Edge robotics involves frequent exchanges of large-volume multi-modal data. Existing methods ignore the interdependency between robotic functionalities and communication conditions, leading to excessive communication overhead. This paper revolutionizes edge robotics systems through integrated perception, motion, and communication (IPMC). As such, robots can dynamically adapt their communication strategies (i.e., compression ratio, transmission frequency, transmit power) by leveraging the knowledge of robotic perception and motion dynamics, thus reducing the need for excessive sensor data uploads. Furthermore, by leveraging the learning to optimize (LTO) paradigm, an imitation learning neural network is designed and implemented, which reduces the computational complexity by over 10x compared to state-of-the art optimization solvers. Experiments demonstrate the superiority of the proposed IPMC and the real-time execution capability of LTO.