Graph Neural Networks for Multi-Robot Active Information Acquisition

TL;DR

Numerical simulations on significantly larger graphs and dimensionality of the hidden state and more complex environments than those seen in training validate the properties of the proposed architecture and its efficacy in the application of localization and tracking of dynamic targets.

Abstract

This paper addresses the Multi-Robot Active Information Acquisition (AIA) problem, where a team of mobile robots, communicating through an underlying graph, estimates a hidden state expressing a phenomenon of interest. Applications like target tracking, coverage and SLAM can be expressed in this framework. Existing approaches, though, are either not scalable, unable to handle dynamic phenomena or not robust to changes in the communication graph. To counter these shortcomings, we propose an Information-aware Graph Block Network (I-GBNet), an AIA adaptation of Graph Neural Networks, that aggregates information over the graph representation and provides sequential-decision making in a distributed manner. The I-GBNet, trained via imitation learning with a centralized sampling-based expert solver, exhibits permutation equivariance and time invariance, while harnessing the superior scalability, robustness and generalizability to previously unseen environments and robot configurations. Experiments on significantly larger graphs and dimensionality of the hidden state and more complex environments than those seen in training validate the properties of the proposed architecture and its efficacy in the application of localization and tracking of dynamic targets.

Figures (5)

• Figure 1: In this Figure we illustrate our graph parametrization of the AIA problem with the I-GBNet. Robot $i$ collects its neighbors' positions and estimates, along with its own attributes and map and feeds them to the network. The latter produces the next action, the robot updates its position takes new measurements. The process is repeated per robot and timestep.
• Figure 2: I-GBNet structure comprising of aggregation functions $\rho^\Omega,\rho^p$, a heatmap projection module $\mathcal{H}$ that projects the posterior distribution of the hidden state on the grid, and a node update function that produces admissible control actions. It only updates the node attributes of the graph, leaving the latter topologically unscathed. The update node function $\phi^v$ comprises of 3 consecutive ResNet Blocks with skip connections, an adaptive average pooling layer and an Action MLP.
• Figure 3: In this Figure we plot the success and flowtime increase for $N\times M$ robots and targets, where each problem instance is run for 100 random environments and initializations. We compare our GNN algorithm to two baselines a Decentralized Sampling-Based (Dec-SB) and a Random method
• Figure 4: This Figure illustrates qualitatively the efficacy of our scheme to the target localization and tracking problem. Fig. \ref{['fig:static_traj']} represents in different colors the executed trajectories of three robots tasked to localize 5 static targets. The evolution of their corresponding uncertainties is depicted in Fig. \ref{['fig:static_sigmas']}. In Fig. \ref{['fig:dynamic_traj']} we show spotlights of the solution with dynamic target and in Fig. \ref{['fig:dynamic_sigmas']} the evolution of the global covariance for each of the targets. In Fig. 4a,4b, the starting and ending position of the robots is illustrated as a triangle and a square respectively, while the targets as red $x$-markers.
• Figure 5: Figure \ref{['fig:resilience1']} depicts the per-node sum of determinants over time, with black lines representing active robots, red the one that fails at $t=10$, and gray area the localization threshold. Figures \ref{['fig:t9_0']}, \ref{['fig:t9_1']} and \ref{['fig:t49_1']} illustrate the hidden state distribution at $t=9$ for robots $k$ and $2$ and at time $t=49$ for robot $2$ respectively. The average mission time for 50 tests is illustrated in Figure \ref{['fig:time_increase']}, where $\mathcal{A}$ refers to the case study with distance-defined communication graph, communication loss and agent failure and $\mathcal{B}$ the one with a static fully connected graph.

Theorems & Definitions (5)

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