  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.
