

howed in this work

RCHITECTURE

ot, as well as the itions between the t and the obstacle. of the velocity and

relative position of the robot, taaxis of the abscissas. To simplifbe reached and an obstacle tcalculations. The following nosystem:

Fig. 1 Representation of the Roboto

XOY: world coordinates in

ptar ε R2: position of the targ

vtar ε R2: velocity of the targ

p ε R2: position of the robot

v ε R2: velocity of the robot

pobs ε R2: position of the obs

vobs ε R2: velocity of the obs

prt = ptar - p: relative position

pro = pobs-p: relative position

pot =ptar - pobs: relative positi

Ψ: angle of prt;

θtar: angle of vtar;

θro: angle of pro;

θot: angle of pot;

θobs: angle of vobs;

θ: angle of v.

In this paper was consideripotential field. The assumptions

Assumption 1. The positionvtar and vobs are all known.

Assumption 2. The obstacconvex polygon. In this papercover by a circle.

Assumption 3. The robot, treated as point mass.

The following assumptions the robot are also made:

arget and obstacle done with the fy the modeling only one goal to to avoid are considered in the otations are used to describe the

ot Positioning in Relation to Target and o Obstacle [9]

the workspace;

get;

get;

t;

t;

stacle;

stacle;

n from robot to target;

n from robot to obstacle;

ion from obstacle to target;

ing three assumptions mainly to s are:

ns p, ptar and pobs and velocities v,

cle is covered by a circle or a r is considered that obstacle is

the target and the obstacle are

on the limits of the operation of

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Assumption 4. The maximum linear and the robot are vmax and ωmax respectively.

Assumption 5. The speed of the targ││vtar││<=vmax.

In simulation that will be presented, velocity measurements of the target and obsby the ultrasound sensors. The vmax and ωmaccording with the engine used.

B. Planning of theVelocity of the Robot The velocity of the robot will be random

distance of influence of the obstacle. Attracrepulsive potential acts in the robot when tline. Nevertheless, only attractive potentialwhen it is in the black surface, because there the obstacle in this moment. Therefore, therpotential when the robot is in the black surfac

Fig. 1 shows the angles formed betweenhorizontal axis and the angle between the hthe projected path by the target. Fig. 1 alsobetween the horizontal axis and velocity element participant.

According with L. Huang in [9] the direction of the robot as there is attractrepulsive potential are represented by the equrespectively. | | || | | |||| || || || / sin / ||

Where

tan sin sin cos cos| | || ||

|| || ,0 , | |

The velocity and the direction of the robattractive potential are represented by the equrespectively. |v| |v | 2ε |p | |v | cosε ||p || / sin / ||

©2013 IEEE

angular speeds of

get is limited by

the positions and stacle are obtained max are determined

m according to the ctive potential and the robot is in the l act in the robot is not influence of

re is not repulsive ce.

n the robot and the horizontal axis and o shows the angle

vectors of each

velocity and the tive potential and uations (1) and (2),

(1) || (2)

s (3)

(4)

bot as there is only uations (5) and (6),

s θ ψ (5) || (6)

In equations (1) and (5) εcorresponds to the scaling factohigher the value of the ε1 highrobot. In the equation (4) thedepends of ε2, ρ, ρo and ρro to(4) ε2 correspond to the scpotential, ρ denotes the minimand the obstacle and ρo is thobstacle.

C. Applying the Method of FuzThe potential field method

needed to determine the velorobot shall follow, so a fuzzy sydimensionality of the system [has eight inputs, but using theare required by the potential fithree inputs fuzzy.

