Using Control Barrier Functions to Incorporate Observability: Application to Range-Based Target Tracking

Abstract

In many nonlinear systems, the observability of the system is dependent on its state and control input. Thus, incorporating observability into a control scheme can enhance an observer's ability to recover accurate estimates of unmeasured states, minimize estimation error, and ultimately, allow the original control objective to be achieved. The accommodation of observability, however, may conflict with the original control goal at times. In this paper, we propose the use of control barrier functions (CBFs) to enforce observability and thereby facilitate the convergence of the state estimate to the true state while accommodating the original control objectives. Motivated by practical applications for autonomous robots operating in global positioning system-denied environments, we focus on the problem of target tracking for a unicycle model when only the distance to the target is measured. The proposed approach is compared in simulation with a model predictive control (MPC) approach that treats an observability-related metric as part of the cost function, where several different options for the observability metric are explored. It is found that the CBF-based approach achieves control and estimation performance that is comparable to that of the MPC approach, but with significantly less computational complexity. These findings are further experimentally verified in range-based target tracking with a swimming robotic fish.