Real-world planning domains Real-world domains are complex and dont 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!
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 cant always be separated
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 agents goals are another agents actions!
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
SIPE-2 Image from:
Blocksworld in SIPE-2 ;;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 Image taken from Sussman Anomaly Excerpt from SIPE-2 Blocksworld Definition
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 & Norvigs representation only includes variable bindings, but more generally we can introduce a wide array of variable constraints
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
Truth criterion in SIPE-2 Heuristic: prove that there is one possible ordering of the actions that makes the formula true – but dont 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
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 toTable Theres a problem with this operator: can you spot what it is? Negated and disjunctive goals Universally quantified preconditions and effects
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
Other real-world planning issues Conditional planning Partial observability Information gathering actions Execution monitoring and replanning Continuous planning Multi-agent (cooperative or adversarial) planning
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)
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 ps 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
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-specific heuristics