Learning Hidden Markov Models with Geometrical Constraints

TL;DR

This paper introduces a method for learning Hidden Markov Models with geometrical constraints, improving model quality and robustness in robot navigation environments by incorporating domain-specific information and new estimation techniques.

Contribution

It presents novel initialization heuristics, update rules, and a strategy for enforcing geometrical consistency in HMMs, tailored for better learning in spatial environments.

Findings

Enhanced model quality and convergence speed

Robustness to limited and noisy data

Effective in real and simulated robot navigation scenarios

Abstract

Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) form a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office buildings, which are typical for robot navigation and planning. The work presented here is concerned with acquiring such models. We demonstrate how domain-specific information and constraints can be incorporated into the statistical estimation process, greatly improving the learned models in terms of the model quality, the number of iterations required for convergence and robustness to reduction in the amount of available data. We present new initialization heuristics which can be used even when the data suffers from cumulative rotational error, new update rules for the model parameters, as an instance of generalized EM, and a strategy for enforcing complete geometrical consistency in the model. Experimental results demonstrate the effectiveness of our approach for both simulated and real robot data, in traditionally hard-to-learn environments.