In this paper, we present an advanced strategy for the coordinated control of a multi-agent aerospace system, utilizing Deep Neural Networks (DNNs) within a reinforcement learning framework. Our approach centers on optimizing autonomous task assignment to enhance the system's operational efficiency in object relocation tasks, framed as an aerospace-oriented pick-and-place scenario. By modeling this coordination challenge within a MuJoCo environment, we employ a deep reinforcement learning algorithm to train a DNN-based policy to maximize task completion rates across the multi-agent system. The objective function is explicitly designed to maximize effective object transfer rates, leveraging neural network capabilities to handle complex state and action spaces in high-dimensional aerospace environments. Through extensive simulation, we benchmark the proposed method against a heuristic combinatorial approach rooted in game-theoretic principles, demonstrating a marked performance improvement, with the trained policy achieving up to 16\% higher task efficiency. Experimental validation is conducted on a multi-agent hardware setup to substantiate the efficacy of our approach in a real-world aerospace scenario.