6. NEURAL NETWORK BASED PATH PLANNING ALGORITHM 6.1 INTRODUCTION

Transcription

1 6 NEURAL NETWORK BASED PATH PLANNING ALGORITHM 61 INTRODUCTION In previous chapters path planning algorithms such as trigonometry based path planning algorithm and direction based path planning algorithm were developed which belongs to the category of conventional or traditional path planning methods The conventional methods work in a sequential way, which can perform only one task at a time, is performed These methods functions logically with the set of rules and calculations The conventional method learns by rules On the other hand neural network based methods have the ability of processing things in a parallel way and do many things at once The neural networks will learn by example While conventional methods can be programmed using any high level language, the neural networks can be self programmed A sensor based navigation scheme which makes use of a global representation of the environment by means of self organizing or Kohonen network is presented in [68] A neural map which offers a promising alternative to the distance transform and harmonic function methods for both global and local navigation is presented in [69] A neural network model learned from human driving data, introduced to model obstacle avoidance through dense areas of obstacles is presented in [70], and is tested in different scenarios, and compared using cross validation to determine the optimal network structure A method of construction of a collision free path for moving a robot among obstacles based on two neural networks is presented in [71] The path planning of a mobile robot by using a modified Hopfield neural network is presented in [77] A collision avoidance scheme is proposed in [80] for a multiple robot system Based on the above works a neural network based path planning algorithm is developed based on the parallel distributed neural network model in order to extinguish fire in both types of environment, ie, environments with and without obstacles

2 62 NEURAL NETWORKS 621 A SIMPLE NEURON An Artificial Neural Network (ANN) is a mathematical model inspired by structure as well as the functional aspects of biological neural networks [146] ANNs have been employed in various areas such as computing, medicine, engineering, economics, and many others ANNs are composed of a number of simple computational elements called neurons, organized into a structured graph topology made out of several consecutive layers and are interconnected through a series of links, called the synaptic weights Synaptic weights are often associated with variable numerical values, which can be adapted so as to allow the ANN to change its behavior based on the problem being tackled A simple neuron with a single R-element input vector is shown in Figure 621 P 1 W 1, 111 P 2 n F o b P R W 1,R11 Figure 621 Simple neuron Here the individual element inputs p 1,p 2,,p R are multiplied by weights

3 w 1,1,w 1,2 w 1,R and the weighted values are given as input to the summing junction Their sum is simply Wp, the dot product of the (single row) matrix W and the vector p 622 ARCHITECTURE OF NEURAL NETWORKS The Architecture of Neural Networks can be classified into a Feed forward neural network b Feed backward neural network These network architectures can be either simulated using software or implemented using hardware a Feed-forward neural network Feed-forward ANNs allow signals to travel only in one direction ie, from the input to the output There is no feedback in the feed forward network; ie, the output of any layer does not affect that same layer Feed forward neural network is shown in Figure 622 Feed-forward ANNs tend to be straight-forward networks that associate inputs with outputs They are widely used in pattern recognition This type of organization is also referred to as bottom-up or topdown Feed forward networks are static networks in the sense, that given an input value they produce only one set of output values not a sequence of values Feed forward networks are memory less networks in the sense, that the output of a feed forward network is not dependent on the previous state of the network

4 Figure 622 Feed forward neural network b Feedback neural network Feedback networks can have signals travelling in both directions by introducing loops in the network Feed backward neural network is shown in Figure 623 Feedback networks are very powerful and can get extremely complicated Feedback networks are dynamic in the sense, which their state changes continuously until they reach an equilibrium point They remain at the equilibrium point until the input changes and a new equilibrium needs to be found Feedback networks are also referred to as interactive or recurrent networks The term recurrent is often used to denote feedback connections in single-layer organizations

5 Figure 623 Feed backward neural network 623 LEARNING IN NEURAL NETWORKS All learning methods used for adaptive neural networks can be classified into two major categories: a Supervised learning b Unsupervised learning a Supervised learning In supervised learning, both the inputs and outputs are provided The network then processes the inputs and compares the resulting outputs against the desired outputs Errors are then propagated back through the system, causing it to adjust the weights, which control the network This process occurs again and again, and the weights are continually changed till convergence The set of data, which enables the training, is called the "training set" During the training of a network, the same set of data is processed many times, as the connection weights are ever refined An important issue concerning supervised learning is the problem of error convergence, which is the minimization of error between the desired and the computed unit values The aim is to determine a set of weights which minimizes the error One well-known method, which is common to many learning paradigms, is the least mean square (LMS) convergence b Unsupervised learning In this type, the network is provided with inputs, but not with the desired outputs The system itself must then decide what features it will use to cluster the input data This is referred to as self-organization or adaptation These networks use no external influences to adjust their weights Instead, they monitor their performance internally These networks look for regularities or

