D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 1998. To appear.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....considered pragmatic multi robot map making. Several existing approaches operate in the sonar domain, where it is relatively straightforward to transform observations from a given position to the frame of reference of the other observers thereby exploiting structural relationships in the data ([10, 5, 1]) One approach to the fusion of such data is through the use of Kalman Filtering and its extensions ( 15, 14] In other work, Rekleitis, Dudek and Milios have demonstrated the utility of introducing a second robot to aid in the tracking of the exploratory robot s position ( 12] and introduced ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 1998. To appear.

....it can be accomplished. An essential aspect of this knowledge is a map. That is, information which enables the robot to estimate where it is, where it s going, and how to get there. To date, many researchers have devoted a significant amount of work to solving these three tasks, given a prior map [22, 38, 16, 33]. A few have tackled the problem of constructing a map semi autonomously[47, 24] and some have attempted the map acquisition problem in a fully autonomous setting [20, 8, 31] Of the latter works, the majority commit to a particular sensing modality (sonar) and assume that the world can be ....

....using a camera [11] This work is significant in that it can be exploited as an alternative to the map representation we will employ in Section 5.2. It should be noted that both the Kalman Filter and Markov based approaches to map building are motivated by previous successes in robot localization [22, 42, 16, 10]. The algorithm for map construction presented by Thrun is satisfying in that no specific representation of the underlying uncertainties is required. However, this approach assumes that the robot has already performed the task of exploration the collection of observations from which to build ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 1998. To appear.

....observations from the environment while performing other tasks. In our work, we address the active localization problem where the robot can execute actions with the only purpose of gaining information about its location. The active localization problem has been addressed by some authors before [4], 5] 6] 7] 9] Despite the general approach of these works is the same as that of ours (action selection based on entropy) they left large room from improvement. For instance, a problem that remains open is how to efficiently obtain a sensor model of the environment. In some of the ....

....moment, the action u to be executed next is the one with lower H(u) since, the lower the entropy H(u) the more informative the action u is likely to be. B. Implementation The entropy based action selection formalism just described is quite general and similar to that described, for instance, in [4]. However, the localization framework presented in section III allows an efficient implementation of this action selection theory. The basic idea is to exploit the particle filter and the appearance based training set to discretize the double integral of equation 4. First, we discretize the ....

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 25(3-4):195--207, 1998.

.... implemented by several families of SLAM algorithms [11, 18, 5, 3] Region II represents integration of motion control and mapping exemplified by virtually all exploration strategies [10, 20, 16, 17, 14] Region III which integrates localization and motion control is the field of active navigation [8, 6, 15] and sensor management [12] Full integration of all three components [5, 1] in Region IV is the goal of this work and will be referred to as integrated exploration. This paper considers an exploration strategy which balances coverage, accuracy, and the speed of exploration the basic driving ....

....distribution of the localizability metric is calculated o# line using an a priori occupancy grid map. The localizability metric introduced in this paper is intended for use on line and in the context of SLAM. SLAM and Active localization (I III) Active stochastic localization is implemented in [6]. The algorithm selects from a list of possible motion actions by weighing the resulting reduction in localization uncertainty against the associated cost. The task of exploration is not considered. Integrated exploration (IV) Feder et al. 5] is the most closely related work. The vehicle ....

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 1998.

....an enormous impact on broad areas in computer vision. In recent work on active object recognition [2, 5, 11, 12] it has already been shown that sensible selection of viewpoints improves recognition rate, especially in settings, where multiple ambiguities between the objects exist. The work of [8] is another example from robotics, where such ideas have been implemented for self localization tasks. Besides the success in the area of active object recognition no comparable work is known for selecting the right sensor data during object tracking. The advantages are quite obvious: For a ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 25:195--207, 1998.

