Coordinating heterogeneous teams of mobile robots for tasks such as search and rescue is highly challenging. This is due to the complexities of perception, decision making and planning in such environments, with agents' non-synchronous operation, constrained communication, and limited computational resources. This paper presents the Cooperative and Asynchronous Transformer-based Mission Planning (CATMiP) framework, which leverages multi-agent reinforcement learning (MARL) to effectively coordinate agents with heterogeneous sensing, motion, and actuation capabilities. The framework introduces a Class-based Macro-Action Decentralized Partially Observable Markov Decision Process (CMD-POMDP) model to handle asynchronous decision-making among different agent classes via macro-actions. It also extends the Multi-Agent Transformer (MAT) architecture to facilitate distributed, ad hoc communication among the agents. CATMiP easily adapts to mission complexities and communication constraints, and scales to varying environment sizes and team compositions. Simulations demonstrate its scalability and ability to achieve cooperative mission objectives with two classes of explorer and rescuer agents, even under severe communication constraints. The code is available at https://github.com/mylad13/CATMiP.
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