The inputs required by therelative position of the robot totarget (vtar), angle of the target (θtar), the relative position of tvelocity of the obstacle (vobs), the axis of abscissas (θobs), angrobot to the obstacle (θro) and th

By using the fuzzy system the tilt of the line (ψ), and between θtar and ψ. This differoutput of the fuzzy system. Tused in the equation 1 to deterThe output of the fuzzy systemBy using the difference betweefuzzy system, the efficiency ofthat in the potential field methofield method the variables θtar aTherefore, the scaling error iconventional because there arethe simulations that will be shousing the fuzzy system the robshort time. Therefore, the fuzzyinputs required and improves ef

For determining the directioto establish θro, which is obtaiinfrared sensors. It is only necthe robot detects the edge, repulsive potential. While the there is only attractive potentialequal ψ.

The fuzzy system employerobot with two wheels and configuration shown in Figure 2

Fig. 2 System R

ε1 is an empirical constant that or of the attractive potential. The her the speed determined for the e variable η is showed, which o be determined. In the equation caling factor of the repulsive

mum distance between the robot he distance of influence of the

zzy Potential Field d has a large number of inputs ocity and the direction that the ystem is used to reduce the high [10, 11]. Originally the method e fuzzy system only four inputs field, nevertheless there are only

e potential field method are: the o the target (prt), velocity of the in relation the axis of abscissas the robot to the obstacle (pobs), angle of the obstacle in relation gle of the relative position from he angle related to the prt (ψ).

the only inputs are prt, vtar, and get from them the difference

rence between θtar and ψ is the he value of the fuzzy output is rmine the velocity of the robot.

m used has a range of [-π/2, π/2]. en θtar and ψ how output of the f the direction planning is better od conventional. In the potential and ψ are determined separately. is bigger in the potential field e two variables to determine. In wed in this paper is verified that bot gets to range the target in a y system reduces the number of fficiency.

on of the robot is also necessary ined through the position of the cessary to set this variable when

because in this case there is robot does not detect the edge, l, so η will be zero and ψ will be

ed herein is used for an active one support wheels, with the 2.

Robot Locomotion [12]

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In this research two fuzzy systems have been used. The two fuzzy systems have three input variables and one output variable. In the first system each variable has three linguistics terms with two triangular membership functions for the two first terms and one trapezoidal membership function for the last term. In the second system two fuzzy input variables have three linguistics terms and one has five linguistics terms with a triangular membership function for each term.

In the first fuzzy system each variable of the system has three linguistic terms. The system inputs and related linguistic terms are: Distance (prt) (Small, Medium, High), Target Velocity (vtar) (Low, Medium, High), Tilt Straight Line (ψ) (Low, Medium, High). The system output and related linguistics terms is represented as Difference (Low, Medium, High), which corresponds to the difference between variables ψ and θtar. The two first membership functions of each linguistic variable are triangular and the last membership function is trapezoidal.

The inputs of the second fuzzy system are equivalent the inputs of the first fuzzy system. The difference between two fuzzy systems is that in the second system all membership functions are triangular and the linguistic variable (ψ) has five terms linguistics. The linguistic terms of (ψ) are: Very Low, Low, Medium, High and Very High.

A total of 27 rules are required to implement the first fuzzy system while the second system fuzzy requires 45 rules. The system is based on fuzzy IF-THEN rules. A sample of the system is shows:

R1: IF Distance is Small AND Target Velocity is Low AND Tilt Straight Line is Low THEN Difference is Low

R2: IF Distance is Small AND Target Velocity is Low AND Tilt Straight Line is Medium THEN Difference is Low

R3: IF Distance is Small AND Target Velocity is Low AND Tilt Straight Lime is High THEN Difference is Medium

The inference output from these rules is computed by mean of the Mamdani (max-min) operator for composition, minimum operator for implication and centroid for defuzzification [5]. The fuzzy systems used are shown in Fig. 3 and 4, which presents a little scheme with the inputs and output of the fuzzy system.

To validate this system, a simulation is studied regarding to the direction that the robot must follow to find your target. This simulation is presented in a Cartesian coordinate system and from simulation is obtained the result regarding the relative distance between the robot and the target and velocity of the robot at each moment.

