Collaborative perception allows for information sharing between multiple agents, such as vehicles and infrastructure, to obtain a comprehensive view of the environment through communication and fusion. Current research on multi-agent collaborative perception systems often assumes ideal communication and perception environments and neglects the effect of real-world noise such as pose noise, motion blur, and perception noise. To address this gap, in this paper, we propose a novel motion-aware robust communication network (MRCNet) that mitigates noise interference and achieves accurate and robust collaborative perception. MRCNet consists of two main components: multi-scale robust fusion (MRF) addresses pose noise by developing cross-semantic multi-scale enhanced aggregation to fuse features of different scales, while motion enhanced mechanism (MEM) captures motion context to compensate for information blurring caused by moving objects. Experimental results on popular collaborative 3D object detection datasets demonstrate that MRCNet outperforms competing methods in noisy scenarios with improved perception performance using less bandwidth.