Learning from Sparse Demonstrations

This paper proposes an approach which enables a robot to learn an objective function from sparse demonstrations of an expert. The demonstrations are given by a small number of sparse waypoints; the waypoints are desired outputs of the robot's trajectory at certain time instances, sparsely located within a demonstration time horizon. The duration of the expert's demonstration may be different from the actual duration of the robot's execution. The proposed method enables to jointly learn an objective function and a time-warping function such that the robot's reproduced trajectory has minimal distance to the sparse demonstration waypoints. Unlike existing inverse reinforcement learning techniques, the proposed approach uses the differential Pontryagin's maximum principle, which allows direct minimization of the distance between the robot's trajectory and the sparse demonstration waypoints and enables simultaneous learning of an objective function and a time-warping function. We demonstrate the effectiveness of the proposed approach in various simulated scenarios. We apply the method to learn motion planning/control of a 6-DoF maneuvering unmanned aerial vehicle (UAV) and a robot arm in environments with obstacles. The results show that a robot is able to learn a valid objective function to avoid obstacles with few demonstrated waypoints.