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1. Artificial Intelligence Chapter 11: Planning
2. Introduction Like problem-solving agents, planning agents have goals, states, and actions
A plan is a sequence of actions to achieve some goal
3. Why plan, when you can search?
4. From Problem Solving to Planning Planners can
Use FOL (for example) for representing states, goals, and actions
Break hard problems into manageable subproblems
Solve some subproblems independently of others
5. Planning Could use standard FOL inference (e.g., resolution) to find plan
But this isn’t practical: Huge search space
Instead, use special-purpose (=efficient) algorithms, each with its own restricted (= smaller search space) language
6. STRIPS Representation for Planning STRIPS language
States = conjunctions of function-free ground literals
Goals = same thing, but can also have variables (assumed to be existentially quantified)
7. STRIPS Representation for Actions Actions have three components:
Action description = just the name
Precondition = conjunction of positive literals that says what must be true to make the action applicable
Effect = conjunction of positive or negative literals that says what changes in the state when the action is applied
Can be separated into an add list and a delete list
8. Representations for Plans Relative ordering of plan steps
Total order (linearization): all steps in order
Partial order: some steps in order
9. Plan Solutions Problems with linearized, totally ordered plans
Which linearization to choose?
What if agent can perform some steps in parallel?
When combining plans (e.g., for subproblems), partial ordering gives flexibility
Solution = an executable plan that guarantees reaching the goal
Complete plans: all preconditions of all steps are achieved by prior steps
Consistent plans: no inconsistencies in ordering constraints or causal links
10. Plan Space Searching through plan space
Each node is a partial plan, which represents a set of complete plans
Search operators modify plans: add steps, reorder steps, etc.
Progression (forwards) vs. Regression (backwards) planning
11. The Plan Data Structure A Plan data structure contains:
A set of plan steps, Si
A set of step ordering constraints
A set of open preconditions
A set of causal links
Initial plan: Steps = Start and Finish
Start’s effects = initial state. No preconditions.
Finish’s preconditions = goal state. No effects.
13. Partial-Order Planning Start with the minimal partial plan
Each point in planning adds a step (and causal links) that achieves some precondition
Can use standard search algorithms
The key is the formulation: Nodes aren’t world states, they’re partial plans
14. Partial-Order Planning Example Start at home
Goal = return home with milk, bananas, and drill
Only add steps that achieve an unachieved precondition -> Reduces search space
Causal links help prune bad plans quickly, before going too far down the dead end