PLANNINGand

INTELLIGENT SYSTEMSAn Introductory Overview

byMichail G. Lagoudakis

TR-96–2–1

Submitted to

Dr. Kimon P. Valavanis

The Center of Advanced Computer StudiesUniversity of Southwestern LouisianaP.O. Box 44330, Lafayette, LA 70504

December 1996

Planning and Intelligent Systems 1

by Michail G. Lagoudakis

TR-96–2–1

Abstract

Planning, as an inseparable component of intelligent behavior, became aresearch interest as early as AI was founded. The possibility of an automatedplanning system has been studied at different levels of complexity and over awide area of application domains. Many methodologies have been proposed andseveral planning systems have been built, nevertheless there is a long way to gobefore we can speak of practical success. A planning system must meet the realworld requirements. It must respond in real time and cope with the unpredictabilityand uncertainty which are inherent characteristics of the real environments.

Planning as a component of Intelligent Systems and the corresponding re-search are the objectives of this report which is organized in three parts. The firstpart contains an introduction and the statement of the problem. The second partreviews the proposed techniques and methodologies, as well as the related prob-lems and difficulties. Finally, in the last part four well-known planning systemsare described: STRIPS, NOAH, SIPE, FORBIN.

1 This report serves as a partial fulfillment for the requirements of CMPS 619 course during Fall 1996 semester.

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Contents

Chapter 1 Planning: An Overview . . . . . . . . . . . . . . . . . 1Section 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1Section 2 Artificial Intelligent Systems . . . . . . . . . . . . . . . 2Section 3 Classical Planning . . . . . . . . . . . . . . . . . . . . . 4Section 4 Practical Planning . . . . . . . . . . . . . . . . . . . . . 7

Chapter 2 Planning Techniques . . . . . . . . . . . . . . . . . 12Section 1 Knowledge Representation . . . . . . . . . . . . . . 12Section 2 Plan Synthesis . . . . . . . . . . . . . . . . . . . . . . 14Section 3 The difficulty of planning . . . . . . . . . . . . . . . . 18

Chapter 3 Planning Systems . . . . . . . . . . . . . . . . . . . 20Section 1 STRIPS . . . . . . . . . . . . . . . . . . . . . . . . . . 20Section 2 NOAH . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Section 3 SIPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Section 4 FORBIN . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

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Chapter 1Planning: An Overview

1.1 Introduction

Intelligence is a common feature found in all live beings. Of course, thedegree of intelligence differs from one to an other, but it can be easily seen thatall of them have the ability to act in an “intelligent” manner and affect theirenvironment. In most cases (if not in all), the actions performed by the intelligentbeing (its behavior) are directed by the desire of achieving a particular goal.There is a reason behind each action and there is a mechanism that “predicts” theconsequences of actions, instead of experiencing them and dictates what action todo next, looking forward to some goal. This process of reasoning about actionsis referred asplanning and the sequences of actions are referred asplans.

Planning appears at several different levels in the everyday life. We are sofamiliar with this process that some times it is taken as a mechanical one. Butthere are many cases where we cannot cope with its complexity. Picking up anobject, driving a car, cooking a food, playing chess, solving a problem, designinga computer program, managing a group of people, or even more, bringing up achild, are only a few examples where planning issues arise. Even more, beingswith lower intelligence than that of human have the ability of planning theiractivities, for example, the ants that collect food into their nest for the winter. Itis obvious that the “success” of an intelligent being depends heavily on its ability

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to plan its actions “effectively”, where the terms “success” and “effectively” maybe defined differently for different cases.

Studies of human intelligence have been performed for well over the past2,000 years, but only in the last few decades (in parallel with the impressiveevolution of computers), research led to the possibility of buildingArtificial In-telligent Systems. The result was the development of a broad research area, namedArtificial Intelligence (AI) , which has succeeded in many practical domains. Cer-tainly, the goal of building a “thinking machine” has not been accomplished (andperhaps will never be accomplished), but there are many positive results so far.

Planning, as an inseparable component of intelligent behavior, became aresearch interest as early as AI founded. The possibility of an automated planningsystem, that is, an Artificial Intelligent System capable of reasoning about its“actions” , has been studied at different levels of complexity and over a widerange of application domains. Many methodologies have been proposed andseveral planning systems have been built, nevertheless, there is a long way to gobefore we can speak of practical success. An Artificial Intelligent System andtherefore its planning component must meet the real world requirements. Thesystem must respond in real time and cope with the unpredictability, uncertaintyand error occurrences, which are inherent characteristics of the reality. Thus, inthis sense, planning and AI are still on-going research areas.

Planning is not only an area of AI, but it has been studied also at higherlevels (Cognitive Science) [Hoc, 1989] or lower ones (Control Theory) [Dean& Wellman, 1991]. This “vertical” dimension of planning should be consideredfor a more-in-depth study of the area. The combination of the results at thesedifferent levels will help not only the automation of the problem, but, also, thedeeper understanding of the human planning mechanism.

Planning as a component of Artificial Intelligent Systems and the correspond-ing research are the objectives of this report. Chapter 1 presents the statementof the problem and its components. Chapter 2 presents a review of the proposedtechniques and methodologies, as well as the related problems arising in the con-text of planning. In Chapter 3 some of the best known planning systems aredescribed and analyzed.

1.2 Artificial Intelligent Systems

A definition of the Artificial Intelligent Systems is not attempted here, as there

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is no common definition approved by all the researchers and perhaps the conceptof intelligence, as we know it, is far away from what is “true intelligence”.The demanding reader can be referred to any well-known book on ArtificialIntelligence or Intelligent Machines. The concept of Intelligent Agent as recentlydescribed in [Russell & Norvig, 1995] might be the most satisfactory.

We will bypass the problem by simply providing the definition of Intelligencetaken from the Webster’s Dictionary2:

“ Intelligence is the ability to perceive one’s environment, to deal with itsymbolically, to deal with it effectively, to adjust to it, to work toward a goal.”

Briefly speaking, an Artificial Intelligent System is nothing else than an artifactwith the ability above in some degree. In the rest of this report, the term ArtificialIntelligent System will be referred as Intelligent System, or simply System, orAgent, where there is no confusion, since all the discussion will be restricted toArtificial Intelligent Systems.

Before proceeding any further, a list of Intelligent Systems where planningissues arise is provided:

1. Intelligent Robotic Systems (IRSs)

• Robot Navigation• Path Planning• Goal-Oriented Robot Programming

2. Problem Solvers

• Theorem Proving• Game Playing

3. Automated Program Generators4. Natural Language Processors5. Expert Systems

• Decision Support System• Management (Strategic) Planning

2 Philip Babcock Gove (editor), Webster’s Third International Dictionary, G & C Merriam Company, 1981, Springfield,MA

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6. Computer Integrated Manufacturing (CIM)

• Production Planning Systems• Factory Scheduling Systems• Flexible Manufacturing Systems (FMSs)• Automated Manufacturing Systems (AMSs)

7. Distributed Agents

• Agent Coordination• Agent Cooperation

1.3 Classical Planning

In this section, a more formal definition of the problem is attempted. Theterm classical planning has been used for the early definition of the problem basedon several assumptions. There are a lot of other terms that come up within thecontext of planning so the exposition of the problem is elaborated step-by-stepby incorporating new terms.

World (Environment)It is impossible to think of an Intelligent System outside of an application

domain. Any system acts within a certainworld or environment. It can bethought asthe set of all the “entities” that can affect or be affected by the systemand their properties, where the term entity is taken in its broadest meaning. Aworld can be virtual (e.g. the domain of a logic problem) or real (e.g. a factoryfloor). In general, the system itself is part of the world.

The termworld statestands for the full description of the entities and theproperties of the world at a particular time (snapshot). The result of the applicationof an action by the system to a world state is the derivation of another world state.Actions when applied transform, is some manner, the world from state to state, bychanging one or more properties. A stretch of consequent world states is calledworld history or chronicle.

ActionAction is a common characteristic of all intelligent systems. It is“the pro-

gressive alteration of mental states or of mental and physical states coordinately,

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especially when resulting in an observable effect on the external world”3. In otherwords, it is the way an Intelligent System exhibits its capabilities to the outer en-vironment. We can think of action(s) as the “output” of the system. The necessityof a such an output is obvious, since its absence implies the useless of the system.

In most cases, there is a particular (finite or infinite) set of actions thesystem is capable of performing. These actions which are indivisible into simplercomponents are calledprimitive actions. The term action when used in this reportwill be referred to such primitive actions. Not all the actions can be performed atany world state. An action is said to beapplicablewith respect to a world stateif the system is capable of performing it at this state.

OperatorOperators represent or characterize classes of similar actions. Anoperatoris a

parameterized full description of an action, in the sense that it contains informationconcerning not only the identity of the action but also the situations (world states)where it is applicable and the effects of its application to the world. In otherwords, an operator connects the action and the environment.

The parameters of an operator can be instantiated and theinstancederivedis a primitive action. In this way, an infinite class of actions can be representedby a finite set of operators. For example, the operator MOVE may represent theclass of all the movement actions to any arbitrary direction.

GoalAn Intelligent System performs actions in order to achieve a particular goal.

Action not oriented to a specific goal is meaningless, and this random behavioris not a feature of intelligence. In most cases, agoal is described asa desiredproperty of the world state. Then the mission of the system is to transform thecurrent world state into a state where this property is held (goal state). In general,there are more than one goal states. If the goal is the solution of some problemdescribed in the initial world state, then the ability of the system to achieve thegoal reflects its ability to solve the problem.

