Fuzzy Control of Swarm Ad-Hoc Network Based Systems for Locating Emission Sources Debdutta Bhattacharya Roll No. 05EC1008 Department of Electronics and Electrical Communication Engineering Indian Institute of technology, Kharagpur – 721302, India E-mail: [email protected]

Abstract A swarm based fuzzy logic control of robots is proposed for the finding of a source of contaminant/aerosol leak in a hazardous environment where human exploration is difficult. The objective is to locate the source of a contaminant emission. Each robot communicates with others in vicinity with its limited communication capabilities via an ad-hoc wireless network. Thus, all robots in vicinity provide data which are the contaminant values measured by appropriate sensors for determining next direction of motion of a robot. Each robot thus finds its next location using the data by the fuzzy logic control embedded in it and finally zero in onto the location. Partial failure of sensors and failure of a particular robot does not affect the search to a great extent. Fuzzy logic is used to accommodate various approximate ranges of values of contaminant concentration and also write down approximate rules regarding orientation (direction) of the robot. Problem Definition Leakage of contaminants/aerosols in a particular area is sometimes a problem in plants dealing with hazardous products like nuclear power plants. Once this happens, the general approach is to deploy an automated robot with sensors. It is time taking and expensive. It follows one of the three techniques - spiral surge, bias-random walk and gradient seek. However the downside of using a single robot is that it is susceptible to local maxima of pollutant/aerosol concentration. Instead, a swarm based system of robots each with limited communication and sensing abilities would do the same job in a much faster time with each robot communicating with its neighbors to move in the direction of highest contaminant reading. This is the main approach to the problem. A swarm is deployed to find the source of contamination. They communicate via an ad-hoc wireless network with all bots in proximity which act as extended sensors. Three properties of a swarm system are realized- separation, cohesion and alignment assuring that wide regional coverage and stable connectivity is maintained. The emission source is located in a fewer number of steps by this method.

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Details about the problem The fuzzy variables for such a swarm based system can be found from the inputs that a robot would need to move to the next location. It would require the maximum concentration and the robot in vicinity that reports such a maximum concentration. Thus the variables used are: • Concentrations of contaminant (as reported by all extended sensors) • Direction of robots which report concentrations In general, the problem approach may be given by the following chart (Figure 1):

Figure 1 – Working of the Fuzzy Logic Control

Fuzzification of the problem (Membership functions) The two variables mentioned are: 1.) Concentration of contaminant 2.) Direction of reporting sensor They are fuzzified in the following manner: 1. Concentration of contaminant (as reported by the extended sensors) We obtain a set of values:S= {s1,s2…,sn} from all readings obtained from robots. The MAX and MIN values in the figure equal the minimum value and maximum value of all sensors’ reading data that the robot collected from other robots at each time-step. This data keeps changing continuously and graphs are redrawn with this data. (as shown in Figure 2) As seen in the graph, LOW – 0% to 50% of the range obtained. (Trapezoidal function used.) MEDIUM – 30% to 70% of the range obtained. (Triangular Function used.) HIGH – 50% to 100% of the range obtained. (Trapezoidal function used.)

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Figure 2 -The concentration membership function

• •

Two typical sets are shown as an example – When the robot is far from the leak : S = {0.6,1.2,0.45,7.5,8,0.87} When the robot is near the leak : S = {30.5,40.6,85,67.6,50}

Thus, we fuzzify the concentrations with the help of the maximum and minimum concentration reported. The concentration reading itself may range from 0 to 100(in this case, it is so). And this reading helps in deciding which direction the robot should head. The dynamic change of the limits ensure flexibility of the system. 2. Directions of robots which report the concentrations Each robot has the set of directions and concentrations of all other robots in vicinity with which it can communicate via the ad-hoc network. The directions reported may range from -1800 to 1800 out of which 8 angles have been designated names. The angles when fuzzified are expressed in terms of these broad directions.(Shown in Figure 3)

Figure 3(a) - The Broad Directions

Figure3(b) - Robots nearby acting as extended sensors

The entire area is divided into a matrix or into cells into which the robots may move. Thus each cell has 8 surrounding cells. However, this is the localized picture for a particular robot. It is not necessary that the cell of one robot will be the cell in another’s map. Its area may well be part of two cells. The main point is that the robots can be at any angle with respect to a robot and thus the need to fuzzify the direction.The robots that are in the vicinity are given directions on the basis of angles measured from the line of sight of the robot. Thus a robot has 8 directions (Back, Back Left, Left, Front Left, Front, Front Right, Right, and Back Right). The membership function is as shown in Figure 4.