....on pattern recognition [15] Related to our work the approach in [8] covers one step of our sequential decision process. 21 In the general area of active vision and action selection information theoretic concepts have been investigated recently. Examples are active localization of robots [9], active view point selection for object recognition [1] and sensor planning for active object search [23] The most rigorous application of information theory in image processing and computer vision can be found in [10] The image formation process in 3D is completely embedded in an information ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Technical report, Carnegie Mellon University, 1998. 34

....that depends on the number of grid cells. Moreover, robots based solely on proximity sensors get easily confused because the sensors often return similar readings at different locations. Many efforts have been made to solve the problem of uncertainty in robot localization for proximity sensors [3,4]. By comparison, vision is much more informative, since it provides information regarding vhere is what . Nature provides many examples of visual systems that are successful in supporting long range navigation. For example, insects such as bees and ants exhibit remarkable homing abilities, ....

D. Fox, W. Burgard, S. Thrtm, "Active Markov Localization for Mobile Robots", Robotics and Autonomous Systems, 1998.

....motion. ii) The sequence of actions is not reduced to a parametrized trajectory. Then Markov decision processes (MDPs) and partially observable MDPs optimization problems need to be solved [25, 5] The robot actions and the environment are modeled in a statistical framework. Solutions proposed in [21, 5, 8] are based on minimization of a probabilistic metric (entropy) The method developed in [5] is applied under positional uncertainty; the approach proposed here is suitable under both positional and orientation uncertainty. The rest of the paper is structured as follows. Section 2 describes the ....

D. Fox and W. Burgard, Active Markov localization for mobile robots, Robotics and Autonomous Systems 25 (1998), no. 4, 195--207.

....functions [6, 7] To this group belongs the approach, proposed in the present paper. ii) The sequence of actions is not reduced to a parameterized trajectory. Then Markov decision processes (MDPs) and partially observable MDPs optimization problems need to be solved [8] Solutions proposed in [9, 8, 10] are based on minimization of a probabilistic metric (entropy) The method developed in [8] is applied under positional uncertainty; the approach proposed here is suitable under both positional and orientation uncertainty. The rest of the paper is structured as follows. Section 2 describes the ....

D. Fox and W. Burgard, "Active Markov localization for mobile robots," Robotics and Autonomous Systems, vol. 25, no. 4, pp. 195--207, 1998.

....it is optimal in the sense of the reduction in uncertainty and ambiguity. We will demonstrate our approach in an active object recognition scenario. The general problem of optimal sensor data acquisition has been discussed before. Examples can be found in the area of active robot localization [6] and active object recognition [1] where a similar metric has been used, but the sequential implementation is missing. The most related approach, not only from the application point of view, but also from a theoretical point of view is the work of [11] The commonness, differences and ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Technical report, Carnegie Mellon University, 1998.

....overcome this drawback, we use a novel form of performance curve, namely a plot of the cumulative cost of the training examples against performance. This is related to the form of the performance curves used by Fox et al. in which performance is plotted against a particular resource, namely time [17]. Performance should be measured as the average performance of the hypotheses generated during a particular iteration of the learning cycle. This is the correct performance measure because it rewards learners which discriminate between competing hypotheses. Another obvious option would be to the ....

....does not exhibit the tradeo between exploration (experimentation) and exploitation. It would do if one sought to maximise gain of information per unit cost. The work in robotic discovery that is perhaps most closely related to ASE Progol is by Fox, Burgard, and Thrun on active localisation [17]. Localisation is the problem of a robot estimating its present position from sensor data. In their approach to localisation, the robot controls its various e ectors so as to most eciently localise itself. More speci cally, they employed a greedy approach analogous to the one proposed by ....

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 25(3-4):195-207, 1998.

....environment; they are detected and recognized using a camera mounted vertically on the observer s platform [1] Natural landmarks could be used as well [8, 15] but would require more sophisticated vision techniques. Proximity sensor readings could be integrated for grid based Markov localization [2, 13], but would require more elaborate ltering techniques. Whenever the observer sees a landmark, it localizes itself in the workspace with a given precision (on the order of 1 2in) that has been experimentally established. When the robot does not see any landmark, the imprecision of its location ....

