International Journal of Advancements in Computing Technology Volume 2, Number 3, August, 2010
Path Planning of Mobile Robot Based on Modification of Vector Field Histogram using Neuro-Fuzzy Algorithm Ali H. Hamad*1, Fatima B. Ibrahim*2 Information and communication engineering, Baghdad University, Baghdad, Iraq *2 Information and communication engineering, Baghdad University, Baghdad, Iraq
[email protected],
[email protected]
*1
doi: 10.4156/ijact.vol2.issue3.14
Abstract In this paper, a neuro-fuzzy algorithm has been implemented to improve the path planning of a mobile robot based on modification of vector field histogram (VFH) approach using neuro-fuzzy algorithm. A back propagation neural network has been used for detection of unknown obstacle to avoid collision. A neural network model is used to learn (off line) many critical status of obstacle topology. Fuzzy rules were applied to steer the mobile robot to the target direction. The candidate valleys generated by neural network from local sensor data in the robot would be fuzzified to select a winning valley that is nearest to the target direction. The simulation result of the proposed algorithm shows good navigation properties and ability to overcome the limitation of traditional vector field histogram approach. This work was implemented using Matlab® and Mobotsim®
Keywords: Mobile robot, Neuro-fuzzy,Vvector field histogram. 1. Introduction The path planning is one of the key issues in mobile robot navigation. Path planning is traditionally divided into two categories: global path planning and local path planning. In global path planning, prior knowledge of the workspace is available which means that the robot navigates in a known environment, while the local path planning methods use ultrasonic sensors, laser range finders, and on-board vision systems to perceive the environment to perform on-line planning, in this case a prior knowledge of the environment is not necessary and the robot navigate in an unknown environment [1]. Mapping is the process of generating models of a mobile robot's environment based on sensory information with aim to determine the location of various entities, such as landmarks or obstacles. Most successful navigation algorithms require the availability of dynamic and adaptable maps. An accurate model of the environment surrounding a robot enables it to complete complex tasks quickly, reliably and successfully. Without such a model, a robot neither can plan a path to a place not currently sensed by its sensors nor may effectively search for an object or place [2]. A method for real-time building with mobile robot in motion was recently developed by Borenstein and Koren at the University of Michigan[3] this method entitled Histogramic In-Motion Mapping, Algorithm Uses a two-dimensional Cartesian histogram grid for obstacle representation. A pioneering method for probability of obstacles in a grid-type world model has been developed at Carnegie-Mellon University (CMU) developed by Moravec [4]. This world model called a certainty grid is especially suited to the accommodation of inaccurate sensor data such as range measurements from ultrasonic sensors. To be useful in the real world, robots need to move safely in unstructured environments and achieve their given goals despite unexpected changes in their surroundings. The environments of real robots are rarely predictable or perfectly known so it does not make sense to make precise plans before moving. The robot navigation problem can be decomposed into the following two problems • Getting to the goal: This is a global problem because short paths to the goal generally cannot be found using only local information. The topology of the space is important in finding good routes to the goal. • Avoiding obstacles: This can often be solved using only local information, but for an unpredictable environment it cannot be solved in advance because the robot needs to sense the obstacles before it can be expected to avoid them.
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Path Planning of Mobile Robot Based on Modification of Vector Field Histogram using Neuro-Fuzzy Algorithm Ali H. Hamad, Fatima B. Ibrahim
2. The Basic VFH The Vector Field Histogram (VFH) method, introduced by Borenstein and Korem, is a real-time obstacle avoidance method that permits the detection of unknown obstacles and avoids collisions while simultaneously steering the mobile robot towards the target. The three main steps of implementation of the VFH method can be summarized as the following: Step 1: Builds a 2D Cartesian histogram grid of obstacle representation, as shown in figure (1). Step 2: From the previous 2D histogram grid, considers an active window around the robot, and filters that 2D active grid onto a 1D polar histogram, can be shown in figure (2). Step 3: Calculates the steering angle and the velocity controls from the 1D polar histogram, as a result of an optimization procedure [5].
