1. Complexity of STRIPS SHAKEY the Robot October 8, 2003

2. 1.Backwards planning 2.Why planning is hard 3.SHAKEY the robot

3. Backwards Planning Node = set of states h’(n, i) = MIN{ h(i,n’) | n’ instantiates n }

4. Sussman’s Anomaly An example from the blocks world in which divide and conquer fails Interacting goals A B C goal A B C Initial state On (A,B) On (B,C)

5. Sussman’s anomaly 1.Assume we want to satisfy On (A,B) first A B C Initial state A B C A B C B C A But now we cannot satisfy On (B,C) without undoing On (A,B) 2.Assume we want to satisfy On (B,C) first. But now we cannot satisfy On(A, B) without undoing On(B, C)

6. Planning is PSPACE-Complete PSPACE = can be computed in polynomial space PSPACE-Complete = as hard as anything in PSPACE Proof: Reduce ANY (space bounded) Turing machine to a STRIPS planning problem

7. Proof Propositions: in(i,x)symbol x in tape position i at(i,q)head is at i in state q trans(q,x,y,q’)transition table Actions: action do(i,q,x,y,q’) precondition: in(i,x), at(i,q), trans(q,x,y,q’) effect: at(i+1,q’), in(i,y),  in(i,x),  at(i,q)

8. Is Planning Possible? SHAKEY the robot –Brains: STRIPS style planner –Stanford Research Institute, 1969 –Funded by DARPA (as was the Internet!) VIDEO

9. What Else Did Shakey Have? Sensing Error Recover –Regress goal backwards to latest state that matches “real world” Learning –“Macro operators” – MACROPS –Potential pitfall?

10. courtesy JPL Started: January 1996 Launch: October 15th, 1998 Experiment: May 17-21