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Abstract In various applications of multi-robotics in disaster response, warehouse management, and manufacturing, tasks that are known a priori and tasks added during run time need to be assigned efficiently and without conflicts to robots in the team. This multi-robot task allocation (MRTA) process presents itself as a combinatorial optimization (CO) problem that is usually challenging to be solved in meaningful timescales using typical (mixed)integer (non)linear programming tools. Building on a growing body of work in using graph reinforcement learning to learn search heuristics for such complex CO problems, this paper presents a new graph neural network architecture called the covariant attention mechanism (CAM). CAM can not only generalize but also scale to larger problems than that encountered in training, and handle dynamic tasks. This architecture combines the concept of covariant compositional networks used here to embed the local structures in task graphs, with a context module that encodes the robots’ states. The encoded information is passed onto a decoder designed using multi-head attention mechanism. When applied to a class of MRTA problems with time deadlines, robot ferry range constraints, and multi-trip settings, CAM surpasses a state-of-the-art graph learning approach based on the attention mechanism, as well as a feasible random-walk baseline across various generalizability and scalability tests. Performance of CAM is also found to be at par with a high-performing non-learning baseline called BiG-MRTA, while noting up to a 70-fold improvement in decision-making efficiency over this baseline. 

As city populations continue to rise, urban air mobility (UAM) seeks to provide much needed relief from traffic congestion. UAM is enforced by electrical vertical takeoff and landing (eVTOL) vehicles, which operate out of a vertiport, akin to the relationship between planes and airports. The vertiport has an air traffic controller (ATC) tasked with managing each eVTOL, ensuring they reach their destinations on time and safely. This task allocation problem can be difficult due to inadvertent issues such as mechanical failure, inclement weather, collisions, among other uncertainties that may arise. This paper provides a novel solution to this Urban Air Mobility - Vertiport Schedule Management (UAM-VSM) problem through the utilization of graph convolutional networks (GCNs). GCNs allow us to add abstractions of the vertiport space and eVTOL space as graphs, and aggregate information for a centralized ATC agent to help generalize the environment. We use Unreal Engine combined with Airsim for high fidelity simulation. The proposed GRL agent will be trained in an environment without extra uncertainties and then tested with and without those uncertainties. The performance will be examined side by side with a random and first come first serve (FCFS) baseline. 

Abstract This paper introduces a new graph neural network architecture for learning solutions of Capacitated Vehicle Routing Problems (CVRP) as policies over graphs. CVRP serves as an important benchmark for a wide range of combinatorial planning problems, which can be adapted to manufacturing, robotics and fleet planning applications. Here, the specific aim is to demonstrate the significant real-time executability and (beyond training) scalability advantages of the new graph learning approach over existing solution methods. While partly drawing motivation from recent graph learning methods that learn to solve CO problems such as multi-Traveling Salesman Problem (mTSP) and VRP, the proposed neural architecture presents a novel encoder-decoder architecture. Here the encoder is based on Capsule networks, which enables better representation of local and global information with permutation invariant node embeddings; and the decoder is based on the Multi-head attention (MHA) mechanism allowing sequential decisions. This architecture is trained using a policy gradient Reinforcement Learning process. The performance of our approach is favorably compared with state-of-the-art learning and non-learning methods for a benchmark suite of Capacitated-VRP (CVRP) problems. A further study on the CVRP with demand uncertainties is conducted to explore how this Capsule-Attention Mechanism architecture can be extended to handle real-world uncertainties by embedding them through the encoder.