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The main objective of this paper is to develop an efficient method for learning and reproduction of complex trajectories for robot programming by demonstration. Encoding of the demonstrated trajectories is performed with hidden Markov model, and generation of a generalized trajectory is achieved by using the concept of key points. Identification of the key points is based on significant changes in position and velocity in the demonstrated trajectories. The resulting sequences of trajectory key points are temporally aligned using the multidimensional dynamic time warping algorithm, and a generalized trajectory is obtained by smoothing spline interpolation of the clustered key points. The principal advantage of our proposed approach is utilization of the trajectory key points from all demonstrations for generation of a generalized trajectory. In addition, variability of the key points' clusters across the demonstrated set is employed for assigning weighting coefficients, resulting in a generalization procedure which accounts for the relevance of reproduction of different parts of the trajectories. The approach is verified experimentally for trajectories with two different levels of complexity.