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Finite-time stabilisation of cyclic formations using bearing-only measurements. (English) Zbl 1291.93259

Summary: This paper studies decentralized formation control of multiple vehicles in the plane when each vehicle can only measure the local bearings of their neighbors by using bearing-only sensors. Since the inter-vehicle distance cannot be measured, the target formation involves no distance constraints. More specifically, the target formation considered in this paper is an angle-constrained cyclic formation, where each vehicle has exactly two neighbors and the angle at each vehicle subtended by its two neighbors is prespecified. To stabilize the target formation, we propose a discontinuous control law that only requires the sign information of the angle errors. Due to the discontinuity of the proposed control law, the stability of the closed-loop system is analyzed by employing a locally Lipschitz Lyapunov function and nonsmooth analysis tools. We prove that the target formation is locally finite-time stable with collision avoidance guaranteed.

MSC:

93D15 Stabilization of systems by feedback
93A14 Decentralized systems
93C10 Nonlinear systems in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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