Minimum Sensing Strategy for a Path-following Problem via Discrete-time Control Barrier Functions

This paper presents a minimum sensing strategy for a path-following task where a mobile robot is required to satisfy a prescribed localization accuracy by measuring known landmarks. Specifically, we design a sensing strategy that confines the covariance of a robot to the pre-required locational accuracy along a path by controlling the degree of attention to each landmark. We first present a novel discrete-time control barrier function (DCBF) that confines the covariance of the robot inside of the pre-planned locational requirement. We then integrate the proposed DCBF into the optimization problem, which is designed to allocate the attention of a robot to each landmark so that the overall sensing effort is minimized. In the proposed optimization problem, we evaluate the sensing cost as the minimum information gain, namely the minimum number of bits that must be included in the sensor data, and formulate how the specified attention level affects the estimation of the robot state. Finally, we demonstrate the effectiveness of the proposed method in simulation studies.