Learned Regions of Attraction for Safe Motion Primitive Transitions

Estimating regions of attraction (ROAs) of dynamical systems is critical for understanding the operational bounds within which a system will converge to a desired state. In this paper, we introduce a neural network-based approach to approximating ROAs that leverages labeled data generated by offline sampling and simulation of initial conditions, with labels determined by flow membership in an "explicit region of attraction." This framework is designed to estimate ROAs with a level of precision suitable for integration into a motion primitive transition framework as conditions to switch between candidate primitive behaviors. To account for gaps between the simulated environment and the real world, online learning is employed; this refines the offline-learned model of the ROA based on observed discrepancies between predicted and actual system behaviors. We validate this methodology on a quadrupedal robot, demonstrating that our ROA estimates can effectively model regions of attraction for a high-dimensional system. We show this for multiple primitive behaviors and in environments different from the training data. The outcomes highlight the usefulness of our method in estimating regions of attraction and informing transition conditions between primitive behaviors.