Encirclement of Moving Targets Using Noisy Range and Bearing Measurements

This paper presents theoretically justified controllers that use relative range and bearing measurements to steer a team of autonomous vehicles, operating without inertial position information, to circular trajectories around a constant-acceleration, constant-velocity, or stationary target. An extended Kalman filter is used to improve the noisy relative measurements and estimate the velocity of the moving target. These estimated values are used in the control laws to encircle constant-velocity moving targets. Lyapunov techniques are utilized to show that the vehicle will converge to the desired circular formations. Additionally, cooperating vehicles are shown to converge to a circular formation with equal temporal spacing using each vehicle’s estimate of the target’s velocity to define a common reference frame. Numerical simulations validate the efficacy of these control laws.