A Directional Approach to Uncertainty Representation for Robotics

Robotic Perception tasks typically involve processing uncertain quantities that are defined on inherently nonlinear domains. The most important among these domains involve the 2d and 3d manifolds of orientations and poses (which combines position and orientation). Typical approaches of representing uncertainty on these domains assume small uncertainties allowing for making use of local linearity for defining distributions on the tangent space. This talk will focus on using distributions from directional statics, which are inherently defined on this manifold starting off with the Bingham distribution and its role in representing uncertain unit quaternions. The discussion will involve the challenges in designing state estimators based on directional distributions by covering orientational counterparts to the Kalman Filter and the Unscented Kalman Filter. We will also give an overview of some interesting problems such as efficient computation of the normalizing constants and representing a broader variety of uncertain directional quantities.