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Questions and Answers
What is a core characteristic of classical planning environments?
What is a core characteristic of classical planning environments?
- Deterministic and static environment (correct)
- Dynamic changes independent of agent actions
- Stochastic outcomes of actions
- Incomplete observability of the environment state
In classical planning, how are world states and goals represented?
In classical planning, how are world states and goals represented?
- World states are represented as probability distributions, goals as utility functions.
- World states and goals are implicitly defined within the planning algorithm.
- World states are represented with objects and Boolean predicates, goals are conjunctions of predicates. (correct)
- World states are represented using neural networks, goals as reward functions.
What does the term 'ground' refer to in the context of PDDL representation?
What does the term 'ground' refer to in the context of PDDL representation?
- An aspect of the world that changes over time.
- Absence of variables; all arguments in the predicate are constants. (correct)
- A metaphorical representation of a solid and secure state.
- Refers to actions that involve physical contact with the ground.
What is the significance of successor-state axioms in logic-based planning?
What is the significance of successor-state axioms in logic-based planning?
In PDDL, what does the 'closed-world assumption' imply?
In PDDL, what does the 'closed-world assumption' imply?
Why is the explicit representation of time not required in classical planning, unlike in logic-based planning?
Why is the explicit representation of time not required in classical planning, unlike in logic-based planning?
In the context of classical planning, what does the term 'fluent' refer to?
In the context of classical planning, what does the term 'fluent' refer to?
Within classical planning, actions are defined by their preconditions and effects. What are preconditions?
Within classical planning, actions are defined by their preconditions and effects. What are preconditions?
When formulating a planning problem, why might 'ground' be referenced directly in operators instead of a general 'location'?
When formulating a planning problem, why might 'ground' be referenced directly in operators instead of a general 'location'?
Consider a planning domain where actions are deterministic and the environment is fully observable. Which search algorithm guarantees an optimal plan if all actions have the same cost?
Consider a planning domain where actions are deterministic and the environment is fully observable. Which search algorithm guarantees an optimal plan if all actions have the same cost?
Consider a scenario where removing a tire from an axle requires the condition On(tire, axle) to be true. How is this condition represented in a PDDL action schema?
Consider a scenario where removing a tire from an axle requires the condition On(tire, axle) to be true. How is this condition represented in a PDDL action schema?
In the context of the tire-changing problem, the initial state includes On(flat_tire, axle) and On(spare_tire, trunk). What does the application of the action Remove(flat_tire, axle) achieve?
In the context of the tire-changing problem, the initial state includes On(flat_tire, axle) and On(spare_tire, trunk). What does the application of the action Remove(flat_tire, axle) achieve?
Given the operator 'Put(tire, loc)' with a precondition 'Empty(loc)', what does 'Empty(loc)' signify?
Given the operator 'Put(tire, loc)' with a precondition 'Empty(loc)', what does 'Empty(loc)' signify?
After applying the action Remove(tire, trunk), which predicates should be added to the new state?
After applying the action Remove(tire, trunk), which predicates should be added to the new state?
In classical planning, which statement accurately describes the relationship between states and predicates?
In classical planning, which statement accurately describes the relationship between states and predicates?
What is the main strategy employed by linear planning to solve complex problems that can be represented as a conjunction of goal predicates?
What is the main strategy employed by linear planning to solve complex problems that can be represented as a conjunction of goal predicates?
In linear planning, what is done if a later action invalidates a previously achieved goal?
In linear planning, what is done if a later action invalidates a previously achieved goal?
What is a potential issue when applying linear planning to problems with interacting goals, as illustrated by Sussman's Anomaly?
What is a potential issue when applying linear planning to problems with interacting goals, as illustrated by Sussman's Anomaly?
Compared to linear planning, what is the key difference in how non-linear planning addresses multiple goals?
Compared to linear planning, what is the key difference in how non-linear planning addresses multiple goals?
What is an action schema composed of in classical planning?
What is an action schema composed of in classical planning?
Given the operators 'Put(tire,loc)' and 'Remove(tire, loc)', and the initial conditions 'On(flat, axle)' and 'On(spare, trunk)', which operator can be applied first?
