1. Instructor: Eyal Amir Grad TAs: Wen Pu, Yonatan Bisk Undergrad TAs: Sam Johnson, Nikhil Johri CS 440 / ECE 448 Introduction to Artificial Intelligence Spring 2010 Lecture #14

2. Today Planning and SAT technologies Combining planning and motion planning Review before midterm

3. SAT Technologies SATLIB –Library of test problems for SAT solvers SAT Live –http://www.satlive.org/http://www.satlive.org/ DIMACS format for SAT problems –Standard format for CNF knowledge bases Annual conference –http://www.satisfiability.org/http://www.satisfiability.org/

4. Planner Technologies Many planners –http://www4.ncsu.edu/~stamant/planning- resources.htmlhttp://www4.ncsu.edu/~stamant/planning- resources.html Planning competitions http://www.icaps- conference.org/index.php/Main/Competitionshttp://www.icaps- conference.org/index.php/Main/Competitions PDDL (Planning Domain Description Language) –Standard format for specifying planning problems Extensions: parallel actions, actions off varying duration, non-deterministic actions (actions that may fail or have different effects than intended). Separate: Motion Planning

5. Factored Planning for Robot Motion

6. Motivation – AI Planning Only Strength of AI planning and description (PDDL) –Planning with logical constraints in state space Weakness of AI planning –Executing (or actuating) real-world robots –i.e. How to push a button (key1)? If we plan with kinematics constraints, –Incomplete (require details): In many cases, an action (i.e. push a button) is not straightforward to incorporate kinematic constraints into logic states. Moreover, there is no guarantee that there is a path for the action. –Ambiguous: there are many ways to interpret an action. Assumption: executable actions are given. act key1 Pre:  pushed key1 Eff: pushed key1

7. Example Goal: button (key1) is on (lit) Problem: Find a motion+logical plan that achieves Goal act key1 Pre:  pushed key1  on key1 Eff: pushed key1  on key1 P key1 (c)=1 P key1 (c)=0 PDDL CSpace We have two different representations A graph built by a motion planner (i.e. PRM) in CSpace Actions in PDDL (Planning Domain Description Language) Two representations share predicates (P key1 (.) = pushed key1 )

8. Our Representation (Assumption) Assumption: pair of shared predicates (P i, P’ i ) are given. –P i : CSpace  {0,1} and P’ i : State Space of PDDL  {0,1} In the example –P 1 =P key1 and P’ 1 = Pushed key1 C 1, C 2, C 3,…,C N-1, C N P 1, P 2, …, P M-1, P M S 1, S 2, S 3,…,S K-1, S K P’ 1, P’ 2, …, P’ M-1, P’ M CSpaceState Space of PDDL P key1 (c)=1 act key1 Pre:  pushed key1  on key1 Eff: pushed key1  on key1 PDDL P key1 (c)=0 CSpace Shared Space

9. Problem Definition Given –A CSpace* for a robot and objects –PDDL (Planning Domain Description Language) –Initial configuration (c init ) in CSpace –Initial/Goal conditions (q init /q goal ) in PDDL –Predicates † map between PDDL and CSpace Goal –Finding a path from the c init  q init to q goal The path is collision free in CSpace Each action in the path changes states according to PDDL description. *CSpace is the set of all the possible configurations. † A predicate is a function which maps a configuration to a discrete value

10. act key1 Pre:  P’ i  P’ j  pushed key1 Eff: P’ i  P’ j  pushed key1 Algorithm: Plan with Motion 1. Find a plan (sequence of actions) with the PDDL Using AI planner (e.g. FF, GraphPlan, SATPlan, …) 2. Find a path which passes through the PDDL actions in order act’ key1 act unkey1 act’ key2 … act unkey1 Pre: P i   P j Eff:  P i   P j

11. Experimental Setting in Simulation  Initial: no button is pushed  Goal: Call (A)dam, (B)en, and (C)olin  Constraints encoded in PDDL  Called_A: Push Call after Push A  Called_B: Push Call after Push B  Called_C: Push Call after Push C  Unlock: Push unlock after On key1 and On key2  Unlock causes  On key1 and  On key2  Lock: Push Call  Call causes Lock

12. Result Video

13. Summary of Technical Today SAT solvers technology – can be downloaded from the web. Many free implementations Planning technologies – same Combining planning and motion planning: Many times done in a hierarchy when the AI planning algorithm requests motions from the lower-level motion planner

14. Now… Review! Search Game playing (2-players, full information) FOL FOL Theorem Proving Propositional reasoning Planning

15. Questions Driven Appetizer question: how to prove What axioms are needed?