Robotic manufacturing systems are essential in the post-pandemic world owing to their high level of flexibility and automation during a labor crisis. However, designing a suitable robotic manufacturing system for small- and mid-sized enterprises (SMEs) is challenging, considering both their financial burdens and the current supply chain disruptions of component suppliers. To address these challenges, this study proposes a distributed multi-agent collaborative conceptual design method involving designers and suppliers to assist SMEs in implementing robotic manufacturing systems. First, we propose a common data model that enables knowledge interaction between different agents during collaborative conceptual design. Subsequently, based on the proposed data model, the agent-based collaborative conceptual design process is developed, which enables different agents to communicate, interact, and negotiate with each other according to their experiences and knowledge. Third, an integrative algorithm based on 2-additive fuzzy measures, Choquet integral, and stochastic multi-criteria acceptability analysis is implemented to support the multi-agent decision-making process to robustly select architecture alternatives. As a case study, a real industrial design project of a robotic manufacturing system required by our industrial partner, is adopted to demonstrate the effectiveness of the proposed method.