Given the operators 'Put(tire,loc)' and 'Remove(tire, loc)', and the initial conditions 'On(flat, axle)' and 'On(spare, trunk)', which operator can be applied first?
A robot can perform three actions: MoveToTable(block, location), Move(block, location1, location2), and Grasp(block). For the action Move(block, location1, location2) what is a likely Precondition?
A robot can perform three actions: MoveToTable(block, location), Move(block, location1, location2), and Grasp(block). For the action Move(block, location1, location2) what is a likely Precondition?
Consider the initial state where On(A, Table), On(B, Table), and On(C, A) are true. What action should be performed first to achieve the goal state where On(A, B) and On(B, C) are the predicates?
Consider the initial state where On(A, Table), On(B, Table), and On(C, A) are true. What action should be performed first to achieve the goal state where On(A, B) and On(B, C) are the predicates?
An action in the blocks world is specified with the following. Action(Move(b,x,y),PRECOND: On(b,x) / Clear(b) Clear(y) Block(b) Block(y) (b≠x) ^ (b≠y)^(x≠y),EFFECT: On(b,y) ^ Clear(x) ^ «On(b,x) ^ «Clear(y)). What does Clear(y) refer to?
An action in the blocks world is specified with the following. Action(Move(b,x,y),PRECOND: On(b,x) / Clear(b) Clear(y) Block(b) Block(y) (b≠x) ^ (b≠y)^(x≠y),EFFECT: On(b,y) ^ Clear(x) ^ «On(b,x) ^ «Clear(y)). What does Clear(y) refer to?
Given the goal On(A, B) ^ On(B, C) and the initial state On(A, Table) ∧ On(B, Table) ^ On(C, A). Why is simply executing Move(A,Table,B) and Move(B,Table,C) is not a valid plan?
Given the goal On(A, B) ^ On(B, C) and the initial state On(A, Table) ∧ On(B, Table) ^ On(C, A). Why is simply executing Move(A,Table,B) and Move(B,Table,C) is not a valid plan?
In the blocks world, consider two actions: Action(pickup(X)) and Action(putdown(X)). Under what condition would you have to add a clear action, Action(clear(X)), as part of your plan?
In the blocks world, consider two actions: Action(pickup(X)) and Action(putdown(X)). Under what condition would you have to add a clear action, Action(clear(X)), as part of your plan?
What is the advantage of using the closed-world assumption in classical planning?
What is the advantage of using the closed-world assumption in classical planning?
If your goal is to put the spare tire on the axle, what would be a well-formed goal statement written as a conjunction of predicates, assuming states are expressed such that On(object, location)?
If your goal is to put the spare tire on the axle, what would be a well-formed goal statement written as a conjunction of predicates, assuming states are expressed such that On(object, location)?
How does classical planning primarily differ from search planning?
How does classical planning primarily differ from search planning?
In propositional logic planning, how are different time steps handled in terms of representing world state?
In propositional logic planning, how are different time steps handled in terms of representing world state?
In the context of classical planning, particularly in the operators such as Put(tire, loc) and Remove(tire, loc), what does loc != ground refer to as a precondition?
In the context of classical planning, particularly in the operators such as Put(tire, loc) and Remove(tire, loc), what does loc != ground refer to as a precondition?
Which of the following options is a suitable strategy in non-linear planning?
Which of the following options is a suitable strategy in non-linear planning?
In what ways can classical planning be applied to handling the tire-changing scenario?
In what ways can classical planning be applied to handling the tire-changing scenario?
What does the term 'action schema' mean in classical planning? Note, 'schema' can be thought of as a template.
What does the term 'action schema' mean in classical planning? Note, 'schema' can be thought of as a template.
Which is the correct order needed to ensure to put the spare tire on the axle based on our classical planning example?
Which is the correct order needed to ensure to put the spare tire on the axle based on our classical planning example?
What do state and goals have in relation to predicates?
What do state and goals have in relation to predicates?
How are operators used?
How are operators used?
In what manner do classical planning operators change the state?
In what manner do classical planning operators change the state?
When can actions be used?
When can actions be used?
What type of search is breadth-first search?
What type of search is breadth-first search?
