Incorporating Observability via Control Barrier Functions with Application to Range-based Target Tracking

Abstract

In nonlinear systems, the control input often directly impacts observability of the system. In this paper, we investigate the use of control barrier functions (CBFs) for enforcing observability of a mobile robot in target tracking, when only the distance to the target is measured. The problem is motivated by practical applications for autonomous robots when operating in GPS-denied environments. To address the tradeoffs between localization accuracy and tracking performance, a tracking controller is augmented by a control barrier function based on an observability metric. Two examples are used to show the efficacy of the approach, one with unicycle dynamics on a plane, and the other based on gliding robotic fish with complex 3D dynamics. The approach taken in this work is compared to a model predictive controller that optimizes a joint cost function of tracking error and observability metric. While both approaches are shown to maintain observability and enable tracking, the CBF-based approach is shown to have several advantages