Generally speaking, a goal can be described in more complex ways than asingle property of the world state. It could be the maintenance or prevention of

3 Philip Babcock Gove (editor), Webster’s Third International Dictionary, G & C Merriam Company, 1981, Springfield,MA

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some condition, or a relation between some initial and some final world states.In such cases, the goal is structured by several subgoals. Goals can be posed bythe outer environment to the system, but self-generated goals are also possible.

Plan

Plan is a detailed and systematic formulation of actions4. In other words,it is a set of actions (or better, instantiated operators) grouped together with aspecific structure dictated, in general, by some goal. Note that “structure” doesnot necessarily means sequence. The structural components may be sequencing,choice (condition), iteration, recursion, parallelism, and in the most extremeform, nondeterminism [Georgeff, 1987]. Given such components, a plan canbe decomposed into subplans, and recursively, subplans into other subplans andso on.

A plan is said to beapplicableto the current world state if it can be carried outcompletely starting at this state, i.e. at each step the current action is applicableto the current world state. A plan is said to be a solution to a problem (goal)if its application to the current world state leads to a goal state. A goal maybe achieved by many different plans, that is, there might exist more than onesolutions. The different solutions can be evaluated and ordered in terms of someefficiency measures, differing from domain to domain.

Plan Execution

Plan execution is the system’s process of carrying out an applicable plan.This is the real output of the system and this output taken over time consists itsbehavior. The behavior of the system affects the environment and perhaps itselfand exhibits the intelligence of the system.

Planning

Given the primitive actions, the operators and the current world model ofan Intelligent System along with a goal,planning (or plan synthesis) istheprocess of formulating an applicable plan that achieves the goal when executed.The intelligence of the system is reflected to its ability to produce “efficient” or

4 Philip Babcock Gove (editor), Webster’s Third International Dictionary, G & C Merriam Company, 1981, Springfield,MA

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“optimal” plans, where efficiency and optimality are defined with respect to theapplication domain.

Planning Execution

WORLD

INTELLIGENT SYSTEM

Plan

WorldModel

OperatorsActions

GoalGeneration

Self GoalGeneration

Figure 1.1 Intelligent System and Planning

Figure 1.1 shows a block diagram of the concepts discussed so far. Rectan-gular represent components whereas circles represent processes. The lines andthe arrows designate the communication among them.

1.4 Practical Planning

The problem discussed so far is known as classical planning. When it isconsidered in the real world context then it takes an other dimension and is calledpractical planning.

Time, Scheduling and ConstraintsAll real environments involve the time dimension. Therefore, in this context,

the planning process and the generated plans must be projected over time. Whenplanning comes down to the assignment of actions over time periods then itis known asscheduling. Thus, scheduling can be viewed as a special case ofplanning [Georgeff, 1987] when the system has to cope with timing issues.

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Things become complicated when the system is not free to make arbitrary se-lections (especially in time decisions) but there are severalconstraints(deadlines,preferences, etc.) that must be met. In this case, the system faces theconstraintsatisfaction problem. Scheduling with resources, deadlines and constraints has avery practical importance, especially in manufacturing [Zweben & Fox, 1994].

Real Time

Planning in the real environments should not be seen as a static process, thatis, after a plan has been produced for a given goal, a new goal is given and theprocess continues. In real world, it should be seen as a continuous process. Thegoals “arrive” randomly (sometimes conflicting) and the system must respond inreal time, planning and replanning continuously. The plan must continually beexecuted (although it may be incomplete in its overall length) to meet the real-time response requirement. In this context, planning can been seen as a methodof controlling processes [Dean & Wellman, 1991].

Execution Monitoring

Real environments are characterized by uncertainty, unpredictability, erroroccurrences and faults. In the ideal case, the world changes exactly as the systempredicts using its world model. But in reality, the real world state becomes verysoon incompatible to the world model state. Therefore, the execution of the planwill fail to achieve the goal state. Moreover, it might cause undesirable situations.

As a consequence, the system must additionally monitor the execution of theplan, update the world model when an unexpected event occurs and revise thecurrent plan (replanning) to meet the new conditions. It is obvious that the successof execution monitoring, error recovery and replanning relies on the ability of thesystem to perceive the real world. Note that perception is not a part of the planningprocess although it plays an important role in the execution monitoring.

Hierarchy

From the discussion above, the reader can recognize three different levels ofprocessing into the system: planning, scheduling, monitoring. Planning consiststhe higher level, scheduling is the intermediate and finally monitoring is the lowest.Moreover, since the world can be viewed at different levels of abstraction, this

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could be the case also for a plan and therefore each of the three levels abovecould consist of several sublevels, provided they preserve the hierarchy.

It is also obvious that the “amount” of intelligence required decreases as wemove from planning to monitoring, whereas the precision of the plan increases.This comes to agreement with the“Principle of Increasing Precision with De-creasing Intelligence”for Intelligent Systems, defined in [Valavanis & Saridis,1992].

Metaplanning and Learning

The term metaplanning is used to characterize the intelligence and theknowledge that guides the planning process. If planning is reasoning about actionsand plans, then metaplanning isreasoning about planning.

Effective planning requires the system to be able toacquire planning knowl-edge from its environment and its experience. This process is referred aslearning[Minton, 1993]. Learning provides to the system adaptivity (the real environmentoften changes over time) and a dynamic internal structure.

The figure below represents a more realistic view of a planning system.

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Planning

Execution

WORLD

INTELLIGENT SYSTEM

Plan

WorldModelOperatorsActions

GoalGeneration

Self GoalGeneration

Perception

Scheduling

Monitoring

Metaplanning Learning

Planning Knowledge Learning Knowledge

Figure 1.2 Intelligent System and Planning revisited

Multiagent Domain

In the description given so far, it has been assumed that the world wherethe system acts, is a static environment. The world state can be changed onlyby the actions of the system. However, this is not the case for the real worldenvironments which are characterized by a highly dynamic nature. Then thesystem is not the exclusive “dominator” of what occurs in the world and theproblem becomes harder.

This concept becomes more understandable if we drop the convenient as-sumption that there is only one system acting in the world. The realistic case isthat the world is, in general, populated with a number of agents (other intelligentsystems, not necessary identical). Some of them are cooperative, some adversarialand other simply disinterested [Georgeff, 1987]. In this case, the changes of theworld state become a very complicated function.

Planning considered in multi-agent domains is a very difficult problem. Insuch domains, planning should not be established only on individual basis, but

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it should be generalized on a group basis. In the latter form, it is knownas Distributed Planning. Concepts like agent cooperation, agent beliefs andintentions, agent communication, deadlocks, action interference, etc. arise inthis context and add a large amount of complexity.

Practical PlanningThe assumptions made for the classical form of the problem prevent the

classical approaches from being applied into real world environments. Thus,when the real world and practical applications are considered, the problem takesa new form, known aspractical planning. The concepts discussed so far in thislast section define the outline of this “assumption-free” form.

It is obvious that practical planning poses a much more difficult problem thanthe classical one. Unfortunately, we can speak of real success of the research inplanning only with respect to the practical form. From this perspective, the areais still open and challenging.

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Chapter 2Planning Techniques

This chapter presents a review of the currently existent approaches proposedfor the planning problem. The concept of knowledge representation and the relatedassumptions are discussed first . Then, the different planning methodologies arepresented and the chapter concludes with the inherent difficulties of the problem.

It is noted that the presented review is by no means a complete overview. Itshould be seen as an introduction to the concepts of planning for the unfamiliarreader.

2.1 Knowledge Representation

An important issue in every intelligent system is the way the knowledge isrepresented in it. It is a fact that the efficiency of the system depends not onlyon the quality of its knowledge but also on the way it is structured.

Formal ModelsIt is common in the planning research to useformal models[Allen, 1990] to

describe and analyze the different approaches. It is easy to define the capabilitiesand the limitations of the different approaches specifying formal models. More-over, the class of problems for which an approach is suitable can be determined

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prior to implementing it. This is important especially when the research movescloser to the real environment.

There are many aspects in the framework of planning that can be formalized.However, most researchers have focused on the representation of the actions andthe world.

First-Order Predicate CalculusThe simplest approach for representation is to use first-order predicate calculus

taking advantage of its expressive power. Then the world state is represented bya set ofwell-formed formulas (wffs)that specify the properties held in this state.An operator can be represented as a collection of three lists of wffs:

1. Precondition List2. Add List3. Delete List

The first list determines whether the operator (action) is applicable to thecurrent world state or not. The precondition must be true prior to applying theoperator. The add and the delete lists contain information about the effects ofthe operator and the next world state, i.e. the state resulting from the applicationof this operator (action). The add list contains the properties that become true,whereas the delete list contain the properties that are no longer true.

This approach first appeared in STRIPS, the most influential planning systemtoday and is known as STRIPS-based representation. There are two assumptionsassociated with this approach:

Closed World Assumption: Any negated property of the world is true, unlessits unnegated form is explicitly stated in the current world state.

STRIPS Assumption: The world state remains unchanged unless an actionspecify explicitly some changes in this. In other words, the only available changesare that specified by the action.

It is obvious that this approach, although important, is very restrictive. Therepresentation is static and atemporal, i.e. it lacks the concept of time. Moreover,only one action can occur at any time and actions have to occur instantly [Allen,1990].

