In this work, we consider the problem of localizing a team of robots, without access to direct pose measurements, under the influence of nonuniform environmental disturbances and measurement bias. Specifically, we are interested in the conditions under which teams remain range-only localizable when the environmental disturbances vary from robot to robot. We approach this problem through nonlinear observability and graph theory. After analyzing the system’s observability properties, we present theorems that identify the structural conditions under which the system maintains local weak observability. We demonstrate that rigid structures are important not only in defining multi-robot interactions, but also in characterizing the influence of nonuniform disturbances. We also give several example systems to cement intuition on the derived conditions. An observability-based planner is then presented that guides a subset of robots toward trajectories that are highly observable through finite-horizon optimization on robot headings. Simulations are then presented, along with an extended Kalman filter for state estimation, and a comparison to previous methods, to corroborate and demonstrate the results derived.

中文翻译：

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受非均匀环境干扰的单轮多机器人团队的非线性可观测性

在这项工作中，我们考虑了在不均匀的环境干扰和测量偏差的影响下，无法直接进行姿势测量的情况下将机器人团队本地化的问题。具体来说，我们对当环境干扰因机器人而异时，团队只能在范围内进行本地化的条件感兴趣。我们通过非线性可观性和图论来解决这个问题。在分析了系统的可观察性之后，我们提出了确定系统维持局部弱可观察性的结构条件的定理。我们证明了僵化结构不仅在定义多机器人交互中很重要，而且在表征非均匀干扰的影响方面也很重要。我们还给出了一些示例系统，以根据导出的条件巩固直觉。然后提出了一个基于可观察性的计划程序，该计划程序将引导机器人的子集朝向通过在机器人方向上进行有限水平的优化而高度可观察到的轨迹。然后介绍仿真，以及用于状态估计的扩展卡尔曼滤波器，以及与以前方法的比较，以证实和证明所得出的结果。