Integrating Online Learning and Connectivity Maintenance for Communication-Aware Multi-Robot Coordination

TL;DR

A Data-driven Connectivity Maintenance (DCM) algorithm that combines online learning of the communication signal strength and a bi-level optimization-based control framework for the robot team to enforce global connectivity of the realistic multi-robot communication graph and minimally deviate from their task-related motions is proposed.

Abstract

This paper proposes a novel data-driven control strategy for maintaining connectivity in networked multi-robot systems. Existing approaches often rely on a pre-determined communication model specifying whether pairwise robots can communicate given their relative distance to guide the connectivity-aware control design, which may not capture real-world communication conditions. To relax that assumption, we present the concept of Data-driven Connectivity Barrier Certificates, which utilize Control Barrier Functions (CBF) and Gaussian Processes (GP) to characterize the admissible control space for pairwise robots based on communication performance observed online. This allows robots to maintain a satisfying level of pairwise communication quality (measured by the received signal strength) while in motion. Then we propose a Data-driven Connectivity Maintenance (DCM) algorithm that combines (1) online learning of the communication signal strength and (2) a bi-level optimization-based control framework for the robot team to enforce global connectivity of the realistic multi-robot communication graph and minimally deviate from their task-related motions. We provide theoretical proofs to justify the properties of our algorithm and demonstrate its effectiveness through simulations with up to 20 robots.

Figures (6)

• Figure 1: Example distributions of Received Signal Strength Index (RSSI) as inter-robot communication signal strength measurements in the real world. a) The lab environment depicting the real-world setting, b) RSSI value (dB) distribution over the space from the Wi-Fi transmitter Robot $1$, and c) RSSI value (dB) distribution over the space from the Wi-Fi transmitter Robot $2$. The white contour edges denote the level sets of RSSI = -25dB in (b) and (c), respectively, highlighting the asymmetric communication performance in real-world scenarios, e.g., the strength of wireless signal received by robot 2 from robot 1 is weaker than the one received by robot 1 from robot 2.
• Figure 2: Example of our considered communication model: black and red contour edges indicate the level sets of RSSI values of $\psi$dB and $\epsilon$dB ($\psi<\epsilon$), respectively. $\mathcal{R}_{1,3}> \epsilon$ indicates that robot $3$ is strongly connected to transmitter robot $1$ with $\mathcal{R}_{1,2}> \psi$ and $\mathcal{R}_{1,3}> \psi$ indicates that robots $3$ and $2$ can reliably measure the RSSI value of signals sent from robot $1$.
• Figure 3: Simulation example of 5 robots and tasked to corresponding colored task places. The red dash lines in this figure denote the currently optimal strongly connected communication graph $\mathcal{G}^\mathrm{c*}$. The white and red boxes represent the obstacles. The robot diameter is $0.16$m. Compared baseline method MCCST luo2020behavior under different parameter settings include (e) MCCST ($R_\mathrm{c} = 0.7$m), and (f) MCCST ($R_\mathrm{c} = 1.2$m).
• Figure 4: The contour plot for the $h^\mathrm{gp}_{i,j}(\mathbf{x})$ at different time step: a) the ground truth 0-superlevel set calculated by $\mathcal{R}_{i,j}(\mathbf{x})-\epsilon$, b) the predicted $h^\mathrm{gp}_{i,j}(\mathbf{x})$ with 0-superlevel set at $t =0$ denoted as red dash line, and c) the predicted $h^\mathrm{gp}_{i,j}(\mathbf{x})$ with 0-superlevel set at $t=700$ denoted as red dash line.
• Figure 5: Comparative analysis of the simulation example shown in Fig. \ref{['fig:our_simulation']} with respect to different metrics a) Minimum distance to robots/obstacles $D_{min}$ to verify the safety constraints' satisfaction ($R_\mathrm{s}$ = $R_\mathrm{obs} = 0.28$m), b) Average algebraic connectivity to indicate whether the graph is strongly connected ($\lambda_2 >0$) or not $\lambda_2 =0$, where $\lambda_2$ is the second-smallest eigenvalue of the Laplacian matrix calculated from the adjacency matrix. The elements in our adjacency matrix indicate whether the pairwise robots $i$ and $j$ are strongly connected with each other ($\mathcal{R}_{i,j}(\mathbf{x})\geq -25$dB and $\mathcal{R}_{j,i}(\mathbf{x})\geq -25$dB), and c) Average control perturbation (computed by $\frac{1}{N}\sum_{i=1}^N|| \mathbf{u}_i-\mathbf{u}^\mathrm{ref}_i||^{2}$ measuring the accumulated deviation from nominal controllers).

Theorems & Definitions (6)

• Lemma 1
• Lemma 2
• Lemma 3
• proof
• Proposition 4
• proof