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Situation CalculusThe restrictions of the STRIPS state-based representation gave rise to a more

powerful representation known assituation calculus[McCarthy & Hayes, 1969].A situation is a snapshot of the world at some instant in time, hence there areinfinite situations. The situation calculus provides a language for specifyingknowledge about situations, by taking situations as objects in the domain anddescribed by terms in the logic, instead of listing all the properties. The notionof fluent is introduced. Afluent is a function corresponding to a property of theworld. Given a situation, it returns the value of the property in this situation. Thepredicates in situation calculus are used to specify statements about the valuesof the fluents in several states (situations). The situation transitions are specifiedin terms of theResultfunction which, given an action performed in a particularsituation, returns the resulting situation.

Situation calculus is more powerful mainly because the assumptions above arenot any more part of the formalism. However, an other problem arises, discussedlater, known as the frame problem. Moreover, simultaneous actions and externalevents can not be specified.

Temporal LogicTemporal logic introduces various temporal operators that describe properties

of world histories. Assertions are associated over time intervals rather than timeinstants. External events, simultaneous actions or any kind of overlapping actionscan be represented. The frame problem is not present but the representation mustdeal now with future situations.

It is widely believed that the notion of temporal logic is the most natural andconvenient way to represent real world environments.

2.2 Plan Synthesis

Domain Dependent/Independent PlanningThe distinction between these two approaches is based on the application

domain where the system is to be applied. In the case of the domain dependentapproaches the system takes advantage of the domain knowledge and uses domainspecific heuristics to control its operation. This makes the system very efficient.

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However, it is not applicable to other domains. On the other hand, the domainindependent approach deals with general mechanisms behind planning. Thepurpose is to reduce the amount of the domain knowledge required and the effortof incorporating it into the system. Note that in either case domain specificknowledge is necessary.

From a research point of view the second approach is more interestingalthough more difficult because it makes the system applicable to several differentdomains while little effort.

Linear/Non-Linear PlanningThe distinction is based on the so calledlinearity assumption: given a goal

it can be decomposed into subgoals, a subplan can be constructed for each one ofthem and the final plan can be formed by combining these subplans sequentially.This assumption is true only for some domains where the goal can be decomposedlinearly into subgoals. In general, there are strong interactions between thesubgoals, and thus between the corresponding subplans, that makes linear planningimpossible. In such cases, planning should be interleaved between subgoals andsubplans, leading to the alternative termsnon-interleaved(linear) andinterleaved(non-linear) planning.

Total Order/Partial Order PlanningThe distinction here is based on theprinciple of least commitment: the

choices made at any time (e.g. ordering) are only those that are necessary. Allthe others must be delayed as long as possible. A plan may be represented at anytime as a set of operators totally ordered, i.e. all the ordering choices have alreadybeen committed (total order planning) or, as a set of partially ordered operators,i.e. only the necessary choices have been committed (partial order planning).

In the later case, the planning system is more flexible. It will not undo earlierdecisions in case of a problem discovered later. Note also that a partially orderedplan corresponds to several totally ordered plans.

Theorem ProvingThis is the simplest approach. Planning can be viewed as the ability to

prove that there exists a sequence of actions that achieves the goal. However,it is essential for the theorem prover to provide the right kind of constructive

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proof [Green, 1969]. Other deductive approaches that synthesize the plan usingadditionally conditions, recursion and iteration have been proposed.

Planning as SearchEach world state defines a set of states that are directly reachable by applying

some action. Then a search space among world states is defined. From thisperspective, planning can be seen as a straight forward search problem:Find thesequence of world states that “connects” the initial state with a goal state.

On the other hand, a partially completed plan defines a set of more completeplans that can be produced directly by extending it. That defines a search spaceamong partial plans and planning can be viewed again as a search problem:Findthe suitable extensions to construct a plan that achieves the goal.

In either case, the search space grows exponentially, so several heuristictechniques are used to guide the search. For example, means-ends analysis, branchand bound, backtracking, beam search, etc.

Hierarchical planningThe hierarchical planning method is used to solve the problem in an abstract

level, that is, to construct an abstract plan without specifying the details, thenrefine it to a more detailed level and so on until the final plan has been produced.The point in this approach is that each abstract space level must behomomorphicto the original (ground) problem [Georgeff, 1987]. That is, there exists a solutionat an abstract level if an only if there exists a solution at the ground problem.

This approach is considered to be the most natural way to plan, as it is closerto the way humans plan.

Reactive SystemsThe idea of the reactive systems isacting without planning using only the

perception of the world. A reactive system chooses actions, one at a time, fromsome kind of knowledge base that maps external situations to actions. Theadvantage of the reactive systems is that they operate robustly in complex andunpredictable domains which are difficult to be modelled [Rich & Knight, 1990].Also, they are extremely responsive since they don’t spend time for planning andthat makes them suitable for real time tasks where there is no time to “think”.The drawback is that they cannot respond in complex tasks.

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A good intelligent system should have both a planning and a reactive compo-nent. Some times there is no time for planning at all, but there are also situationswhere planning is necessary. The system should be able to decide when to planand when to react for best performance. Of course, there is no clear distinguish-ing line between the two components and it is up to the system to “redraw” thisline intelligently.

The idea of reactive systems is very close to the way live intelligent systemsact in some cases based on their instincts and/or reflex actions.

Distributed PlanningThis approach is suitable for multiagent domains. There are three cases

according to the amount of distribution of the problem:

1. A plan is constructed by a central agent and it is distributed to all agentsfor execution.

2. A partial plan is constructed by a central agent and it is distributed for furtherplanning and execution to the agents.

3. The problem is given to all agents and each one is responsible for his ownplan.

An important issue is the interference between the different actions. Thatrequires interagent communication and knowledge of all the possible interactions.The main technique used for the communication is theblackboard architecture,where the agents communicate through a centralized structure accessible by allof them.

The idea of distributed planning can be applied also to a single agent. Plan-ning is performed by independent communicating planning subsystems (experts),usually using a blackboard architecture.

Rational AgentsThis is a very promising approach that considers agents endowed with the

psychological attitudes ofbelief, desire and intention[Georgeff, 1987]. Theseattitudes are related with the reasoning about actions and such an agent will beable to (re)configure its decision-making theory, which is very useful especially inhighly dynamic environments. This is important in cases where the goals conflictor in multiagent domains. The difficulty in this approach is in the formalizationof such ideas. There is very little work in this area and the challenge remains.

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2.3 The difficulty of planning

The Real World

There are many difficulties associated with planning. Most of them arisewhen planning meets the reality. The real-time response requirement and thedynamic nature of the real world make the problem extremely difficult. There isa trade off between the complexity of the problem and the (realistic) generosityof the application domain. The closer to the real world, the harder the problem.This problem was overcome in the past by assuming ideal worlds far away fromthe reality.

An important issue is how accurate is the representation of the world main-tained into the system. The representation model should be expressive enoughand assumption-free for best results. Flexibility and adaptivity also are necessaryand the monitoring and learning methods seem to be very helpful in this case.

The Frame Problem

The frame problemappears in many areas of AI. Briefly speakingit is theproblem of determining which things change and which do not into the worldwhere the system acts. When logic is used for the world representation thenthe properties that change are described by the effects of the actions but wemust provide also a large (perhaps infinite) number of axioms to describe whatproperties are unaffected for each one action. These axioms, known asframeaxioms, need to be given or to be deducible for all the property-action pairs,which seems to be unreasonable. The problem usually is bypassed by posingsome closed-world-like assumptions.

Many researchers have dealt with the frame problem. The reader is referred to[Raphael, 1970; Hayes, 1973; Shoham, 1987; Brown, 1987]. In [Georgeff, 1987]a general form is given and five related problems are described. It is taken asthe problem of constructing a formulation in which it is possible to readily specifyand reason about the properties of actions and world states (or situations). Thefive related problem derived are:

1. The Combinatorial Problem:The large number of the frame axioms.2. The Precondition Qualification Problem:The conditions under which an

action effects certain changes in the world.

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3. The Frame Qualification Problem:The extent of influence of the action orwhat remains unaffected by the action.

4. The Ramification Problem: The ability to write down certain axioms ofinvariance regarding world states.

5. The Independence Problem:The independency of the activities of the agentsin multiagent domains.

Many approaches have been proposed for these problems (e.g. using differentkinds of logic) but all can be viewed as metatheories regarding the making ofappropriate assumptions about the given problem domain [Georgeff, 1987].

IntractabilityViewing planning as search, it is very easy to conclude that the search space

grows exponentially. That makes the problem intractable and several techniquesmust be used to reduce the search space, like reformulation of the problem in anappropriate way, restriction of the class of the problems that can be handled oruse of domain heuristics for selective search.

The heart of a planning system is itstruth criterion [WIlkins, 1988], thatis, the algorithm to determine if a given formula (property) is true or not at acertain world state or situation. This algorithm is used again and again duringthe planning process. But it is widely known that the satisfiability problem isNP-complete and that adds intractability. An in-depth study of such problem islocated at [Chapman, 1987] and at [Erol et. al., 1992].

Moreover, the special case of scheduling is itself an NP-complete problem[Garey et. al., 1987]. An other combinatorial problem arises when the systemtraverses a plan to detect interactions and conflicts between actions.

It is an open question how so many problems can be handled together.However, there is a lot of progress so far and that makes the area hopeful andpromising.

