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MOBILE ROBOT NAVIGATION USING MONTE CARLO LOCALIZATION Amina Waqar [email protected] ___________________________________________________________________________________________ Abstract— This paper presents an algorithm for the mobile Previously people have done a lot of work on tracking using navigation of a robot using Monte Carlo. Previously, people did a Kalman filter which is a form of Phase Locked Loop (PLL) lot of work for the tracking of mobile robot. Previously people and is less efficient , because of it , it can be used as tracking. used grid-based approach that used high resolution 3D grids to Fig.1 shows working of Kalman filter. The black boxes show represent the state space. Whereas this method is quite the original position , green stars show the estimated position computationally efficient. Using Monte Carlo Localization we apply the sampling approach to divide the state space into and red crosses show the modified position by taking averages samples. We can increase the number of samples where required. of both. Monte Carlo Localization is easy to implement. Several results proved that Monte Carlo yields more accurate results. And also, C. Markov Localization Markov localization caters the problem of state estimation it is computationally very efficient. I. INTRODUCTION Throughout the last decade, sensor-based localization has been recognized as a key problem in mobile robotics (Cox 1991; Borenstein, Everett, & Feng 1996). In Localization, a mobile robot estimates its position in a global co-ordinate frame. There are two types of localizations: Global Localization and position tracking. In global localization, a robot does not know its original position whereas in position tracking the robot knows its original position.Global Localization is also known as “hijacked robot problem” (Engelson 1994)in which the robot has to determine its position from scratch.Many of the previous researches were on tracking but now many people are working on both types of localizations.In this paper we shall represent the robot’s belief by probability density over the region in its range. The range is determined by the range in which the sensors will be able to work effectively. Figure 1 .Tracking using Kalman Filter A. B. Previous Works from sensor values. Markov localization is a probabilistic algorithm: Instead of maintaining a single hypothesis as to where in the world a robot might be, Markov localization maintains a probability distribution over the space of all such hypotheses. The probabilistic representation allows it to weigh these different hypotheses in a mathematically sound way. Before we delve into mathematical detail, let us illustrate the basic concepts with a simple example. Consider the environment depicted in Fig 2. For the sake of simplicity, let us assume that the space of robot positions is one-dimensional, that is, the robot can only move horizontally (it may not rotate). Now suppose the robot is placed somewhere in this environment, but it is not told its location. Markov localization represents this state of uncertainty by a uniform distribution over all positions, as shown by the graph in the first diagram in Fig 2. Now let us assume the robot queries its sensors and finds out that it is next to a door. Markov localization modifies the belief by raising the probability for locates next to doors, and lowering it anywhere else.Consider that the resulting belief is multi-modal, reflecting the fact that the available information is insufficient for global localization. Notice also that places not next to a door still possess non-zero probability. This is because sensor readings have noise, and a single sight of a door is typically insufficient to exclude the possibility of not being next to a door. Now let us assume the robot moves a meter forward. Markov localization incorporates this information by shifting the belief distribution accordingly, as visualized in the third diagram in Fig 2. To account for the inherent noise in robot motion, which inevitably leads to a loss of information, the new belief is smoother (and less certain) than the previous one. Finally, let us assume the robot senses a second time, and again it finds itself next to a door. Now this observation is multiplied into the current (nonuniform) belief, which leads to the final belief shown at the last diagram in Fig 2. At this point in time, most of the probability is centered around a single location. The robot is now quite certain about its position. Figure 3 : Monte Carlo Simulation Bel (l)=∫P(l|l’,a)Bel(l’)dl’ Bel is the belief of the robot that was uniform distribution initially. To update a belief there must an action ‘a’ done by the robot. The belief at position l, Bel(l) is updated using the previous belief at position l’, Bel(l’).Then we convolve the both the beliefs to get the new belief which guides the robot where to go. D. Monte Carlo Localization In the Monte Carlo localization we discretize the space into random samples. Since it is using global localization, it can represent into multimodal distributions .Due to this reason, less memory is required and is computationally efficient. Grid-based approaches were also used but they were computationally cumbersome.Grid-based approaches required more memory also because they were using 3-D figures. In our experiment we have modelled the robot with four sensors on each side. Each of it emits a signal which is reflected back as 1 if there is a wall and 0 if there is door or any empty space. The range in our cases is five units ( 0-4).As it moves along the path from door to wall the signals will convert from 0’s to 1’s.Fig.3 explains the above simulation. Fig.3(a) represents first belief of the robot after an action. Fig.3(b) is an updated PDF based the previous PDF. Fig3.(c) shows the convolution of both the PDF’s where the door actually is and that way the robot should move. II. CONCLUSIONS In this paper we have concluded that Monte Carlo Localization is an easy to implement and requires less memory and is computationally efficient. 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