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