Planning under Resource Constraints

This paper outlines the basic principles underlying reasoning about resources in IPP, which is a classical planner based on planning graphs originally introduced with the graphplan system. The main idea is to deal with resources in a strictly action-centered way, i.e., one speciies how each action consumes or produces resources, but no explicit temporal model is used. This avoids the computational problems of solving general constraint satisfaction problems by using instead interval arithmetics and propagation of resource requirements over time steps in the planning graph. 1 Actions that provide, produce, and consume Resources The starting point for the language extension is the ADL subset that is available in IPP 3.0 7]. It ooers universally quantiied and conditional eeects, atomic negation, equality as well as quantiied and conditional goals. To reason about resources, an action description is extended in the following way: 1. Following the \ordinary preconditions" (which are logical facts) resource requirements can be speciied. 2. EEect descriptions are extended to specify which of the resource variables is provided, produced or consumed by the action. 3. Database query schemata allow for a compact representation of resource requirements and resource eeects. As an example, consider the following two actions that are part of our version of the airplane example used by the ZENO planner 9]. y(?x ?y:airport) :pre plane-at(?x) ($gas distance(?x ?y)/3) :eff plane-at(?y) not plane-at(?x); ALL ?p:passenger boarded(?p) => at(?p ?y) not at(?p ?x); $gas-= distance(?x ?y)/3; $time += distance(?x ?y) * (3/20). The action y speciies what happens when an airplane ies from airport x to airport y. As a precondition it needs to be at airport x and as a resource requirement there must be enough gas in the tank to y the distance between the two airports speciied with $gas distance(?x ?y) / 3. We allow the distinguished binary predicates =; ; , which mean that the current amount of the resource variable $gas speciied as the rst argument must be either equal, lower-or-equal, or higher-or-equal the arithmetic expression following as the second argument. An arithmetic expression can contain a database query schema such as distance(?x ?y) together with an arithmetic term built out of the four basic mathematical operations and real numbers. When the action gets instantiated, the query schema is instantiated into a database query such as distance(Basel Paris) for which the speciic value is found in the associated database. Together with the arithmetic term …