Figure 1. Construction of the 2D Histogram grid map. Reproduced from [5]
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Figure 2. (a) 1D polar histogram of obstacle occupancy around ( b) Polar histogram shown in polar form [5]
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International Journal of Advancements in Computing Technology Volume 2, Number 3, August, 2010 The active grid S* is mapped to a 1D structure known as a polar histogram H, where, the contents of each active cell in the histogram grid are now treated as an obstacle vector, the direction of which is determined by the direction α from the cell to the Vehicle Center Point (VCP)
y j − yo
α ij = tan −1
xi − x o
(1)
and the magnitude is given by
mij = C ij2 * (d max − d ij )
(2)
Where: dmax= Distance between the four farthest cell of S* and VCP. Cij = Certainty value of active cell (i,j). dij = Distance between active cell (i,j) and the VCP. mij =Magnitude of the obstacle vector at cell (i,j). xo, yo = Present coordinates of the VCP. xi, yj = Coordinates of active cell (i,j). αij= Direction from active cell (i,j) to the VCP. H has an arbitrary angular resolution ξ such that n=360/ ξ is an integer (e.g., ξ=5 and n=72). Each sector k corresponds to a discrete angle ρ quantized to multiples of ξ, such that ρ=k×ξ, where k = 0, 1, 2... n-1. Correspondence between S* and sector k is established through this equation:
k = int(
α ij ) ξ
(3)
For each sector k, the polar obstacle density is calculated by
hk = ∑ mij
(4)
i, j
In order to alleviate this problem, we use the following function to smooth the polar obstacle density: p
h = ' k
∑h
l =− p
k −l
2 p +1
(5)
Where hk’ is the smoothed polar obstacle density POD. The parameter p determines how much the polar histogram is smoothed, and we found that p=5 produces the best results. The POD of each sector represents the level of difficulty of moving in the corresponding direction [6]. In the certainty grid, the robot's work area is represented by a two-dimensional array of square elements, denoted as cells. Each cell contains a certainty value (CV) that indicates the measure of confidence that an obstacle exists within the cell area. With the CMU method, CVs are updated by a heuristic probability function[7] . The polar Obstacle Density of each sector with angles of sectors are from 5 degree to 355 degree. {Excluding 0 degree and 360 degree for calculation reasons} steps 5 degree {5 degree is the best in calculation} are used to make a histogram which will be used later to find the robot tragedy. The basic VFH algorithm is an obstacle avoidance method and is not fully target-oriented. In other words, it doesn’t necessarily guarantee the robot to reach the target in all cases when it is used in a navigator. In this work an improvement over the VFH algorithm has been made based neural network and Fuzzy logic algorithm to overcome the drawback of VFH. A “candidate valley” is a cluster of consecutive sectors with PTIs below a certain threshold (e.g., there are two candidate valleys in Figure (3). The candidate valley determining the robot’s next heading direction is called the “winning valley.” In the basic VFH algorithm, the winning valley is always the one that is closest to the target direction. We call this approach the “closest-valley-wins” scheme. In the proposed TFH algorithm the winning valley does no longer have to be the one closest to the target direction. The modified approach helps avoid certain trap-situations. Once a winning valley
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Path Planning of Mobile Robot Based on Modification of Vector Field Histogram using Neuro-Fuzzy Algorithm Ali H. Hamad, Fatima B. Ibrahim is identified, the algorithm selects a sector in the winning valley as the robot’s next heading direction. The basic VFH algorithm is an obstacle avoidance method and is not fully target-oriented. In other words, it doesn’t necessarily guarantee the robot to reach the target in all cases when it is used in a navigator. The robot may miss a target if the robot moves in a wide candidate valley and the target is not on the robot path of obstacle avoidance maneuvering; or a target locates very close to an obstacle [6].
