This paper solves the simultaneous localization and formation (SLAF) problem for a multi-agent system moving in 2D plane. The multi-agent system consists of leaders who have the knowledge of their absolute positions in the global coordinate frame, and followers who do not know their absolute positions but have angle-only measurements and communication with respect to their neighboring agents. The aim of SLAF is to simultaneously localize and control the followers such that a desired formation among the leaders and followers can be achieved by using locally available sensing and communication information. To handle the challenging situation where the formation becomes unlocalizable at some nongeneric configurations, a perturbation-based SLAF algorithm is proposed such that the SLAF task can be achieved with an asymptotic convergence. To meet different tasks’ requirements, three types of distributed SLAF algorithms are designed for the followers when the leaders are static, move with constant, or time-varying velocities, respectively. The effect of measurement noises, extension to other types of sensor measurements, requirement on agents’ coordinate frames, collision and collinearity avoidance are also discussed. To validate the theoretical results, simulation examples corresponding to the discussed scenarios are carried out.

本文解决了同步定位问题多智能体系统在 2D 平面上移动的形成（SLAF）问题。多智能体系统由知道其在全局坐标系中的绝对位置的领导者和不知道其绝对位置但仅具有角度测量和与其相邻代理通信的跟随者组成。SLAF 的目标是同时定位和控制跟随者，从而可以通过使用本地可用的传感和通信信息来实现领导者和跟随者之间的期望编队。为了处理在某些非泛型配置下编队变得不可定位的挑战性情况，提出了一种基于扰动的 SLAF 算法，使得 SLAF 任务可以通过渐近收敛来实现。满足不同任务的需求，当领导者是静态的、以恒定的速度移动或随时间变化的速度时，分别为跟随者设计了三种分布式 SLAF 算法。还讨论了测量噪声的影响、扩展到其他类型的传感器测量、对代理坐标系的要求、碰撞和共线性避免。为了验证理论结果，进行了与所讨论场景相对应的模拟示例。