## Learning Topological Maps with Weak Local Odometric Information (1997)

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Venue: | IN PROCEEDINGS OF IJCAI-97. IJCAI, INC |

Citations: | 137 - 4 self |

### BibTeX

@INPROCEEDINGS{Shatkay97learningtopological,

author = {Hagit Shatkay and Leslie Pack Kaelbling},

title = {Learning Topological Maps with Weak Local Odometric Information},

booktitle = {IN PROCEEDINGS OF IJCAI-97. IJCAI, INC},

year = {1997},

pages = {920--929},

publisher = {}

}

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### Abstract

Topological maps provide a useful abstraction for robotic navigation and planning. Although stochastic maps can theoretically be learned using the Baum-Welch algorithm, without strong prior constraint on the structure of the model it is slow to converge, requires a great deal of data, and is often stuck in local minima. In this paper, we consider a special case of hidden Markov models for robot-navigation environments, in which states are associated with points in a metric configuration space. We assume that the robot has some odometric ability to measure relative transformations between its configurations. Such odometry is typically not precise enough to suffice for building a global map, but it does give valuable local information about relations between adjacent states. We present an extension of the Baum-Welch algorithm that takes advantage of this local odometric information, yielding faster convergence to better solutions with less data.

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Citation Context ...gorithm is a straightforward extension of BaumWelch to deal with the relational information and the factored observation sets. The Baum-Welch algorithm is an expectation-maximization (EM) algorithm [ =-=Dempster et al., 1977-=- ] ; it alternates between the E-step of computing the state-occupation probabilitiessat each time in the sequence given E and the current model , and the M-step ofsnding a new model that maxim... |

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Citation Context ...1 Such models have proven particularly useful as a basis for robot navigation in buildings, providing a sound method for localization and planning [ Simmons and Koenig, 1995; Nourbakhsh et al., 1995; =-=Cassandra et al., 1996-=- ] . Much previous work has required that the model be specied manually; this is a tedious process and it is often dicult to obtain correct probabilities. An ultimate goal is for an agent to be able... |

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Citation Context ...iscrete states, observations and possibly actions. 1 Such models have proven particularly useful as a basis for robot navigation in buildings, providing a sound method for localization and planning [ =-=Simmons and Koenig, 1995-=-; Nourbakhsh et al., 1995; Cassandra et al., 1996 ] . Much previous work has required that the model be specied manually; this is a tedious process and it is often dicult to obtain correct probabili... |

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Citation Context ...aranteed to provide monotonically increasing convergence of Pr(Ej). Baum-Welch has been proven to be an EM algorithm; it has also been provably extended to real-valued observations [ Liporace, 1982; =-=Juang, 1985-=- ] . Our algorithm introduces an additional matrix, and enforces thesrst two geometric consistency constraints on the M-step, but like the standard Baum-Welch it is still guaranteed to converge to a l... |

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Citation Context ...ns and possibly actions. 1 Such models have proven particularly useful as a basis for robot navigation in buildings, providing a sound method for localization and planning [ Simmons and Koenig, 1995; =-=Nourbakhsh et al., 1995-=-; Cassandra et al., 1996 ] . Much previous work has required that the model be specied manually; this is a tedious process and it is often dicult to obtain correct probabilities. An ultimate goal is... |

14 | Learning hidden Markov models with geometric information
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(Show Context)
Citation Context ...l matrix, and enforces thesrst two geometric consistency constraints on the M-step, but like the standard Baum-Welch it is still guaranteed to converge to a local maximum of the likelihood function [ =-=Shatkay and Kaelbling, 1997-=- ] . The proof is along the lines of the one presented by Juang et al [ 1986 ] for the standard BaumWelch algorithm, and is beyond the scope of this paper. 4.1 Computing State-Occupation Probabilities... |

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