Computing robust plans in continuous domains

Abstract

We define the robustness of a sequential plan as the probability that it will execute successfully despite uncertainty in the execution environment. We consider a rich notion of uncertainty over continuous domains that includes stochastic action effects, and changes to state variables due to unpredictable exogenous events. Given a characterization of this uncertainty in terms of probability distributions (e.g., Gaussian) our contributions are two-fold: First, we describe a novel approach to computing the robustness of a plan in the situation calculus, which (a) separates the projection problem from the problem of reasoning about probability, and (b) explicitly reveals the relevance and statistical independence of random variables and events (i.e., conditions that contain random variables). Then, building on this approach, we describe a forward search based planner that generates maximally robust plans, exploiting the revealed structure for speed-up. Preliminary empirical results demonstrate that our approach can realize exponential savings in both time and space compared to the classical sampling approach. Copyright ?? 2009, Association for the Advancement of Artificial Intelligence. All rights reserved.