Not yet reviewed by Pith; the record is open.

Programming by demonstration has recently gained much attention due to its user-friendly and natural way to transfer human skills to robots. In order to facilitate the learning of multiple demonstrations and meanwhile generalize to new situations, a task-parameterized Gaussian mixture model (TP-GMM) has been recently developed. This model has achieved reliable performance in areas such as human-robot collaboration and dual-arm manipulation. However, the crucial task frames and associated parameters in this learning framework are often set by the human teacher, which renders three problems that have not been addressed yet: (i) task frames are treated equally, without considering their individual importance, (ii) task parameters are defined without taking into account additional task constraints, such as robot joint limits and motion smoothness, and (iii) a fixed number of task frames are pre-defined regardless of whether some of them may be redundant or even irrelevant for the task at hand. In this paper, we generalize the task-parameterized learning by addressing the aforementioned problems. Moreover, we provide a novel learning perspective which allows the robot to refine and adapt previously learned skills in a low dimensional space. Several examples are studied in both simulated and real robotic systems, showing the applicability of our approach.