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Chapter 3Planning Systems

3.1 STRIPS

Perhaps the single most influential planning system to date is the STRIPSplanner. Although there are about 25 years since STRIPS first appeared, themethods of representing actions it introduced are still employed in many currentsystems and are still the subject of actual theoretical study. This section containsa general description of the system and the ideas followed during its design. Formore details the reader should be referred to [Fikes & Nilsson, 1971].

Introduction

STRIPS stands for the words STanford Research Institute Problem Solver andit is a problem-solving program developed by the Artificial Intelligence Group atSRI and more precisely by Richard Fikes and Nils Nilsson in the early ’70s. Theinitial version implemented in LISP on a PDP-10 and it had used in the generationof control plans for the SRI Shakey Robot.

STRIPS belongs to the class of problem-solvers that search through a spaceof several world models in order to find one in which a particular given goal isachieved. It is assumed that for each world model, there exists a set of applicableoperators, each of which transforms this world model to some other world model.

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The task of the solver is to find a sequence of operators that transforms the giveninitial world model into a desired goal-satisfying one.

The first attempt in this class had done by Newell, Shaw and Simon in theearly 1960s which resulted to the General Problem Solver (GPS) [Ernst & Newell,1969]. The main influence of GPS was the use of Means- Ends Analysis as atechnique to direct search. In the late 1960s Green at SRI [Green, 1969]presentedthe QA3 (Question-Answering) Problem Solver. QA3 depended exclusively onformal theorem proving techniques but it suffered by the so called "frame problem”that prevented it from solving non-trivial problems.

The searching mechanism of STRIPS applies the previous two approachesseparately during the searching through the space of world models. Theoremproving methods are used only within a given world model to answer questionabout it concerning which of the operators are applicable and whether or not goalshave been satisfied. For search through the space of world models, a GPS- likemeans-ends analysis is used. This combination provides more powerful searchheuristics and allows much more complex world models than in the previoussystems.

The Problem Space

The problem spaceof STRIPS is defined by the following entities:

1. An initial world model2. A set of operators on world models3. A goal condition

STRIPS represents aworld modelas an arbitrary collection of well-formedformulas (wwfs) of first order predicate calculus. Using wwfs we can representquite complex world models and we can use theorem-proving programs to answerquestions about a model.

The operators are the basic elements from which a solution is built. Theavailable operators are grouped into families calledschemata. Each schemacontains "similar" operators that can be described by a single parameterizedoperator. Thus, a particular operator can be obtained by substituting specificconstants for the parameters in the description of the schema it belongs to. InSTRIPS, when an operator is applied to a world model, specific constants willalready have been chosen for the operator parameters.

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Eachoperator is defined by an operator description consisting of two mainparts: a description of the effects of the operator, and the conditions under whichit is applicable. Theeffectsof an operator are simply defined by a list of wffsthat must be added to the model (add list) and a list of wffs that are no longertrue and therefore must be deleted (delete list). The applicability condition, orprecondition, is stated as a wff schema. To determine whether or not there is aninstance of an operator schema applicable to a world model, it must be provedthat there is an instance of the corresponding wff schema that logically followsfrom the model.

A goal condition is simply a wff that describes the desired goal(s). Theproblem is solved when STRIPS produces a world model that satisfies the goalwff.

The Search Strategy

Searching into the space of the world models in abreadth- first fashion(application of all applicable operators to the initial world model and then to itssuccessors and to their descendants and so on until the goal model is produced)will lead to an undesirable large tree of world models and thus it is impractical.

Instead, the GPS strategy of extracting "differences" between the present worldmodel and the goal and of identifying operators that are "relevant" to reducingthese differences has been adopted. Once a relevant operator has been determined,we attempt to solve the subproblem of producing a world model to which it isapplicable. If such a model is found, then we apply the relevant operator andreconsider the original goal in the resulting model.

It suffices to explain the terms "difference" and "relevant" used above.STRIPS begins by employing a theorem prover on an attempt to prove that thegoal wff G0 follows from the set M0 of wffs describing the initial world model.If G0 does follow from M0, the task is trivially solved in the initial model. Oth-erwise, the theorem prover will fail to find a proof. In this case, the uncompletedproof is taken to be the "difference" between M0 and G0. Next, operators thatmight be "relevant" to reducing this difference are sought. These are the opera-tors whose effects on world models would enable the proof to be continued. Indetermining relevance, the parameters of the operators may be partially or fullyinstantiated. The corresponding instantiated precondition wff schemata (of therelevant operators) are then taken to be new subgoals.

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STRIPS works on a subgoal using the same technique. Suppose the precondi-tion wff schema G is selected as the first subgoal to be worked on. STRIPS againuses a theorem prover in an attempt to find instances of G that follow from theinitial world model M0. Here again, there are two possibilities. If no proof can befound, STRIPS uses the incomplete proof as a difference, sets up (sub)subgoalscorresponding to their precondition wffs and the process continues. If STRIPSdoes find an instance of G that follows from M0, then the corresponding operatorinstance is used to transform M0 into a new world model M1. STRIPS thencontinues by attempting to prove G0 from M1. However, if no proof could befound, subgoals for this problem would be set up and the process would continue.

The hierarchy of goal, subgoals and models generated by the search process isrepresented by asearch tree. Each node of the search tree has the form(<world-model>,<goal-list>) and represents the problem of trying to achieve the subgoalson the goal list (in order) from the indicated world model. An example of sucha tree is shown below.

(M0,(G0))

(M0,(Ga,G0))

(M1,(G0))

(M0,(Gb,G0))

(M0,(Gc,Gb,G0))

(M2,(Gb,G0))

(M3,(G0))

(M3,(Gd,G0))

(M4,(G0))

OPa

OPb

OPc

OPd

Terminal

Figure 3.1 An example of STRIPS search tree

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The top node (M0,(G0)) represents the main task of achieving goal G0 fromworld model M0. Let us assume that two alternatives subgoals Ga and Gb are setup. These are added to the front of the goal lists in the successor nodes. Pursuingone of these subgoals, suppose that in the node (M0,(Ga,G0)), goal Ga is satisfiedin M0; the corresponding operator, say OPa, is then applied to M0 to yield M1.Thus, along this branch, the problem is represented by the node (M1,(G0)). Alongthe other branch, suppose Gc is set up as a subgoal for achieving Gb and thusthe node (M0,(Gc,Gb,G0)) is created. Suppose Gc is satisfied in M0 and thusOPc is applied to M0 yielding M2. Now STRIPS must still solve the subproblemGb before attempting the main goal G0. Thus, the result of applying OPc isto replace M0 by M2 and to remove Gc from the goal list to produce the node(M2,(Gb,G0)). The process continues until STRIPS produces the node (M4,(G0))where suppose that G0 can be proved directly from M4. This node is terminal.The solution sequence of operations is (OPc,OPb,OPd).

Note that when an operator is found to be relevant, it is not known where itwill occur in the completed plan. That is, it may be applicable to the initial modeland therefore be the first operator applied. Or, its effects may imply the goal sothat it is the last operator applied, or it may be some intermediate step towardthe goal. This flexible search mechanism embodied in STRIPS combines manyof the advantages of both forward search (from the initial model to the goal) andbackward search (from the goal to the initial model).

Whenever a successor node is generated, STRIPS immediately tests to seeif the first goal in the goal list is satisfied in the new node’s model. If so,the corresponding operator is applied, generating a new successor node. If not,the difference (the uncompleted proof) is stored with the node. Except forthose successor nodes generated as a result of applying operators, the processof successor generation is as follows:

1. STRIPS selects a node.2. It uses the difference stored within the node to select a relevant op-

erator.3. It uses the precondition of this operator to generate a new successor

node.4. If all of the node’s successors have already been generated, STRIPS

selects some other node still having uncompleted successors.

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The whole search process in STRIPS is summarized in the following flow-chart.

Start

M<-INITIAL WORLD MODELGOAL-LIST<-(MAIN GOAL)NODE<-(M,GOAL-LIST)

G<-FIRST GOAL IN GOAL-LIST

DOES M SATISFY G?YES NO

YES NO ATTACH DIFFERENCE TONODE AND STORE NODE

SELECT A STORED NODE HAVING UNCOMPUTED SUCCESSORS

NODE<-THE NODE SELECTEDM<-WORLD MODEL OF NODEGOAL-LIST<-THE GOAL-LIST OF THE NODE

IS G THE LAST GOAL IN GOAL-LIST?

EXITFAILURE

EXITSUCCESS

GENERATION OF A SUCCESOR NODE

GENERATION OF A SUCCESOR NODE

M<-World Model formed by applying the Operstor associated with M to GGOAL-LIST<-List formed by removing G from GOAL-LISTNODE<-(M,GOAL-LIST)

Select an operator OP relevant to Reducingthe differnce attached to NODEGOAL-LIST<-List formed by adding the Precondition of OP to the front of GOAL-LISTNODE<-(M,GOAL-LIST)

No such nodes

Initial Node Creation

Figure 3.2 The search algorithm of STRIPS

STRIPS employs a heuristic mechanism to select nodes with uncompletedsuccessors to work on next. For this purpose an evaluation function is usedwhich takes into account such factors as the number of remaining goals in thegoal list, the number and types of predicates in the remaining goal formulas andthe complexity of the difference attached to the node.

