Estimating a Mean-Path from a set of 2-D curves

To perform many common industrial robotic tasks, e.g. deburring a work-piece, in small and medium size companies where a model of the work-piece may not be available, building a geometrical model of how to perform the task from a data set of human demonstrations is highly demanded. In many cases, however, the human demonstrations may be sub-optimal and noisy solutions to the problem of performing a task. For example, an expert may not completely remove the burrs that result in deburring residuals on the work-piece. Hence, we present an iterative algorithm to estimate a noise-free geometrical model of a work-piece from a given dataset of profiles with deburring residuals. In a case study, we compare the profiles obtained with the proposed method, nonlinear principal component analysis and Gaussian mixture model/Gaussian mixture regression. The comparison illustrates the effectiveness of the proposed method, in terms of accuracy, to compute a noise-free profile model of a task.