Learning Topological Maps with Weak Local Odometric Information

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 odo-metric information, yielding faster convergence to better solutions with less data. 1 Introduction Hidden Markov models (HMMs), as well as their extension to partially observable Markov decision processes (POMDPs) model a variety of nondeterministic dynami-cal systems as abstract probabilistic state-transition systems with discrete 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 a/., 1995; Cassandra et a/., 1996]. Much previous work has required that the model be specified manually; this is a tedious process and it is often difficult to obtain correct probabilities. An ultimate goal is for an agent to be able to learn such models automatically, both for robustness and in 1 Actions are modeled by POMDPs but not by HMMs. order to cope with new and changing environments. The Baum-Welch algorithm [Rabiner, 1989] is frequently used to learn HMMs. Since POMDPs are a simple extension of HMMs, they can, theoretically, be learned with a simple extension to the Baum-Welch algorithm. However , without 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, and is often stuck in local minima. In this paper, we consider a special case of HMMs (extendable to POMDPs) for robot navigation, in which states are associated with points in a metric configuration space. We assume the robot has some odometric ability to measure relative transformations between its configurations. Such odometry is typically not precise enough …