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Planning I: Total Order Planners

Planning I: Total Order Planners. Sections 11.1 - 11.4. Problem. Mechanically find a sequence of actions that take us from the start state to the goal state now we want a mechanical way of doing the “proof” efficiently Define a start (initial) state, a goal state, & some operators

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Planning I: Total Order Planners

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  1. Planning I: Total Order Planners Sections 11.1 - 11.4

  2. Problem • Mechanically find a sequence of actions that take us from the start state to the goal state • now we want a mechanical way of doing the “proof” efficiently • Define a start (initial) state, a goal state, & some operators • Find a plan • sequence of operators/actions that leads from the start to the goal state

  3. Assumptions • Goals are conjunctions of atoms • to achieve a goal, you achieve a set of subgoals • Actions are deterministic • no uncertainty in performing an action • The agent is the only “operator” in the world • World is accessible [the agent is omniscient] • Closed world assumption (sometimes is adopted) • negation by failure

  4. Approaches to planning • Situational calculus • State-space search

  5. Situational calculus [Ch. 7] • FOL plus a “timestamp” added to most predicates • result(action, state) function returns the next state after applying action in state • Frame problem • effect axioms describes what changes, but doesn’t specify what stays the same • frame axioms describe what stays the same, but many are required (representation problem) and you have to reason with them (inferential problem). • Successor-state axioms: combine frame axioms with effect axioms • Good representation; slow inference procedure: too fine grained

  6. State-space search [Ch. 3-4] • Initial state, goal test, operators [actions] • Doesn’t allow reasoning about the states & operators • operators are just used to generate the next state • can’t reason about which operators should occur before which other operators which would greatly reduce the number of states needed to test • goal test is a black box that doesn’t allow us to reason about how to get to the goal • heuristic is simply a numeric score of distance from the goal • Weak in terms of representation & ability to reason about the world

  7. Solution • Combine the two approaches • simplify the representation language • allows us to reason about how to achieve the goal • inference procedure is faster than resolution • “open up” the representation of state, operators & goal test in the search • rather than blindly applying operators, reason about which ones are most important • reduce the number of nodes that are considered

  8. STRIPS • Facts: conjunction of ground atoms • Goal: conjunction of atoms • variables allowed: assume all variables in a goal description are existential • Operators/Actions [e.g., StackOnto] • precondition: conjunction of atoms • action • effects: add (positive literals) & delete (negative literals) list • assumption: everything stays the same unless explicitly on the delete list [avoids the frame problem]

  9. Approaches to planning • Situation-space search • search the space of all possible situations • initial state is one node • goal node is all of the sub-goals solved • plan is the sequence of actions from start -> goal • Plan-space search • search the space of all (partial) plans • node is a partial plan • start node is an initial node • goal node contains the complete plan • arcs (typically) add to or modify a previous node’s plan

  10. Situation-space planners • Progression: forward chaining • similar to state-space search except for representation • inefficient due to large state space to explore • Regression: backward chaining • start from the goal state & solve its sub-goals [preconditions] • more efficient & goal-directed than progression [fewer applicable operators]

  11. STRIPS: goal-stack based regression planner • Goal stack: what to do next • Current state: facts that are true • Pick order of achieving (sub-)goals • find operator that achieves the goal • push the operator on to the stack • push its preconditions (in some order) on to the stack • check that when we eventually get back to the original goal, that all of the preconditions that we needed to satisfy are still satisfied

  12. Key assumption • Sub-goals are independent of each other • divide & conquer the problem without worrying about other parts of the “equation” • e.g., buying items: the order doesn’t matter; buying milk before eggs doesn’t usually make it impossible to then buy eggs • whole plan = sum of all sub-plans • STRIPS makes this assumption • thus, incomplete • Sussman anomaly • sub-goals interfere with each other

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