Learning abstraction of a swarm to control a parent system

Many high-dimensional systems can be decomposed into a swarm of subsystems manipulating a parent system, each with its own dynamics. Rather than design control laws directly on this state space, we propose a method that uses deep learning to learn an abstract state of the swarm that encapsulates the interactions between the swarm and parent system. In addition, controllers for the swarm and parent system that utilize this abstract state are also learned. Further, the controller for the swarm is designed to be pseudo-distributed, where the policy for each member is only dependent on that member's state, the abstract representation of the swarm, and the desired abstract representation. We set up neural networks for each part of the architecture and assemble them into a recurrent neural network wherein the mapping to the abstract state and the control laws for the parent and swarm systems are learned simultaneously. This method is applied to an example problem consisting of a tilting plane with a swarm of robots driving on top of it, with the goal being to balance the plane. The results are compared to those of an iterative Linear Quadratic Regulator as well as a prescribed abstract state with hand-crafted controllers for the swarm and parent systems. Our results show that the performance of the learned method is comparable to these more demanding methods.