6 trends in the input signals, and make adaptations according to the function of the network Even without being told whether it's right or wrong, the network still must have some information about how to organize itself This information is built into the network topology and learning rules An unsupervised learning algorithm might emphasize cooperation among clusters of processing elements In such a scheme, the clusters would work together Examples of unsupervised learning are hebbian learning and competitive learning Human neurons are different from the artificial neurons in that the aspect of learning concerns the distinction or not of a separate phase, during which the network is trained, and a subsequent operation phase We say that a neural network learns off-line, if the learning phase and the operation phase are distinct A neural network learns on-line if it learns and operates at the same time Usually, supervised learning is performed off-line, whereas unsupervised learning is performed on-line 624 TRANSFER FUNCTION The result of the summation function is transformed into an output through an algorithmic process, known as the transfer function In the transfer function the summation can be compared with some threshold to determine the neural output If the sum is greater than the threshold value, the processing element generates a signal, and if it is less than the threshold, no signal is generated Both types of responses are significant The transfer function is classified into: a linear transfer function b threshold transfer function c sigmoid transfer function a Linear transfer function

7 For linear units, the output activity is proportional to the total weighted output Linear transfer function is shown in Figure 624 Figure 624 Linear transfer function b Threshold transfer function For threshold units, the outputs are set at one of two levels, depending on whether the total input is greater than or less than some threshold value Threshold transfer function is shown in Figure 615 y 1 0 T x Figure 625 Threshold transfer function c Sigmoid transfer function For sigmoid units, the output varies continuously but not linearly as the input changes Sigmoid units bear a greater resemblance to real neurons

8 than do linear or threshold units, but all three must be considered as rough approximations Sigmoid transfer function is shown in Figure Figure 626 sigmoid transfer function 63 ASSUMPTIONS USED IN THE MODEL 1 The forest domain is decomposed into M x N grids of square cells 2 The forest domain decomposition into 20 x 20 grids of square cells is shown in Figure Each cell in the grid contains an anchor sensor node which knows the location based on integers 4 The actor (Robot) is available at cell 1, which is always the start cell and the cell in which fire occurs is always the goal cell 5 Once a fire occurs inside a particular cell, it will be detected by the sensor placed inside the cell first, and the sensor sends a message containing the coordinates of the cell to the actor Thus, the actor knows both the start and goal cells Then it uses

9 the algorithm implemented using the neural network to find a path Figure 631 Decomposition of the forest using 20 x 20 grids with coordinates based on integers 6 Obstacles are static and the size of the obstacle is similar to the size of the cell 7 Two adjacent cells will have obstacles either lengthwise or breadth wise, but not combined 8 Since the actor is available at cell 1, and based on assumptions 6 and 7, only 3 movements are sufficient to navigate the entire domain They are (i) UP denoted by 0 (ii) DIAGONAL denoted by 1 and (iii) LEFT denoted by 2, as shown in Figure 632, where CPA denotes the Current position/cell of the Actor

10 1 0 2 CPAA Figure 632 Directional movements of the actor 64 PATH PLANNING ALGORITHM The actor placed in the cell whose location is 1 uses the algorithm shown below to estimate the sequence of points which does not contain any obstacle Then, it will move through these points to reach the goal cell where the fire has occurred and start to extinguish it The algorithm is shown below: 641 Algorithm for estimating the path Let s be the start position, g be the goal position and n be the number of cells in a row or column location = 0 Store the start position in the first location of the memory path while (s not equal to g) location =location +1 if ((absolute value (s-g)) mod (n+1) = 0) then if (location s+n+1 contain obstacle) then

11 Check up move cell; ie, s+n and left move cell s+1 If (both cells do not contain an obstacle or left move cell contains an obstacle) then s = s+n If (up move cell only contains an obstacle) then s = s +1 else s = s + n+1 else if ((absolute value (s-g)) mod n = 0) then if (location s+n contain obstacle) then Check diagonal move cell; ie, s+n+1 and left move cell s+1 If (either cells do not contain obstacle or left move cell contains an obstacle) then