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Figure 4 – The direction membership function For each given angle, this function is referred to, to get the probability of firing of each rule. It is triangular in shape. The Fuzzy Interface: These fuzzy rules are described in IFTHEN form and use the above linguistic variables. Our objective is to take the linguistic values and find the next direction of movement of the robot. The diffusion of pollutant/aerosol in the contaminated area will induce a gradient phenomenon. A high concentration indicates a location near the source. The rules set should tend to steer all robots to the vicinity of the highest reported concentration. Thus, the rules we use are: 1) If concentration is HIGH and direction is FRONT, move FRONT. 2) If concentration is HIGH and direction is FRONT LEFT, move FRONT LEFT. 3) If concentration is HIGH and direction is FRONT RIGHT, move FRONT RIGHT. 4) If concentration is HIGH and direction is BACK, move BACK. 5) If concentration is HIGH and direction is BACK LEFT, move BACK LEFT. 6) If concentration is HIGH and direction is BACK RIGHT, move BACK. 7) If concentration is HIGH and direction is LEFT, move LEFT. 8) If concentration is HIGH and direction is RIGHT, move RIGHT. Equal weightage is given to concentration and direction. These are the rules applied to each reading that is obtained from the set of readings. Defuzzification The sensors (extended and normal) submit a set of data to the robot. For the reading of each sensor, the robot has to fuzzify each data set for each extended sensor and report the direction in which it has to move. Now, we may get different directions for different sensors. Thus in final results we have a few directions to move and we need a crisp output. The membership function for output direction is also the same as the direction membership function. Since the task of the fuzzy controller is steering the robot move toward the highest reported concentration, the center of gravity method is used to get a crisp output to control the robot’s next moving direction. This is the next optimal deployment direction.

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Figure 5 – The de-fuzzification function for finding direction Thus, as shown in the figure 5, we have two selected directions for two different readings and then we find center of gravity and thus the direction in which the robot should move in the next step. In this case, it will be 22.50. Simulation and Results A virtual grid is created with the concentration gradient expressed as the function of distance from the source and contaminant release speed given by the equation: C(x,y) = N(x,y) + K * P/r for single source. C(x,y) = N((x,y) + K * Σ (Pi/ri) for multiple sources. where C is the concentration in the (x,y)th cell N is the noise variation P is the emission rate r is the distance from emission source All robots can be randomly deployed in the grid, or they can be deployed based on the requirements of different approaches. The time for a robot to move from one cell (point) to its neighbor cell (point) equals 1 simulation time-step. The time that a robot consumed for sampling, measuring the concentration in each cell is a random number that ranges from 1 to 4 time-steps, and this number is unknown to the robot before it moves into its new cell. One such case with 11 robots applied is shown in Figure 6. The ‘+’ refers to the centroid of all moving robots. The robots take 576 steps in this case to locate the source. The change in the time of search along with the failure of sensors is shown by the graph of Figure 7. •

Performance criterion : Number of steps required to locate the source

Performance is given here for both Swarm-based and Gradient Seek techniques for 30 simulations(Table -1). The Swarm based technique turns out to be faster.

