Invariant Smoothing on Lie Groups

Paul Chauchat (1, 2) , Axel Barrau (3) , Silvere Bonnabel (1)

1 CAOR - Centre de Robotique
2 SAFRAN Group
3 SAFRAN Electronics & Defense

In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the proposed algorithm is based on a maximum a posteriori estimator, determined by optimization. But owing to the specific properties of the considered class of problems, the involved linearizations are proved to have a form of independence with respect to the current estimates, leveraged to avoid (partially or sometimes totally) the need to relinearize. The method is validated on a robot localization example, both in simulations and on real experimental data.

Mots clés: Smoothing Algorithm; Smoothing Methods; Geometric Methods

Domaines: Robotique [cs.RO]; Géométrie algorithmique [cs.CG]; Optimisation et contrôle [math.OC]

Paul Chauchat, Axel Barrau, Silvere Bonnabel. Invariant Smoothing on Lie Groups. IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2018, Oct 2018, Madrid, Spain. ⟨hal-01725847⟩