Models and methods for plan diagnosis Brian Sulcer 10 March 2009 - - PowerPoint PPT Presentation

Models and methods for plan diagnosis

Brian Sulcer 10 March 2009

Source

• Roos, N & Witteveen, C. (2007). Models and methods for plan diagnosis.

Autonomous Agents and Multi-Agent Systems 19(1):30-52

Model-based plan diagnosis

• plan performed by some agent(s) is considered as a system to be diagnosed
• plan execution can be monitored by making partial observations of plan

states

• compare observed states with predicted states based on normal plan

execution

• deviations between observed and predicted states explained by qualifying a

subset of plan states as behaving abnormally

Definitions

• state: assignment of values to variables
• partial state: state assignment in which some variables are unassigned
• partial state ordering: partial states can be ordered with respect to their

information content

• compatibility: states are compatible if they could characterize the same state
• f the world
• information fusion: compatible states can be combined to form a new partial

state

Actions, plan operators and plan steps

• actions: activity that changes some part of the world; considered the only

source of state changes

• plan operator: formal definition of action in a plan; maps partial state to partial

state

• plan step: specific instance of a plan operator applied to a specific partial

state

Plans and plan execution

• a plan consists of a set of operators, a set of steps and a partial order

between plan steps (execution order)

• steps take unit time to execute and are executed at the earliest possible time

step according to the execution order

• no plan step will affect inputs of any other step occurring at the same time
• there is no overlap in the variables affected by plan steps executing at the

same time

Qualifications, predictions

• health modes: set of possible modes of malfunction of a plan step, including

normal operation; includes predicted output for each mode

• qualified plan: plan plus set of step qualified as abnormal
• resulting state from execution of a step is undefined if
• the step is qualified as abnormal
• one or more of the inputs to the step are undefined

Observations and diagoses

• observation: pair of partial states resulting at times t and t’ such that t < t’
• diagnosis is performed by comparing this observation with the predicted

state at t’ following the state at t

• if the predicted state is not compatible with the observed state, then

execution has gone wrong

• plan diagnosis: a qualification such that the predicted state under the

qualification is compatible with the observed state

Preferred diagnoses

• subset minimal plan diagnosis: no smaller subsets can be used as diagnosis
• minimum plan diagnosis: assigns the the minimal number of abnormal steps
• prefer diagnoses with smaller number of undefined variables (precision)
• predictive power: the number of predicted variable values that are compatible

with the observed values

• the maximum predictive power of any diagnosis is the predictive power of the

null diagnosis (normal operation)

Preferred diagnoses

• maxi-diagnosis (maximally informative): diagnosis such that there exists no

diagnosis with greater predictive power

• mini-maxi diagnosis (minimal maximally informative): maxi-diagnosis such

that there exists no maxi-diagnosis that is a subset

• finding minimum diagnoses is NP-hard (reducible in polynomial time to the

minimum cover problem)

Generating maxi-diagnois

• create the disagreement set (the set of variables that are defined in both the

predicted and observed state, but with different values)

• working backward in time, identify the plan step that effects variables in the

disagreement set, add it to the diagnosis and remove those variables from the disagreement set

• the diagnosis now contains the latest steps that could have caused all the

disagreements

Distributed plans and mini-maxi diagnoses

• assume partitioning of the plan steps among agents
• agents label their own steps with preliminary labels, then propagate labels to
• ther agents and resolve final labelings

Label setting phase

• steps producing variables in the disagreement set are labeled faulty or maybe

faulty, depending on their dependence on prior step output

• steps not producing variables in the disagreement set are labeled healthy or

maybe healthy, depending on their dependence on prior step output

• steps are labeled ‘no’ if they are not enabled within the observation time

window

Label propagating phase

• agents retrieve preliminary labels from others and use them to resolve all

maybe labels

labels of predecessors current label definite label ∃f mf/mh no ∃no mf/mh no ∃mf mf/mh no ∀h mh h ∀h mf f

Conclusions

• the simple framework presented allows diagnosis using partial observations
• f plan execution
• minimum diagnosis difficult, but minimal maximum informative diagnosis can

be found efficiently

• mini-maxi diagnosis can be found efficiently in a distributed environment