....imprecision of the estimate of the observer s position (and consequently that of the target) whenever this does not immediately con ict with keeping the target in the observer s eld of view. Robot navigation based on active Markov localization was also achieved using only raw proximity sensors [2, 13] in which case the robot may plan motions for position disambiguation. Landmark based navigation has been addressed from di erent points of view in the literature (e.g. see [4, 23, 25, 19] The principle is simple: if the robot primarily localizes itself relative to landmarks, the planner must ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 25(3-4):195207, 1998.

....pragmatic multi robot map making in particular. Most existing approaches operate in the sonar domain, where it is relatively straightforward to transform observations from a given position to expected observations from nearby positions, thereby exploiting structural relationships in the data [16, 17, 18, 7]. These approaches successfully apply the probabilistic expectation maximization (EM) paradigm[19] to the task by iteratively re ning the map and the estimates of the observation points. In other work, Rekleitis, Dudek and Milios have demonstrated the utility of introducing a second robot to aid ....

D. Fox, W. Burgard, and S. Thrun, \Active markov localization for mobile robots", Robotics and Autonomous Systems, 1998, To appear.

....solve the global localisation problem in environments with high levels of perceptual aliasing. A variety of methods have been proposed for resolving perceptual ambiguity by accumulating sensory evidence over time. The most popular is the probabilistic approach known as Markov localisation (e.g. [2, 5, 7, 8], etc. which can be applied to either topological or metric maps. The main paradigm for probabilistic navigation using topological maps is that of Hidden Markov Models, and their extension to Partially Observable Markov Decision Processes [7, 8] Here, the robot maintains a probability ....

....the robot s motor actions depend upon its current position estimate, so there is no guarantee that the robot will take appropriate actions to relocalise itself should it become lost. One solution to this problem would be to choose actions designed to improve localisation quality, as in Fox et al. [5]. Alternately, the robot could revert to wall following in order to relocalise whenever it believed it might be lost, e.g. using the entropy based novelty lter described in [5] to detect a decrease in localisation quality. 8 Summary In this paper, we have introduced an approach for combining ....

[Article contains additional citation context not shown here]

D. Fox, W. Burgard and S. Thrun, Active Markov Localization for Mobile Robots, Robotics and Autonomous Systems, to appear, 1998.

....probabilistic planning (Cassandra, Kaelbling, Littman 1994) So far, they have been used mainly to solve low level planning tasks Copyright c fl 2000, American Association for Artificial Intelligence (www.aaai.org) All rights reserved. for mobile robots such as path following and localization (Fox, Burgard, Thrun 1998; Mahadevan, Theocharous, Khaleeli 1998; Cassandra, Kaelbling, Kurien 1996; Simmons Koenig 1995) In this paper, we show that POMDPs can also be used to solve higher level planning tasks for mobile robots such as sensor planning. The key idea behind our robot architecture is that POMDP ....

Fox, D.; Burgard, W.; and Thrun, S. 1998. Active markov localization for mobile robots. Robotics and Autonomous Systems 25:195--207.

....requests examples from a region of uncertainty [6] which in turn has obvious similarities with the version space approach to proposing experiments. The work in robotic discovery that is perhaps most closely related to the proposed work is that of Fox, Burgard, and Thrun on active localization [11]. Localization is the problem of a robot estimating its present position from sensor data. In their approach to localization, the robot controls its various e ectors so as to most eciently localize itself. More speci cally, they employed a greedy approach analogous to the one proposed by ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. To appear Robotics and Autonomous Systems, 1999.

....(expressed as a percentage of the limit on experimental resources) against performance. Costs may be in time, money etc. providing that they are converted into the same units. This is a more general form of the learning curves used by Fox et al. in which performance is plotted against time [18]. 5 Experiment to Test Hypothesis 1 5.1 Aim of the Experiment to Test Hypothesis 1 The aim of the Experiment is to test Hypothesis 1 (see Section 1) by investigating whether the cost of converging upon an accurate hypothesis is signi cantly reduced if ASE Progol samples trials at random, ....

