Practical Planning: Scheduling and Hierarchical Task Networks

1. CMSC 471 Practical Planning:Scheduling and Hierarchical Task Networks Chapter 12.1-12.2 Adapted from slides by Tim Finin and Marie desJardins.

2. Outline • Intelligent scheduling • Hierarchical task network (HTN) planning • Increasing expressivity

3. Real-world planning domains • Real-world domains are complex and don’t satisfy the assumptions of STRIPS or partial-order planning methods • Some of the characteristics we may need to deal with: • Modeling and reasoning about resources • Representing and reasoning about time • Planning at different levels of abstractions • Conditional outcomes of actions • Uncertain outcomes of actions • Exogenous events • Incremental plan development • Dynamic real-time replanning }a.k.a. scheduling!

4. Planning vs. scheduling • Planning: given one or more goals, generate a sequence of actions to achieve the goal(s) • Scheduling: given a set of actions and constraints, allocate resources and assign times to the actions so that no constraints are violated • Traditionally, planning is done with specialized logical reasoning methods • Traditionally, scheduling is done with constraint satisfaction, linear programming, or OR methods • However, planning and scheduling are closely interrelated and can’t always be separated

5. Hierarchical decomposition • Hierarchical decomposition, or hierarchical task network (HTN) planning, uses abstract operators to incrementally decompose a planning problem from a high-level goal statement to a primitive plan network • Primitive operators represent actions that are executable, and can appear in the final plan • Non-primitive operators represent goals (equivalently, abstract actions) that require further decomposition (or operationalization) to be executed • There is no “right” set of primitive actions: One agent’s goals are another agent’s actions!

6. HTN operator: Example OPERATOR decompose PURPOSE: Construction CONSTRAINTS: Length (Frame) <= Length (Foundation), Strength (Foundation) > Wt(Frame) + Wt(Roof) + Wt(Walls) + Wt(Interior) + Wt(Contents) PLOT: Build (Foundation) Build (Frame) PARALLEL Build (Roof) Build (Walls) END PARALLEL Build (Interior)

7. HTN planning: example

8. SIPE-2 • SIPE-2 is an HTN planner with many advanced features: • Plan critics • Resource reasoning • Constraint reasoning (complex numerical or symbolic variable and state constraints) • Interleaved planning and execution • Interactive plan development • Sophisticated truth criterion • Conditional effects • Parallel interactions in partially ordered plans • Replanning if failures occur during execution

9. SIPE-2 Image from: http://www.ai.sri.com/~sipe/architecture.html

10. Blocksworld in SIPE-2 Excerpt from SIPE-2 Blocksworld Definition Sussman Anomaly ;;some colored blocks for other problems (ON R1 B1) (ON B1 TABLE) (ON B2 TABLE) (ON R2 TABLE) ;true in all problems (CLEAR TABLE) END PREDICATES STOP OPERATOR: PUTON1 ARGUMENTS: BLOCK1, OBJECT1 IS NOT BLOCK1; PURPOSE: (ON BLOCK1 OBJECT1) PLOT: PARALLEL BRANCH 1: GOALS: (CLEAR OBJECT1) BRANCH 2: GOALS: (CLEAR BLOCK1) END PARALLEL PROCESS ACTION: PUTON; ARGUMENTS: BLOCK1,OBJECT1 RESOURCES: BLOCK1 EFFECTS: (ON BLOCK1 OBJECT1) END PLOT END OPERATOR Excerpt taken from http://www.ai.sri.com/~sipe/blocks-sipe.txt Image taken from http://www.ai.sri.com/~sipe/sussman-derivation.html

11. HTN operator representation • Russell & Norvig explicitly represent causal links; these can also be computed dynamically by using a model of preconditions and effects (this is what SIPE-2 does) • Dynamically computing causal links means that actions from one operator can safely be interleaved with other operators, and subactions can safely be removed or replaced during plan repair • Russell & Norvig’s representation only includes variable bindings, but more generally we can introduce a wide array of variable constraints

12. Truth criterion • Determining whether a formula is true at a particular point in a partially ordered plan is, in the general case, NP-hard • Intuition: there are exponentially many ways to linearize a partially ordered plan • In the worst case, if there are N actions unordered with respect to each other, there are N! linearizations • Ensuring soundness of the truth criterion requires checking the formula under all possible linearizations • Use heuristic methods instead to make planning feasible • Check later to be sure no constraints have been violated

13. Truth criterion in SIPE-2 • Heuristic: prove that there is one possible ordering of the actions that makes the formula true – but don’t insert ordering links to enforce that order • Such a proof is efficient • Suppose you have an action A1 with a precondition P • Find an action A2 that achieves P (A2 could be initial world state) • Make sure there is no action necessarily between A2 and A1 that negates P • Applying this heuristic for all preconditions in the plan can result in infeasible plans

14. Increasing expressivity • Conditional effects • Instead of having different operators for different conditions, use a single operator with conditional effects • Move (block1, from, to) and MoveToTable (block1, from) collapse into one Move (block1, from, to): • Op(ACTION: Move(block1, from, to),PRECOND: On (block1, from) ^ Clear (block1) ^ Clear (to)EFFECT: On (block1, to) ^ Clear (from) ^ ~On(block1, from) ^ ~Clear(to) when to≠Table • There’s a problem with this operator: can you spot what it is? • Negated and disjunctive goals • Universally quantified preconditions and effects

15. Reasoning about resources • Introduce numeric variables that can be used as measures • These variables represent resource quantities, and change over the course of the plan • Certain actions may produce (increase the quantity of) resources • Other actions may consume (decrease the quantity of) resources • More generally, may want different types of resources • Continuous vs. discrete • Sharable vs. nonsharable • Reusable vs. consumable vs. self-replenishing

16. Other real-world planning issues • Conditional planning • Partial observability • Information gathering actions • Execution monitoring and replanning • Continuous planning • Multi-agent (cooperative or adversarial) planning

17. SATPlan

18. SATPlan • Formulate the planning problem as a CSP • Assume that the plan has k actions • Create a binary variable for each possible action a: • Action(a,i) (TRUE if action a is used at step i) • Create variables for each proposition that can hold at different points in time: • Proposition(p,i) (TRUE if proposition p holds at step i)

19. Constraints • Only one action can be executed at each time step (XOR constraints) • Constraints describing effects of actions • Persistence: if an action does not change a proposition p, then p’s value remains unchanged • A proposition is true at step i only if some action (possibly a maintain action) made it true • Constraints for initial state and goal state

20. Now apply our favorite CSP solver!

21. Planning summary • Planning representations • Situation calculus • STRIPS representation: Preconditions and effects • Planning approaches • State-space search (STRIPS, forward chaining, ….) • Plan-space search (partial-order planning, HTN, …) • Constraint-based search (GraphPlan, SATplan, …) • Search strategies • Forward planning • Goal regression • Backward planning • Least-commitment • Nonlinear planning

22. Applications of Planning • Military operations • Autonomous space operations • Construction tasks • Machining tasks • Mechanical assembly • Design of experiments in genetics • Command sequences for satellite Most applied systems use extended representation languages, nonlinear planning techniques, and domain-specificheuristics

23. Oil-Spill Response in SIPE-2 Image taken from http://www.ai.sri.com/~sipe/oil.html