A POMDP approach to the hide and seek game

Projecte final de Màster Oficial fet en col.laboració amb Institut de Robàtica i Informàtica IndustrialPartially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in uncertain and dynamic environments. They have been successfully applied to various robotic tasks. The modeling advantage of POMDPs, however, comes at a price exact methods for solving them are computationally very expensive and thus applicable in practice only to simple problems. A major challenge is to scale up POMDP algorithms for more complex robotic systems. Our goal is to make an autonomous mobile robot to learn and play the children's game hide and seek with opponent a human agent. Motion planning in uncertain and dynamic envi- ronments is an essential capability for autonomous robots. We focus on an e cient point-based POMDP algorithm, SARSOP, that exploits the notion of optimally reachable belief spaces to improve computational efficiency. Moreover we explore the mixed observability MDPs (MOMDPs) model, a special class of POMDPs. Robotic systems often have mixed observability: even when a robots state is not fully observable, some components of the state may still be fully observable. Ex- ploiting this, we use the factored model, proposed in the literature, to represent separately the fully and partially observable components of a robots state and derive a compact lower dimensional representation of its belief space. We then use this factored representation in conjunction with the point-based algorithm to com- pute approximate POMDP solutions. Experiments show that on our problem, the new algorithm is many times faster than a leading point-based POMDP algorithm without important losses in the quality of the solutio