Robotic Demonstration Learning Stability-Accuracy Trade-Off: From an Energy Function Learning Viewpoint

Learning a globally asymptotically stable (GAS) autonomous dynamic system (ADS) is one of the most popular approaches for the robotic demonstration learning. However, the GAS guarantee will inevitably scarify the demonstration learning accuracy. In this paper, we try to ease the stability-accuracy contradiction by focusing on ensuring the ADS's local stability instead of its global stability. Specifically, an energy function with locally unique-minimum property, called NS-QLF, is designed and learned on the demonstration set to serve as a local stability certificate of the ADS. Then, a locally stable ADS with a predefined region of attraction (RoA) is learned based on the NS-QLF and sequentially optimization techniques. Both simulation and experiments are conducted to validate that the learned ADS can accurately transfer human-like skills to the robot.