Curved surface contact patches with quantified uncertainty

We introduce a set of 10 bounded curved-surface patch types suitable for modeling local contact regions both in the environment and on a robot. We present minimal geometric parameterizations using the exponential map for spatial pose both in the usual 6DoF case and also for patches with revolute symmetry that have only 5DoF. We then give an algorithm to fit any patch type to point samples of a surface, with quantified uncertainty both in the input points (including nonuniform variance, common in data from range sensors) and in the output patch. Finally, we outline how such patches can be composed into a spatial patch map of the available contact surfaces both on and around a robot.