Finite time distributed distance‐constrained shape stabilization and flocking control for d‐dimensional undirected rigid formations

Abstract

Most of the existing results on distributed distance-constrained rigid formation control establish asymptotic or exponential convergence. To further improve the convergence rate, we explain in this paper how to modify existing gradient controllers to obtain finite time stability. For point agents modeled by single integrators, the controllers proposed in this paper drive the whole formation to locally converge to a desired shape with finite settling time. We also show for undirected triangular formation shape control, if all the agents start with non-collinear positions, then the formation will converge to the desired shape in finite time. For agents modeled by double integrators, the proposed controllers allow all agents to both achieve the same velocity and reach a desired shape in finite time. All controllers are totally distributed. Simulations are also provided to validate the proposed control strategies. FINITE TIME SHAPE STABILIZATION AND FLOCKING CONTROL 2825 the displacement-based formation system. Along this direction, several recent papers [4,5,[10][11][12][13] have studied distance-constrained rigid formation control for different formation shapes, all with asymptotic convergence (or sometimes exponential convergence) to the desired shape (irrespective of the orientation or absolute position of the formation). We note that there exist other approaches to achieve formation stabilization, such as the complex-Laplacian-based approach proposed in [14] and the orientation-alignment-based approach discussed in [15]. They differ from the rigidity-based approach in underlying graph requirement, control objective, and sensing/communication requirement for each individual agent. We refer readers to [3] for a detailed comparison on different approaches for formation control.One objective of this paper is to design closed-loop controllers to stabilize rigid formation shapes with a finite settling time, that is, to bring a formation with incorrect distances to one with the correct distances in a finite time, at least for a neighborhood of initial conditions around the correct formation. Suppose that a formation is traveling in a particular direction and it needs to adjust the formation shape perhaps by shrinking to avoid an obstacle. Then one wants to achieve the formation adjustment in a limited time-before arriving at the obstacle. Actually, finite time convergence also brings about many benefits, which include not only a faster convergence rate but also improved disturbance rejection and robustness properties [16,17]. Because of these favorable properties, recent years have witnessed increasing efforts on finite time convergence control for networked and distributed systems because the convergence time is always a critical factor for such systems. This motivates the current work on formation control of networked agents with a finite convergence time. We note that finite time formation control using different measurements/control strategies has been reported in, for example, [18] and [19]. In [18], the control s...

Cooperative Event-Based Rigid Formation Control

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Quantization effects and convergence properties of rigid formation control systems with quantized distance measurements

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