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Fixing the consistency issues of the extended Kalman filter for simultaneous localization and mapping (SLAM)

SLAM is a problem of robotics that has been extensively studied over the past two decades. The ability of a robot to build a map of an unknown environment and localize itself in this map is indeed the key to true autonomy. Mathematically, the problem is formalized as a non-linear Bayesian estimation/filtering problem (estimate robot’s trajectory and map given all the observations). The problem was historically tackled using the conventional extended Kalman filter (EKF), which is the state of the art for navigation and guidance. Yet, it was soon abandoned, due to inconsistencies, and then replaced by particle filters and optimization based SLAM algorithms. The catch is as follows indeed : as all observations are made by sensors attached to the robot, and are thus relative to the robot’s frame, the origin and orientation of the global frame are unobservable (i.e. the robot can not acquire information through measurements on, e.g., where the north is). Yet, the EKF tends to « think » it can gain information on those unobservable quantities, due to the linear approximations it makes use of. In turn, this leads to degraded performance. In this talk, we will show that a simple modification to the EKF, rooted in differential geometric motivations, allows to theoretically solve those inconsistency issues. In terms of performance, the resulting novel EKF compares favorably with state of the art sophisticated SLAM techniques, albeit way simpler.

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46