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

Velocity and Direction Planning in a Sumo Robot Type Using the Method of Potential Field with Fuzzy

Systems 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 Tianjin University Teresina, Brazil

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

Ricardo de Andrade Lira Rabêlo, Thiago Allison 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 application of the potential field method is presented in this paper for autonomous sumo robot class navigation with dynamic environments including moving target and static obstacle. The method used in this paper aims to planning the velocity and the direction taken by the robot in order to reach your target in the possible shortest time. The design velocity is determined from the relative velocities between the robot and the target as well as the relative positions between them. This work uses a hybrid method to determine the velocity and position of a sumo robot class, which is intended to push the opponent out of the arena. This hybrid method applies the potential field with fuzzy logic and use the Mamdani model to obtain the necessary variables for determining the velocity and direction to be followed by the robot. For determining the time necessary to find the target two simulations were done in the MATLAB. The obtained results show that the hybrid method overcomes the local minimum problem within any stationary or dynamic environment with static obstacles.

Keywords— Potential field; velocity planning; direction planning; mobile robot; fuzzy system;

I. INTRODUCTION Currently, there are several approaches to planning of

velocity and direction of a mobile robot, but the approaches most employed only work with static environments, or only with the moving obstacle [1]. Currently, the main approaches used to planning the velocity and direction of a mobile robot are: visibility graph or roadmap, probabilistic roadmap, path planning and velocity planning method and potential field

approach [2-4]. The potential field approach is the only method that deals with environment totally dynamic, which is environment where the target and the obstacle are in movement [5].

The potential field has been widely used in robotics for generating paths. The method considers the goal to be achieved corresponding to an attraction force and the obstacles corresponding to a repulsive force [6]. The direction to be followed by the robot to avoid the obstacles and to find your target is considered as a vector resulting from the sum of all the force vectors involved [6].

The conventional potential field method is not suitable for determining the trajectory of a robot in a dynamic environment, [7]. This occurs because the original method exhibits problems such as local minimum, no passage for the robot between obstacles, and goals no reachable with obstacles nearby [7].

In this paper a modified model of the potential field is used due to the problems above-mentioned. This model was proposed by [7] and it overcomes the convergence to local minimum and goal non reachable with obstacles nearby problems. This approach 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; therefore the robot has difficulty in finding the target in this situation [7].

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The disadvantage of the model proposed bby using a fuzzy system. This new approach a fuzzy system to establish guidelines to brobot, whatever the distance and velocity ofto the target. Therefore, the hybrid methopaper does not have the disadvantage of when it is very close and the velocity of tgreater than the velocity of the target.

Another disadvantage of the potential fcalculation. This problem also has been ovesystems, 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[8].

The approach used in this paper has planning the velocity and direction of an sumo class to participate in challenges war roout this approach was considered that the oppin movement and the edge of the arena is thwork the obstacle is in stationary movemearticle uses the hybrid fuzzy-potential metrobots class, its use can be extended to othesuch as the follower’s line and class soccer. Iin industry in unstructured environments owith limited information regarding the provdynamic objects.

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. To simplify the modelinbe reached is considered in the calculationnotations are used to describe the system:

XOY: world coordinates in the workspace

ptar ε R2: position of the target;

vtar ε R2: velocity of the target;

p ε R2: position of the robot;

v ε R2: velocity of the robot;

prt = ptar - p: relative position from robot to

Ψ: angle of prt;

θtar: angle of vtar;

θ: angle of v.

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by [7] is overcome is developed using e followed by the f the robot relative od showed in this finding the target the robot is much

field is the heavy ercome 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 robot obots. For carrying ponent is the target he obstacle. In this ent. Although this thod to the sumo er types of robots, It can be deployed or semi structured vision of static or

RCHITECTURE

ot, as well as the itions between the

ng only one goal to ns. The following

e;

o target;

Fig. 1 Representation of the

In this paper was consideripotential field. The assumptions

Assumption 1. The positionv, vtar 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:

Assumption 4. The maximuthe robot are vmax and ωmax resp

Assumption 5. The speed││vtar││<=vmax.