....exploration (experimentation) and exploitation. As a result algorithms such as E 3 and prioritised sweeping are not directly applicable to CLML. The work in robotic discovery that is perhaps most closely related to our approach to CLML is by Fox, Burgard, and Thrun on active localisation [18]. Localisation is the problem of a robot estimating its present position from sensor data. In their approach to localisation, the robot controls its various e ectors so as to most eciently localise itself. More speci cally, they employed a greedy approach analogous to the one proposed by ....

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 25(3-4):195-207, 1998.

....expected discounted reward (using policy iteration) where the reward for visiting cell i is H(L t ) 1 H(M t (i) 1 H(L t ) H(M t (i) where H( is the normalized entropy. Hence, if the robot is lost , so H(L t ) 1, the robot will try to visit a cell which it is certain about (see [6] for a better approach) otherwise, it will try to explore uncertain cells. After learning the map, the robot spends its time visiting each of the doors, to keep its knowledge of their state (open or closed) up to date. We now brie y consider some alternative approximate inference algorithms. ....

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 1998.

....[Niemann, 1990] Related to our work the approach in [Fisher and Principe, 1997] covers one step of our sequential decision process. In the general area of active vision and action selection information theoretic concepts have been investigated recently. Examples are active localization of robots [Fox et al. 1998], active view point selection for object recognition [Arbel and Ferrie, 1999] and sensor planning for active object search [Ye, 1997] The most rigorous application of information theory in image processing and computer vision can be found in [Huck et al. 1996] The image formation process in ....

D. Fox, W. Burgard, and S. Thrun, "Active Markov Localization for Mobile Robots," Technical report, Carnegie Mellon University, 1998.

....it can be accomplished. An essential aspect of this knowledge is a map. That is, information which enables the robot to estimate where it is, where it s going, and how to get there. To date, many researchers have devoted a signi cant amount of work to solving these three tasks, given a prior map [22, 38, 16, 33]. A few have tackled the problem of constructing a map semi autonomously[47, 24] and some have attempted the map acquisition problem in a fully autonomous setting [20, 8, 31] Of the latter works, the majority commit to a particular sensing modality (sonar) and assume that the world can be ....

....using a camera [11] This work is signi cant in that it can be exploited as an alternative to the map representation we will employ in Section 5.2. It should be noted that both the Kalman Filter and Markov based approaches to map building are motivated by previous successes in robot localization [22, 42, 16, 10]. The algorithm for map construction presented by Thrun is satisfying in that no speci c representation of the underlying uncertainties is required. However, this approach assumes that the robot has already performed the task of exploration the collection of observations from which to build the ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 1998. To appear.

.... a Bayesian approach in which we view the map as a (matrixvalued) random variable, which can be updated by Bayes rule in just the same way that the other hidden state variables, such as the robot s pose (position and orientation) are updated in the widely used techniques of Markov localization [FBT98] and Kalman filtering. To do Bayesian updating, we must specify the observation model (how the state predicts what the robot should see) and the transition model (how the state changes, both over time and in response to the robot s actions) We use the formalism of factored POMDPs (Partially ....

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 1998.

....it is difficult to evaluate exactly what happens in the presence of noise uncertainty. However, recently approaches explicitly dealing with sensing, model, and movement uncertainty have appeared [ Koenig and Simmons, 1998; Simmons and Koenig, 1995; Kaelbling et al. 1996; Thrun et al. 1998; Fox et al. 1999b ] Common to these approaches is that they use a probabilistic formulation to represent and update the pose of the robot which has the advantage of enabling them to handle uncertainty in a natural and convenient manner. These approaches, also known as Markovian methods, use a spatially ....

....sensible movement sensing strategy, i.e. to do active sensing, since moving randomly in general does not bear the promise of gaining evidence efficiently enough. The approaches described in [ Koenig and Simmons, 1998; Simmons and Koenig, 1995; Kaelbling et al. 1996 ] and in [ Thrun et al. 1998; Fox et al. 1999b ] respectively, mainly differ in the chosen discrete pose representation. The former approaches use a coarse, topological representation (cell size approx. 1 meter) whereas the latter ones use a fine grained grid (cell size approx. 0.1 meter) representation similar to the well known occupancy ....

