AbstractIn this paper we investigate the problem of finding a suitable roto-translation achieving the optimal matching between two uncertain three-dimensional vector sets. State-of-the-art approaches for vector registration are based on strict assumptions on the covariance matrices describing the uncertainty on the vectors, hence they can be too conservative or inaccurate when the actual uncertainty differs from the employed model. After discussing the problem we propose two iterative solutions for matching the 3D vectors, showing that a suitable uncertainty model allows reducing the estimation error while preserving the real-time nature of the computation. We further derive the covariance matrices for such estimates, evaluating their consistency through extensive numerical experiments. The results appear particularly suitable for robotic applications, since the vector sets constitute a natural representation of three-dimensional perception of a robot, interacting with complex non-planar environments.