1 observers data only fault detection bo wahlberg automatic control lab & access kth, sweden...
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Observers Data Only Fault Detection
Bo WahlbergAutomatic Control Lab & ACCESSKTH, SWEDEN
André C. BittencourtDepartment of Automatic Control UFSC, Brazil &
Linköping University, SWEDEN
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Residual based fault detectionDifference between a sensor output and a corresponding
model-based prediction
Usual caseRaw measurements available
Integrated sensorsNo access to the raw measurements
Problem Description
SensorMB filter
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Integrated
Sensor
???-
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Residual Generation using Observers Estimates ONLY
Simplification: The sensors are integrated with standard observers/Kalman filters
Faults are now mixed through the observer
The sensor structures, i.e. the observer gains, will affect the fault influence to the estimates
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Different Approaches
1. Try to reconstruct the output as
- Sensitive to errors- Requires a reliable observer model- Redundant solutions
2. Assume there are at least 2 observers (sensors)
Model is not used
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3. Augment sensor states
Use the augmented state model to design an overall observer to generate the residuals
QuestionsAre faults still observable?What if is unknown?How to compare the performance?
Idea!
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Fault Observability
• Suppose and augment the fault to the states (e.g. Törnqvist, 2006)
• Analyze the observability of the augmented system
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Fault Observability is OK, IF
• Original pair is observable• is full column rank
Same conditions as if the raw measurements were available (we can access the same information)
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The internal sensor structure
is abstracted, with some simplifications, to
The simplified model is then used to generate residuals
, the artificial measurement noise can be used to adjust for jitter, lost samples, etc
Unknown Sensor Structure
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Performance comparison
Analyze the residual-fault transfer functions (fault sensitivity) for the different methods
Some indications of improvements using the overall observer i.e. Steady state analyzes
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Robot Example – where am I?
Localization is crucial in autonomous systems
Typical situations• Wheel slippages• Skidding• Wall grasping• Pushed away• Collision
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Two Localization Providers
Odometry
• Integration of velocity meas• Based on the linear
displacement caused by wheel rotations
• Reliability < 15m (acc errors)
Laser Scan Matching
• Integration of relative displacement measurements
• Hough transform (heading) + Iterative Closest Point (ICP)
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Behavior – No faults
• Odometry bias quickly (badly calibrated tires)Will increase the amount of false alarms
• Model disturbances affects considerably more
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Preliminary Results
Basic idea: A. Extended system (system + sensor).B. Design an overall observer to generate residualsC. Do standard fault detection
• Fault observability conditions have been derived• Evaluation on a mobile robot – real data
Remaining open questions:More thorough performance analysis neededUse of more complex sensor modelsMethods to support observer design to residual gen
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Unknown Sensor Structure
Two approximations
1.
2.
Then, use the simplified model
to tune, for example, a Kalman filter
, the artificial measurement noise can be used to adjust for jitter, lost samples, etc
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Scan matching
• Estimate the transform relating two scans
• is the hardest to estimate
• is estimated through spectrum correlation in the Hough domain [Censi05]
Rotations are phase shifts in the HD
• ICP solves the translation estimation
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Robot Models
• Odometry model based on the relation between wheel rotation to linear displacement
Model valid for differential drive robot
• Simple kinematics modelRobot as a rigid-bodyMoving in a plane