Classical Planning Chapter 10

Outline The challenges in planning with standard search algorithm Representing Plans – the PDDL language Planning as state-space search Planning Graphs and the GRAPHPLAN Algorithm Other Approaches

Classical Planning What is planning: The task of coming up with a sequence of actions to achieve a given goal is called planning Classical planning: When the environment is Fully observable Deterministic Static Discrete

Challenges in Planning with Standard Search Method (A*, etc) Why real-world planning problem with state-space search is hard: Too many irrelevant actions – goal oriented search would help Difficult to find a good heuristic function So the language for planning should make it easy for algorithms to exploit the logical structure of the problem

Challenges in Planning – too many choices!

PDDL Language State: represented by a conjunction of ground atoms without function symbols Action: represented by a set of action schemas

A specific planning problem Goal state – a conjunction of literals (positive + negative) that may contain (existentially quantified) variables A set of action schemas Clearly a planning problem can be seen as a search problem

Example – the blocks-world

Complexity of classical planning PlanSAT: Is there a plan for a planning problem Both are decidable if the planning language is function-free – finitely many states Both in the class of PSPACE – more difficult than NP! But for many domains: Bounded PlanSAT: NP-complete PlanSAT: P – thus finding A (possibly suboptimal) plan may be not so hard!

Algorithms for planning as state-space search Backward (regression) relevant-states search

Heuristics for planning Adding edges in the state-space graph Ignoring pre-conditions Ignoring delete list Key idea: decomposition – dividing the problem into parts (which may be independent) and solve each part independently, then combine the subplans Subgoal independence assumption

Planning Graphs - motivation A big source of inefficiency in search algorithms is the branching factor One way to reduce branching factor: First create a relaxed problem Remove some restrictions of the original problem Want the relaxed problem easy (polynomial time) The solutions to the relaxed problem will include all solutions to the original problem Then do a modified version of the original search (backward search) Restrict the search space to include only those actions that occur in solutions to the relaxed problem

Planning Graphs Search space for a relaxed version of the planning problem Alternating layers of states (ground literals) and actions Nodes at action-level i: actions that might be possible to execute at time i Nodes at state-level i: literals that might possibly be true at time i Edges: preconditions and effects Mutual exclusion links

Sample Planning Graph

Mutual Exclusions Two actions at the same action-level are mutex if Inconsistent effects: an effect of one negates an effect of the other Interference: one deletes a precondition of the other Competing needs: they have mutually exclusive preconditions Two literals at the same state-level are mutex if Inconsistent support: one is the negation of the other, or all ways of achieving them are pairwise mutex

The GRAPHPLAN Algorithm graph  Initial-planning-graph(problem) goals  Conjuncts(Problem, GOAL) nogoods  an empty hash table For t = 0 to infinity do if goals all non-mutex in St of graph then solution  Extract-solution(graph, goals, num-lev(graph), nogoods) if solution != failure, then return solution if graph and nogoods have both leveled off then return failure graph  Expand-graph(graph, problem)

The spare tire problem

The spare-tire problem

Extract-solution as a search problem Initial state: the last level of the planning graph Sn Actions at state level Si: select any conflict-free subset of actions in Ai-1 that covers the goals of the state. The result state: level Si-1, the goals at the new state = the pre-conditions of the selected actions Goal of the backward search: reach a state at S0 such that all goals are satisfied. The cost of each action is 1 When extract-solution fails to find a solution for a set of goals at a level, a pair (level, goals) is added as a no-good.

Other Classical Planning Approaches Classical Planning as Boolean satisfiability Planning as a first-order logical deduction: Situation calculus Planning as constraint satisfaction