Rigid motion estimation using mixtures of projected Gaussians

Modeling the position and orientation in three-dimensional space is important in many applications. In robotics, the position and orientation of objects as well as the rigid motions of robots are derived from sensor data that are uncertain. The uncertainties of these sensor data result in position and orientation uncertainties that can be very widely spread or have several peaks. In this paper we describe a class of probability density functions (pdf) on the group of rigid motions that allows for modeling wide-spread and multi-modal pdf and offers most of the operations that are available for the mixtures of Gaussians on Euclidean space. The use of this class of pdf is illustrated with an example from robotic perception.