As assembly tasks grow in complexity, collaboration among multiple robots becomes essential for task completion. However, centralized task planning has become inadequate for adapting to the increasing intelligence and versatility of robots, along with rising customized orders. There is a need for efficient and automated planning mechanisms capable of coordinating diverse robots for collaborative assembly. To this end, we propose a Stackelberg game-theoretic learning approach. By leveraging Stackelberg games, we characterize robot collaboration through leader-follower interaction to enhance strategy seeking and ensure task completion. To enhance applicability across tasks, we introduce a novel multi-agent learning algorithm: Stackelberg double deep Q-learning, which facilitates automated assembly strategy seeking and multi-robot coordination. Our approach is validated through simulated assembly tasks. Comparison with three alternative multi-agent learning methods shows that our approach achieves the shortest task completion time for tasks. Furthermore, our approach exhibits robustness against both accidental and deliberate environmental perturbations.

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