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Complexity of STRIPS SHAKEY the Robot

Complexity of STRIPS SHAKEY the Robot. October 8, 2003. Backwards planning Why planning is hard SHAKEY the robot. Backwards Planning. Node = set of states h’(n, i) = MIN{ h(i,n’) | n’ instantiates n }. Sussman’s Anomaly. An example from the blocks world in which divide and conquer fails

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Complexity of STRIPS SHAKEY the Robot

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  1. Complexity of STRIPSSHAKEY the Robot October 8, 2003

  2. Backwards planning • Why planning is hard • 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 C B A B C goal Initial state On (A,B) On (B,C)

  5. Sussman’s anomaly • Assume we want to satisfy On (A,B) first A C B C A B Initial state • But now we cannot satisfy On (B,C) without undoing On (A,B) • Assume we want to satisfy On (B,C) first. B C C A B A Initial state 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. Started: January 1996 Launch: October 15th, 1998 Experiment: May 17-21 courtesy JPL

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