6D Pose Uncertainty in Robotic Perception

Robotic perception is fundamental to important application areas. In the Joint Research Project DESIRE, we develop a robotic perception system with the aim of perceiving and modeling an unprepared kitchen scenario with many objects. It relies on the fusion of information from weak features from heterogenous sensors in order to classify and localize objects. This requires the representation of wide spread probability distributions of the 6D pose. In this paper we present a framework for probabilistic modeling of 6D poses that represents a large class of probability distributions and provides among others the operations of fusion of estimates and uncertain propagation of estimates. The orientation part of a pose is described by a unit quaternion. The translation part is described either by a 3D vector (when we define the probability density function) or by a purely imaginary quaternion (which leads to a prepresentation of a transform by a dual quaternion). A basic probability density function over the poses is defined by a tangent point on the 3D sphere (representing unit quaternions), and a 6D Gaussian distribution over the product of the tangent space of the sphere and of the space of translations. The projection of this Gaussian induces a distribution over 6D poses. One such base element is called a Projected Gaussian. The set of Mixtures of Projected Gaussians can approximate the probability density functions that arise in our application, is closed under the operations mentioned above and allows for an efficient implementation.