1 Observers Data Only Fault Detection Bo Wahlberg Automatic Control Lab & ACCESS KTH, SWEDEN André C. Bittencourt Department of Automatic Control UFSC, Brazil & Linköping University, SWEDEN

2 Residual based fault detection Difference between a sensor output and a corresponding model-based prediction Usual case Raw measurements available Integrated sensors No access to the raw measurements Problem Description Sensor MB filter - Integrated Sensor ??? -

3 Motivational Applications Navigation/Localization systems i.e. GPS, odometry, SLAM

4 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

5 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

6 3. Augment sensor states Use the augmented state model to design an overall observer to generate the residuals Questions Are faults still observable? What if is unknown? How to compare the performance? Idea!

7 Fault Observability Suppose and augment the fault to the states (e.g. Törnqvist, 2006) Analyze the observability of the augmented system

8 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)

9 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

10 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

11 Robot Example – where am I? Localization is crucial in autonomous systems Typical situations Wheel slippages Skidding Wall grasping Pushed away Collision

12 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)

13 Known Challenges Odometry Model simplifications and assumptions Driving on uneven floor Wheel slippage External forces Scan Matching Computational burden Changing environments (people passing by) Environment informativiness (the corridor problem)

14 Residuals Used 1.Simple approach 2.EKF using the augmented state matrix model Aug states EKF

15 Distance Measure and Test Mahalanobis distance measure Robustification with CUSUM

16 Behavior – No faults Odometry bias quickly (badly calibrated tires) Will increase the amount of false alarms Model disturbances affects considerably more

17 Behavior – Faults Succesfull detection in many cases t+1 t+2 t+3 t+4 t t+1 t+2 t+3 t+4 t

18 Preliminary Results Basic idea: A.Extended system (system + sensor). B.Design an overall observer to generate residuals C.Do standard fault detection Fault observability conditions have been derived Evaluation on a mobile robot – real data Remaining open questions: More thorough performance analysis needed Use of more complex sensor models Methods to support observer design to residual gen

19 ¿ Questions ?

20 Unknown Sensor Structure Two approximations 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

21 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

22 Robot Models Odometry model based on the relation between wheel rotation to linear displacement Model valid for differential drive robot Simple kinematics model Robot as a rigid-body Moving in a plane

23 Detection - rotation and are affect with a transient behavior Input 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 t+1 t+2 t+3 t+4 t t+1 t+2 t+3 t+4 t