Planning under Uncertainty in Dynamic Domains - Carnegie Mellon ...

Chapter 3Planning under UncertaintyIn this chapter I provide an overview of the prodigy 4.0 planning algorithm anddiscuss extensions made to allow it to create and evaluate plans under conditions ofuncertainty. I present extensions to prodigy 4.0's model to represent uncertaintyinSection 3.2. I give the meaning of the elements of this language in terms of a Markovdecision process in Section 3.3. I illustrate the chapter with an example domain, aplan and the domain's derived mdp in Section 3.4.3.1 Overview of prodigy 4.0prodigy 4.0 takes as input a representation of a planning problem and attempts toproduce a solution. The problem consists of the allowable object types, the actionsthat can be taken, a set of specic objects, an initial state and a goal state description.A solution, if found, will be a sequence of operators that can be applied to the initialstate to produce some state satisfying the goal description. prodigy 4.0 uses meansendsanalysis to search for plans. In this section I give a detailed description of thelanguage prodigy 4.0 uses to represent planning problems, how it constructs a planand how it searches a space of partial plans to nd a solution.3.1.1 Domains, problems and plansA planning domain in prodigy 4.0 consists of a type hierarchy T , a set of literalsL and a set of operators O 1 , based on the strips domain denition [Fikes & Nilsson1971]. Each operator is dened by specifying its preconditions and eects. Thepreconditions specify conditions about the world that must be true in order for theoperator to be applied, and are made of combinations of literal terms, that mayinclude typed variables and may be combined using conjunction, disjunction, negationand existential and universal quantication. The eects specify literals that are either1 A domain also contains inference rules, which are very similar to operators but add inferencesto the state rather than changing it. Full details can be found in [Carbonell et al. 1992].19