In simulation that will bevelocity measurements of the tby the ultrasound sensors. Thaccording with the engine used

B. Planning of Velocity of the As the velocity planning is

influence of the obstacle is lowattraction is used to planning of

Fig. 1 show the angles forhorizontal axis and between projected path by the targetbetween the horizontal axis element participant.

According with [7] the veloinfluence of the obstacle is:

|v| = |vtar| 2+2ε1 prt |vtar

In this equation, is assumed

Robot Positioning in Relation to Target when p> po, [7]

ing three assumptions mainly to s are:

ns p, ptar and pobs and velocities

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

um linear and angular speeds of pectively.

d of the target is limited by

e presented, the positions and target and obstacle are obtained

he vmax and ωmax are determined .

Robot when p>po done to a sumo robot class, the

w, therefore only the potential of f the velocity.

rmed between the robot and the n the horizontal axis and the . Fig.1 also shows the angle and velocity vectors of each

ocity of the robot as there is not

r| cos ( θtar-ψ +ε12| prt |

2)1/2

(1)

d that vtar and ||prt|| are nonzero.

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The direction of the robot, according to [The direction represents the angle of the robof abscissas.

θ=ψ+ sin-1 ((vtarsen θtar-ψ )/(||v|In the equations (1) and (2) ε1 is an empi

corresponds to the scaling factor of the attrachigher the value of the ε1 higher the speed drobot.

C. Applying the Method of Fuzzy Potential FThe potential field has a large number o

determine the velocity and the direction thfollow, so a fuzzy system is used to dimensionality of the method [8]. Originally tinputs, but using the fuzzy system only required by the potential field. These inputmeans of ultrasonic sensors [9, 10].

The inputs required for the potential fielposition of the robot to the target (prt), velo(vtar), angle of the target in relation to the axiand the angle related to the prt (ψ). The variabplaced in the conventional method in termcoordinates. By using the fuzzy system the ovtar and the tilt straight line (ψ), and thouobtained the difference between θtar and ψ. the output of the fuzzy system. This value is to determine the velocity and direction of the

The fuzzy system employed herein is urobot with two wheels and one support configuration shown in Fig. 2.

Fig. 2 System Robot Locomoti

Each variable of the fuzzy system used hterms. The system inputs and related lingDistance (prt) (Small, Medium, High), Tar(Low, Medium, High), Tilt Straight Line (ψHigh). The system output and related linrepresented as Difference (Low, Mediumcorresponds to the difference between variabl

The membership functions used to invewere defined as triangular and trapezofunctions, and the system is based on fuzzy total of 27 rules are required to implement ththe following ways:

R1: IF Distance is Small AND TargetAND Tilt Straight Line is Low THEN Differe

R2: IF Distance is Small AND TargetAND Tilt Straight Line is Medium THEN Di

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[7] is given by (2). bot relative to axis

|) ) (2)

irical constant that ctive potential. The determined for the

Field f inputs needed to hat the robot will reduce the high

the method has six three inputs are

ts are obtained by

ld are: the relative ocity of the target s of abscissas (θtar) bles prt and vtar are

ms of the x and y only inputs are prt, ught them can be This difference is used in (1) and (2) robot.

used for an active wheels, with the

ion [11]

has three linguistic guistic terms are: get Velocity (vtar) ψ) (Low, Medium, nguistics terms is m, High), which les ψ and θtar.

stigate the system oidal membership IF-THEN rules. A he fuzzy system in

t Velocity is Low ence is Low

t Velocity is Low ifference is Low

R3: IF Distance is Small AND Tilt Straight Lime is High

The outputs of the set of means of the Mamdani (max-For implication is used thedefuzzification is used the centis shown in Fig. 3, which prinputs and outputs of the system

Two simulations are studiesimulations are regarding the follow to find your target. The a Cartesian coordinate system. and the target and the velocity simulations.

In the simulations, the robthree parts. The first part of thinitial acceleration motion. In thhigh due to the high torque appthe slip of the wheels during aaccelerating but it is not changi

When the wheels of the robstart to move. The robot accelspeed, which depends of the ethe second part of the movemereached its maximum speed, values established by the hybrThis movement will be descrisection.

