This paper describes a new model to range data registration algorithm, specifically designed for accuracy, speed, and robustness. Like many recent registration techniques, our Robust-Closest-Patch algorithm (RCP) iteratively matches model patches to data surfaces based on the current pose and then re-estimates pose based on these matches. RCP has several novel features: 1) on-line registration is driven by low curvature patches computed from the model off-line; 2) an approximate normal distance between a patch and a surface is used, avoiding the need to estimate local surface normal and curvature from noisy data; 3) pose is solved exactly by a linear system in six parameters, using a symmetric formulation of the rotation constraint; 4) robustness is ensured using an M-estimator that estimates both the rigid pose parameters and the error standard deviation. Results are shown using models and range data from turbine blade inspection.