Adapting Ocean Surveys to the Observed Fields Characteristics Maria-João Rendas I3S, CNRS-UNSA

Outline The goals of Sumare Using prior information Exploiting reactive behaviors Conclusions and perspectives

The goals of SUMARE “design strategies for environmental monitoring using autonomous sensors” Traditional means Oceanographic ships; networks of buoys; divers A priori determination of the surveyed region and of the spatial sampling rate Difficult to focus on features of interest. Limited operating conditions (shallow waters, under ice,....) Autonomous sensors Sensors carried by mobile robots (cheaper, easier to operate) Sensor trajectory can be determined on-line during survey Ability to concentrate (track) features of interest Wide range of operating scenarios test their added-value in two applications: sand bank and maerl mapping

Two approaches Exploiting prior knowledge give to the sensor a mathematical (statistical) model of the possible appearances of the field use data together with the prior model to extrapolate the data in the observed region over an extended domain Exploiting reactive behaviour track interesting features (contours, canyons, iso-depth lines,...) adapt the spatial sampling rate identify the regions which are more informative with respect to the end- user’s goals. use environment’s features to navigate, decreasing dependability on artificial references or surfacing for GPS fixes

Goal: efficiently use prior knowledge about the observed field (which constrains the possible set of actually occuring field patterns) Efficiency gain comes from being able to extrapolate across spatial regions, and to direct the sensor to the most informative regions ? Using prior knowledge

Case studies: 1.current fields (mouth of the Rhone river) 2.sand banks (Kwintebank, Belgium)

Current fields Problem: map a natural field (currents in the mouth of the river Rhone) Framework: Bayesian (use prior knowledge to characterize the set of possible observed maps) Prior knowledge: predictions made using mathematical models (MUMM) (Navier-Stokes equation)

41 maps (15 x 22 grid) provided by MUMM (Brussels, Belgium) 10 maps reserved for testing A PRIORI KNOWLEDGE

KNOWLEDGE REPRESENTATION Learn from data Geometric model c = V  + U  V T U=0 Statistical model  : N (  , diag( i ))  : N (0, L+1 I)  c: N (V   V T, V   V  +   )

Allows extrapolation of local observations: EXTRAPOLATION + Maximum a posteriori estimate

Uncertainty of the resulting field can be determined showing how matrix S (the choice of observation points) impacts performance

INFORMATION GAIN Points can be chosen (a priori) to maximise overall expected information gain (minimize the covariance of the a posteriori estimate)

If only a specific feature is of interest (e.g. a given contour level) its uncertainty can be computed, and the vehicle guided in order to optimise its observation performance INFORMATION GUIDANCE Example map the line of constant current intensity ||c||=C te

Local minimax criterion: optimize the accuracy of the worst estimated neighbour contour point d Using a 1 st order Taylor expansion

Adaptive determination of next observation point  - robot position  - best identified point true contour estimated contour ( using current values observed along trajectory and prior statistical model) trajectory

Sand bank profiles Problem: observation of the variation of sand bank profiles (Kwintebank, Belgium) Prior knowledge: observations (oceanographic surveys) provided by MUMM.

Reconstruction Low-dimensional statistical model learned from data set using a wavelet representation of the profiles

Approach: 1.build (for each profile) a statistical model of the variations of the profile with respect to the “average profile” 2.use this model to extrapolate across distinct regions of the profile, and to identify the most informative sections. Problem: Which interval of length I provides, according to the identified model, the largest information with respect to the total volume? What is the uncertainty of the volume estimate given those observations ? Can we repeat this step iteratively, identifying the next better region on the basis of the already observed regions ?

Observation strategies Design of observation strategies is meaningless for one- dimensional observation spaces (lines). Full 2½D statistical model of the Kwintebank will be learned, and adaptive observation algorithms will be designed on the basis of the learned statistical model. For the sand bank, since it is a dynamical phenomenon, it makes more sense to learn a model of the variations than of the shape of the bank itself.

Directly acquire distinctive features of the environment Exploiting reactive behavior

Classification of sea-bottom Allows on-line guidance based on the sea- bed occupancy. Requires training data to recognize the type of bottom Provides direct geometric features that allow the navigation of the robot with respect to natural features