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Figure 6 – Location of Emission Source in simulation

Figure 7- Time Steps required with failure of sensors Table 1 - Comparison between Fuzzy Controlled Swarm-based approach and Traditional Gradient Seek Approach Number of simulations

Mean number of steps required to locate source

Fuzzy Control Swarm based (11 robots used)

30

548

Gradient Seek

30

1635

Method

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Table 1 illustrates the advantage of using Swarm based Fuzzy logic controlled system to find the source of contaminant leakage in a hazardous environment as compared to Gradient Seek algorithm applied by a single sophisticated robot. Thus, this method is superior to the traditional method. Also , failure of a robot/robots doesn’t affect the search much as it is a group of robots co-ordinating with each other to find the source and even the failure of a sensor means that it can still use the other’s data to move on. Summary This paper proposes the use of a swarm based system to locate an emission source. This approach is a better way to deal with leakage in hazardous environments as compared to deployment of a single robot using the gradient seek technique. It is faster and requires lesser number of steps as is seen from simulation results. This is also a better method in terms of robustness of the system (as in failure handling capability).One of the most interesting aspects of this problem is that the fuzzy variable for concentration does not have fixed values for maximum and minimum. The values for the boundaries of LOW, MEDIUM and HIGH are real-time and keep changing with the readings the robot gathers as it moves each step. This makes the control flexible.

Future projections Two things are discussed in this section. Firstly, a possible problem in the current method and how it can be averted. Secondly, the entire concept applied for a different task where it would function just as well. Improvement in Fuzzy Model A possible problem in this approach to finding and searching the source of contaminant leak is that this method may fail if there are local maximas or there are sources of multiple leaks. For ensuring that all the robots do not converge onto a single point in case of a leak, it is proposed to include a third fuzzy variableNo. of robots in vicinity for each robot So, at each point of time, a robot will have 3 sets of data from its extended sensors • Concentration of contaminant • Direction of the distant robot from this base robot • No. of robots in vicinity for the distant robot Now, the third variable may have a plot like the concentration variable wherein we define no. of robots below a fixed number as low (say less than 5), a range as medium (say 3 to 8) and high (7 and above). The fuzzy rules may be modified such that 1) If concentration is HIGH and direction is FRONT and robots in vicinity is LOW, move FRONT. 2) If concentration is HIGH and direction is FRONT and robots in vicinity is MEDIUM, move FRONT. …… and so on for the other rules. This ensures that only for LOW and MEDIUM numbers, more robots will converge, else they’ll search for other locations. Once the leak is located, the search can be called off. A Different Application A scenario where the same method may be applied is exploring an unknown surface (Eg. Exploring the Mars surface). This problem, which has formed a part of some coding competitions, can be integrated with Swarm Based Fuzzy Logic Controlled Scanning Robots. The method would be quite the same as presented in this paper with the fuzzy variables being: i. Area explored by a robot (Its limits will be flexible like the concentration variable in this paper) ii. Number of robots in vicinity of that robot iii. Direction of that robot from the base robot.

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Again, making a similar rule base for this scenario, we can determine the next optimum direction that a robot should take. For eg. one rule might be • If area covered is LOW and direction is FRONT and robots in vicinity is LOW, move FRONT. • If area covered is MEDIUM and direction is FRONT and robots in vicinity is LOW, move FRONT. … and so on for all directions and for each reading set obtained. Also, here the robots must keep communicating between themselves (those in vicinity) by the ad-hoc wireless network to keep themselves updated about the area already so that they do not explore it again. This area can be added to the already scanned area in the local maps of the robots. This is an interesting application the fuzzy logic controller can be put to. References [1] X. Cui , T. Hardin, R. K. Ragade, and A. S. Elmaghraby, “A Swarm Approach for Emission Sources Localization”, The 16th IEEE International Conference on Tools with Artificial Intelligence, Nov, 2004, Boca Raton, Florida [2] Venayagamoorthy G.K., Doctor S., "Navigation of mobile sensors using PSO and embedded PSO in a fuzzy logic controller," Industry Applications Conference, 2004. 39th IAS Annual Meeting. Conference Record of the 2004 IEEE , vol.2, no. pp. 1200- 1206 vol.2, 3-7 Oct. 2004

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Fuzzy Control of Swarm Ad-Hoc Network Based ...

Indian Institute of technology, Kharagpur – 721302, India. E-mail: debdutta.iitkgp@gmail.com. Abstract. A swarm based fuzzy logic control of robots is proposed ...

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