12 s = s+n+1 If (diagonal move cell only contains obstacle) then s = s +1 else s = s + n else if (location s+1 contain obstacle) then Check up move cell; ie, s+n and diagonal move cell s+n+1 If (both cells do not contain an obstacle or up move cell contain obstacle) then s = s+n+1

13 If (diagonal move cell only contains obstacle) then s = s + n else s= s + 1 Store the point s in location 642 Parallel distributed neural network model: The parallel distributed neural network model is shown in Figure 642 It uses 3 neurons which take two inputs cell s multiplied by the weight and bias and sums them It uses reinforcement learning; ie, the network is designed in such a way that each time the best next move will be selected out of three possible moves The move selected means it is rewarded, and moves not selected mean they are punished The weights used in the model are binary weights and takes the value of either 0 or 1The weight will be calculated for each neuron separately using the formula shown below: w1 = 1 if ((abs(s-g)) mod (n+1) = 0) 0 other wise

14 w2 = 1 if ((abs(s-g)) mod n = 0) 0 other wise w3 = 1 if (((abs(s-g)) mod (n+1)! = 0) && ((abs(s-g)) mod n! = 0)) 0 other wise abs(x) is a function which takes an integer argument x, which can be either positive or negative, and returns a positive value of the argument n+1 s = o, store s W1 AF1 No n s W2 AF2 O o has obstacle 1 W3 AF3 Yes Check for next cells without obstacle and assign to s store s Figure 642 Parallel distributed neural network model where s - the starting cell in the first iteration and it is the next sequence of cells where the actor has to move, calculated in the next iterations g - it is the goal cell where the fire has occurred

15 n - the number of cells in a row or column of the decomposed forest domain w1, w2, w3 - weights connected to the neurons AF1,AF2,AF3 - Activation functions for neurons 1, 2 and 3 respectively o - Net output of the Activation functions summed together The output of each neuron is calculated as follows: Output of neuron1 = s+n+1 if w1 = 1 n+1 if w1 = 0 Output of neuron2 = s+n if w2 = 1 n if w2 = 0 Output of neuron3 = s+1 if w3 = 1 1 if w3 = 0 The weight will vary from iteration to iteration, due to a change in the value of s in each iteration The cell g is always constant, and it is not shown explicitly in the model shown below: The model also uses 3 activation functions, which are calculated as AF1 = s+n+1 if output of neuron1 is s+n+1 0 otherwise AF2 = s+n if output of neuron 2 is s+n

16 0 otherwise AF3 = s+1 if output of neuron 3 is s+1 0 otherwise Initially the input value s is fed to the neural network It is assumed that g is available as an environment variable, as it is constant The weight will be calculated for each neuron separately The output of each neuron is fed as input to the activation function The net value of three activation functions decides which move is selected Then the selected move is tested for the presence of an obstacle If there is no obstacle in the cell selected for the next move, then stores the cell number and assigns the cell number to s If any obstacle is present in the cell selected for next move, then the two cells obtained using the remaining two movements will be checked for obstacles If anyone cell is free (definitely one cell will be free because of the assumptions of the shape of the obstacles) then store the cell number in the memory and assign the cell number to s The process is repeated with the new s till the cell number of s is the same as that of cell g The actor will use the sequence of cell numbers stored in the memory to reach the cell where the fire has occurred, and extinguish it by suitable means once the computation of the path using the cell numbers is complete 65 Simulation Results In this work the forest domain is considered as a grid decomposed into m x n cells based on integer values The developed model is assumed to work with single instance of fire occurrence, since for the entire forest domain the assumption is only one actor is available The path planning algorithm developed is based on the parallel distributed neural network model for the actor in order to extinguish fire in both types of environment, ie, environments with and without obstacles The software java is used for simulation purposes The

17 algorithm was implemented on a 20 x 20 grid and was executed for 100 times To test the effectiveness of the proposed algorithm, the fire is created in various cells by varying start and end coordinates including all the quadrant regions, horizontal lines and vertical lines The number of obstacles is also varied This is achieved by properly designed test cases The test cases are designed in such a way that 123 statements, 6 independent paths and 1 loop in the program get executed at least once The actor is represented by a green square located at the top left corner, the cells containing obstacles are represented using black color, and the cell where the fire occurs is shown in red, and a line in red color shows the path planning of the actor to travel and reach the target area to extinguish the fire The simulated results are shown in Figures 651 and 652 Figure 651 Environment without obstacles

18 Figure 652 Environment with Obstacles