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Theorem ProvingSTRIPS employs theresolutiontheorem-proving technique when attempting

to prove goals or subgoals. The technique has been extended in two ways to handlethe parameters occurring in wwf schemata. The standard unification algorithm isused to compute appropriate instances of schema parameters according to thefollowing substitution rule: The terms that can be substituted for a parameterare constants, parameters and functional terms not containing Skolem functions,variables or the parameter itself. Moreover, due to the multiple occurrences ofa parameter in a set of clauses, a substitution for a particular parameter must beperformed in all of the descendant clauses.

Difference and Relevant OperatorsOne of the most important steps during the search process in STRIPS is the

determination of the difference between the present world model and the goal, aswell the identification of the relevant operators.

Let us assume that we have achieved a particular node of the tree, (M,(Gi,Gi-1,...,G0)). The first subgoal on the goal list, Gi, is then selected to be worked on.The theorem prover is applied on an attempt to prove the unsatisfiability of theset {MU˜Gi}. If a contradiction is found that means that M |= Gi, so the operatorwith precondition Gi is applied to M and the process continues.

The difficulty arises when such a proof can not be found after some prespec-ified amount of effort. The set of clauses P constituted by the negation of thegoal (˜Gi), plus all of their descendants, less any clauses already eliminated bythe theorem prover during the unsuccessful proof, forms the uncompleted proof.This set P is taken to be thedifferencebetween M and Gi. If P is very large,several heuristics are used to selectively reduce it.

The selection of arelevant operatoris performed in two steps:

1. Selection of all the candidate operators.This selection is based on the comparison between the clauses of thedifference and the clauses in the add lists of the operators.

2. Identification of the operator that "minimizes" the difference.That means that the clauses in the add list of this operator can be usedto "resolve away" a maximum number of clauses in the difference, andthus, the proof can be continued.

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RemarksThe heuristics used in STRIPS directs the search towards the goal, and give

a large depth-first component that sometimes leads to a feasible, but not optimal,solution. Moreover, there are problems that can not be solved by STRIPS. In[Lifschitz, 1987] a careful study on the semantics of STRIPS can be found andthe classes of problems where STRIPS is sound and where is not. However, thecontribution of STRIPS in the planning research is of major importance.

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3.2 NOAH

In this section, we describe theNOAH (Nets of Action Hierarchies) planningsystem which appeared in the middle ’70s. NOAH is the result of the DoctoralThesis of Earl Sacerdoti at the Stanford Research Institute. Its primary purposewas to support the Computer-Based Consultant (CBC) project at SRI, which wasto produce a computer capable of filling the role of an expert in the cooperativeexecution of complex tasks with a relatively inexperienced human apprentice.NOAH was implemented in QLISP on a PDP-10 computer. For a generaldescription the reader is referred to [Sacerdoti, 1975]. A complete descriptionwith many examples is available in [Sacerdoti, 1977].

Knowledge Representation

The structure used in NOAH for the knowledge representation is calledprocedural network and this is the major source of the solving and monitoringpower of the system. Aprocedural network is a strongly connected networkof nodes, each of which represents a particular action at some level of detail.An action is an operation that changes the state of the world when applied.Each node contains bothproceduralanddeclarativeknowledge. The proceduralcomponent represents the domain knowledge, whereas the declarative componentin conjunction with the network links represents the plan knowledge. Thisstructure enables NOAH to be, in some manner, self-aware about the state ofits own reasoning process.

Each node at some level of detail when expanded produces a number ofchild-nodes (actions) at the next level of detail. All these nodes but the last one,form the preconditionsfor the last node, in the sense that their purpose is theestablishment of some expressions in order to make the last action applicable.The last node is referred as thepurposeof the preconditions.

A procedural net represents a plan of actions at hierarchical levels of de-scription. Nodes at each level are interconnected in a two-dimensional pattern."Horizontal" links form a partial order with respect to time among the nodes ofthe same hierarchical level. "Vertical" links form a tree-hierarchy consisting ofthe different levels of the plan and the "expansions" from one level to another.The figure below shows the graphic representation of the components of a pro-

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cedural network. The next figure shows a sample procedure net with three levelsof hierarchy.

QueryQuery S J

GOAL PHANTOM AND SPLIT AND JOIN

Parent

Children

Predecessor(s) Successor(s)

Figure 3.3 Graphic Representation of Nodes: Basic Types and Links

PLANHEAD Achieve (ON A B)Adds: (ON A B)

S J

S J

PLANHEAD

Clear AAdds: (CLEARTOP A)

Adds: (CLEARTOP B)

CLear BAdds: (CLEARTOP B)

PLANHEADAdds: (CLEARTOP B)

(ON A B)

CLear BAdds: (CLEARTOP B)

CLear BAdds: (CLEARTOP B)

PUT B ON TABLEAdds: (ON B TABLE) (CLEARTOP A)Deletes: (ON B A)

Put A on BAdds: (ON A B)Deletes: (CLEARTOP B)

Put A on BAdds: (ON A B)Deletes: (CLEARTOP B)

A

BA

B

Initial State: (ON A B) (CLEARTOP B)

Goal State: (ON B A) (CLEARTOP A)

Figure 3.4 A Procedural Network (two levels of expansion) for the Simple Problem Above.

There are many different types of nodes. The most important of themare shown in the figure above. GOAL nodes represent a goal to be achieved.

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PHANTOM nodes represent a goal that should already be true at the time theyare encountered. A PHANTOM node is just like a GOAL node except that it willnot be expanded to greater detail. SPLIT nodes have a single predecessor andmultiple successors and represent a forking of the partial ordering. JOIN nodeshave multiple predecessors and a single successor and represent a rejoining ofsubplans within the partial ordering.

Each node is associated with code representing the procedural knowledgeassociated with that node. The action represented by the node can be "simulated"by evaluating the body of that code. This evaluation will lead to create new nodes(children of the original) representing more detailed actions in the next level ofthe plan. The code is written inSOUP (Semantics Of User’s Problem) languagewhich is an extension of QLISP.

Each node is associated with an add and a delete list of symbolic expressions(declarative knowledge). These lists contain theeffectsof the action (representedby the node) to the world. NOAH employs ahybrid distributed world modelrepresentationto overcome the frame problem. The unchanged expressions ofthe world (i.e. the frame axioms) are maintained in a global world model. Thetruth value of the expressions that have been affected by the actions of the planare indicated by the add and the delete list of the headnode (PLANHEAD) of theplan. The model query algorithm firstly checks the global model and if it fails,then it checks the portion contained in the current plan.

Plan Generation

NOAH begins with a given goal to achieve. A one step plan is built directly,which consists of the PLANHEAD node and a single GOAL (the given). Thisprocedural network is the highest level of abstraction and it should be expanded.

Theplanning algorithmof NOAH takes as input a procedural net and producesa new procedural net with one more level (the expanded plan) of detail. Theexpansionis done on each node of the lowest-level (most-detailed) plan, accordingto the procedural knowledge and several child nodes are produced. After thecompletion of the expansion a new, more detailed plan has been added to theprocedural network.

The previously produced plan should be tested by the system to ensure thatthe local expansions already done make sense in the global plan. For this purpose

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a set of constructive criticsis provided, designated to add constraints in the planin order to make it consistent.

A summary of the two-step planning algorithm is provided bellow:

1. Expand the most detailed plan in the procedural network. A newprocedural net with one more lever (more detailed) is produced.

2. Apply the critics on the new plan to make it consistent. Add constraints,perform ordering or eliminate redundant tasks. A complete proceduralnet is produced.If this step cannot be accomplished report failure.

3. Goto 1.

Constructive Critics

The purpose of the critics is to ensure the consistency of the plan after eachexpansion. In other words, the arrangement of the several expansions in a globalsense.

The criticism (as it is called) allows greater modularity with respect to thesemantics of the task domain. The model of each action does not have to includeinformation about all the potential interactions with other actions. Also, theinsertion of a new action is easier in the sense that it does not require the revisionof the already modelled actions, thus reduces the complexity.

Therefore, the set of critics is a collection of modules each one containinginformation about one type of interaction. Then a computer expert system can bebuilt over them. The critics are distinguished between general purpose (domainindependent) and task specific (domain dependent).

• The "Resolve Conflicts" Critic : Examines the portions of the plan thatrepresent conjunctions to be achieved in parallel for conflicts between thepreconditions and the purposes of the nodes. In general, a linearization (timeordering) of the conflicting nodes resolves the conflict.

• The "Use Existing Objects" Critic : The correct ordering of the actions ina complete plan requires the specification of the objects that the actions areto manipulate. In NOAH, this is accomplished by binding the unboundedvariables in the goal. NOAH avoids binding a variable to a specific objectunless a best choice is clear. If this is not the case, aformal object(a placeholder for an entity not yet specified) is bound to the variable. This prevents

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the system from making arbitrary choices, possibly wrong, and allows it todeal with partially ordered plans. When the plan has been completed at thesame level of detail, the "Use Existing Objects" critic will replace formalobjects by real ones. This may involve merging nodes from different portionsof the plan resulting in reordering or partial linearization.

• The "Eliminate Redundant Precondition" critic : The individual expansionof each goal may lead to redundant duplication of several preconditions. Thiscritic eliminates the redundant preconditions which leads to better storageusage and avoidance of redundant planning effort.

• The "Resolve Double Cross" critic :A special kind of conflict, called "dou-ble cross" arises when each of the conjunctive purposes denies a preconditionfor the other and it cannot be resolved by linearization. This critic attemptsto make each subplan innocuous to the other. After examining the assertionor denials that led to the conflict and determining the variable bindings thatcaused them, it inserts appropriate steps in the plan to ensure that the variablesare bound differently at the time of the conflict.

