## Heading in the Right Direction (1998)

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Venue: | in Proceedings of the Fifteenth International Conference on Machine Learning |

Citations: | 6 - 2 self |

### BibTeX

@INPROCEEDINGS{Shatkay98headingin,

author = {Hagit Shatkay and Leslie P. Kaelbling},

title = {Heading in the Right Direction},

booktitle = {in Proceedings of the Fifteenth International Conference on Machine Learning},

year = {1998}

}

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### Abstract

Stochastic topological models, and hidden Markov models in particular, are a useful tool for robotic navigation and planning. In previ- ous work we have shown how weak odometric data can be used to improve learning topological models, overcoming the common problems of the standard Baum-Welch algorithm. Odometric data typically contain directional information, which imposes two difficulties: First, the cyclicity of the data requires the use of special circular distributions. Second, small errors in the head- ing of the robot result in large displacements in the odometric readings it maintains. The cumu- lative rotational error leads to unreliable odomet- ric readings. In the paper we present solutions to these problems by using a circular distribution and relative coordinate systems. We validate their effectiveness through experimental results from a model-learning application.

### Citations

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(Show Context)
Citation Context ...gs when moving from state qt-1 to state qt, as well as the change of the robot's heading, 0, between these states. An arbitrary initial model ho is assumed. Then an expectation maximization algorithm =-=[3]-=- is executed as follows: 2We discuss here HMMs rather than POMDP models. Extension to POMDPs is straightforward, but notationally more cumbersome. ab Figure 1: Robot changes heading from state a to st... |

4556 | A tutorial on hidden markov models and selected applications in speech recognition
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(Show Context)
Citation Context ...ess and in order to cope with new and changing environments. Since POMDP models are a simple extension of HMMS, they can, theoretically, be learned with a simple extension to the Baum-Welch algorithm =-=[15]-=- for learning HMMS. However, without a strong prior constraint on the structure of the model, the Baum-Welch algorithm does not perform very well: it is slow to converge, requires a great deal of data... |

1388 |
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Citation Context ...s are quantitatively compared to the actual model that generated the data. Each of the models induces a probability distribution on strings of observations; the asymmetric Kullback-Leibler divergence =-=[11]-=- between the two distributions is a measure of how far the learned model is from the true model. We report our simulation results in terms of a sampled version of the KL divergence, as described by Ju... |

511 | Factorial hidden Markov models
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(Show Context)
Citation Context ... directional data. Probabilistic models are widely used within the AI community. Such models may allow continuous probabilities, as demonstrated in work on Bayesian networks [7], hidden Markov models =-=[5, 8]-=-, probabilistic clusters [2] and stochastic maps [19], to name a few. However, the assumption underlying all the above work is that continuous distributions are linear -- that is -- distributions that... |

460 | Globally consistent range scan alignment for environment mapping
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Citation Context ...on-circular distribution is justified when the estimation of a position is based only on readings a-priory known to be taken near this position, (see for example work by Thrun et al [20] and Lu et al =-=[12]-=-). However, we do not know in advance the angles between states. The data is a sequence of measurements recorded at all the states. We estimate the probabilities of the states in which they were recor... |

263 |
Statistics of Directional Data
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(Show Context)
Citation Context ...r handling directional data. In particular we concentrate on the von Mises distribution -- a circular version of the normal distribution. Further discussion can be found in the statistical literature =-=[6, 10, 13]-=-. Section 3.3 returns to show how the theory is applied in our model and learning algorithm. 3.1 STATISTICS OF DIRECTIONAL DATA Directional data in the 2-dimensional space can be represented as a coll... |

190 | Acting under uncertainty: discrete Bayesian models for mobile-robot navigation
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(Show Context)
Citation Context ...ly observable Markov decision processes (POMDP models), are a useful tool for representing environments such as road networks and office buildings, which are typical for robot navigation and planning =-=[1, 14, 18]-=-. Previous work on planning with such models typically assumed that the model is manually provided. Manual acquisition of these models can be very tedious and hard. It is desirable to learn such model... |

171 |
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Citation Context ...ly observable Markov decision processes (POMDP models), are a useful tool for representing environments such as road networks and office buildings, which are typical for robot navigation and planning =-=[1, 14, 18]-=-. Previous work on planning with such models typically assumed that the model is manually provided. Manual acquisition of these models can be very tedious and hard. It is desirable to learn such model... |

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Citation Context ... within the AI community. Such models may allow continuous probabilities, as demonstrated in work on Bayesian networks [7], hidden Markov models [5, 8], probabilistic clusters [2] and stochastic maps =-=[19]-=-, to name a few. However, the assumption underlying all the above work is that continuous distributions are linear -- that is -- distributions that assign density to each point on the real line so tha... |