In this simulation, has been creates the movements of the robot. The movements of the robot are described in three parts. The first part of the movement corresponds to the initial acceleration motion. In this case the acceleration is quite high due to the high torque applied. This high torque provides the slip of the wheels during a certain time where the robot is accelerating but it is not changing its position in space.

When the wheels of the robot stop slipping, the robot starts to change its position in space. In this moment the robot

accelerates to reach to its maximum speed, which depends of the engine that is being used. This is the second part of the movement. Finally, when the robot has reached its maximum speed, it begins to move through the values established by the method used.

Fig. 3 Fuzzy Inference System, with three inputs and one output (First

System Fuzzy)

Fig. 4 Fuzzy Inference System, with three inputs and one output (Second System Fuzzy)

III. SIMULATION OF THE TRAJECTORY OF A SUMO ROBOT CLASS

One simulation has been conducted in the MATLAB to validate the hybrid method used. In this simulation an environment which represents the displacement of the object and of the robot, within a circle with diameter of 152 centimeters has been established. This environment is shown in Fig. 5. In this representation the target firstly moves in a straight line with an acceleration of 8 m/s2. This occurs until it reaches its maximum speed.

In the moment that the target reaches its maximum speed, the motion becomes linear with constant speed until it reaches a certain point in space. In the moment which the target reaches this point it attempts to escape of the robot instead of trying to find it. In this moment the target is moving in a sinusoidal path with an acceleration of 8 m/s2.

In this simulation the target is initially set in position [50 114] while the robot is in position [50 38]. The positions determine to the robot and the target were chooses therefore the minimum distance between the robot and the target in the start of the combat should be 24 centimeters. Therefore, the simulation was initialized with the robot and target to place in opposite sides in the center of the radius of the circle.

The maximum speed established for the target is of 20 cm/s, which is the average speed achieved by the majority of robots used in the competition. The obstacle is represented for the circle and it velocity is zero [13].

This movement of the target was designed so that it obtains some possible movement of the target during the match. In the first moment, the target tries to find the robot. This movement

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occurs while the target is moving in straight line. As the movement of the form sinusoidal, this corresponds to the time in which the target is trying to escape. In this interval, the target describes its movement in the form of a parabola trying to difficult the perception of the robot that is trying to find it.

The motion that the robot describes to find the opponent is shown in Fig. 5. To better illustrate the movement which the target describes its movement is shown in Fig. 6 in expanded form.

Fig. 5 Trajectory made for robot to find the target

Two graphics were generated from this environment, the first relative position between the robot and the target and the second corresponding to velocity of the robot. These graphics are generated in relation to time, and they show the difference between the time obtained using only potential field and the time obtained to using hybrid fuzzy potential field method. These graphics are shown in Fig. 7 and 8, respectively.

In the analysis of the graphic of Fig. 7 and 8 it can be verified that the robot find more quickly the target through of the fuzzy potential field method. This occurs because the fuzzy system establishes specific conditions to determine the velocity and direction of the robot in order to decrease the mistake in the measuring.

Fig. 6 Trajectory Described by Target

Fig. 7 Distance between Robot and Target, with Target Movement with

Random Velocity

Fig. 8 Velocity of the Robot with Target Movement with Random

Velocity.

The mistake in the measuring occurs mainly due to the difficult to establish the value of the θtar. On the simulation of the potential field this value is obtained deriving the movement equation. In the fuzzy potential method is not established the value of the θtar. In this hybrid method is obtained the difference between the angles θtar and ψ. This difference is the output of the fuzzy system.

The output difference is obtained according to (1), (2), (5) and (6). According to this equations, as higher the velocity of the robot lower is the difference between the angles, therefore this value depend of the cosine. The opposite occurs with the direction therefore depend of the sine of the difference between the angles.