Fig. 3 Fuzzy Inference Systin

III. SIMULATIONS OFSUMO ROB

Two simulations have beenvalidate the hybrid method usedtarget movement in a straight simulation is used to determinresults. The scaling factor with second simulation. The first simIn this simulation the target desconstant velocity, wherein the [0 70] while the robot is in posi

The maximum speed establis the average speed achieved bthe competition. [12].

AND Target Velocity is Low h THEN Difference is Medium

inference rules are obtained by -min) operator for composition. e minimum operator and for troid [8]. The fuzzy system used esents a little scheme with the

m.

ed to validate this system. The direction that the robot must

two simulations are presented in The distance between the robot of the robot are obtained of the

bot's movement is described in he movement corresponds to the his case the acceleration is quite plied. This high torque provides a certain time when the robot is ng its position in space.

bot stop slipping, the robot will lerates until reach its maximum

engine that is being used; this is ent. Finally, when the robot has it starts to move through the

rid fuzzy-potential field method. ibed in more detail in the next

tem Using Mamdani method, with three nputs and one output

F THE TRAJECTORY OF A BOT CLASS n conducted in the MATLAB to d. The first simulation tracks the path parallel to the x-axis. This

ne the scaling factor with better better results will be used in the

mulation is shown in the Fig. 4. scribes a rectilinear motion with target is initially set in position

ition [0 0].

ished to target is 20 cm/s, which by the majority of robots used in

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Two graphics were generated from thisfirst relative to position between the robot athe latter relative to velocity of the robot. Tgenerated in relation to the time and are showrespectively.

Fig. 4 Trajectory described by the robot

Three values for the constant ε1 wedetermine the shortest time required to thtarget. This constant influences mainly in velocity of the robot and direction that it willthe value of ε1 greater the speed set for the rthis constant is established accordingly to mathe robot should have, which depend of the mreduction ratio gears.

Fig. 5 Distance among Robot and Target – RLine (ε1=0.5), Cyan Line

In the Fig. 5 the robot finds more quicklthe value of the constant ε1 is higher. Thervelocity for the robot is higher when the valNevertheless the largest possible value of ε1value causes a speed greater than the maximby the engine used. The engine used for thePittman [13] with reduction ratio of 29.5highest speed that the robot of this simulaticm/s. The time required to find the target is othe scaling factor is 0.5. For other values shothe time is 4.161 and 5.266 seconds as the equivalent to 0.6 and 0.4, respectively.

The robot has 4.52 N.m of torque using thwhich enables the robot to load an object wi

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s environment, the and the target and These graphics are wn in Fig. 5 and 6,

t to find the target

ere established to he robot finds the

the value of the l follow. As higher obot. The value of aximum speed that motor, battery and

Red Line (ε1=0.4), Blue e (ε1=0.6)

ly the target when refore, the defined lue of ε1 is higher. 1 is 0.5. A greatest

mum speed allowed e calculus was the 5:1. Therefore the ion can have is 51 of 4.616 seconds as own in the graphic, scaling factors are

he highest speed it, ith a five times its

weight. Therefore, this robot mass is 3 kg.

The Fig. 6 shows the variaduring the movement, which iFig. 7 shows the first part orobot's wheels are slipping. In perform any movement in space

In Fig. 6 the second and tshown. The second part of thein which the robot starts to acceIn this moment the hybrid fuzzthe calculation of the directionThe third part of the movemenits maximum speed. The moveto the speed and direction impo

Fig. 6 Velocity of the Ro(ε1=0

Fig. 7 Representation of the

In the Fig. 7 the robot is sl0.015 seconds, and its speed 0.1766 cm/s. The robot will b0.1766 cm/s, which is represegraphic.

