Autonomous range acquisition for 3D modeling requires reliable range registration, for both the precise localization of the sensor and combining the data from multiple scans for view-planning computation. We introduce and present a novel approach to improve the reliability and robustness of the ICP (Iterative Closest Point) 3D shape registration algorithm by smoothing the shape's surface into multiple resolutions. These smoothed surfaces are used in place of the original surface in a coarse-to-fine manner during registration, which allows the algorithm to avoid being trapped at local minima close to the global optimal solution. We used the technique of multiresolution anaysis to create the smooted surfaces efficiently. Besides being more robust, convergence is generally much faster, especially when combined with the point-to-plane error metric of Chen and Medioni. Since the point-to-plane error metric has no closed-form solution, solving it can be slow. We introduce a variant of the ICP algorithm that has convergence rate close to it but still uses the closed-form solution techniques (SVD or unit quaternion methods) of the original ICP algorithm.