## 11.3.3 The Probabilistic Case: POMDPs

Example 11.14 generalizes nicely to the case of states. In operations research and artificial intelligence literature, these are generally referred to as partially observable Markov decision processes or POMDPs (pronounced pom dee peez''). For the case of three states, the probabilistic I-space, , is a -simplex embedded in . In general, if , then is an -simplex embedded in . The coordinates of a point are expressed as . By the axioms of probability, , which implies that is an -dimensional subspace of . The vertices of the simplex correspond to the cases in which the state is known; hence, their coordinates are , , , . For convenience, the simplex can be projected into by specifying a point in for which and then choosing the final coordinate as . Section 12.1.3 presents algorithms for planning for POMDPs.

Steven M LaValle 2012-04-20