An optimization problem is at the heart of many robotics estimating, planning, and optimum control problems. Several attempts have been made at model-based multi-robot localization, and few have formulated the multi-robot collaborative localization problem as a factor graph problem to solve through graph optimization. Here, the optimization objective is to minimize the errors of estimating the relative location estimates in a distributed manner. Our novel graph-theoretic approach to solving this problem consists of three major components; (connectivity) graph formation, expansion through transition model, and optimization of relative poses. First, we estimate the relative pose-connectivity graph using the received signal strength between the connected robots, indicating relative ranges between them. Then, we apply a motion model to formulate graph expansion and optimize them using g$^2$o graph optimization as a distributed solver over dynamic networks. Finally, we theoretically analyze the algorithm and numerically validate its optimality and performance through extensive simulations. The results demonstrate the practicality of the proposed solution compared to a state-of-the-art algorithm for collaborative localization in multi-robot systems.
翻译：优化问题是许多机器人估算、规划和最佳控制问题的核心。 在基于模型的多机器人本地化方面做了几次尝试,很少有人将多机器人协作本地化问题设计成一个要素图形问题,以便通过图形优化来解决。在这里,优化的目标是以分布方式将估计相对位置估计数的错误最小化。我们用于解决这一问题的新颖的图形理论方法由三个主要组成部分组成;(连接性)图形形成,通过过渡模型扩展,以及优化相对配置。首先,我们利用所接收的与连接的机器人之间的信号强度来估计相对的方位关联性图表,指出它们之间的相对范围。然后,我们应用一个运动模型来用G$$2$o的图形优化作为动态网络的分布解析器来制定图表扩展和优化它们。最后,我们从理论上分析算法,并通过广泛的模拟来从数字上验证其最佳性和性。结果表明,拟议解决方案与多机器人系统中协作本地化的最新算法相比是实用的。
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