Abstract:
This study addresses the problem of cooperative target localization for stationary multi-agent systems, aiming to localize a stationary target within a specifically designed planar environment by proposing a novel leader-follower-based distributed cooperative control strategy that does not rely on distance measurements. Existing approaches to the cooperative target localization problem frequently rely on the geometric relationships between adjacent agents and the target, or the measurement distances from some agents to the target, to design cooperative pointing controllers. However, these methods generally require complex geometric analyses or precise distance measurements, which inherently limit their applicability within complex environments. To overcome the limitations of complex geometric analyses and precise distance measurements, a novel distributed target estimator was designed in this study. This estimator requires only two leader agents to provide the direction angle and scaling factor of the observed target, without the need for direct distance measurement, and it is suitable for any deployed stationary agent or stationary target. In this setup, each agent possesses knowledge of its own global position, and its deployment is arbitrary. The designed distributed target estimator requires only directional information (orientation angles) of the target, as perceived by the 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 measure the target's orientation angles, and that the three entities –two leader agents and the target – are not collinear. Although this assumption implicitly determines the target's position, the spatial information regarding the target remains unknown to the leader agents and 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. Therefore, the proposed estimator embeds the local orientation angle information acquired by the leader agents into a distributed estimation algorithm by introducing a projection matrix. This operation ensures that the leader’s estimates of the target converge along the line of sight toward the target position. Thus, the system eliminates the need for distance measurement. Only two orientation angles are utilized to facilitate the exponential convergence of the estimates of all agents for the target position, thereby achieving global localization under simple information conditions. Furthermore, the projection matrix, owing to its positive semi-definite property, increases the difficulty and complexity of theoretical analysis. The introduction of a scaling factor ensures convergence of the cooperative control algorithm and provides quantifiable parameters based on this scaling factor, thereby quantifying its convergence speed of the cooperative control algorithm to a certain extent. Theoretical analysis has proven that followers gradually approach and converge on the target position through local information exchange. Finally, the efficacy and performance of the proposed leader-follower-based distributed cooperative control strategy are demonstrated via a numerical simulation of an agent system with 11 agents in a planar environment of sufficient scope.