Theory and Practice - Automated Planning - Lecture Slides, Slides of Computer Science

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Chapter 1

Introduction

Lecture slides for

Automated Planning: Theory and Practice

3. A systematic arrangement of elements or important parts; a configuration or outline: a seating plan; the plan of a story.
4. A drawing or diagram made to scale showing the structure or arrangement of something.
5. A program or policy stipulating a service or benefit: a pension plan.

plan n.

1. A scheme, program, or method worked out beforehand for the accomplishment of an objective: a plan of attack.
2. A proposed or tentative project or course of action: had no plans for the evening.

Some Dictionary Definitions of “Plan”

• Which of these do you think this course is about?

Conceptual Model

• Σ is an abstraction
  • Deals only with the aspects that the planner needs to reason

about

State transition system Σ = ( S,A,E ,γ) S = {states} A = {actions} E = {exogenous events} γ = state-transition function

Example

• Σ = ( S,A,E ,γ)
  • S = {states}
  • A = {actions}
  • E = {exogenous events}
  • State-transition function γ: S x ( A ∪ E ) → 2 S
• Example:
  • S = {s 0 , …, s 5 }
  • A = {move1, move2, put, take, load, unload}
  • E = {}
  • γ: see the arrows

Dock Worker Robots (DWR) example

take

put

move

put

take

move

move2^ move

unload^ load

move

move

loc1 loc

s 0

loc1 loc

s 1

s 4

loc1 loc

s 5

loc1 loc

loc1 loc

s 3

loc1 loc

s 2

Controller

• Control may involve lower-level planning and/or

plan execution

• e.g., how to do move

Given observation o in O , produces action a in A

Instructions to the controller

move2^ move

loc1 loc

s 1

loc1 loc

s 3 Observation function h : S → O

Depends on whether planning is online or offline

Planning problem Planning problemPlanning problem

Planner

Instructions to the controller

Plans

• Classical plan : a sequence of actions 〈take, move1, load, move2〉
• Policy : partial function from S into A { (s 0 , take), ( s 1 , move1), ( s 3 , load), (s 4 , move2) }

take

put

move

put

take

move

move2^ move

unload^ load

move

move

loc1 loc

s 0

loc1 loc

s 1

s 4

loc1 loc

s 5

loc1 loc

loc1 loc

s 3

loc1 loc

s 2

take

move

load

move

Dock Worker Robots (DWR) example

Scheduler

Planning Versus Scheduling

• Scheduling
  • Decide when and how to perform a given set of actions - Time constraints - Resource constraints - Objective functions
  • Typically NP-complete
• Planning
  • Decide what actions to use to achieve some set of objectives
  • Can be much worse than NP-complete; worst case is undecidable

1. Domain-Specific Planners (Chapters 19-

• Most successful real-world planning systems work this way - Mars exploration, sheet-metal bending, playing bridge, etc.
• Often use problem-specific techniques that are difficult to generalize to other planning domains

Types of Planners

2. Domain-Independent

• In principle, works in any planning domain
• No domain-specific knowledge except the description of the system Σ
• In practice,
  • Not feasible to make domain- independent planners work well in all possible planning domains
• Make simplifying assumptions to restrict the set of domains - Classical planning - Historical focus of most research on automated planning

Classical Planning (Chapters 2-9)

• Classical planning requires all eight restrictive assumptions
  • Offline generation of action sequences for a deterministic, static, finite system, with complete knowledge, attainment goals, and implicit time
• Reduces to the following problem:
  • Given (Σ, s 0 , S (^) g )
  • Find a sequence of actions ( a 1 , a 2 , … an ) that produces a sequence of state transitions ( s 1 , s 2 , …, s (^) n ) such that s (^) n is in S (^) g.
• This is just path-searching in a graph
  • Nodes = states
  • Edges = actions
• Is this trivial?

Classical Planning (Chapters 2-9)

• Generalize the earlier example:
  • Five locations, three robot carts, 100 containers, three piles - Then there are 10 277 states
• Number of particles in the universe is only about 10 87 - The example is more than 10 190 times as large
• Automated-planning research has been heavily dominated by classical planning - Dozens (hundreds?) of different algorithms

loc1 loc

s 1

take

put

move2^ move

Planning Graphs (Chapter 6)

• Rough idea:
  • First, solve a relaxed problem - Each “level” contains all effects of all applicable actions - Even though the effects may contradict each other
  • Next, do a state-space search within the planning graph
• Graphplan, IPP, CGP, DGP, LGP, PGP, SGP, TGP, ...

Level 0 Level 1 Level 2

All appli- cable actions

All effects of those actions

All actions applicable to subsets of Level 1

All effects of those actions

Initial state

Heuristic Search (Chapter 9)

• Heuristic function like those in A*
  • Created using techniques similar to planning graphs
• Problem: A* quickly runs out of memory
  • So do a greedy search instead
• Greedy search can get trapped in local minima
  • Greedy search plus local search at local minima
• HSP [Bonet & Geffner]
• FastForward [Hoffmann]