The Belief Roadmap: Efficient Planning in Linear POMDPs by Factoring the Covariance

Summary

In this paper we address the problem of trajectory planning with imperfect state information. In many real-world domains, the position of a mobile agent cannot be known perfectly; instead, the agent maintains a probabilistic belief about its position. Planning in these domains requires computing the best trajectory through the space of possible beliefs. We show that planning in belief space can be done efficiently for linear Gaussian systems by using a factored form of the covariance matrix. This factored form allows several prediction and measurement steps to be combined into a single linear transfer function, leading to very efficient posterior belief prediction during planning. We give a belief-space variant of the Probabilistic Roadmap algorithm called the Belief Roadmap (BRM) and show that the BRM can compute plans substantially faster than conventional belief space planning. We also show performance results for planning a path across MIT campus without perfect localization.