Figure 3. The Traversability Field Histogram[6]
3. Proposed neuro-fuzzy algorithm Neural networks and others methods are used to solve the behavior learning problem. Learning allows autonomous robots to acquire knowledge by interacting with the environment and subsequently adapting their behavior and solve the problem of insufficient knowledge for designing the controller rule-base [8]. Multivalued fuzzy logic control is well suited for controlling the complex robot navigation because it is capable of representing degrees of truth on a numeric scale and making inferences even under uncertainty, which allows to express partial preferences and to combine them using logical operators [9]. In this paper a neuro-fuzzy algorithm has been implemented and tested to navigate a mobile robot in unknown obstacle work space. The navigation is basically divided into two phases: Phase (1) the local phase and phase (2) the global phase as shown in the flow chart below and figure (4). Robot Window Sensor Data Feature Extraction Neural Network for local robot motion
Fuzzy Rule for global robot motion Robot Motion toward the target
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International Journal of Advancements in Computing Technology Volume 2, Number 3, August, 2010 Fuzzification
n O1 Fuzzy Reasoning . .
Robot Motion toward target safely
. O72 n
Defuzzification
Input layer Hidden layer output Local phase
Global phase
Figure 4. Neuro – fuzzy based local and global robot motion
3.1 Neural network for local obstacle avoidance[10] In local phase we use a neural network based multilevel feed-forward back propagation algorithm which use the sensor data from environment. After getting the data from 24 ultrasonic sensors and mapping the histogram that divides the window into 72 sectors each indicates the Polor Obstacle Histogram POD. Two examples shown in figure 5(a,b). Simulation to this phase will be as follows, at first the mobile robot opens a window 33*33 cells where the robot is in the center of the window, the ultrasonic sensor will transceive its wave (24 sensors). The histogram loop includes dividing the window into 72 sectors each sector have specific value (Polar Obstacle Density) that indicates the measure of confidence that an obstacle exists within the sector. In the second stage, the Polar Obstacle Density of each sector would be an input to Neural Network; this means that the input layer has 72 neurons .
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Path Planning of Mobile Robot Based on Modification of Vector Field Histogram using Neuro-Fuzzy Algorithm Ali H. Hamad, Fatima B. Ibrahim 1800 1600 1400 1200 1000 800 600 400 200 0
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(b) Figure 5. the two examples that have been taken of POD The output will be a 72 index, if the index is one, this mean that sector is free and if it is zero means this sector is not free. The angle of sectors is from 5˚ to 355˚ steps 5˚. The free zone starts from 70 ˚ to 300˚ and the other angles indicate that an obstacle exists within the area. The Neural Network learning is off-line based on several I/O patterns, after learning is completed offline using a Matlab, the weights are fixed and the final values are then used during recall sessions. The candidate sector results from the neural network phase will be fuzzified. The winning sector which the mobile robot will take its direction is the nearest to the angle between mobile r obot and the target.
3.2 Target finding based fuzzy logic. The input sectors are defined with linguistic variables Far, Near, Very Near. The membership function for Very Near linguistic variable will respect to ON and OFF condition, while Far and Near MF considered as a triangular type. The Fuzzy inference rules for selecting the winning sector are as follows: If sector is VN Then sector is winning. If sector is N and sector is VN Then sector is winning If sector is F Then sector is candidate If sector is F and sector is N Then sector is candidate The mobile robot will move towards the target depending on the free zone of the winning sector. The input target angle are defined with linguistic variables around 0 , around 45 ,….., around 315 . This can be shown in figure (8). The membership function will be considered here as a triangulation type. The fuzzy inference rules which guide the robot are explained as the following: If Target Angle is Around 0 Then Desired Direction is Forward If Target Angle is Around 45 Then Desired Direction is Right Forward If Target Angle is Around 90 Then Desired Direction is Right If Target Angle is Around 135 Then Desired Direction is Backward-Right hen Desired Direction is Backward If Target Angle is Around 180 T If Target Angle is Around 225 Then Desired Direction is Backward-Left If Target Angle is Around 270 Then Desired Direction is Left If Target Angle is Around 315 Then Desired Direction is Forward-Left
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International Journal of Advancements in Computing Technology Volume 2, Number 3, August, 2010 Far
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Figure 6. Fuzzy membership The defuzzification is the output of the fuzzy system, it is a decision-making logic (written in a formula) adopted for the computation of the real value of the output. The final decision (defuzzification) is achieved to give the output of fuzzy controls and to convert the fuzzy output value produced by rules. The system must decide how to give the right output using fuzzy logic from a fuzzy linguistic formulation. The generation of rules operates itself according to the distribution of the whole training in fuzzy linguistic terms. The final decision (deffuzification) is accomplished to convert input of the fuzzy system after treatments with the inference rules.[1] The direction of the robot to turn is achieved by the MIN fuzzy logic operator as: µ direction = µ desired AND µ winning = MIN(µ desired, µ winning) Figures (9),(10) and (11) show the behavior of the mobile robot to find the target after applying the neuro fuzzy algorithm.
