Learning motions from human demonstrations provides an intuitive way for non-expert users to teach tasks to robots. In particular, intelligent robotic co-workers should not only mimic human demonstrations but should also be able to adapt them to varying application scenarios. As such, robots must have the ability to generalize motions to different workspaces, e.g. to avoid obstacles not present during original demonstrations. Towards this goal our work proposes a unified method to (1) generalize robot motions to different workspaces, using a novel formulation of trajectory optimization that explicitly incorporates human demonstrations, and (2) to locally adapt and reuse the optimized solution in the form of a distribution of trajectories. This optimized distribution can be used, online, to quickly satisfy via-points and goals of a specific task. We validate the method using a 7 degrees of freedom (DoF) lightweight arm that grasps and places a ball into different boxes while avoiding obstacles that were not present during the original human demonstrations.

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