Distributed model predictive control (DMPC) is promising to achieve optimal cooperative control in multi-robot systems (MRSs). However, real-time DMPC implementation relies on numerical optimization tools to periodically calculate local control sequences online. This process is computationally demanding and lacks scalability for large-scale, nonlinear MRSs.

   In this article, we propose a novel distributed learning-based predictive control (DLPC) framework for scalable multirobot control. Unlike conventional DMPC methods that calculate open-loop control sequences, our approach centers around a computationally fast and efficient distributed policy learning algorithm that generates explicit closed-loop DMPC policies for MRS without using numerical solvers.  The policy learning is executed incrementally and forward in time in each prediction interval through an online distributed actor-critic implementation. The control policies are successively updated in a receding-horizon manner, enabling fast and efficient policy learning with the closed-loop stability guarantee. The learned control policies could be deployed online to MRS with varying robot scales, enhancing scalability and transferability for large-scale MRS. 

  Furthermore, we extend our methodology to tackle the multirobot safe learning challenge through a force field inspired policy learning approach. We validate our approach's effectiveness, scalability, and efficiency through extensive experiments on cooperative tasks of large-scale wheeled robots and multirotor drones. Our results demonstrate the rapid learning and deployment of DMPC policies for MRS with scales up to 10,000 units.