Formation Control and Guidance using Bearing-only Measurements

In this thesis, we study formation control and guidance algorithms using only bearing measurements. First, an angle based leader–follower formation control problem is considered. In this problem, there are three leaders which have access to their own global positions. The other agents are followers which sense relative bearing measurements with regard to three neighbors. We propose a control strategy for leaders and followers. Under the proposed control law, the formation shape is proved to be locally asymptotically stable by mathematical induction. Second, we study a guidance problem with three stationary beacons. An agent wants to navigate to its desired position in the plane. We develop a control law using bearing vectors and the subtended bearing angles to guide the agent asymptotically to its destination. Lastly, we consider a guidance problem with N beacons on the n dimensional space. An agent wants to reach the point that minimizes the weighted sum of distances to N stationary beacons. This problem is usually known as the Fermat–Weber location problem. Different from existing solutions in the literature, we propose a continuous time control law using only bearing vectors to steer an agent to the solution of this problem. Moreover, when the beacons are moving exponentially fast to their desired positions, a corresponding control law is also provided. Our analyses are based on Lyapunov theory and input-to-state stability for cascade systems. Simulations and experiments are included to validate our theoretical results. ©2014 Minh Hoang Trinh ALL RIGHTS RESERVED