Learning Hidden Markov Models with Geometrical Constraints

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.