Decentralized Multi-Robot Line-of-Sight Connectivity Maintenance under Uncertainty

TL;DR

This work tackles the challenge of maintaining Line-of-Sight connectivity in multi-robot teams under Gaussian localization uncertainty. It develops Probabilistic LOS Connectivity Barrier Certificates (PrLOS-CBC) to define a probabilistic, yet tractable, admissible control space, and Uncertainty-Aware LOS Least Constraining Tree (ULOS-LCT) to select a minimally disruptive LOS edge set. A fully decentralized algorithm (Dec-LOS-LCT) interleaves edge selection with distributed constrained optimization, supported by C-ADMM, to preserve global and subgroup LOS connectivity with high probability while keeping control deviations near nominal tasks. Theoretical guarantees, plus extensive simulations, CoppeliaSim scenarios, and real hardware experiments, demonstrate robust LOS maintenance, safety, and real-time performance, highlighting the method’s practicality for scalable autonomous teams under localization noise.

Abstract

In this paper, we propose a novel decentralized control method to maintain Line-of-Sight connectivity for multi-robot networks in the presence of Guassian-distributed localization uncertainty. In contrast to most existing work that assumes perfect positional information about robots or enforces overly restrictive rigid formation against uncertainty, our method enables robots to preserve Line-of-Sight connectivity with high probability under unbounded Gaussian-like positional noises while remaining minimally intrusive to the original robots' tasks. This is achieved by a motion coordination framework that jointly optimizes the set of existing Line-of-Sight edges to preserve and control revisions to the nominal task-related controllers, subject to the safety constraints and the corresponding composition of uncertainty-aware Line-of-Sight control constraints. Such compositional control constraints, expressed by our novel notion of probabilistic Line-of-Sight connectivity barrier certificates (PrLOS-CBC) for pairwise robots using control barrier functions, explicitly characterize the deterministic admissible control space for the two robots. The resulting motion ensures Line-of-Sight connectedness for the robot team with high probability. Furthermore, we propose a fully decentralized algorithm that decomposes the motion coordination framework by interleaving the composite constraint specification and solving for the resulting optimization-based controllers. The optimality of our approach is justified by the theoretical proofs. Simulation and real-world experiments results are given to demonstrate the effectiveness of our method.

Figures (8)

• Figure 1: Simulation example of 24 robots divided into $M=3$ subgroups with different colors and tasked to three different places. Robots in blue subgroup 1 execute biased rendezvous behaviors towards the blue task site 1, while robots in red subgroup 2 and green subgroup 3 perform circle formation behaviors around the red task site 2 and green task site 3, respectively. The $R_\mathrm{s},\; R_\mathrm{obs}$ and $R_\mathrm{c}$ are 0.2 m, 0.2 m and 0.8 m in this experiment. The red lines in this figure denote the currently optimal LOS communication graph $\mathcal{G}^\mathrm{slos*}$ and the gray dash lines are the current LOS communication graph $\mathcal{G}^\mathrm{los}$. The black boxes represent the obstacles. The confidence level in this experiment is set as $\sigma^\mathrm{s}=\sigma^\mathrm{obs} = \sigma^\mathrm{c} = 0.90,\; \sigma^\mathrm{los} = 0.99\; (i.e.,\; \sigma^\mathrm{graph}=0.9 )$. The robot diameter is 0.16 m. The Multivariate Gaussian covariance matrix for measurement noise is $\mathrm{diag}[0.03,0.04]$. Compared baseline methods include (d) MCCST luo2020behavior, (e) Our method without considering occlusion avoidance, (f) Enforcing edges from fixed initial ULOS-LCT (red edges in Figure \ref{['fig1:subfiga']}), and (g) Enforcing edges from fixed initial LOS connectivity graph (gray edges in Figure \ref{['fig1:subfiga']}).
• Figure 2: Performance comparison of the simulation example in Fig. \ref{['fig:our_simulation']} w.r.t. different metrics: a) Minimum distance to robots/obstacles to verify the safety constraints' satisfaction, b) Average algebraic LOS connectivity to indicate whether the LOS graph is LOS connected ($\lambda_2 >0$) or not $\lambda_2 =0$, where $\lambda_2$ is the second-smallest eigenvalue of the LOS Laplacian matrix calculated from the LOS adjacency matrix. The elements in the LOS adjacency matrix indicate whether the pairwise robots are LOS connected), c) Average distance to target region to indicate the overall task efficiency, and (d) Average control perturbation (computed by $\frac{1}{N}\sum_{i=1}^N|| \mathbf{u}_i-\tilde{\mathbf{u}}_i||^{2}$ measuring the accumulated deviation from nominal controllers).
• Figure 3: Testing environments with different initial positions of robots, numbers of robot subgroups, and obstacles with different lengths, positions, and shapes.
• Figure 4: Quantitative results on different sizes of robot team. Error bars show the standard deviation.
• Figure 5: Numerical results under different levels of noisy observations.

Theorems & Definitions (18)

• Lemma 1
• Definition 2
• Lemma 3
• Remark 4
• Definition 5
• Theorem 6
• Remark 7
• Proposition 8
• Proposition 9
• Proposition 10