[Article contains additional citation context not shown here]

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robots and Autonomous Systems, 25(3-4):195--207, 1999.

....and exploitation. As a result algorithms such as E 3 and prioritized sweeping are not directly applicable to Closed Loop learning. The work in robotic discovery that is perhaps most closely related to our approach to Closed Loop learning is by Fox, Burgard, and Thrun on active localization [Fox et al. 1999]. Localization is the problem of a robot estimating its present position from sensor data. In their approach to localization, the robot controls its various effectors so as to most efficiently localize itself. More specifically, they employed a greedy approach analogous to the one proposed by ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. To appear Robotics and Autonomous Systems, 1999.

....solve the global localisation problem in environments with high levels of perceptual aliasing. A variety of methods have been proposed for resolving perceptual ambiguity by accumulating sensory evidence over time. The most popular is the probabilistic approach known as Markov localisation (e.g. [2, 5, 7, 8], etc. which can be applied to either topological or metric maps. The main paradigm for probabilistic navigation using topological maps is that of Hidden Markov Models, and their extension to Partially Observable Markov Decision Processes [7, 8] Here, the robot maintains a probability ....

....the robot s motor actions depend upon its current position estimate, so there is no guarantee that the robot will take appropriate actions to relocalise itself should it become lost. One solution to this problem would be to choose actions designed to improve localisation quality, as in Fox et al. [5]. Alternately, the robot could revert to wall following in order to relocalise whenever it believed it might be lost, e.g. using the entropy based novelty filter described in [5] to detect a decrease in localisation quality. 8 Summary In this paper, we have introduced an approach for combining ....

[Article contains additional citation context not shown here]

D. Fox, W. Burgard and S. Thrun, Active Markov Localization for Mobile Robots, Robotics and Autonomous Systems, to appear, 1998.

No context found.

Fox, D., Burgard, W. and Thrun, S. (1998). Active Markov localization for mobile robots, Robotics and Autonomous Systems 25: 195--207.

No context found.

Dieter Fox, Wolfram Burgard, and Sebastian Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems. to appear.

....a comparison of MCL to an alternative localization algorithm capable of global mobile robot localization. In particular, we compared MCL to grid based Markov localization, our previous best stochastic localization algorithm and one of the very few algorithms capable of localizing a robot globally [7,23]. The gridbased localization algorithm relies on a fine grained piecewise constant approximation for the belief Bel, using otherwise identical sensor and motion models. The fact that our implementation employs identical sensor and motion models and is capable of processing the same data greatly ....

D. Fox, W. Burgard, S. Thrun, Active Markov localization for mobile robots, Robotics and Autonomous Systems 25 (3--4) (1998) 195--207.

....of robots which is equivalent to computing distributions over the joint space of all robots. Active localization: The collaboration described here is purely passive. The robots combine information collected locally, but they do not change their course of action so as to aid localization. In [10, 22], we proposed an algorithm for active localization based on information theoretic principles, where a single robot actively explores its environment so as to best localize itself. A desirable objective for future research is the application of the same principle to coordinated multi robot ....

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 25:195--207, 1998.

....than a few meters, the robot must use information from its environment to track where it is. There are many successful localization methods that can determine the robot s position (relative to a map) using sonar, laser and camera data (MacKenzie Dudek 1994; Dudek Zhang 1996; Sim 1998; Thrun, Fox, Burgard 1998; Fox, Burgard, Thrun 1998; Kaelbling, Cassandra, Kurien 1996) However, most localization methods fail under common environmental conditions. Proximity sensors such as laser or sonar range finders have finite range, which means that in sufficiently wide open spaces, they cannot see anything ....

....the robot must use information from its environment to track where it is. There are many successful localization methods that can determine the robot s position (relative to a map) using sonar, laser and camera data (MacKenzie Dudek 1994; Dudek Zhang 1996; Sim 1998; Thrun, Fox, Burgard 1998; Fox, Burgard, Thrun 1998; Kaelbling, Cassandra, Kurien 1996) However, most localization methods fail under common environmental conditions. Proximity sensors such as laser or sonar range finders have finite range, which means that in sufficiently wide open spaces, they cannot see anything to use as a reference point. ....

