Bearing-Only Formation Control With Prespecified Convergence Time

Abstract

This paper considers the bearing-only formation control problem, where the control of each agent only relies on relative bearings of their neighbors. A new control law is proposed to achieve target formations in finite time. Different from the existing results, the control law is based on a timevarying scaling gain. Hence the convergence time can be arbitrarily chosen by users, and the derivative of the control input is continuous. Furthermore, sufficient conditions are given to guarantee almost global convergence and interagent collision avoidance. Then a leader-follower control structure is proposed to achieve global convergence. By exploring the properties of the bearing Laplacian matrix, the collision avoidance and smooth control input are preserved. A multi-robot hardware platform is designed to validate the theoretical results. Both simulation and experimental results demonstrate the effectiveness of our design.Index Terms-Bearing-only formation control, finite-time formation control, prescribed-time consensus.

Free‐will arbitrary time consensus protocols with diffusive coupling

“…where 0 < t 1 < t f and 𝜂 2 > 1. From ( 25) and (26), each agent i needs to communicate the sum of the relative states ∑ j∈ i (x j − x i ) and the sum of the relative velocities…”

Coordination of multi‐agent systems with arbitrary convergence time

“…Note that finite-time convergence property of estimation/control law is beneficial in coordinating multiple tasks in multi-agent systems, as demonstrated in orientationestimation based formation control [4] or pointing consensus [5]. Recently, fixed-time bearing-based network localization [25,26] and bearing-based leader-follower formation control [27] were also proposed.…”

“…In comparison with the fixed‐time consensus and bearing‐based network localization laws in [17, 25], the upper bound of the settling time of the control laws in this paper can be easily selected. The structure of the proposed coordination laws in this paper is also simpler than the one studied in [27], where a dynamic auxiliary time‐varying gain is introduced to the control law.…”

Free-Will Arbitrary Time Consensus Protocols with Diffusive Coupling

“…Consensus laws with prespecified convergence time using an auxiliary time-varying gain are proposed in [5]. An extension of [5] to prespecified time bearing-only formation control is given in [13]. Recently, free-will arbitrary time (FwAT) consensus protocols, built upon the results in [14], are presented in [1], [15].…”

“…The settling time bound t f is explicitly available in the designed consensus laws and can be prespecified arbitrarily [1], [15]. Furthermore, the design and convergence analysis of FwAT consensus laws [1], [15] are simpler than those in [5], [13]. However, existing works in prespecified time consensus [1], [5], [15] have been proposed for only first-order integrator dynamics.…”