A Topologically Inspired Path-Following Method with Intermittent State Feedback

Autonomous systems often operate in environments where state feedback may not be available, such as in anti-access and area denial environments. In these environments, it is often required that an agent track a path, despite interruptions in state feedback. As a result, the class of Relay-Explorer problems has emerged, where a switched system approach is used to account for intermittent state feedback. Past work on these problems established a framework for developing dwell-time conditions for stable tracking using these methods. However, existing work only applies to a limited class of reference paths and feedback region geometries. This letter advances a topologically inspired method for guaranteeing re-acquisition of feedback for nearly arbitrary geometries in arbitrary dimensions, all while relaxing the dwell-time conditions and retaining the uniformly ultimately bounded stability result from preceding work. Numerical experiments in the plane demonstrate an increase of hundreds of percentage points-even for fairly generic geometries-in the tracking error the agent could afford, using the proposed method, without sacrificing stability.