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

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2 Chapter 1. Introductionif the primary rockets should fail during the critical minutes of orbit insertion. Thespacecraft cannot wait until this point to think about the problem, and reactivesystems that explicitly prime the secondary rocket beg the question of how suchbehaviour could be designed automatically.To deal with such problems, a planning system must be able to prioritise thedierent possible situations that might occur when a candidate plan is executed,and produce a plan that covers the most important ones while leaving others to becompleted as more information is available during execution. One way to approachthis problem, adopted in this thesis, is to assign probabilities to the various sourcesof uncertainty in the planning domain and use them to derive probabilities for eachof the dierent possible outcomes when the plan is executed. The outcomes withhigher probability are treated as having higher priority. This approach is attractivebecause a single parameter | a minimum acceptable value for the probability of plansuccess | can be used to control the planner and values can be combined using thestandard axioms of probability. Computing the probability of success of a plan canbe expensive, however.This thesis describes an implemented algorithm to produce plans that meet athreshold probability of success in uncertain domains. The thesis concentrates onplan generation and does not address plan execution, plan monitoring or re-planningalthough these are important pieces of a complete system for planning in uncertaindomains. The central contributions of the thesis are described below after the keyconcepts of planning under uncertainty are covered in more detail.1.1 Planning under uncertaintyPlanning, in the absence of uncertainty, is the process of nding a sequence of operatorsto transform an initial state into one that matches a goal description. The initialstate is usually specied by giving a list of facts that hold in it, and the goal descriptionis usually a logical sentence using a subset of the facts as terms. Operators areusually described in terms of preconditions and eects, where the precondition of anoperator is a logical sentence describing the states in which the operator can legallybe applied, and the eects describe the changes that will be brought about in a stateif the operator is applied. Following strips [Fikes & Nilsson 1971], the eects areusually represented as a list of facts to be deleted from the current state and a list offacts to be added.This thesis builds on the Prodigy planner [Minton et al. 1989; Carbonell et al.1992; Veloso et al. 1995], a domain-independent planner that was designed as a testbedfor learning and problem solving. Prodigy provides a rich language for specifyingsearch control knowledge and includes a number of independent machine learningmodules that can produce control knowledge from experience in a particular domainor use saved cases.
1.2. An example planning problem 3Uncertainty can enter a planning domain through a number of dierent types ofcause. The initial state may not be completely known, either because it is not completelyobservable by the agent or because of delays between forming and executinga plan. The outcomes of actions taken in the domain may be non-deterministic andother agents may bechanging the world though exogenous events that are not completelyknown or predictable. Finally the goals of the agent maychange over time,perhaps unpredictably. For each of these sources, partial information is still useful,for example a subset of the possible initial states that is guaranteed to contain theactual initial state, or a probability that some new goal will be given over a xed timescale can be helpful in building a working plan.This thesis presents a planner that can handle uncertainty from three types ofcause: more than one possible initial state, non-deterministic outcomes of actionsand non-deterministic exogenous events. For each of these, the planner requires aprobabilistic representation. It then attempts to nd a plan that exceeds a minimumdesired probability of success.The presence of exogenous events means that each step in a plan that has an appreciableduration is eectively nondeterministic. Explicitly considering each of thesealternative outcomes could lead to a combinatorial explosion in the separate cases thata planner would need to consider. The planning algorithm present in the thesis, calledWeaver, addresses this problem by lazily including sources of uncertainty in its evaluationof a plan. This is done building creating a plan in two alternating steps, plancreation and plan evaluation. In the plan creation step, Weaver chooses an outcomefor a step that is desired in order to achieve a goal and does not explicitly considerthe other outcomes, although it does make sure the outcome is reasonably likely. Inthe plan evaluation step, all sources of uncertainty can potentially be considered, butonly those that are shown to have an aect on the plan's chance of success are explicitlyrepresented. After this, the plan creation step is then re-entered, with one ormore of the sources of uncertainty that are known to be important being explicitlyconsidered.1.2 An example planning problemConsider for example a planning domain describing an oil tanker that has run agroundnear the coast and is beginning to leak oil into the sea. The goal is to stop theoil from polluting the water or reaching any ofseveral areas of coastline along theshore. The available actions include pumping the oil from the tanker into a secondaryvessel, surrounding the tanker with booms to contain the oil, using booms and otherequipment to prevent the oil from reaching the shore and cleaning oil up from eitherthe sea or the shore. Cleaning up oil from the water is successful with 70% probability.The amount of oil spilled from the tanker is a stochastic process represented as anexogenous event. Its path of travel once in the water is also treated as an exogenousevent. Many of the pieces of equipment used in the recovery process require good
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158 BIBLIOGRAPHY[Blythe & Veloso 19
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