Entrapping a target in an arbitrarily shaped orbit by a single robot using bearing measurements

The problem of entrapping a static target by a robot with a single integrator dynamic model using bearing-only measurements is studied in this paper. Existing works need to either estimate the position of the target with the robot position a priori, or finally maintain an exact circular motion around the target. In this paper, we propose an estimator–controller framework for the robot, where the estimator is designed to estimate the relative position with bearing measurements by exploiting the orthogonality property, based on which the controller is proposed to achieve the desired relative position. Within this framework, the robot can entrap the target without any prior position information in an arbitrarily shaped orbit. We characterize sufficient conditions on the desired orbiting shapes which can support the robot for successful localization and entrapment simultaneously. It is proved that the estimation and tracking errors both converge to zero as time goes to infinity. Extensions to a moving target and multiple robots are also discussed and analyzed respectively. Simulations testify the effectiveness of the proposed method.