4. Conclusion The neural fuzzy algorithm shows good navigation and obstacle avoidance and good ability to overcome many limitation in mobile robot path planning. The proposed approach can deal a wide number of environments. Around 135° Around 0°
Around 225°
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Figure 7. Fuzzy membership Using fuzzy logic combined with the neural network capture human expert knowledge to decide about the best avoidance direction getting a big safety of obstacle danger.
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Path Planning of Mobile Robot Based on Modification of Vector Field Histogram using Neuro-Fuzzy Algorithm Ali H. Hamad, Fatima B. Ibrahim Forward 0°
Left 270°
Right 90°
Mobile Robot
Backward 180° Figure 8. Robot directions
Sensor range is 40cm & time required is
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(1:60sec) Sensor range is 15cm & time required is (1:27sec)
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Figure 9.. Robot behaviors in narrow corridor with different sensor range
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International Journal of Advancements in Computing Technology Volume 2, Number 3, August, 2010
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(a) complex maze.
(b) complex maze.
Figure 10. Behavior of the robot in maze-like environment.
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The illusion straight line between the start & end point
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Figure 11. The behavior of the mobile robot in an office like environment.
5. References
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Path Planning of Mobile Robot Based on Modification of Vector Field Histogram using Neuro-Fuzzy Algorithm Ali H. Hamad, Fatima B. Ibrahim [1] O. Hachour , “The proposed fuzzy logic navigation approach of autonomous mobile robots in unknown environment “ , International journal of mathmatical models and methods in applied scienes . Issue 3, Volume 3, pp. 204-218. 2009. [2] Maki K. Habib,”Real time mapping and dynamic navigation for mobile robots”, International journal of advanced robotic systems, VOL.4, No.3, pp.323-338. 2007. [3] Broenstein J. and Koren, Y.,”real time obstacle avoidance for fast mobile robot”, IEEE Transactions on Systems, Man and Cybernetics, Vol. 19, No. 5, pp. 1079-1187, Sept 1989. [4] Moravec, H. P. and Elfes, A., “ High Resolution Maps from Wide Angle Sonar”. IEEE Conference on Robotics and Automation, Washington D.C , pp. 116-121.1985 [5] Broenstein J. and Koren, Y,” The vector field histogram- fast obstacle avoidance for mobile robot”, IEEE transaction on robot and automation , Vol. 7, No. 3, pp.278-288, 1991. [6] Cang Ye, “Navigating a Mobile Robot by a Traversability Field Histogram” , IEEE Transactions On Systems, MAN, and Cybernetics-Part B, Vol. 37, No. 2, April 2007. [7] U.Raschke & J.Borenstein, “ A Comparison of Grid-type Map-building Techniques by Index of Performance” , IEEE, pp.1828-1832, 1990. [8] M.Figueiredo and f. Gomile, "Design of fuzzy system using neuro-fuzzy works", IEEE Trans. Neural Networks, 10:815-827,Aug,1999. [9] A. Saffiotti, K. Konolige and H. Ruspini, "A multivalued logic approach to integrating planning and control", Artificial Intelligence, 76:481-526, 1995. [10] Mozeal.M. “Sensor-Based Neural twork Mobile Robot Obstacle Avoidance”, M.Sc. Thesis Dep.of Mechatronics Engineering, University of Baghdad, 2009.
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