The study of distributed optimisation for mobile robots has become a cutting-edge topic of great interest in the mobile edge computing environment. In this paper, we propose a semi-distributed power allocation algorithm by introducing millimetre wave communication (mmW) technology and the innovative application of integrated circuits (ICs), aiming at the efficient allocation of resources and power in mobile robot systems. Through the introduction of graph theory and Lagrangian duality, we design an integrated framework that decouples the distributed optimisation problem into two phases of local computation and global collaboration, making full use of the computational and communication resources in ICs. Experimental results show that the semi-distributed approach outperforms the centralised approach in terms of energy consumption, but slightly improves the time-averaged delay. Further parameter sensitivity analyses reveal the impact of the weight parameter V in the Lyapunov drift-penalty transformation on the system performance. By tuning V, we can achieve a targeted trade-off between energy consumption and time-averaged delay, providing a feasible solution for mobile robot performance optimisation in different task scenarios. This research not only deepens the theoretical foundation of distributed optimisation for mobile robots, but also provides practical guidance for the design and tuning of real systems in mobile edge computing environments. From a technical point of view, the application of millimetre wave communication and integrated circuits provides a broader communication and computation space for mobile robot systems. In addition, the semi-distributed algorithm and the sensitivity analysis of Lyapunov drift-penalty weights in this paper provide new theoretical and technical support for the future development of intelligent mobile robots.