Learning from demonstration allows to encode task constraints from observing the motion executed by a human teacher. We present a Gaussian-process-based learning from demonstration (LfD) approach that allows robots to learn manipulation skills from demonstrations of a human teacher. By exploiting the potential that Gaussian process (GP) models offer, we unify in a single, entirely GP-based framework, the main features required for a state-of-the-art LfD approach. We address how GP can be used to effectively learn a policy from trajectories in task space. To achieve an effective generalization across demonstrations, we propose the novel Task Completion Index (TCI) for temporal alignment of task trajectories. Also, our probabilistic GP-based representation allows encoding variability throughout the different phases of the task. Finally, we present a method to efficiently adapt the policy to fulfill new requirements and modulate the robot behavior as a function of task variability. This approach has been successfully tested in a real-world application, namely teaching a TIAGo robot to open different types of doors.

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