• The "Optimal Disjuncts" critic : It used for the system to choose betweenthe alternative ways of expanding a goal, referred as disjunctive (sub)goals.Several criteria are considered, like the number of actions in the (sub)goal,the amount of interaction, etc. After the plan has been expanded in somedetail, the critic selects the superior of them and ignores the other.

Hierarchical Kernel

A plan that appears to be feasible at a higher level may be inconsistent aftera number of expansions. For example, the expansion of an earlier action maycause side-effects that might obliterate a higher level precondition of a subsequentaction. Therefore, the planning mechanism should check each level of expansionto ensure that the higher level plans are in fact carried out.

Utilizing the hierarchical structure of the procedural network, it suffices tocheck only a subset of the higher level actions, referred ashierarchical kernel,instead of all. The check of the kernel is done after each expansion by checkingthe effects of the preceding (in time sequence) siblings of the node currentlybeing expanded and the preceding siblings of each of its ancestor nodes. If allthe elements on the add lists and none of the elements on the delete lists aretrue in the current model, then the process terminates successfully. If there is

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any "problem", NOAH reestablishes the purpose of the node whose effects areno longer preserved.

The process above can be seen as "hierarchical debugging". Unfortunately,although it provides a checking mechanism that captures most unwanted interac-tions it does not guarantee that a problem will not arise.

Iterative Actions

The structure of the procedural network and the SOUP language allow thespecification of iterative actions, which are quite common in everyday planningproblems. An iteration is modelled as a single action at a higher level. Whenexpanded, the expansion of only one cycle is created, together with the specialnodes REPLICATE, LOOPSPLIT, JOINSPLIT that form the iteration model. TheREPLICATE node, added in parallel with the expansion of the single cycle,contains all the required information for the remaining iterations and the possibledifferences from cycle to cycle.

Plan Execution

NOAH has the ability not only to create, but also to execute action plans.It makes a clear distinction between plan generation and plan execution, but theworking data structure is the same for both cases, the procedural network. Theplanning process views the procedural network as hierarchy of plan in differentlevels of detail, whereas the execution process views it as a collection of actionhierarchies. An action hierarchy consisting of the node representing the action,together with all of its children nodes, together with their descendant nodes,referred as awedge. In other words, a wedge is the subtree (of the hierarchy tree)under a particular node (action). The figure below shows the two perspectives.

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(a) The Planner’s View

(b) The Execution Monitor’s View

Figure 3.5 The Two Perspectives of a Procedural Net

The execution monitor interacts with the user in the following manner:

1. Start with the top wedge of the procedural net.2. Ask the user to accomplish the action at the head (root) of the current

wedge.3. If the response is positive, assume that the action has been accom-

plished and the current wedge has been successfully executed.4. If the response is negative, assume the user needs a more detailed

breakdown of the action, and so execute in turn all the subwedgesheaded by the children of the head of the current wedge.

5. If the top wedge of the procedural net has been successfully accom-plished , then terminate.

6. Go to 2.

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Error RecoveryNOAH has the ability to expand a node of a partially executed plan, due to

some unexpected events that changed the world and made it inconsistent withthe model in NOAH. This operation is accomplished by first building a dummyPLANHEAD node that contains the "new" image of the world. The new subplanis built following this node. The procedural network representation allows asmuch as possible of the existing plan to be reused, during the recovery process.

RemarksThe significant features of NOAH may be summarized as follows:

• Representation of a plan at many different levels of detail.• The actions at each level are partially ordered with respect to time.• Hierarchical planning mechanism.• Plan monitoring and execution capability.

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3.3 SIPE

IntroductionIn the recent years, research focus in planning has been shifted to the domain

independent planning, that is the study of methods of representation and reasoningapplicable to many different domains. Of course, the encapsulation of domainspecific knowledge is inevitable for the system to be successful, but this is oneof the purposes of the idea above: to provide mechanisms that help the encodingof domain specific knowledge and heuristics.

In this section, a planning system that belongs to this class is presented.SIPE(System for Interactive Planning and Execution monitoring) has been developedat SRI International by David Wilkins. SIPE can be viewed as an extension ofthe ideas hidden in previous systems like STRIPS, NOAH, NONLIN, DEVISERand PLANX10. It has been implemented in INTERLISP and it has workedsuccessfully in four different domains: an extended blocks world, cooking, aircraftoperations and travel planning.

The major ideas inside SIPE is the hierarchical planning and the parallelactions. The former has been accepted as the natural way of planning in anyphysical or artificial planning system. The later has been derived from theproperties of the real environment where planning is applied.

In the sequel, a brief description has been attempted. The demanding readershould be referred to [Wilkins, 1984] for more, and to [Wilkins, 1988] for a fulldescription.

Knowledge RepresentationKnowledge representation is a major concept in any planning system, since

the efficiency of the inference mechanism relies basically on the power and theexpressiveness of the underlying representation. In SIPE a plan is represented asa procedural network(see NOAH) and it is a partially ordered collection of goalsand actions. A plan is refined by applying operators (the system’s description ofthe possible actions) and several critics are employed to ensure that the refinements"converge" to the desired goal. The parts involved in the SIPE representationscheme are objects, goals, classes, operators, deductive operators, constraints andresources presented below.

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Domain objects, classes and goals The domain objects and their invariantproperties are represented by nodes linked in a hierarchy, calledsort hierar-chy. Each node can have several attributes associated with it and the hierarchicalstructure enables the inheritance of properties from other nodes, as well as theposting of constraints on the values of the attributes. There are different types ofnodes for each of the following: variables, objects and classes.

The properties of the system that vary and the relationship between them arerepresented using a restricted form of first- order predicate calculus. It is also usedto describe goals, as well as the preconditions and the effects of the operators.This scheme combines the advantages of the frame-based representation and thepower of the predicate calculus.

Operators The operators represent the actions the system is capable to perform.An operator description contains the objects involved in the action, the goal ofthe action, the effects of the action when performed and the preconditions forthe action. SIPE provides the known add and delete lists for the effects of anaction but employs additionally adeduction mechanismthat deduces effects notexplicitly described as part of the operator using general frame axioms. At thefinal plan all the effects are mentioned explicitly.

SIPE makes the following two assumptions for the world representation:

1. STRIPS assumption:All relations mentioned in the world model remainunchanged unless an action in the plan specifies that some relation haschanged.

2. Closed-world assumption:Any negated predicate is true unless the unnegatedform of the predicate is explicitly given in the model or in the effects of anaction that has been performed.

It is remarkable that SIPE separates the preconditions of an operator from thegoals. So the system will not make any effort to make the precondition true. Afalse precondition simply means that the operator is not appropriate. This givesflexibility for two reasons. First, there are some actions suitable to be triggeredonly in undesired situations (preconditions). The system will not cause them forthe sake of performing that action. On the other hand, a planner that tries toachieve all the preconditions, might make the situation worse in order to applyits "emergency" operators. SIPE’s preconditions provides instructions of how toachieve a goal. Second, it provides an interface between different levels of detail

37

in the hierarchy. The precondition of an operator specify that certain higher-level conditions must be true, while an operation itself specifies goal at a moredetailed level.

The interface described above is enhanced by allowing the operators to specifyexplicitly the purpose they are trying to achieve at the different levels of detail.There is a small difference between the GOAL and the PURPOSE of an operator.The GOAL is what an operator tries to achieve at a higher level of detail andis used to determine when to apply the operator. The PURPOSE is what theoperator tries to achieve at a lower level of detail and it is used to determine"why" it is in the plan (plan rationale).

Each operator contains also a PLOT, that is a (small) procedural net thatrepresents how the operator expands a node in the next level of detail or how theaction is to be performed in terms of actions and goals. The plot of an operatorcan be described in two ways. First, in terms of goals to be achieved, that issome predicate to be true). In this case, we don’t care about which action is tobe used, but about a situation to be achieved. Second, in terms of processes to beinvoked, that is some action to be performed. In this case, we don’t care aboutwhich situation is to be achieved, but about a certain action. The selection ofthe appropriate way is dominated by where the emphasis is on; on the situationor on the action.

Constraints

SIPE has the ability to construct partial descriptions for objects that havenot been specified yet during the planning process. For this purpose a constraintlanguage is used for expressing the several constraints applied on the variablebindings, in other words, for specifying the possible values of the planningvariables that have not been instantiated yet.

A constraint can be a restriction on the properties of an object or on therelationship between an object and other objects. Constraints can be encoded aspart of the operator description or can be posed by the system dynamically duringthe planning process based on the interactions within the plan. In either case, theconstraints should be propagated to the variables into the related parts of the plan,in order to be satisfied by the final variable bindings.

SIPE assumes that a constraint is satisfiable, if it cannot be proved unsatisfiablewithin the current world state (Closed-World Assumption). Actual checking by

38

the system is done once per level in the hierarchy. Although the existenceof constraints adds complexity and the necessity of a constraint satisfactionalgorithm, at last it yields some means of efficiency. The expressiveness of thedomain representation is improved (objects with varying degree of abstractnesscan be represented in the same formalism), as well as the process of finding asolution (since decisions can be delayed and problems can be discovered quickly).

