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The advantages of modular robot systems stem from their ability to change between different configurations, enabling them to adapt to complex and dynamic real-world environments. Then, how to perform the accurate and efficient change of the modular robot system, i.e., the self-reconfiguration problem, is essential. Existing reconfiguration algorithms are based on discrete motion primitives and are suitable for lattice-type modular robots. The modules of freeform modular robots are connected without alignment, and the motion space is continuous. It renders existing reconfiguration methods infeasible. In this paper, we design a parallel distributed self-reconfiguration algorithm for freeform modular robots based on multi-agent reinforcement learning to realize the automatic design of conflict-free reconfiguration controllers in continuous action spaces. To avoid conflicts, we incorporate a collaborative mechanism into reinforcement learning. Furthermore, we design the distributed termination criteria to achieve timely termination in the presence of limited communication and local observability. When compared to the baselines, simulations show that the proposed method improves efficiency and congruence, and module movement demonstrates altruism.