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This paper analyses and discusses an automatic control system model for mobile robot, uses fuzzy neural networks. Cardenas research (Cardenas, 2004) aimed to build intelligent mobile robot for car parking by using fuzzy neural networks. The researcher divided the task of car parking into two subtasks which are path projection and traffic control. The researcher proved this invented model can predicate and calculate accurate location for going to target location (car parking). This invented model has little weakness when comparing with other researches of the same idea. This model works in limited working area, but the parking robot may carry out tasks with high reliability in parking space. In addition, the researcher has used traditional robot equations without any modification, so this model may be missing the automatic driving because the control system is not built-in.
Mobile robot is an important vehicle of intelligent behaviour by having artificial intelligent brain (Cardenas, 2004). Mobile robot is able to make own decision, so it can do several tasks in order to help human in working life. For example, it is used in agriculture, mineral extraction, and exploration. Car parking is a good task to study by finding shorter and safe path to reach a target location. Cardenas (2004) showed that mobile robot has a control system which is responsible and can think about shortest target path in a confined specific working area. This control system has complex structure of the fuzzy neural network, which has intelligence ability as human brain has in dealing with any complex problem. Figure (1) (Safa & Sabah, 2001) shows the control system is closely related to feedback concept. In feedback, the output signals are fed back in order to improve style by increasing or reducing the input signals.
According to Cardenas (2004), artificial neural network and fuzzy logic have been constructed as a hybrid system named fuzzy neural network. The defining neural network is taken in a very broad view of several researchers; for example (Safa & Sabah, 2001) and (Safa & Hayder, 2009). Neural network is intelligent software consist of three consecutive connected layers: input, hidden and output layers. Each layer has several numbers of neurons, and all neurons in one layer are connected with all neurons in previous and next layers of it as in figure (2).
The information is transmitted from input layer to hidden layers, and the outputs of hidden layer are sent to output layer. The outputs of output layer represent the outputs of neural network. The neurons reflect their operation by using activation function, which is sigmoid function, which has non-linear feature (Temme and Moraga, 1999) as in the following relation defined by :
Y = f(ï¡) = 1 / [1-exp(-ï¡)] -----------------------------------(1)
Where ï¡ = Sum (Si * ï·ij) ï€¢ i=1,2,â€¦..n; j=1,2,â€¦,h
and ï·ij : connection weight between neurons i and j; Wij ïƒŽ(0,1).
The neural network's information is stored in neurons connection among layers, which have weight value (ï·) in the range (0,1). These weights will update as in the following relation, after information feedback. These new updated weights help control system to reach an optimum decision.
ï·ij (new) = ï·ij (old) + ï„ï·ij ------------------------------------(2)
ï€¢ i=1,2,â€¦..n; j=1,2,â€¦,h
This control system uses the principles of fuzzy logic and neural network to be able to adapt and think about any control problem. The activation function in fuzzy neural network has a generalised logical function according to Temme and Moraga's (1999) definition, which they defined in the following relation:
f(x,y) = f(x) * f(y) --------------------------------------------------(3)
After several steps of derivations of relations 3 and 1, the base mathematical relation for fuzzy neural control system is reached, which has symmetric summation as in the following:
s(x,y) = f(x,y) / [f(1-x,1-y) + f(x,y)] ------------------------------(4)
The explanation of standard idea of fuzzy neural network system is necessary. Unfortunately, Cardenas (2004) produced one example but it is ambiguous because missing the fuzzy rules. There are several good models; Nguyen and Lee (2007) showed good fuzzy neural network structure example as in figure (3). One important thrust of this example has produced fuzzy rules that define the relationship between system behaviour (outputs) with inputs types. This system has five layers; two inputs X & Y and one output. Neurons in the input layer are divided into two groups; two neurons to X and the remainder to Y. While this system must depend on rule (IF-THEN) depending on fuzzy logic rule, there are two rules:
Rule 1: If X is A1 and Y is B1, then T1 = p1X + q1Y + r1
Rule 2: If X is A2 and Y is B2, then T2 = p2X + q2Y + r2
This system consists of five layers which are: fuzzification, fuzzy AND, normalization, fuzzy inference and defuzzification layers. The information is converted to fuzzy inputs by fuzzification layer to send to layer 2 and then to layer 3. These fuzzy inputs are transmitted by the rules of fuzzy inference layer to the defuzzification layer after being converted to fuzzy outputs. The fuzzy outputs are converted by defuzzification layer into numerical values which will be outputs of this system.
Cardenas (2004) viewed four steps to design fuzzy neural network, which are:
1- System designing must use the participation of neural network and fuzzy logic.
2- The connection weights may get values through random functions.
3- Cost function may be selected, which depends on a problem.
4- The weights of connection may be updated to improve the cost function.
The researcher showed this type of controller is better than others because used only neural network in its design, and it has more intelligence and is more similar to human brain. Also, the number of connection weights is less than in a structure using neural network alone. Depending on the fuzzy logic and neural network properties this design can train everything in a good way.
