Academic Research interests
• Probabilistic robotics
• Systems and control
• Optimization on manifolds
• Navigation and object tracking
Industrial applications :
• Crane control with the world leader MANITOWOC (POTAIN). See this picture
of me experimenting the real-time controller on a 30 meters high crane. It has also been successfully tested on the recent crane Hup (see picture below, courtesy of Manitowoc).
• Guidance and navigation with SAGEM, the No. 1 company in Europe and No. 3 worldwide (in terms of revenue) for inertial navigation systems (INS). Our algorithm is embedded in the new drone Patroller (see picture below, courtesy of Safran Electronics & Defense).
• Radar tracking with THALES.
• High pressure polyethylene reactor of TOTAL PETROCHEMICALS. Carling- France.
Invariant Extended Kalman Filtering
For linear systems, the well-known Kalman filter has a well-characterized behaviour that is independent of the underlying system's trajectory in the following sense: the covariance matrix of the estimate, and the Kalman gain, are identical for all trajectories. On the other hand, for non-linear systems, due to linearizations around the estimated trajectory, the extended Kalman filter (EKF) covariance matrix, gain, and more generally behaviour, do depend on the system's estimated trajectory, leading to possible divergence when the estimated trajectory is not close to the true one.
For non-linear systems possessing symmetries, the invariant extended Kalman filter (IEKF) is an emerging methodology aimed at modifying the conventional EKF so as to account for those symmetries. The resulting filter's behaviour is less (and sometimes not) dependent on the system's trajectory, leading to improved stability and robustness properties.
It has been successfully implemented by Safran Electronics and Defense (formerly Sagem) for an inertial navigation application where it has lead to substantial improvements over the existing industrial methods. See the patent "Alignment method for an inertial unit. A. Barrau, S. Bonnabel. SAGEM/ARMINES. 2013. FR3013830. WO/2015/075248" for experimental results. This patent was awarded a Sagem Innovation Award, as the most innovative patent filed by the company in 2015.
To study IEKF theory, a good starting point is this article
Optimization on manifolds
The geometry in algorithms can also stem from probabilistic considerations (information geometry), or from the intrinsic geometry of the problem. Indeed, in optimization and machine learning, some constraints on the search space (orthogonality constraints, low rank etc.) make the search space a submanifold. This has lead to the realm of optimization on manifolds. The search space can generally be endowed with several geometries, but here again, the relevant geometries are often encoded in the invariances of the problem (see this nice presentation
of Bamdev Mishra).
I have also obtained some convergence results of stochastic gradient methods when the search space is a Riemannian manifold in this paper
Flatness theory allows to move the load from a point A to a point B easily in open loop (the only sensor is the length of the cable, available in any crane). The problem is that crane operators use a joystick to indicate a desired velocity of the load, not a point "B" for the load to meet. This results in
rapidly changing required velocities, and the corresponding load trajectory lacks the smoothness necessary to apply flatness (the desired velocities must be differentiated several times). The required velocities must thus be smoothened, prior to being differentiated, in a way such that the velocity and acceleration constraints of the various motors are met at all times.
But at the same time, the smoothened desired velocities must not be "too" smooth otherwise the crane operator will consider the control system as not reactive and will not accept to use it. This tradeoff (i.e., smooth but still reactive) is not easily achieved. Especially considering that optimal control techniques are too demanding computationally for the crane controller.
Experiments have been conducted in the field with MANITOWOC (POTAIN). It turns out the control system allows unexperienced operator to safely move the load, and it also allows more experienced driver to move the load as fast as before, but with less efforts.