In robotic networks relying on noisy range measurements between agents for cooperative localization, the achievable positioning accuracy strongly strongly depends on the network geometry. This motivates the problem of planning robot trajectories in such multi-robot systems in a way that maintains high localization accuracy. We present potential-based planning methods, where localizability potentials are introduced to characterize the quality of the network geometry for cooperative position estimation. These potentials are based on Cramer Rao Lower Bounds (CRLB) and provide a theoretical lower bound on the error covariance achievable by any unbiased position estimator. In the process, we establish connections between CRLBs and the theory of graph rigidity, which has been previously used to plan the motion of robotic networks. We develop decentralized deployment algorithms appropriate for large networks, and we use equality-constrained CRLBs to extend the concept of localizability to scenarios where additional information about the relative positions of the ranging sensors is known. We illustrate the resulting robot deployment methodology through simulated examples and an experiment.
翻译:在依赖合作定位代理物之间噪音测距的机器人网络中,可实现的定位精确度在很大程度上取决于网络几何测量,这促使在多机器人系统中规划机器人轨迹的问题,从而保持高本地化精确度。我们提出了潜在的规划方法,其中引入了可定位性潜力,以确定网络几何质量特征,用于合作定位估计。这些潜力以Cramer Rao Lower Bounds(CRLB)为基础,为任何不偏倚的测位器所能实现的误差共差提供了较低的理论约束。在此过程中,我们建立了CRLBs与图形刻度理论之间的联系,而该理论曾被用来规划机器人网络的移动。我们开发了适合大型网络的分散部署算法,我们利用平等限制的CRLBs,将可定位概念扩大到已知有关测距传感器相对位置的其他信息的情况。我们通过模拟实例和实验来说明由此产生的机器人部署方法。