ResourcesThe representation of an operator provides same means of specifying that

some of the variables associated with an action or goal will actually serve asresources for this action or goal. Resources are employed during the executionof an action and released after that. A resource declared as part of an actionis interpreted as a precondition of the action (the resource must be availableprior to the execution of the action). There are mechanisms in the planningsystem, that checks for resource availability and conflicts over resources duringallocation and deallocation. The ability of representing resources is very helpfulin the axiomatization and representation of the domain. Also, it is known for anoperation which resources are required before it is applied. Therefore, conflictscan be detected before the expansion and so the search process can be directedeffectively.

Plan RationaleThe rationale of an action in a plan is the reason for being in this plan, or

’why’ this action is there. This is necessary for the planner to determine:

• how long a condition must be maintained• what changes in the world cause problems in the plan• what is the relationship between the different levels

This information is contained in the PURPOSE of the node.

During the expansion of a node by an operator, the PURPOSE is used todetermine the node in the expansion that achieves the operators purpose. If thereis no PURPOSE information available then it is assumed that the last node in theexpansion is such a node. After the determination of this node, the higher leveleffects are copied down to this node and its rationale is that it achieves the highergoal. If the rationale of some node is not to achieve a higher level goal then itis assumed that it is there to prepare some later action.

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Deductive OperatorsBesides the regular operators, SIPE supports alsodeductive operators, that

deduce facts from the current world state. Using deductive operators is better thanrepresenting explicitly the effects in the operators, especially in complex world.Moreover, its necessary for execution monitoring in order to deduce facts due toexternal events (e.g. tracked by sensors).

The effects deduced by SIPE are considered to be side-effects. All thedeductions are made at the time of the expansion and recorded in the proceduralnet. This may lead to ’achievement’ of some goals, in the meaning that it isdeduced that they have already been achieved. In this case, no action is requiredto achieve them.

The deductive operators have the same form as the regular ones, so they canbe handled by the same mechanism. There is a trade off between the deductionexpressiveness and the general efficiency of the system. For this reason SIPE hasa controlled deductive capability. Each deductive operator has triggers for thecontrol of its application.

Parallel ActionsTwo segments of a plan can be executed in parallel if the partial ordering of

the plan does not specify that one of them must precede the other. Parallelism isdesirable, so SIPE keeps as much parallelism as possible, then detects and correctsthe interactions between the parallel branches.

An interaction is defined to occur between two parallel branches if a goalthat is trying to be achieved in one of them (at any level) is made either trueor false by an action at the other. It is easy to recognize interactions, since theeffects of the actions are listed explicitly in the plan. However, they may notappear until some level of detail has been reached. There is a distinction betweenhelpful and harmful interactions.

A helpful interaction occurs when a goal in one branch is made true inanother branch. We can take advantage of this by simply ordering the branches.In general, this will cause other problems, so several heuristics are employedbefore the acceptance of such a decision.

A harmful (or problematic) interactionoccurs when an action in one branchmakes false a goal in an other branch. In this case, the plan is not a validsolution any more. It is very difficult to resolve such interactions. Domain specific

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knowledge is required. SIPE simplifies this by not shuffling actions between twoparallel branches.

The action rationale is used to resolve harmful interactions. Suppose thata predicate is made false at some node in a branch and true at some node atanother branch. Depending on the rationale for including these nodes in the plan,it may be the case that the predicate is not relevant to the plan (an extraneous sideeffect), or must be kept permanently true (the purpose of the plan), or must be keptonly temporarily true (a precondition for later achievement of a purpose). SIPE’sability to specify a plan rationale flexibly and to separate side effects from maineffects enables it to distinguish these three cases accurately. Then the resolutionfollows the rules below:

1. If both of them are side effects then there is no any problem becausein fact no real conflict exists.

2. If one of them is a precondition then resolve the interaction by orderingthe segments, first doing the one with the precondition. The precon-dition sometime will be unnecessary so its negation will not affect theplan.

3. If the interaction is between a purpose and a side effect, order the sideeffect before the purpose.

4. If both are purposes then the problem is not solvable at this level andmust be posted to the higher levels.

Reasoning About Resources

When some object is listed as a resource in an action, the system prevents thatparticular object from being mentioned as either a resource or an argument in anyaction or goal in parallel. This is a very strong restriction, so SIPE permits the, socalled,shared resources. A resource in one branch can be an argument in an otherparallel branch but not a resource. However, this may lead to harmful interactions.SIPE employs a heuristic to resolve such resource-argument conflicts, based onthe assumption that when an object is used as a resource, it will have its ’state’changed by such use. So, the corresponding action must be done first to ensurethat the object will be ’in place’ when it will be used later as an argument.

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Search ControlThe automatic search employed by SIPE is a depth-first search to a given

depth limit. There is no knowledge for making choices or backtracking. Thatmay lead to poor performance in complex worlds but it is used for the sake of theinteractive planning. The user is enabled to intervene in the planning process atany time and specify certain preferences or constraints. For this communication,SIPE provides a very helpful full-graphic environment.

An other important feature of the search control in SIPE is that it has theability of exploring alternatives in parallel. This is an advantage for the interactiveenvironment , since the user is allowed to conduct a best-first search easily.In addition, to combine breadth-first and depth-first searching, the interactiveoperations allow islands to be constructed (i.e. portions of the plan expanded toarbitrary depth) and then linked together.

Execution Monitoring and ReplanningThe concept of execution monitoring and replanning is critical, since the real

worlds are not perfect and a preproduced plan is not always carried out success-fully. Monitoring introduces other aspects as perception, sensing, identification,communication and so on. Sometimes, monitoring a plan involves planning forhow to monitor it effectively. The replanning mechanism is invoked when someundesired event has been detected by execution monitor. It is important for thesystem to use as much as possible of the old plan, rather than trying to constructa new one from scratch.

Currently, in SIPE the execution monitoring relies on the user who is respon-sible to keep the system aware of any external event, i.e. some predicate changedit not any longer true (or false). Then, SIPE look through the plan to find allthe goals that are affected by this. The plan rationale seems to be very helpfulin this process, to determine how some goal is affected by the event. If it wasa ’helpful’ event, it may lead to the elimination of a portion of the plan, sincethe goal has been accomplished. But if it is a ’harmful’ event then the plan mustbe revised to preserve its purpose.

The following techniques are used for this purpose:

1. Instantiate a variable differently.2. Find relevant operators to accomplish a goal that is no longer true and add

a new subplan into the plan.

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3. Find a higher level from which to replan if the problems are wide.

ConclusionsWe conclude this section with a list of the most important features of SIPE.

• Hierarchical planning• Powerful representation• Constraints on the variables• Deductive operators• Parallel actions• Plan rationale• Reasoning about resources• Interactive environment• Replanning mechanism

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3.4 FORBIN

IntroductionPlanning can be viewed as a process of incremental construction or refinement.

According to this view a planning system can start with a simple partial plan andconstruct the final full-detailed plan applying iterative refinements. This approachhas been followed in the development of a recent planning system, the so calledFORBIN. FORBIN is the result of the work of Thomas Dean, James Firby andDavid Miller at Yale University at about 1988. This section describes its generalcharacteristics and the ideas hidden under its design. For a complete descriptionthe reader should be referred to [Dean et. al., 1988].

The incremental plan constructioninvolves a series of decisions concerninghow to refine the particular partially constructed plan. These decisions determinea search through a space where each state is a partially constructed plan. To directthe search, some means of evaluating a state is necessary. This process involvesprediction of the effects of actions, projection onto the current partial plan anddetermination of whether or not they bring about some desired state of affairs.

Domain knowledge of two types is necessary to support the evaluation:Staticknowledge, that contains the cause-and-effect relations between actions and theirresults and, also, the conditions for using certain methods for refinement.Dynamicknowledge, that contains the current partial plan and the related observations andpredictions.

FORBIN has been built upon an approach to planning referred ashierarchicalplanning. The main intuition behind this is that the search can often be directedso that decisions made early in planning are independent of decisions made later.There are three main components within FORBIN:

• A Representation LanguageIt is used to encode domain-specific information about the possible conse-quences of partially constructed plans. It makes use of a temporal notationbut it lacks even the expressive power of propositional temporal logic. It issufficiently expressive to encode many complex planning problems.

• A Temporal Database ManagerIt keeps track of consequences that are true of every completion of thecurrently partially constructed plan.

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• A Heuristic Task SchedulerIt ensures that all times there exists some completion of the current partiallyconstructed plan that satisfies the top-level planner’s goals.

The temporal database manager and the heuristic task scheduler are used indeciding what refinements to make to a partially constructed plan. Unfortunately,neither program is guaranteed to be complete; that means, that there are situationsin which the system will claim that there is no solution when there actually isone. However, if the system proposes a solution then it is guaranteed correct.

Definitions

A partially constructed planin FORBIN consists of a set of actions and aset of constraints on the expected duration. An action is said to be primitive ifit cannot be broken down into simpler actions. Atask is simply an action in thecurrent partially constructed plan. A task corresponding to a primitive action issaid to beprimitive; otherwise, it is said to beproblematic.

In FORBIN, transforming the current partially constructed plan may involvesplicing in new tasks and imposing additional constraints on existing tasks.Planning proceeds by selecting a problematic task and attempting to replace orsupplement its current specification with a set of other, hopefully less problematic,tasks. This process of transformation referred to asexpansion.

For each non-primitive action, the planner has a set ofmethodsfor carryingout these expansions. Each method specifies a set of actions and constraints ontheir order and duration. In addition, each method is annotated with informationthat describes how good it is in a given set of circumstances.