Cardenas (2004) defined the task of mobile robot as it might start at any location in working area domain to reach a target location by a shorter path without any accident. Mobile robot in Cardenas's research has two car wheel groups, in front and rear. Depending on working area space, it has flexibility in moving backward and turning in any direction. Figure (4) shows that mobile robot stops at position (x,y) in angle ï† respect to X-axis with steer angle (ï¤) , and figure (5) shows the target location in work area is (x*,y*).
Methodology: (Control System Model)
The researcher divided the role of mobile robot control system into two subtasks: path projection and traffic control. In path projection stage, a robot selects a path at any moving location, and chooses a good path dependent on traffic control. The researcher supposed this robot move in a fixed distance r at any stage, and it may follow the relations:
Xi+1 = Xi + ï„Xi
Yi+1 = Yi + ï„Yi ---------------------------------------(5)
ï†i+1 = ï†i+ ï„ï†i
and ï„Xi = r * cos(ï†i)
ï„Yi = r * sin(ï†i) ----------------------------------------(6)
ï„ï†i = 2 * r * tan(ï¤i) / 2L
Where -70 ï€¼ X ï€¼ 70
0 ï€¼ Y ï€¼ 150
-90 ï€¼ ï† ï€¼ 270
ï¤i : front steer angle with a range (-30, 30).
The operation of this robot can begin at any position within working area domain. The research gave to this robot only one target position which is X=0 and Y= 150 with angle (ï†=90). The mobile robot divides this task into two subtasks to avoid any collision with other cars. First it may reach to mid-distance of target by using non-linear driving, and after that uses linear driving to reach a goal. This means, it must get the values X=0 and ï†=90 at first stage, and the value of Y coordinate can be in range (0,150). When it stops at this temporary location, the value of Y coordinate will be increased to 150.
The fuzzy neural controller calculates the coordinates X, Y and ï† in any location depending on relations 5 and 6. It sends two types of signals; first signal to force front and rear wheels to stop or move, and the second one to change the rotation angle of front wheels. This controller resident is in computer (not built in mobile robot) and sends control signals through input-output computer facilities. The cost function (J) of this control system is depended on the values of X=0 and ï†ï€½ï€¹ï€°ï€¬ï€ which is :
J=0.5(X2i + Ï (ï†iï€ ï€ï€ ï€¹ï€°ï€©ï€²ï€©ï€ ï€ ï€ ï€ ï€ -----------------------------------------------ï€¨ï€·ï€©
Xi & ï†i : any X coordinate and any angle to X-axis
Ï: positive weight coefficient
The connection weights of the neural network are updated through training phase by using backpropagation algorithm. This training is done according to the following relation:
ï·ij(new) = Î· * ï¤J/ï¤ï· + Î² * ï„ï·ij(old) ----------------------------(8)
Î· : a learning rate ,
Î² : a momentum coefficient .
Cardenas (2004) showed that this mobile robot had succeeded to reach a target position perfectly without any accident. Furthermore, this success happened in any starting location within work area domain. In figure (6), the researcher showed how the mobile robot can get values X=0 and ï†=90 in an easy way, and figure (7) shows it benefited from symmetries in working area to reduce the coordinates calculation. In figure (8), we can see how this robot goes from position (0,75) to parking location. The efficiency in change driving from non-linear to linear to adapt the road in second stage can be seen clearly in figure (9).
Although Cardenas (2004) supported his model with four experiments, he did not indicate the amount of achievement nor error rate. These values are necessary to measure the efficiency. In contrast, Safa & Hayder (2009) model clearly indicates this. They used error as a critical value for measuring model efficiency. For example, they showed that error is decreased to 0.0018 when car runs straight. Also when car turn to left and right direction, system will achieve minimum errors, which are 0.001 and 0.0001 respectively. In general, the researchers have built a control system which has minimum error (0.0032), which reflects the best efficiency of their model.
Although the methodology of the Cardenas (2004) model has made progress in this area, additional research by Safa & Hayder(2004) deals with automatic control more. This control system works with limited working area, and robot equations were closed according to that area. This robot will fail to do its task when it is put in different work space area. The main important points in the Safa and Hayder model are automatic control driving because the car had a built-in control system, so it uses front and back sensors, which are radars networks. These sensors assist the controller task to accelerate or slow the car speed, and selecte the best stern rotating side. Furthermore, the generalisation of Safa & Hayder control system model means it does a task perfectly in any working area.
With automatic control system we can perform several tasks that are tedious, difficult or dangerous. Cardenas concluded his mobile robot control system which used fuzzy neural controller model for car parking has accurate performance to calculate the mobile robot location at any stage. According to a comparison of this model with Safa & Hyder (2009) model, the Cardenas model lose intelligent automatic behaviour while the system does not have built-in controller. Although the Cardenas submitted good experiments with graphs, he does not use the error rate to measure the model effectiveness.