Beyond of value of the difference between the angles θtar and ψ, another factor that influences the navigation is the constant ε1, therefore as higher ε1, greater be the velocity of the robot. The largest possible value for ε1 is 0.5, because a value above this cause a speed greater than the maximum speed allowed by the engine used. The engine used for the calculus was the Pittman [14] with reduction ratio of 29.5:1. Therefore the highest speed that the robot of this simulation can have is 51 cm/s. The time required to find the target using the potential field method with this scaling factor is 2.261 seconds while for the hybrid fuzzy potential field method is 1.944 seconds. Therefore, the hybrid fuzzy potential field method was 14.2 % bester than the potential field method.

The robot has 4.52 N.m of torque using the highest speed it, which enables the robot to load an object with a five times its weight. Therefore, this robot can load up to 15 kg since its mass is 3 kg.

The Fig. 8 shows the variation of the velocity of the robot during the movement, which is divided into three parts, as already commented previously. The first part of the movement occurs when the robot's wheels are slipping. In this moment the robot does not perform any movement in the space. The second part of the movement corresponds to moment in which the robot starts to change its position in the space. In this part of the movement the method used acts only in the determining of the direction that the robot should follow.

The third part of the movement is divided in two, and these two parts corresponds to the time in which the robot operates on the conditions imposed by the method used. In the first part the target is moving with constant speed while in the second part the target is moving with variable speed. The third part of

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the movement starts when the robot reaches its maximum speed, which is 51 cm/s. The robot reaches this speed in a time period of 0.041 seconds. From this moment the movement of the robot is determined by the velocity and direction defined by the navigation method used. This part of the movement extends until the moment when the robot finds the target.

The performance of the robot using the hybrid fuzzy potential field and conventional potential field method is shows in the Table 1. The Table 1 shows the total distance that the robot moves until find the target and the total time required to find the target. The Table 1 is showed to more adequately express the performance of the proposed system.

TABLE. 1 PERFORMANCE OF THE ROBOT

Total Distance that the Robot Moves until find the target (cm)

Total Time Required to Find the Target (s)

Hybrid Fuzzy Potential Field Method 54.093 1.944

Conventional Potential Field 54.962 2.261

IV. APPLICATION As already mentioned, this method is applied to a robot

sumo category to improve the perception of the robot in relation to the environment and opponent. The robot possess thirteen ultrasound sensors arranged side by side with a tilt angle of 15°, which is set due to the opening angle of the signal emitted by the sensor, which is 15°. This configuration is used to cover the 180° of the front view of the robot. This sensor was chosen because of the small opening angle. With a small opening angle, the grain size is small, which allows more accurate perception of the environment. The location of the sensor that detects an object is used as input to the fuzzy system. The input used is the linguistic variable Tilt Straight Line. In Fig. 9 a representation of the way that these sensors will be arranged is presented. The ultrasonic sensor used is the HC - SR04, which has a range of up to 4 meters [15].

Fig. 9 Representation of Array Sensors; 1 – Opening Angle of the

Sensor

V. CONCLUSION This paper presented an enhancement of the potential

field method through to use of fuzzy systems. In this paper the hybrid fuzzy-potential field method was used to velocity and direction planning of sumo robot class. Two fuzzy systems models have been used to verify the efficiency of the hybrid method. The hybrid method was investigated based on one conducted simulation scenario in the MATLAB.

Through simulations it can be observed that the hybrid fuzzy potential field method is very effective that potential field conventional. By using the hybrid method the robot can find the target in just 1.944 seconds while by using the potential field conventional the time is of 2.261 seconds. Therefore the hybrid fuzzy potential field method is 14 % more effective that potential field method.

The hybrid method showed in this paper takes into account the coefficient of friction between the tire and the contact surface as well as the torque required to drive the robot. Therefore, this hybrid method can be used in various

types of robots, independent of the environment. In the future is expected to combine the hybrid fuzzy potential field method with neural networks to trying to improvement the efficiency of the approach.

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