A partially constructed plan is represented as atask network(a kind of directedacyclic graph). A sample of task networks is given in figure below. Expansionresults in adding subtasks and precedence links to the network. The task networkencodes the basic decisions of the planner.

In general, the effects of one task are contingent upon the effects of precedingtasks. Aninteraction corresponds to a situation in which the effect of one taskserves to undermine the intended effect of another task.

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Time=0

Time=0

Time=35

Time=35

MAKE Widget

MAKE Widget

MAKE Gizmo

MAKE Gizmo

MAKE-T1 W MAKE-T2 W

MAKE-T1 G MAKE-T2 G

(a) Before Expansion

(b) After Expansion

Figure 3.6 Simple Task Networks

To notice and deal with such interactions, the planner must keep track ofthe expected state of the world resulting from each task in the plan it has builtso far. By carefully choosing expansion methods and orderings that preserve theconditions required by actions already specified, interactions can often be avoided.The hard part is anticipating such interactions. One way to accomplish this isannotate methods with expectations concerning what conditions they will require.These expectations are then used to predict certain consequences of the currentpartially constructed plan and guide decision making so that any interactions thatare encountered can easily be resolved. To make good decisions concerningwhich expansion method to use, the FORBIN planner must continually predictthe expected future at each point in its plan. This process of prediction is referredto asprojection and plays an integral role in decision making.

The FORBIN ArchitectureThe figure below shows a simplified version of the FORBIN architecture

in order to emphasize its interesting aspects. The arrows indicate the flow ofinformation between modules, the circles represent static knowledge and the boxes

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represent the dynamic components of the system. In the sequel, a description ofeach component is presented.

TemporalDatabase

Task Network

Task Queue Manager

QueryProcessor

CausalTheory

PlanLibrary

TaskExpander

HeuristicTaskScheduler

Figure 3.7 The FORBIN architecture

The causal theory The causal theory describes the ways that each of theplanner’s actions will change the world. In particular, the theory contains twotypes of rules: those specifying the effects of executing tasks and those specifyingthe way effects interact with one another. Most task effects correspond toatomic propositions that are made true as a result of actions being executed or,more generally, events occurring. Other effects refer to quantities that changecontinuously over time: quantities the planner can add to, subtract from, or changewith processes that continue without intervention once begun. The causal theorymust also concisely capture the interaction that occur between effects. Many ofthe results of a task come about indirectly and it is inappropriate to encode themin the task’s effects. Such results should be encoded in a separate set of rules thatrefer to much more general physical principles.

The plan library The plan library (or task-expansion library) contains themethods that FORBIN has available for accomplishing its tasks. The systemcannot build a plan for a task that does not have an expansion method in thelibrary. Each entry in the library describes one way to carry out an abstract task.

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When there is more than one way to carry out the task, there is more than onentry in the library.

The query processor In order to support the selection of potential expansionmethods, the query processor handles a class of queries known asabductivequeries. An abductive query is made to see whether the assumptions for a methodare satisfied in the current temporal database. The answer returned from such aquery includes a set of additional ordering constraints that may be added to thedatabase to satisfy the assumptions.

The temporal database This is the heart of FORBIN. The database maintainsa picture of the expected future, given the plan so far, the causal theory and anyknown external events. When planning begins, the database contains the initialworld state and the time and nature of any events under external control. Asthe plan is constructed, each new subtask the system commits to is added to thedatabase along with its expected duration and starting time. The database thenapplies (through the query processor) rules from the causal theory to determine theeffects into the future to compute the expected world state at all times. In fact,projection need not terminate. FORBIN gets around this by imposing a lowerlimit on the duration of events and an upper limit on the interval over whichprojected events will be considered. This representation of the future is used fortwo different purposes:

• it gives the expected situation that each task in the plan will encounter (touse when choosing an expansion for the task), and

• it prevents the plan under construction from becoming invalid by ensuringthat task expansion preconditions do not get changed.

The task queue manager FORBIN employs a task queue manager that keepstrack of the tasks in the database that still need further refinement and decideson the best order to make those refinements. These decisions are based on thefollowing criteria:

• Since planning takes time, and some tasks have deadlines, tasks with ap-proaching deadlines are given some priority in expansion.

• Tasks very high in the abstraction hierarchy should be expanded to sufficientdetail that they may be placed in proper perspective in the task network.

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• Heavily constrained tasks should be expanded so that none of their constraintsare accidentally violated.

These criteria enables planning and execution to be overlapped. This is truebecause refinement concentrate on those tasks to be executed earliest so thattheir constituent primitive actions can be "peeled off the front" of the plan andexecuted even while tasks later in the plan are unexpanded. Also, new tasksare allowed to be introduced by the user at any time just like subtasks spawnedthrough expansion.

The heuristic task scheduler To verify abductive queries, FORBIN employsan additional set of procedures for projecting the detailed consequences of thepartially ordered task network. If a query is false in all totally ordered extensionsof the current partial order, then these routines would detect this. The queryroutines of the temporal database (see query processor) act as an initial filter:the detailed projection routines are the final arbiter. These routines are alsoused to score expansion methods by installing each expansion into the plan in atemporary database and then simulating the result considering various consistenttotal orders. Scoring is handled using domain-specific utility functions encodedwith the various expansion methods. By actually looking at total orders, thesimulation procedures are able to make very accurate predictions concerning thepotential value of a given expansion. The simulation routines are collectivelycalled the heuristic task scheduler.

The task expander The routines responsible for performing the expansionsare called the task expander. The database of refinement methods used by thetask expander consists of "recipes" for expanding various tasks into subtasks.Hierarchical refinement is used so that the temporal database always contains allplanning goals, and hence the whole expected future, at some level of detail.Representing the entire future in the database provides a solid basis for each levelof expansion and allows FORBIN to take account of important interactions earlyin planning.

The FORBIN Planning AlgorithmThe FORBIN search algorithm is conceptually quite simple. At any point

in the search there is a partially elaborated plan represented by the current tasknetwork. The object of the search is to expand each task in the network into more

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and more detail until only primitive tasks remain. The final plan produced by thesystem is the network of primitive tasks.

A naive backtracking implementation of this search algorithm is computa-tionally much too expensive; therefore, the FORBIN system makes use of manyheuristics to limit the number of partial task networks considered and the numberof projected futures calculated.

Having described the basic components of the architecture, we can now givethe algorithm used by FORBIN for task expansion.

1. Choose a task2. Find suitable methods by using the results of limited projections.3. Choose the best method by performing detailed projections.4. Expand method and add the results of limited projection.5. Go to 1.

The basic planning algorithm is easy to understand. The task expander selectsa problematic task from the database and looks up all appropriate refinementmethods in the expansion library. It then asks the database which methods can beused in the context of the current task network. If no methods will work, then thetask cannot be carried out in the current plan and FORBIN fails. If one or moremethods will work, then the task expander scores them and chooses the "best".

The heuristic task scheduler efficiently explores the space of total orderings ofthe task network, propagating dynamic effects that occur in each ordering. As itexplores these orderings, it may place any of the possible expansion methods intothe schedule it is building, pursuing those with the greatest utility (and implicitlythose with the shortest overall duration) first. When a feasible schedule is derived,the expansion method used is returned. This is the "best" among the others.

The "best" expansion is then added to the temporal database, and the databaseis updated in accordance with the causal theory. This cycle continues until eithersome task cannot be expanded and failure occurs or all tasks have been reducedto primitive actions and the plan is complete.

RemarksThe main difficulty with hierarchical planning is sorting out the unexpected

interactions involving the expansion method chosen for different tasks. Theactions and the constraints on their order and duration within a single method

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will have been chosen so that they do not interfere with each other. However,when a plan is built for several tasks, subtasks from the different expansions maybecome interspersed and cause interactions that compromise the success of theplan under construction.

The choice of any particular action to add to the plan will usually dependon the situation expected when that action is to be executed. To avoid suchsituations two precautions are taken. First, when a task is added to the database,facts assumed true when choosing the task are recorded along with the task.Second, before choosing a new task to use in the plan, the system checks thedatabase to ensure that adding the task will not cause any previous assumptionsto become invalid. Never adding a new task that violates a previous assumptionavoids the creation of inconsistent futures.

Whenever FORBIN has unexpanded tasks in the task network, it attemptsto expand them but it will not retreat on an expansion decision. So, the orderthat tasks are expanded may be critical to the plan that eventually evolves. Dueto this fact, the algorithm may fail to find a successful plan where one exists.However, the search algorithm as a whole makes expansion decisions flexibly,by considering many alternatives before committing, so that the system is usuallysteered in an appropriate direction.

An important characteristic of FORBIN is its ability to cope with both staticand dynamic facts.Static factsrepresents aspects of the world state that are madetrue until explicitly changed.Dynamic factsrepresent those facets of the worldthat are best modeled as continuous quantities. Very often they are specified interms of a change to their value (hence the new value depends on the old) andonce changed, a dynamic fact may continue to change without further intervention.Within FORBIN dynamic facts are calledquantities.

PerformanceIf FORBIN terminates claiming success, then the solution it provides is

correct. If it fail, that does not necessary means that there exists no solution.FORBIN always terminates in time polynomial in the size of its knowledge base.The temporal database and heuristic evaluation routines exploit the structure oftime and causation to realize high performance. FORBIN represents a practicaland theoretically motivated concession to the complexity of real-world planning.

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