DCL-Sparse: Distributed Range-only Cooperative Localization of Multi-Robots in Noisy and Sparse Sensing Graphs

TL;DR

This work tackles distributed cooperative localization for multi-robot systems operating in GPS-denied, sparse sensing graphs where rigidity and noise hinder convergence. It introduces DCL-Sparse, a multilayer framework that combines Shadow 1-Hop Edges (S1-Edges) with UAV emitters to enhance connectivity and accelerate convergence in unit-disk graphs. The authors derive bounds on the shadow-edge gain $\beta$, prove stability via the spectral radius condition $\rho(I+\alpha L_d+\beta L_s)<1$, and demonstrate that the UAVs significantly improve localization performance. Extensive simulations on the Robotarium show up to a $95\%$ reduction in localization error compared to state-of-the-art methods, with strong robustness to noise and scalability across increasing robot counts.

Abstract

This paper presents a novel approach to range-based cooperative localization for robot swarms in GPS-denied environments, addressing the limitations of current methods in noisy and sparse settings. We propose a robust multi-layered localization framework that combines shadow edge localization techniques with the strategic deployment of UAVs. This approach not only addresses the challenges associated with nonrigid and poorly connected graphs but also enhances the convergence rate of the localization process. We introduce two key concepts: the S1-Edge approach in our distributed protocol to address the rigidity problem of sparse graphs and the concept of a powerful UAV node to increase the sensing and localization capability of the multi-robot system. Our approach leverages the advantages of the distributed localization methods, enhancing scalability and adaptability in large robot networks. We establish theoretical conditions for the new S1-Edge that ensure solutions exist even in the presence of noise, thereby validating the effectiveness of shadow edge localization. Extensive simulation experiments confirm the superior performance of our method compared to state-of-the-art techniques, resulting in up to 95\% reduction in localization error, demonstrating substantial improvements in localization accuracy and robustness to sparse graphs. This work provides a decisive advancement in the field of multi-robot localization, offering a powerful tool for high-performance and reliable operations in challenging environments.

Figures (7)

• Figure 1: Illustration of the proposed UGV-UAV cooperative localization in a typical disaster scenario. Here, the links shown in "Yellow" are the edges of the sparsely-connected sensing and/or communication graph.
• Figure 2: Flipping of sparse (non-rigid) sensing graphs with ground truth location (left) and estimated (flipped due to sparsity of range inference) locations (right). Robots 4,6, 10, and 11 are flipped along the axis connecting the robots 2 and 23 in this example.
• Figure 3: Localization of robots in a network with a unit disk graph where the associated graph G is not ggr. Robots $r_i$, $r_j$, and $r_k$, represented by nodes $v_i$, $v_j$, and $v_k$. Robot $r_i$ can detect robot $r_j$, but cannot detect robot $r_k$ (i.e., node $v_k$ is outside the dashed circle). The blue dotted line indicates a potential shadow edge that might be formed between $v_i$ and $v_k$. Based on the distances $d_{ij}$ and $d_{jk}$, upper and lower bounds for $d_{ik}$ are defined.
• Figure 4: (a) Confirming the bounds of S1-Edge gain (i.e., $\beta$ in \ref{['eqn:n+']}) in the DCL-sparse approach. (b) Determining optimal placement for the Power node among the robots.
• Figure 5: Final localization results for distributed cooperative localization in $\mathbb{R}^2$. Given that our approach is relative localization, the orientation of the achieved formation shape of the estimated positions should be ignored.

Theorems & Definitions (4)

• Theorem 1
• proof
• Remark 1
• Remark 2