Observability-aware Target Tracking with Range Only Measurement

Often times in nonlinear systems, the control input can play a significant role in the system's observability. In this paper, we investigate the trade-off between observability and control performance for 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. A nonlinear model predictive control (NMPC) framework is used to address the dilemma between localization and tracking, by jointly optimizing the tracking performance and an observability metric. Three measures of estimation performance are considered, including the determinant of the observability matrix, the inverse condition number of the observability matrix, and the trace of the covariance matrix in position estimation. By tuning the relative importance of the tracking objective and observation performance, we demonstrate the efficacy of the proposed NMPC approach. The trade-off is captured through two examples, one with unicycle dynamics on a plane, the other based on gliding robotic fish with complex 3D dynamics.