Uncertain geometry in robotics

Robots must operate in an environment which is inherently uncertain. This uncertainty is important in areas such as modeling, planning and the motion of manipulators and objects; areas where geometric analysis also plays an important part. To operate efficiently, a robot system must be able to represent, account for, and reason about the effects of uncertainty in these geometries in a consistent manner. We maintain that uncertainty should be represented as an intrinsic part of all geometric descriptions. We develop a description of uncertain geometric features as families of parameterized functions together with a distribution function defined on the associated parameter vector. We consider uncertain points, curves and surfaces, and show how they can be manipulated and transformed between coordinate frames in an efficient and consistent manner. The effectiveness of these techniques is demonstrated by application to the problem of developing maximal information sensing strategies.