Planning under Uncertainty in Dynamic Domains - Carnegie Mellon ...

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3.12 Reachability graph of literal states in the planning problem from theinitial state, considering only operators. The initial state is shown inthe top left-hand corner, and the four goal states are shown in bold inthe bottom left-hand corner. Actions corresponding to the plan thatis produced for this problem are shown in bold. : : : : : : : : : : : : 393.13 Part of the MDP that would correspond to the example problem if ithad no exogenous events, restricted to the states in which (oil-in-tanker)is true. All transitions and intermediate states correspond to a move-bargeaction. The transitions that correspond to initiating an action are labelledwith their probabilities. Intermediate transitions are not labelled. 403.14 The full set of states for the MDP for the example problem. Thetransitions due to exogenous events are shown with dotted lines, connectingthe two planes into which the states are divided. In the upperplane the state variable (fair-weather) is true and in the lower plane(poor-weather) is true. : : : : : : : : : : : : : : : : : : : : : : : : : 414.1 Weaver's main loop has three modules: a conditional planner, a planevaluator and a plan critic. : : : : : : : : : : : : : : : : : : : : : : : : 434.2 The Pump-Oil and Move-Barge operators are modied respectively torequire and conditionally delete (operational ). The newoperator Make-Ready can add barge-ready. : : : : : : : : : : : : : : 454.3 Aversion of the operator Move-Barge with two possible outcomes. : : 494.4 An initial tail plan to solve the example problem, showing two alternativecourses of action. Step s3 has two dierent possible outcomes,labelled and . The steps along the top row are restricted to outcome of s3, and use barge1 in the situation when it is operational.The steps along the bottom row are restricted to outcome of s3 anduse barge2. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 494.5 A more developed version of the candidate plan. One step has beenmoved to the head plan and now determines two possible current states,given context labels and . : : : : : : : : : : : : : : : : : : : : : : 504.6 A reachability graph of states in the planning problem correspondingto the conditional plan to transfer the oil with one of two barges. Goalstates are marked with a thick border, and the probability of arrivingat each state is shown above it. Time increases from left to right, andthe actions taken are shown with their intervals below the nodes. : : : 524.7 A small example Bayesian belief network. : : : : : : : : : : : : : : : : 534.8 The two-stage algorithm to construct a belief net to evaluate a plan.In the rst stage, nodes are added to the belief net to represent actionsand their preconditions and eects. In the second stage, persistenceassumptions are replaced with nodes representing exogenous eventsand their preconditions and eects when appropriate. : : : : : : : : : 55xii
4.9 Belief nets representing the rst plan created by the conditional plannerfor the example problem, before and after event nodes are added tojustify the persistence of the (weather) variable. In the rst graph, thedotted lines show the unexplored persistence intervals. In the secondgraph, gray nodes represent possible occurrences of external eventsduring one interval. No exogenous events aect the other intervals. : 564.10 The belief net for the rst conditional branch of this section's exampleplan, with marginal probabilities shown. : : : : : : : : : : : : : : : : 584.11 The two nets constructed for the two conditional branches of this section'sexample plan. : : : : : : : : : : : : : : : : : : : : : : : : : : : : 594.12 A version of the Move-Barge operator that depends on the literal(barge-ready ). : : : : : : : : : : : : : : : : : : : : : : : : : : 634.13 Operators in the synthetic domain to illustrate the utility of the constraintson the planner from the critic. The initial plan found by theconditional planner will have a success probability of1=2 n . Either oneconditional branch or one protection step can increase the probabilityto 1. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 654.14 The nondeterminism from the operators in the previous domain is replacedwith a single exogenous event. The operators Final, Alt-Finaland Protect are unchanged and so are the solutions. : : : : : : : : : 654.15 Operators in the synthetic domain to illustrate the utility of the constraintson the evaluator and critic from the planner. : : : : : : : : : 664.16 A modied Pump-Oil operator and a new Deploy-Pump operator thatmake a conditional plan necessary to achieve a probability of successgreater than 0.5 in the example problem. : : : : : : : : : : : : : : : : 685.1 Belief nets from Chapter 4, in which shaded nodes represent specicoccurrences of external events. : : : : : : : : : : : : : : : : : : : : : : 705.2 A belief net representing the same plan but with Markov chains usedto compute changes in the weather over the required time intervalsrather than a series of event nodes. : : : : : : : : : : : : : : : : : : : 715.3 The nodes governing weather from the plan's belief net follow theMarkov chain on the right. : : : : : : : : : : : : : : : : : : : : : : : : 725.4 The event Oil-Spills aects the location of the oil and is partlydetermined by the weather. : : : : : : : : : : : : : : : : : : : : : : : 725.5 The event graph for the example domain, with boxes for eventschemasand ovals for literal schemas. : : : : : : : : : : : : : : : : : : : : : : : 735.6 The Markov model built to model the evolution of the state variable(oil), instantiated by the literal (oil-in-tanker west-coast). : : 745.7 The belief net created to evaluate the rst branch of the example planwith exogenous events aecting both the weather and the oil modelledwith a Markov chain. : : : : : : : : : : : : : : : : : : : : : : : : : : : 77xiii
Page 1 and 2: Planning under Uncertainty in Dynam
Page 3: AbstractPlanning, the process of nd
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Page 20 and 21: 2 Chapter 1. Introductionif the pri
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Page 24 and 25: 6 Chapter 1. Introductionnet nodes
Page 26 and 27: 8 Chapter 1. Introduction
Page 28 and 29: 10 Chapter 2. Related workIn additi
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158 BIBLIOGRAPHY[Blythe & Veloso 19
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164 BIBLIOGRAPHY[Schoppers 1989b] S
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