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Many robotic applications, such as search-and-rescue, require multiple agents to search for and perform actions on targets. However, such missions present several challenges, including cooperative exploration, task selection and allocation, time limitations, and computational complexity. To address this, we propose a decentralized multi-agent decision-making framework for the search and action problem with time constraints. The main idea is to treat time as an allocated budget in a setting where each agent action incurs a time cost and yields a certain reward. Our approach leverages probabilistic reasoning to make near-optimal decisions leading to maximized reward. We evaluate our method in the search, pick, and place scenario of the Mohamed Bin Zayed International Robotics Challenge (MBZIRC), by using a probability density map and reward prediction function to assess actions. Extensive simulations show that our algorithm outperforms benchmark strategies, and we demonstrate system integration in a Gazebo-based environment, validating the framework's readiness for field application.

Multi-Agent Time-Based Decision-Making for the Search and Action Problem