The movement that the accelerated, and the initial accepresented by [11]. It corresponrobot is slipping, and the value

The second part of the moin which the robot starts to accerobot exceeds maximum speedoccurs for a time interval of 0.

can load up to 15 kg since its

tion of the velocity of the robot is divided into three parts. The f the movement, in which the this moment the robot does not e.

third part of the movement are movement corresponds to time elerate until its maximum speed. zy-potential method acts only in n that the robot should follow.

nt occurs when the robot reaches ement is carrying out according

osed by the method used.

obot - Red Line (ε1=0.4), Blue Line

0.5), Cyan Line (ε1=0.6)

time interval in which the wheels of the robot are slipping

lipping during a time interval of at the end of this first step is

begin to move with a speed of ented by the red square in the

robot performs is uniformly eleration is given by the equation nds to acceleration in which the determined was 11.772 m/s2.

vement corresponds to moment elerate until the moment that the

d its. This part of the movement .036 seconds independent of the

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scaling factor value. During this time, the robot is accelerated according to the equation presented by Meggiolaro in [11] to acceleration without slipping, and the obtained value was 12.5 m/s2.

The third part of the movement starts when the robot reaches the target. This part of the movement depends of the scaling factor and as higher the value of the scaling factor shorter the time spent to find the target. The third part of the movement continue until that the robot find the target.

The second simulation studies have 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.

The maximum speed of the target is 20 cm/s. 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.

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 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 moving with variable velocity is shown in the Fig. 8. The movement of the target enlarged form is shows in the Fig. 9 to better illustrate the movement which the target describes.

Fig. 8 Trajectory made for robot to find the target

Fig. 9 Trajectory Described by Target

Two graphics were generated from this environment. The first corresponds to the relative position between the robot and the target and the latter corresponds to the 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. 10 and 11, respectively.

Fig. 10 Distance between Robot and Target, with Target Movement

with Random Velocity

Fig. 11 Velocity of the Robot with Target Movement with Random

Velocity

In the analysis of the graphic of Fig. 10 and 11 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.

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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) and (2). 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 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.

The Fig. 11 shows the variation of the velocity of the robot during the movement. Through of the Fig. 11 can be observed that the movement of the robot is described in three parts as occurs in the first simulation. The first and second parts correspond to the same motion shown in Fig. 5 and 6. The robot will have the same acceleration set for the first environment.

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

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. The difference between them is that firstly the target is moving with constant velocity, and after the target moves with variable velocity. The third part of the movement starts when the robot reaches its maximum speed. The maximum speed of the robot is 51 cm/s. The robot reaches this speed in a time period of 0.041 seconds. From this moment the robot is replaced by its velocity and

direction defined by the method used. The third part of the movement extends until the time that the robot finds the target.

Fig. 12 Velocity of the Robot when the Target is Movement with

Variable Velocity

The Fig. 12 represents the third part of the movement in the moment which the target moves with variable velocity. The velocity of the robot depends of the velocity of the target as is shown in (1). Therefore, as the target accelerates or decelerates, the robot does the same. The variation of the velocity of the robot accordingly with the velocity of the target avoids unnecessary waste of energy supplied by the battery.

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 type was chosen because of the opening angle small. With a small opening angle, the grain size is small, which allows a more accurate perception of the environment. The location obtain for these sensors is used as input to the fuzzy system. The input used is the linguistic variable Tilt Straight Line.

In Fig. 13 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 [14].

Fig. 13 Representation of Array Sensors; 1- Opening Angle of the

Sensor

V. CONCLUSION This paper presented an enhancement of the potential field

method using fuzzy systems. In this paper the hybrid fuzzy-potential field method was used to velocity and direction

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

planning of sumo robot class. The hybrid method was investigated based on two conducted simulation scenarios 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 the hybrid fuzzy potential field method will be combined with neural networks to try to improve the efficiency of the approach.

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[9] S. K. Pradhan, D. R. Parhi, A. K. Pandar, “Fuzzy Logic Techniques for Navigation of Several Robots,” Applied Soft Computing (2009) 290 – 304.

[10] D. R. Parhi, J. C. Mohanta, “Navigational control of several mobile robotic agents using Petri-potential-fuzzy hybrid controller,”Applied Soft Computing 11 (2011) 3546-3557.

[11] M. A. Meggiolaro, “RioBotz Combot Tutorial,” UFRJ, 2009. [12] ROBOCORE. (2013, June, 3) Availible:

http://www.robocore.net/modules.php?name=Forums&file=viewtopic&t=3979

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[14] ULTRASONIC RANGING MODULE HC – SR04. (2013, May. 20) Availible: < http://www.micropik.com/PDF/HCSR04.pdf>