Abstract:
This paper addresses the problem of cooperative target localization for stationary multi-agent systems, aiming to localize a stationary target within a planar environment by proposing a novel leader-follower-based distributed cooperative control strategy. Existing approaches to this problem frequently rely on the geometric relationships between adjacent agents and the target, or measurement distances from some agents to the target, to design cooperative pointing controllers. However, these methods often require complex geometric analysis or precise distance measurements, which inherently limit their applicability within complex environments. To overcome these limitations, a novel distributed target estimator for stationary multi-agent systems and targets situated within the same plane is specifically designed in this paper. In this setup, each agent possesses knowledge of its own global position, and their deployment is arbitrary. The designed distributed target estimator requires only the directional information (orientation angles) of the target as perceived by two designated leader agents, along with a carefully chosen scaling factor, eliminating the need for other distance measurements related to the target. Without loss of generality, it is assumed that the two leader agents measured the target's orientation angles, and that the three entities – the two leader agents and the target – are not collinear. Although this assumption implicitly determines the target's position, this spatial information remains unknown to both the two leader agents and the other agents. Unlike common cooperative controllers, the target estimator imposes a dual requirement: not only must the individual target estimates from each agent converge to a consistent value, but this consistent estimate must also asymptotically approach the target's actual location. To achieve this cooperative consensus task of converging to the target, a specific projection matrix, formulated directly from the sensed orientation angles of the target by the leaders, is integrated into the estimator’s update law for the leader agents. This matrix is strategically designed to ensure the leader agents' estimates of the target's position converge along their respective lines of sight toward the actual target coordinates. Operating autonomously and without direct communication of global information, the follower agents achieve convergence through local information exchange with their neighbors. Under the guidance of the leader-follower distributed cooperative control strategy, these followers gradually refine their estimates, ultimately approximating and converging to the target's actual position. Furthermore, the projection matrix, due to its positive semi-definite property, increases the difficulty of theoretical analysis. The introduction of the scaling factor guarantees the convergence of the cooperative control algorithm and provides quantifiable parameters based on this scaling factor, thereby quantifying the convergence speed of the cooperative control algorithm to some extent. Finally, the efficacy and performance of the proposed leader-follower-based distributed cooperative control strategy are thoroughly demonstrated through numerical simulation results.