Séminaire de mathématiques


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

Silvère BONNABEL, Professeur en Mathématiques


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 abandoned, owing to inconsistencies, and then replaced by particle filters and optimization based smoothing algorithms. In this talk, we will show that a simple modification to the EKF, namely a change of estimation error rooted in differential geometric motivations and Lie group theory, allows to theoretically solve those inconsistency issues. In terms of performance, the resulting novel EKF compares with state-of-the-art SLAM techniques. To conclude the talk, we will briefly discuss two points. First the application of the technique to derive a novel geometric MCSKF for visual inertial odometry (VIO or VINS). Then, the application of our geometric method to smoothing algorithms, where we show the use of an alternative geometric estimation error may alleviate the need for multiple relinearizations. Each of the two latter applications corresponds to a paper presented at IROS 2018.