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 l now we want a mechanical way of doing the “proof” efficiently §Define a start (initial) state, a goal state, & some operators §Find a plan l sequence of operators/actions that leads from the start to the goal state

3. Assumptions §Goals are conjunctions of atoms l to achieve a goal, you achieve a set of subgoals §Actions are deterministic l 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) l 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 l effect axioms describes what changes, but doesn’t specify what stays the same l frame axioms describe what stays the same, but many are required (representation problem) and you have to reason with them (inferential problem). l 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 l 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 l 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 l simplify the representation language allows us to reason about how to achieve the goal inference procedure is faster than resolution l “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 l variables allowed: assume all variables in a goal description are existential §Operators/Actions [e.g., StackOnto] l precondition: conjunction of atoms l action l effects: add (positive literals) & delete (negative literals) list l assumption: everything stays the same unless explicitly on the delete list [avoids the frame problem]

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

10. Situation-space planners §Progression: forward chaining l similar to state-space search except for representation l inefficient due to large state space to explore §Regression: backward chaining l start from the goal state & solve its sub-goals [preconditions] l 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 l find operator that achieves the goal l push the operator on to the stack l push its preconditions (in some order) on to the stack l 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 l 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 l STRIPS makes this assumption thus, incomplete §Sussman anomaly l sub-goals interfere with each other