Fox, D.; Burgard, W.; and Thrun, S. 1998. Active markov localization for mobile robots. Robotics and Autonomous Systems. to appear.

....be a comparison of MCL to previous localization algorithms capable of global mobile robot localization. In particular, we compared MCL to grid based Markov localization, our previous best stochastic localization algorithm and one of the very few algorithms capable of localizing a robot globally [5,20]. The grid based localization algorithm relies on a fine grained piecewise constant approximation for the belief Bel, using otherwise identical sensor 14 (a) Robot position (b) Robot position (c) Robot position Fig. 6. Global localization of a mobile robot using MCL (10,000 samples) a) ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 25(3-4):195--207, 1998.

....it increases the amount of information communicated between the robots. Furthermore, the collaboration described here is purely passive, in that robots combine information collected locally, but they do not change their course of action so as to aid localization as, for example, described in [14]. Finally, the robots update their belief instantly whenever they perceive another robot. In situations in which both robots are highly uncertain at the time of the detection it might be more appropriate to delay the update and synchronize the beliefs when one robot has become more certain about ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 25:195--207, 1998.

....we will begin with an intuitive description of Markov localization, followed by a mathematical derivation of the algorithm. The reader may notice that Markov localization is a special case of probabilistic state estimation, applied to mobile robot localization (see also Russell Norvig, 1995; Fox, 1998 and Koenig Simmons, 1998) For clarity of the presentation, we will initially make the restrictive assumption that the environment is static. This assumption, called Markov assumption, is commonly made in the robotics literature. It postulates that the robot s location is the only state in the ....

....mainly di er in their eciency and how they model the characteristics of the sensors and the map of the environment. In order to combine the strengths of the previous representations, our approach relies on a ne and less restrictive representation of the state space (Burgard et al. 1996, 1998b; Fox, 1998). Here the robot s belief is approximated by a ne grained, regularly spaced grid, where the spatial resolution is usually between 10 and 40 cm and the angular resolution is usually 2 or 5 degrees. The advantage of this approach compared to the Kalman lter based techniques is its ability to ....

[Article contains additional citation context not shown here]

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 25:195-207, 1998.

....of robots which is equivalent to computing distributions over the joint space of all robots. Active localization: The collaboration described here is purely passive. The robots combine information collected locally, but they do not change their course of action so as to aid localization. In [10, 22], we proposed an algorithm for active localization based on information theoretic principles, where a single robot actively explores its environment so as to best localize itself. A desirable objective for future research is the application of the same principle to coordinated multi robot ....

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 25:195--207, 1998.

....we will begin with an intuitive description of Markov localization, followed by a mathematical derivation of the algorithm. The reader may notice that Markov localization is a special case of probabilistic state estimation, applied to mobile robot localization (see also Russell Norvig, 1995; Fox, 1998 and Koenig Simmons, 1998) For clarity of the presentation, we will initially make the restrictive assumption that the environment is static. This assumption, called Markov assumption, is commonly made in the robotics literature. It postulates that the robot s location is the only state in the ....

....mainly di er in their eciency and how they model the characteristics of the sensors and the map of the environment. In order to combine the strengths of the previous representations, our approach relies on a ne and less restrictive representation of the state space (Burgard et al. 1996, 1998b; Fox, 1998). Here the robot s belief is approximated by a ne grained, regularly spaced grid, where the spatial resolution is usually between 10 and 40 cm and the angular resolution is usually 2 or 5 degrees. The advantage of this approach compared to the Kalman lter based techniques is its ability to ....

[Article contains additional citation context not shown here]

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 25:195-207, 1998.

