This paper describes the trajectory learning component of a programming by demonstration (PbD) system for manipulation tasks. In case of multiple user demonstrations, the proposed approach clusters a set of hand trajectories and recovers smooth robot trajectories overcoming sensor noise and human motion inconsistency problems. More specifically, we integrate a geometric approach for trajectory clustering with a stochastic procedure for trajectory evaluation based on hidden Markov models. Furthermore, we propose a method for human hand trajectory reconstruction with NURBS curves by means of a best-fit data smoothing algorithm. Some experiments show the viability and effectiveness of the approach.
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