137 | Learning topological maps with weak local odometric information
- Shatkay, Kaelbling
- 1997
(Show Context)
Citation Context ...imensions; it consists of the changes along the c and the t axis as well as a change in the heading of the robot within a global coordinate system. In our previous work on learning topological models =-=[17]-=- we made several assumptions about the odometric data:sAll odometric measures are normally distributed. Most often the distribution is Gaussian.sAll corridors are perpendicular to each other.sThe robo... |

120 |
A Probabilistic Distance Measure for Hidden Markov Models
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Citation Context ... distributions is a measure of how far the learned model is from the true model. We report our simulation results in terms of a sampled version of the KL divergence, as described by Juang and Rabiner =-=[9]-=-. It is based on generating sequences of sufficient length according to the distribution induced by the true model, and comparing their likelihoods according to the learned model with the true model l... |

84 | Probabilistic navigation in partially observable environments
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(Show Context)
Citation Context ...ly observable Markov decision processes (POMDP models), are a useful tool for representing environments such as road networks and office buildings, which are typical for robot navigation and planning =-=[1, 14, 18]-=-. Previous work on planning with such models typically assumed that the model is manually provided. Manual acquisition of these models can be very tedious and hard. It is desirable to learn such model... |

67 |
Maximum-Likelihood Estimation for Mixture Multivariate Stochastic Observations of Markov Chains
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(Show Context)
Citation Context ... directional data. Probabilistic models are widely used within the AI community. Such models may allow continuous probabilities, as demonstrated in work on Bayesian networks [7], hidden Markov models =-=[5, 8]-=-, probabilistic clusters [2] and stochastic maps [19], to name a few. However, the assumption underlying all the above work is that continuous distributions are linear -- that is -- distributions that... |

44 | Learning Bayesian networks: A unification for discrete and Gaussian domains
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(Show Context)
Citation Context ...he use and manipulation of directional data. Probabilistic models are widely used within the AI community. Such models may allow continuous probabilities, as demonstrated in work on Bayesian networks =-=[7]-=-, hidden Markov models [5, 8], probabilistic clusters [2] and stochastic maps [19], to name a few. However, the assumption underlying all the above work is that continuous distributions are linear -- ... |

24 |
Bees acquire route-based memories but not cognitive maps in a familiar landscape
- Dyer
- 1991
(Show Context)
Citation Context ... of pen-and-ink drawings and the production of animation based on magnetic trackers data requires statistical manipulation of directional data. In cognitive science, modeling routes chosen by animals =-=[4]-=- requires a similar kind of statistical manipulation. In the area of machine learning we often use probabilistic models for robot movement. Most aspects of robot movement (arm movement as well as the ... |

14 | Learning Hidden Markov Models with Geometric Information
- Shatkay, Kaelbling
- 1997
(Show Context)
Citation Context ...nt on the structure of the model, the Baum-Welch algorithm does not perform very well: it is slow to converge, requires a great deal of data, and often becomes stuck in local maxima. In previous work =-=[16, 17]-=- we demonstrated how the simple Baum-Welch algorithm can be enhanced with weak local odometric information to learn better models faster, under the assumption listed above. For the sake of completenes... |

11 |
The Circular Normal Distribution: Theory and Tables
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(Show Context)
Citation Context ...ns the density of any point : on the real line is the same as that of : + k where k is any integer andsis some real number. The need for circular distributions has long been realized by statisticians =-=[6]-=-, but the practice of using them has not found its way into the computer science community and to the machine learning community in particular. One of the goals of this paper is to point out the usefu... |

9 |
et al. Autoclass: A bayesian classification system
- Cheeseman
- 1988
(Show Context)
Citation Context ...c models are widely used within the AI community. Such models may allow continuous probabilities, as demonstrated in work on Bayesian networks [7], hidden Markov models [5, 8], probabilistic clusters =-=[2]-=- and stochastic maps [19], to name a few. However, the assumption underlying all the above work is that continuous distributions are linear -- that is -- distributions that assign density to each poin... |

7 | A probabilistic approach to concurrent map acquisition and localization for mobile robots
- Thrun, Burgard, et al.
- 1998
(Show Context)
Citation Context ...roach of using a non-circular distribution is justified when the estimation of a position is based only on readings a-priory known to be taken near this position, (see for example work by Thrun et al =-=[20]-=- and Lu et al [12]). However, we do not know in advance the angles between states. The data is a sequence of measurements recorded at all the states. We estimate the probabilities of the states in whi... |