We show how a distributed flocking controller can be synthesized using deep learning from a centralized controller which generates the trajectories of the flock. Our approach is based on supervised learning, with the centralized controller providing the training data to the learning agent, i.e., the synthesized distributed controller. We use Model Predictive Control (MPC) for the centralized controller, an approach that has been successfully demonstrated on flocking problems. MPCbased flocking controllers are high-performing but also computationally expensive. By learning a symmetric distributed neural flocking controller from a centralized MPC-based flocking controller, we achieve the best of both worlds: the neural controllers have high performance (on par with the MPC controllers) and high efficiency. Our experimental results demonstrate the sophisticated nature of the distributed controllers we learn. In particular, the neural controllers are capable of achieving myriad flocking-oriented control objectives, including flocking formation, collision avoidance, obstacle avoidance, predator avoidance, and target seeking. Moreover, they generalize the behavior seen in the training data in order to achieve these objectives in a significantly broader range of scenarios.
We show how a high-performing, fully distributed and symmetric neural V-formation controller can be synthesized from a Centralized MPC (Model Predictive Control) controller using Deep Learning. This result is significant as we also establish that under very reasonable conditions, it is impossible to achieve V-formation using a deterministic, distributed, and symmetric controller. The learning process we use for the neural V-formation controller is significantly enhanced by CEGkR, a Counterexample-Guided k-fold Retraining technique we introduce, which extends prior work in this direction in important ways. Our experimental results show that our neural V-formation controller generalizes to a significantly larger number of agents than for which it was trained (from 7 to 15), and exhibits substantial speedup over the MPC-based controller. We use a form of statistical model checking to compute confidence intervals for our neural Vformation controller's convergence rate and time to convergence.
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