How do you use breadth-first search in conjunction of goal predicates in linear planning?
How do you use breadth-first search in conjunction of goal predicates in linear planning?
Flashcards
Classical Planning
Classical Planning
Finding a sequence of actions to achieve a goal in a discrete, deterministic, static, fully observable environment.
Planning Domain Definition Language (PDDL)
Planning Domain Definition Language (PDDL)
A factored representation using languages like PDDL to describe classical planning problems.
Objects/Values in PDDL
Objects/Values in PDDL
Values or entities that are handled distinctly from the state in PDDL.
Predicates in PDDL
Predicates in PDDL
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States in PDDL
States in PDDL
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Goals in PDDL
Goals in PDDL
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State in PDDL
State in PDDL
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Ground Atomic Fluent
Ground Atomic Fluent
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Action Schema
Action Schema
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Parts of an Action Schema
Parts of an Action Schema
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Preconditions
Preconditions
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Effect
Effect
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Operators
Operators
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Non-Linear Planning
Non-Linear Planning
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Sussman's Anomaly
Sussman's Anomaly
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Linear Planning
Linear Planning
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Closed-World Assumption in PDDL
Closed-World Assumption in PDDL
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Breadth-First Search
Breadth-First Search
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Study Notes
Classical Planning
- Also referred to as Symbolic Planning.
Changing a Tire Problem
- Initial state includes a flat tire on the axle and a spare in the trunk.
- Actions include removing and putting a tire on the axle or in the trunk.
- The goal is to replace the flat tire on the axle with the spare from the trunk.
- This problem could be solved with search algorithms like Breadth-First Search (BFS) or with logic.
Search, Logic, and Classical Planning Comparisons
- Search Planning: State representation changes as you act.
- Propositional Logic: represents the world with boolean propositions and successor state axioms, using different symbols for different time points.
- Classical Planning: represents the world with objects and boolean predicates where the state changes as you act.
Definition of Classical Planning
- Classical planning seeks a sequence of actions to achieve a goal in a discrete, deterministic, static, and fully observable environment.
- It uses a factored representation with PDDL (Planning Domain Definition Language).
- PDDL can express all 4Tn2 actions with a single action schema and does not need domain-specific knowledge.
- Basic PDDL handles classical planning domains; extensions handle continuous, partially observable, concurrent, and multi-agent domains.
Classical Planning in PDDL
- Represents objects/values separately from the state, known as instances.
- Defines predicates as true/false functions over these objects.
- States are conjunctions of predicates.
- Goals are conjunctions of predicates.
PDDL State Representation
- A state is a conjunction of ground atomic fluents.
- "Ground" means there are no variables.
- "Fluent" is an aspect of the world that changes over time.
- "Ground atomic" means a single predicate exists, and its arguments are constants.
- Example:
Poor ∧ Unknowncan indicate a hapless agent.At(Truck1, Melbourne) ∧ At(Truck2, Sydney)describes a state in a package delivery problem.
Action Schema
- Operators (action schema) represent families of ground actions.
- An action schema can represent flying a plane from one location to another.
Action Schema Components
- Schema includes action name, variables, preconditions, and effects.
- Preconditions and effects are conjunctions of literals.
- Variable instantiation resulting effect yields a ground (variable-free) action.
- Example:
Action(Fly(P1,SFO,JFK)with preconditions such asAt(P1, SFO) ^ Plane(P1) ^ Airport(SFO) ^ Airport(JFK)and effects such asAt(P1,SFO)^At(P1,JFK).
Action Schema in Operation
- Operators change the state by adding or deleting predicates.
- Actions are executable only if all precondition predicates are true.
- The new state is a copy of current predicates with added or deleted predicates.
Removing a Tire
- If a tire can can be removed from an axle if it is on the axle, then as as a result, the tire is on the ground.
- If a tire can be put on an axle if it is on the ground, then as a result, the tire in on the axle
- If a tire can be removed from the trunk if it is in the trunk, then as a result, the tire is on the ground.
- If a tire can be put in the trunk if it is on the ground, then as a result, the tire is in the trunk.
Rules of Tire Fixing in Classical Planning
- Successor state axioms are defined for each object type.
