Planning and Acting. CITS3001 Algorithms, Agents and Artificial Intelligence. 2018, Semester 2

Transcription

1 Planning and Acting CITS3001 Algorithms, Agents and Artificial Intelligence Tim French School of Computer Science and Software Engineering The University of Western Australia 2018, Semester 2

2 Summary We introduce and motivate planning algorithms based on factored representations We define partial-order planning, and illustrate with examples We describe conditional planning, monitoring, and replanning, and illustrate with examples 1

3 The planning problem So far We have seen two types of problemsolving/searching/ planning mechanisms Searching algorithms such as A* work well for many domains But they need good domain-specific heuristics, which can be hard to identify for complex problems Logical agents are domain-independent But they have tractability issues in large domains What we need is the ability to break up ( factor ) the state and goals of a problem, so that we can address them piece-wise This gives the system much more flexibility in its search 2

4 Planning systems Factored planning systems open up the representations of states, actions, and goals to facilitate Optimal selection and re-ordering of goals Divide-and-conquer by sub-goaling Interleaving of action-sequences 3

5 Planning Systems A state is a conjunction of ground literals e.g. At(Plane1, Sydney) Ù At(Plane2, Melbourne) A goal is a conjunction of literals e.g. At(Plane1, x) Ù At(Plane2, x) An action is defined by A precondition: a conjunction of literals that must be true for the action to be available An open condition is an unfulfilled precondition An effect: a conjunction of literals that is true after the action has been performed Captures everything relevant that has changed e.g. FlyTo(p, x): Precondition: At(p, y) Ù Range(p, r) Ù Distance(x, y) r Effect: At(p, y) Ù At(p, x) 4

6 Partial-order planning In standard search: A node is a concrete world state An operator expands a node to generate its descendant states The search proceeds until a goal state is generated In planning search A node is a partial plan A set of steps, each of which is an action An operator modifies a partial plan by one of Adding a step to fulfil an open condition Asserting an order between two steps Instantiating a bound variable The search proceeds until the plan is complete A plan is complete when no open conditions remain A partial-order planner places an order on steps in its plan only when it is essential to do so AKA a least commitment planner The final result is a directed acyclic graph where Nodes are steps Edges are orderings/dependencies between steps Topological sorting turns this into a linear plan 5

7 Topological sorting A topological sort turns a graph from a partial order into a total order that respects the same dependencies i.e. if X has an arc pointing to Y, X must precede Y in the total order Consider the DAG (copied from l_sorting) The graph has many valid topological sorts, e.g. 7, 5, 3, 11, 8, 2, 9, 10 3, 5, 7, 8, 11, 10, 9, 2 7, 5, 11, 2, 3, 8, 9, 10 3, 7, 8, 5, 11, 10, 9, 2 6

8 Clobbering A precondition for a step is achieved if it is the effect of an earlier step and no intervening step undoes ( clobbers ) it If a step Si achieves a precondition for a step Sj, and a new step Sk clobbers that precondition, Sk must either be Demoted, so that Sk happens before Si Promoted, so that Sk happens after Sj, or If neither of these is possible, then the partial plan cannot be completed and backtracking is required Basically lose Sk and try something else 7

9 An example: Blocks World The initial state: On(C,A) Ù On(A, Table) Ù Clear(B) Ù On(B, Table) Ù Clear(C) The goal state: On(A,B) Ù On(B,C) Action PutOn(x, y): Precondition: Clear(x) Ù On(x, z) Ù Clear(y) Effect: On(x, z) Ù Clear(y) Ù On(x, y) Ù Clear(z) Action PutOnTable(x): Precondition: On(x, z) Ù Clear(x) Effect: On(x, z) Ù On(x, Table) Ù Clear(z) This problem illustrates the Sussman Anomaly It cannot be solved by addressing one goal first, then the other The actions addressing the two goals have to be interleaved 8

10 Example 1 9

11 Example 2 10

12 Example 3 11

13 Real world considerations Agents have to deal with uncertainty Information might be incomplete The agent may not know whether preconditions hold or not Actions may not have the expected outcome Information might be incorrect The current state might be incorrect Actions outcomes might be missing or incorrect These are instances of the qualification problem In a real environment, it is generally impossible to list all preconditions and possible outcomes of any action no plan survives contact with the enemy [Helmuth von Moltke the Elder, 1871] These issues are particularly acute in environments where multiple agents are operating Either cooperatively or competitively 12

14 Two approaches Conditional planning: Anticipate problems and build contingencies into the plan Add observation actions to check preconditions and effects, and create a sub-plan for each possibility But this is expensive because it plans for many unlikely cases Monitoring and replanning: Assume normal, successful execution Continually check the progress of the plan Replan when necessary In general, a combination of the two is a common choice In particular, some monitoring is unavoidable Very difficult to anticipate everything! 13

15 Conditional planning [, if p [true plan] [false plan], ] Check p against the current database, and proceed accordingly If an open condition can be established by an observation action: Add the action to the plan Complete the plan for each possible outcome Insert a conditional step with these sub-plans 14

16 Example 1 15

17 Example 2 16

18 Example 3 17

19 Monitoring Check the progress of the plan during execution i.e. check the state of the world Comes in three flavours Action monitoring The agent checks whether the preconditions of the next action are met Plan monitoring The agent checks whether the preconditions of the remaining plan are met Goal monitoring The agent checks whether changing its goals is appropriate In all cases, failure requires replanning 18

20 Replanning Replanning comes in two flavours Simplest is to replan from scratch Based on the (actual) current state of the world More efficient, but often harder, is to replan to restore the expected state so that the rest of the plan can continue Note that in the extreme in 11.9, P = E = G Then the process defaults to replanning from scratch 19

21 Situated planning The most general (online) approach is sometimes called situated planning The agent interleaves planning and execution It views itself always as part of the way through a plan Activities include Execute a plan step Monitor the state of the world Fix deficiencies in the plan Select an action to resolve open conditions Reorder actions to resolve clobbering Refine the plan in light of new information An example: e.g. execution errors e.g. actions by other agents Transform (a) to (d) 20

22 Example 1 21

23 an unexpected event... 22

24 Execute step (unsuccessful) 23

25 Try again Planning for real world applications requires a mixture of all the techniques we have discussed: tree search, game playing, learning, and logic. It is a challenging field but has great potential. Good luck in your exams. 24