Message-Aware Graph Attention Networks for Large-Scale Multi-Robot Path Planning

TL;DR

The Message-Aware Graph Attention neTwork (MAGAT) is based on a key-query-like mechanism that determines the relative importance of features in the messages received from various neighboring robots and is able to achieve a performance close to that of a coupled centralized expert algorithm.

Abstract

The domains of transport and logistics are increasingly relying on autonomous mobile robots for the handling and distribution of passengers or resources. At large system scales, finding decentralized path planning and coordination solutions is key to efficient system performance. Recently, Graph Neural Networks (GNNs) have become popular due to their ability to learn communication policies in decentralized multi-agent systems. Yet, vanilla GNNs rely on simplistic message aggregation mechanisms that prevent agents from prioritizing important information. To tackle this challenge, in this paper, we extend our previous work that utilizes GNNs in multi-agent path planning by incorporating a novel mechanism to allow for message-dependent attention. Our Message-Aware Graph Attention neTwork (MAGAT) is based on a key-query-like mechanism that determines the relative importance of features in the messages received from various neighboring robots. We show that MAGAT is able to achieve a performance close to that of a coupled centralized expert algorithm. Further, ablation studies and comparisons to several benchmark models show that our attention mechanism is very effective across different robot densities and performs stably in different constraints in communication bandwidth. Experiments demonstrate that our model is able to generalize well in previously unseen problem instances, and that it achieves a 47\% improvement over the benchmark success rate, even in very large-scale instances that are $\times$100 larger than the training instances.

Figures (5)

• Figure 1: Our proposed decentralized framework. (i) illustrates how we process the partial observations of each robot into input tensor ${\mathbf Z}_t^i$, and how we construct the dynamic communication network. (ii) demonstrates the processing pipeline consisting of a feature extractor, a graph convolution module, and an Multi-layer Perceptron (MLP). The optional skip connection represents the bottleneck structure discussed in Sec. \ref{['sec:framework']}. (iii) visualizes how our model gathers features, computes attention weights by a key-query-like attention mechanism (sandy brown), and selectively aggregates useful features.
• Figure 2: The success rate ($\alpha$) and flowtime increase ($\delta_{\mathrm{FT}}$) against the change of environment setup. Here we present the results of GNN models on the left two columns and MAGAT models on the right; we include HCA and Replan as baselines. The first row is for "Same Robot Density Set", while the second is for "Increasing Robot Density Set". These figures show the effects of reducing bandwidth or using bottleneck structure. In the legend ([Graph_Layer_Name]-[Type]-[Num_Features]), Graph_Layeer_Name are GNN or MAGAT, while Type - "F" and solid line refer to normal CNN-MLP-GNN/MAGAT-MLP-Action pipeline, and "B" and dashed line refer to a bottleneck structure. [Num_Features] includes 128 (red), 64 (blue), 32 (black), and 16 (purple).
• Figure 3: Generalization test on Large Scale Map Set. a) shows the success rate. b) shows the percentage of successful robots ($p_{\mathrm{rg}}=\frac{n_{\mathrm{robots\,reach\, goal}}}{n_{\mathrm{robot}}}$), indicating that those model with low success rates can still successfully navigated most of the robots to their goals.
• Figure 4: Histogram of proportion of cases distributed over the number of robots reaching their goal; GNN-F-128(red), MAGAT-F-128(blue), MAGAT-F-32-P4(green) and MAGAT-B-32-P4(yellow), are trained on $20\times 20$ with 10 robots and tested on $200\times 200$ with 500, 1000 robots, and $100\times 100$ with 500 robots.
• Figure 5: The success rate ($\alpha$) and flowtime increase ($\delta_{\mathrm{FT}}$) against the change of environment setup. Here we present some selected results of GNN and MAGAT in both “Same Robot Density Set” (Panel a and b) and “Increasing Robot Density Set” (Panel c and d). The results demonstrated that MAGAT is able to generalize better to more extreme unseen cases. In the legend ([Graph_Layer_Name]-[Type]-[Num_Features]), Graph_Layeer_Name are GNN (dashed line) or MAGAT (solid line), while Type - "F" refer to normal CNN-MLP-GNN/MAGAT-MLP-Action pipeline, and "B" refer to a bottleneck structure. [Num_Features] includes 128 (red), 64 (blue), 32 (black), 16 (purple).

Theorems & Definitions (5)

• Lemma 1
• Proposition 1: Permutation Equivariance of MAGAT
• proof
• Proposition 2: Time Invariance of MAGAT
• proof