- A tire can be removed from an axle/trunk if it is on there; the effect is the tire is on the ground.
- A tire can be put on an axle/trunk if it is on the ground; the effect is the tire is on the axle/trunk.
- Trunk/axle can be empty if nothing is on it.
- At most one thing can be on the trunk/axle.
State Transition Example: Removing a Tire from the Trunk
- Tires: flat, spare
- Locations: axle, trunk, ground
- Possible Predicate: On(tire, loc)
- An old state where the spare tire is in the trunk transitions to a new state where the spare tire is now on the ground and the trunk is free.
- This causes the deletion of
On(spare, trunk)and the effectOn(spare, ground)andEmpty(trunk).
Operator: Removing a Tire From the Trunk
- Precondition: The tire must be in the trunk:
On(tire,trunk). - Effects:
- Add to the state that the tire is on the ground and the trunk is now empty:
On(tire,ground), Empty(trunk). - Delete the original fact that the tire was in the trunk:
On(tire, trunk).
- Add to the state that the tire is on the ground and the trunk is now empty:
Operator: Removing a Tire Location
- Preconditions:
- The tire must be at a specified location:
On(tire,loc). - The location cannot be the ground:
loc != ground.
- The tire must be at a specified location:
- Effects:
- Add to the state that the tire is on the ground:
On(tire,ground). - Add to the state that original location is now empty:
Empty(loc). - Delete from the state that the tire was at the original location:
On(tire, loc).
- Add to the state that the tire is on the ground:
Operator: Putting a Tire
- Preconditions:
- The tire must be on the ground:
On(tire,ground). - The destination location cannot be the ground, which is specified as
loc != ground. - The location must be empty:
Empty(loc).
- The tire must be on the ground:
- Effects:
- Add to the state the tire is at the new location:
On(tire, loc). - Delete from the state the tire is on the ground:
On(tire,ground). - Mark the ground as empty:
Empty(loc).
- Add to the state the tire is at the new location:
Operators for Fixing a Tire
- Put(tire,loc):
- Pre: On(tire,ground), loc != ground, Empty(loc)
- Add: On(tire,loc)
- Delete: On(tire,ground), Empty(loc)
- Remove(tire, loc):
- Pre: On(tire, loc), loc != ground
- Add: On(tire,ground), Empty(loc)
- Delete: On(tire, loc)
- Ground is referenced directly instead of as a location because the ground can be a temporary or universal location.
- Empty fluents are added due to PDDL's closed-world assumption where unmentioned fluents are false.
Matching Operators as Search
- This section showcases matching existing states with applicable operators, which include
On(flat, axle) AND On(spare, trunk)
Finding Plans with Symbolic Representations
- Breadth-First Search (BFS) has certain properties when used with symbolic representations:
- Sound: Yes because all solutions are legal plans.
- Complete: Yes because a solution is found if one exists.
- Optimal: Yes, if all actions have equal costs.
Linear Planning Approach
- Goals are solved one at a time:
- Maintain a stack of achievable goals.
- Use BFS to find a plan for each goal.
- If a later change violates a goal, add that goal back to the stack.
Linear Planning Spare Tire Example
- The start state, goal stack, and action plan are shown to fix tire.
Introducing Tools into the Linear Planning: The Wrench Example
- The start state, goal stack, and action plan are shown to fix tire, using a wrench.
- Linear planning is sound, but not always complete because it cannot always find a plan.
- Linear planning is also not optimal.
Sussman's Anomaly
- A weakness of linear planning that arises when solving goals one at a time results in long plans where one goal is achieved and the second immediately undoes it.
- Some problems will never result in a feasible plan when solving one goal at a time.
- This isn't just a choice of goals
Non-Linear Planning
- Interleaves goals to achieve plans.
- Maintains a set of unachieved goals.
- Searches all interleavings of goals which is very hard in practice.
- Adds a goal back to the set if a later change violates it.
Blocks World
- Blocks world consists of cube blocks on a table
- Blocks can only be be stacked one on top of another
- Robot arms can movie blocks from one position to another.
- Arm can only pick up one block at a time on top of it.
- A typical goal to get block A on B and block B on C
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