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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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Motivational Applications

Navigation/Localization systemsi.e. GPS, odometry, SLAM

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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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Residuals Used

1.Simple approach

2.EKF using the augmented state matrix model

Aug states

EKF

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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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Behavior – Faults

• Succesfull detection in many cases

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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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¿ Questions ?

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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

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Detection - rotation

• and are affect with a transient behaviorInput faults

• Effects in are greater than in because the estimate has a much smaller variance than

is a directly measured quantity is a direvative estimate of the pose

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