Pre-image Backchaining in Belief Space for Mobile Manipulation

As robots become more physically robust and capable of sophisticated sensing, navigation, and manipulation, we want them to carry out increasingly complex tasks. A robot that helps in a household must plan over the scale of hours or days, considering abstract features such as the desires of the occupants of the house, as well as detailed geometric models that support locating and manipulating objects. The complexity of such tasks derives from very long time horizons, large numbers of objects to be considered and manipulated, and fundamental uncertainty about properties and locations of those objects. We have developed an approach to integrated task and motion planning that integrates geometric and symbolic representations in an aggressively hierarchical planning architecture, called HPN [10]. The hierarchical decomposition allows efficient solution of problems with very long horizons and the symbolic representations support abstraction in complex domains with large numbers of objects and are integrated effectively with the detailed geometric models that support motion planning. In this paper, we extend the HPN approach to handle two types of uncertainty: future-state uncertainty about what the outcome of an action will be, and currentstate uncertainty about what the current state actually is. Future-state uncertainty is handled by planning in approximate deterministic models, performing careful execution monitoring, and replanning when necessary. Current-state uncertainty is handled by planning in belief space: the space of sets or probability distributions over possible underlying world states. There have been several recent approaches to integrated task and motion planning [3, 14, 13] but they do not address uncertainty. The use of belief space (and information spaces [11]) is central to decision-theoretic approaches to uncertain domains [9].