Ranging-Based Localizability Optimization for Mobile Robotic Networks

TL;DR

This paper introduces potential-based planning methods for mobile robotic networks that optimize localization accuracy by leveraging CRLBs and graph rigidity theory, enabling decentralized deployment and improved positioning.

Contribution

It presents a novel framework combining CRLBs and graph rigidity for localizability optimization, including decentralized algorithms and extensions for known sensor positions.

Findings

Potential-based planning improves localization accuracy.

Decentralized deployment algorithms are effective for large networks.

The methodology is validated through simulations and experiments.

Abstract

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.