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  1. 1. Outline Artificial Intelligence Planning • • • • Definition of AI planning Key ideas: representation and search STRIPS representation partial-order planning and other techniques for reducing complexity of plan search • limiting assumptions of classical planning • Recent trends on planning research Blocks world example A planning problem is specified by: • an initial state • a goal • a model of the actions that can be performed A solution to a planning problem is a sequence of actions (a plan) that transforms the initial state into a state that satisfies the goal description, and possibly optimizes some measure of performance. B A initial state goal state Plan: Move C from A to table Move B from table to C Move A from table to B Distinctions • Planning is closely-related to problemsolving and search, but there are important differences • Planning is also related to, but different from, scheduling, theorem-proving, automatic programming, and work in control theory, decision theory and operations research, etc. A B C C Applications • • • • • Robot navigation and control Spacecraft control (Deep Space One) factory and manufacturing operations intelligent tutoring natural language generation and understanding (plan recognition) • many others 1
  2. 2. Beginnings of planning research Key issues: Representation and search • A domain-independent planner consists of a language for expressing planning problems and an associated search algorithm for finding plans • Examples: Situation calculus (1959-) QA3 (1969) frame problem Resolution theorem-proving (1965) STRIPS (1972) GPS (1969) Epistemological and heuristic adequacy The two key issues in planning research are: – modeling actions and change – organizing the search for plans “There is a spectrum of more and more expressive languages for representing the world, an agent’s goals, and possible actions. The task of writing a planning algorithm is harder for more expressive representation languages, and the speed of the resulting algorithm decreases as well.” (Dan Weld) – situation calculus and resolution theorem-proving – STRIPS language and planning algorithm – many others STRIPS Language (1) • States and goals described by conjunctions of predicates applied to constant symbols • Example: – constants: blocks A, B, C, table – predicates: • (clear A) = “block A has nothing on it” • (on A, B) = “block A is on block B” • (on B, table) = “block B is on the table” – state: (clear A) ∧ (on A B) ∧ (on B table) STRIPS Language (2) • Actions represented as follows: – name: – precondition list: – delete list: – add list: (move x from y to z) (on x y) ∧ (clear x) ∧ (clear z) (on x y) ∧ (clear z) (on x z) • An action (operator) with variables is called an action (operator) schema Partial descriptions • Only relevant aspects of the world need to be included in state description • STRIPS Assumption: Everything about the world that is not mentioned by the action schema remains unchanged by action – this is “solution” to frame problem 2
  3. 3. Influence • The STRIPS planning algorithm had many deficiencies and was never used again. Many improved planning algorithms have been developed since. • The STRIPS language, and variations of it, continues to be used by most planners Search in situation space Searching for a plan • Besides modeling actions and change, the second important issue in planning is how to make the search for a plan efficient • Distinction between searching in situation space and plan space Situation space for the blocks world • States represent situations • Edges represent actions that transform a situation into a new situation • Search strategies: – forward from initial state (progression) or backward from goal (regression or backward chaining) – total-order planning = plan is build action-byaction in forward or backward direction Search in plan space Plan space for the blocks world • First used by planner called NOAH [1975]. • States represent partially specified plans. • Edges represent plan-refinement operations (e.g. adding actions or ordering constraints). • Search strategies – least-commitment = planner avoids making decisions until a good reason to make a choice – partial-order planning = decide what actions to perform before deciding ordering of actions 3
  4. 4. Example of nonlinear plan (move A from table to B) Finish Start (move B from table to C) Example of partial-order planning Advantages of partial-order planning • By postponing choice about how to order actions, can avoid search of exponential possible orderings • It may take only a few steps to construct a plan that would take thousands of steps using a standard total-order approach • The least-commitment approach means the planner only needs to search in places where subplans interact with each other The null plan for the Sussman anomaly contains two actions: *start* specifies the initial state and *end* specifies the goal. • The following simple blocks-world planning problem is called the “Sussman anomaly” C A B A B C • The next few slides show some of the steps involved in finding a plan using a partial-order planner The plan after adding a causal link to support (on b c) The agenda contains [(clear b) (clear c) (on b table) (on a b)] The plan after adding a causal link to support (clear b) The agenda is set to [(clear c) (on b table) (on a b)] 4