Recent advances in EEG-based BCI technologies have revealed the potential of brain-to-robot collaboration through the integration of sensing, computing, communication, and control. In this paper, we present BRIEDGE as an end-to-end system for multi-brain to multi-robot interaction through an EEG-adaptive neural network and an encoding-decoding communication framework, as illustrated in Fig.1. As depicted, the edge mobile server or edge portable server will collect EEG data from the users and utilize the EEG-adaptive neural network to identify the users' intentions. The encoding-decoding communication framework then encodes the EEG-based semantic information and decodes it into commands in the process of data transmission. To better extract the joint features of heterogeneous EEG data as well as enhance classification accuracy, BRIEDGE introduces an informer-based ProbSparse self-attention mechanism. Meanwhile, parallel and secure transmissions for multi-user multi-task scenarios under physical channels are addressed by dynamic autoencoder and autodecoder communications. From mobile computing and edge AI perspectives, model compression schemes composed of pruning, weight sharing, and quantization are also used to deploy lightweight EEG-adaptive models running on both transmitter and receiver sides. Based on the effectiveness of these components, a code map representing various commands enables multiple users to control multiple intelligent agents concurrently. Our experiments in comparison with state-of-the-art works show that BRIEDGE achieves the best classification accuracy of heterogeneous EEG data, and more stable performance under noisy environments.