Realm: Real-Time Line-of-Sight Maintenance in Multi-Robot Navigation with Unknown Obstacles

TL;DR

Realm addresses real-time line-of-sight connectivity maintenance for multi-robot navigation in unknown environments by deriving LoS constraints directly from point-cloud measurements. It introduces a LoS-distance metric $\hat{d}^{\text{los}}_{ji}$ that encodes urgency and sensitivity, and a fusion function $d^{\text{los}}_{ij}$ to produce symmetric edge weights for distributed connectivity control. A potential-function framework on the graph Laplacian, $V^{\lambda}(\lambda_2)=1/(\lambda_2-\lambda_2^{\min})$, preserves the Fiedler eigenvalue $\lambda_2>0$ to guarantee connectivity and yields a distributed connectivity velocity $\boldsymbol{u}^{\text{c}}_i$. The approach integrates a mapless FAR planner and role-based navigation scaling for LoS-constrained exploration, with validation in Gazebo and real-world drone experiments and open-source code release.

Abstract

Multi-robot navigation in complex environments relies on inter-robot communication and mutual observations for coordination and situational awareness. This paper studies the multi-robot navigation problem in unknown environments with line-of-sight (LoS) connectivity constraints. While previous works are limited to known environment models to derive the LoS constraints, this paper eliminates such requirements by directly formulating the LoS constraints between robots from their real-time point cloud measurements, leveraging point cloud visibility analysis techniques. We propose a novel LoS-distance metric to quantify both the urgency and sensitivity of losing LoS between robots considering potential robot movements. Moreover, to address the imbalanced urgency of losing LoS between two robots, we design a fusion function to capture the overall urgency while generating gradients that facilitate robots' collaborative movement to maintain LoS. The LoS constraints are encoded into a potential function that preserves the positivity of the Fiedler eigenvalue of the robots' network graph to ensure connectivity. Finally, we establish a LoS-constrained exploration framework that integrates the proposed connectivity controller. We showcase its applications in multi-robot exploration in complex unknown environments, where robots can always maintain the LoS connectivity through distributed sensing and communication, while collaboratively mapping the unknown environment. The implementations are open-sourced at https://github.com/bairuofei/LoS_constrained_navigation.

Figures (7)

• Figure 1: Real-time LoS maintenance of four robots while exploring an unknown environment. Robots' visible regions (enclosed by curves with different colors) are constructed from their real-time point cloud measurements. The connectivity between robots is shown by the light green edges. To maintain connectivity, each robot only needs local information from its one-hop neighbors.
• Figure 2: (a) Construction of the visible region liu_StarconvexConstrained_2022; (b) Imbalanced LoS-distance for two robots. Robot $1$ is at a higher risk of losing LoS than robot $2$, as robot $1$ is easier to move beyond the visible region (enclosed by the green curve) of robot $2$ after a delta movement.
• Figure 3: (a) Sensitivity of losing LoS after applying delta movements to two test points (blue and red dots) with a same $d_{k^*}$; (b) Illustration of $\Delta_{d_{k^*}}$ after applying a delta movement $\delta \mathbf{\boldsymbol{q}}$ (red arrow) to $\mathbf{\boldsymbol{q}}_{ji}$ in 2D case.
• Figure 4: The framework of LoS-constrained multi-robot exploration.
• Figure 5: (a) Comparison of the fused LoS-distances between two robots using Eq. (\ref{['eq_weighted_average']}) and using the $\text{Softmin}(\cdot)$ function; (b) Comparison of the derivatives of Eq. (\ref{['eq_weighted_average']}) (solid lines) and that of the $\text{Softmin}(\cdot)$ function (transparent lines).

Theorems & Definitions (5)

• Remark 1
• Proposition 1
• Proposition 2
• proof
• proof