....single step search horizon to generate robot control. Examples include the rich work on robot exploration, in which robots (or teams thereof) select actions so as to maximally reduce their uncertainty about their environments [24, 50, 54, 79, 88, 94] They also include work on active localization [11, 30], where a robot moves to places that maximally disambiguate its pose. Another class of approaches rely on tree search for policy determination, such as the work on active perception and sensor planning by Kristensen [52, 53] His approach uses models of uncertainty to select the appropriate ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 25(3-4):195--207, 1998. 16

.... non Gaussian densities at a fine resolution, one can discretize the interesting part of the state space, and use it as the basis for an approximation of the density p(x k jZ k ) e.g. by a piece wise constant function [3] This idea forms the basis of the grid based Markov localization approach [5, 11]. Methods that use this type of representation are powerful, but suffer from the disadvantages of computational overhead and a priori commitment to the size of the state space. In addition, the resolution and thereby also the precision at which they can represent the state has to be fixed ....

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics andAutonomous Systems, 1998. To appear.

....uncertainty. Throughout this discussion, we will be assuming a known map of the environment [9] The position, x, of the robot is given as the location (x; y) and direction , defined over a space X = X; Y; Theta) Our localization method is a grid based implementation of Markov localization [3, 5]. This method represents the robot s belief in its current position using a 3 dimensional grid over X = X; Y; Theta) which allows for a discrete approximation of arbitrary probability distributions. The probability that the robot has a particular pose x is given by the probability p(x) State ....

....the effect of the robot s sensing and moving actions. The implementation of Markov localization provides the following equations for the tracking the robot s pose from x to x 0 : p(x 0 ju) Z X p(x 0 jx; u)p(x)dx (2) p(x 0 jz) ffp(zjx)p(x) 3) These equations are taken from [3, 12], where equation (2) gives the prediction phase of localization (after motion u) and equation (3) gives the update phase of localization (after receiving observation z) We extend these equations to the fourth dimension as follows: p(sju) hp(xju) H(p(xju) i (4) p(sjz) hp(xjz) H(p(xjz) i ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 25(3-4), 1998.

....experiments, this model is shown in Figure 2. Shown there is the probability of a sonar reading (vertical axis) as a function of the correct distance (determined using ray tracing) and the measured distance. The graph in Figure 2 has been generated from several millions of raw sonar readings (see [FBT98, Fox98] It is the result of fitting a model consisting of a mixture of of a linearGaussian (centered around the correct distance) a Geometric distribution (modeling overly short readings) and a Dirac distribution (modeling max range readings) to this data. ffl The inverse perception model is ....

D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 25(3-4):195--207, 1998.

....is depicted in Table 2. Here the time index is omitted, to emphasize the incremental nature of the algorithm. In experimental tests this method has been demonstrated to localize the robot reliably in static environments even if it does not have any prior knowledge about the robot s position [19,20,51]. Recently, different variants of Markov localization have been developed [19,74,111,139] These methods can be roughly distinguished by the nature of the state space representation. Virtually all published implementations of Markov localization, with (1) Initialization: P ( Gamma Bel pri ....

D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 25(3-4):195--207, 1998.

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D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 1998. To appear.

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D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 1998. To appear.

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D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 1998. To appear.

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D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems (RAS), 25:195--207, 1998.

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Fox, D., Burgard, W., and Thrun, S. 1998. Active markov localization for mobile robots. Robotics and Autonomous Systems.

No context found.

D. Fox and W. Burgard. Active markov localization for mobile robots. Robotics and Autonomous Systems, 1998.

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D. Fox, W. Burgard, and S. Thrun. Active Markov localization for mobile robots. Robotics and Autonomous Systems, 25:195--207, 1998.

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D. Fox, W. Burgard, and S. Thrun. Active markov localization for mobile robots. Robotics and Autonomous Systems, 1998. To appear.

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D. Fox, W. Burgard, and S. Thrun, \Active markov localization for mobile robots," tech. rep., Carnegie Mellon University, 1998.

No context found.

D. Fox, W. Burgard, and S. Thrun, "Active Markov localization for mobile robots," Robotics and Autonomous Systems, vol. 25, pp. 195--207, 1998.

No context found.

D. Fox, W. Burgard, and S. Thrun, "Active Markov localization for mobile robots," Robotic and Autonomous Systems,, Vol. 25, pp. 193-207, 1998.

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