Large Scale Navigation Based on Perception Maria Joao Rendas I3S, CNRS-UNSA

Problem Control the motion of a robot operating in an open region without a priori (or little) knowledge about the region –no need for pre-mission preparation with no global positioning –no returns to surface (stealth...) without getting lost –guaranteeing the return to a pre-specified (homing) region

Approach Map along: identify a set of relevant features and regularly reset the positioing error by returning to them Exploit if the nominal plan takes the robot along uninformative (homogenous) regions, exploit neighbouring regions searching for more features & Quit if need refuse to execute a mission if it may put the robot security at risk

Underwater environment (good) features are rare (widely spaced apart) unstable similar to each other robot’s sensors are myopic no continuous perceptual guidance, high ambiguity situations

Previous work I3S Architecture based on the definition of (Semi) Markov Decision process (corresponding to a partition of the configuration state of the robot determined by the discrete environment features) extensive use of statistical signal processing and of the theory of (sample path properties) of Markov processes to characterise the transition density of the chain guidance conditioned by the current probability of getting lost (absorbing state of the Markov chain) (mostly with terrestrial robots)

Illustration

Underlying Tools uncertainty characterisation –present and future states –probability of absorption in the lost state –ambiguity mapping –update a manageable representation of the features (contours) exploitation / observation strategies & behaviours –search for and acquisition of features

Major limitations Strong Markov property: requires full identifiability of the reached object –architecture is based on an upated state estimate, with an associated uncertainty around it : contradicts the ambiguous nature of the environment and the possibility of large positioning errors. Assumption of existence of discrete bounded features –natural environments are mostly of a continuous nature: more often continuous than discontinuous –features can be unbound: when to stop observing? How much is enough?

Work in progress Makes full use of a Bayesian approach: Ambiguity: propagate an higher-order approximation to the pdf of the robot state Environment representation: instead of the location of individual features, learn a model of their spatial distribution and shape attributes (presentation by Stefan Rolfes) Guidance/exploration : explicitly incorporate the learned model of the environment in the cost functional of the state controller.

Ambiguity problem In large scale environments (& with myopic sensors...) each single feature may be (locally) indistinguishable from another one Common control architecture are based on a single state estimate, obtained with Extended Kalman filters: wrong associations of measures to features lead to divergence of the filter and may lead to robot loss. –approximate the pdf of the state configuration (given the observations) by a mixture of Gauss kernels efficient implementation (bank of dynamically updated EKFs) convenient representation of truly ambiguous solutions (multi-modal pdfs) –use it to characterise a (partially observable) Markov chain, which is the adequate tool to chose optimal disambiguating manoeuvers.

Exploration / observation Use learned (spatial) statistical model to drive the robot to the most informative regions of the workspace (those that are, with high probability, more relevant with respect to its goals) –Case study: acquisition of current maps (in cooperation with MUMM)

Problem: observation of natural (oceanic) parameters in extended areas Common survey strategy ? Guidance by prior information

Goal: efficiently use statistical 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 ?

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

Geometric model Use singular value decomposition M=[col(m 1 ) col(m 2 ) … col(m 41 ) ] In our case we retain L=28 singular vectors of M c = V  + U  V T U=0 Statistical model  : N(  , diag( i ))  : N(0, L+1 I) c: N(V   V T, V   V  +   )

Such a model allows extrapolation of local observations: + Maximum a posteriori estimate z = S c + n S (the observation points) can be chosen to optimise performance

If only a specific feature is of interest its uncertainty can be computed, and the vehicle guided in order to optimise its observation accuracy INFORMATION GUIDANCE perception driven Example map the line of constant current intensity ||c||=C te

Local minimax criterion: optimize the accuracy of the worst estimated neighboor contour point

Approach combining on-line sensor guidance with prior statistical models providing the ability to extrapolate local observations to unobserved regions and the determination of the points more informative with respect to the features of interest. Future work drop constraint on observed points (presently in the same grid as the learning maps) consider the effect of positioning errors consider other types of fields (random closed set models)