The orchestration of agents to optimize a collective objective without centralized control is challenging yet crucial for applications such as controlling autonomous fleets, and surveillance and reconnaissance using sensor networks. Decentralized controller design has been inspired by self-organization found in nature, with a prominent source of inspiration being flocking; however, decentralized controllers struggle to maintain flock cohesion. The graph neural network (GNN) architecture has emerged as an indispensable machine learning tool for developing decentralized controllers capable of maintaining flock cohesion, but they fail to exploit the symmetries present in flocking dynamics, hindering their generalizability. We enforce rotation equivariance and translation invariance symmetries in decentralized flocking GNN controllers and achieve comparable flocking control with 70% less training data and 75% fewer trainable weights than existing GNN controllers without these symmetries enforced. We also show that our symmetry-aware controller generalizes better than existing GNN controllers. Code and animations are available at http://github.com/Utah-Math-Data-Science/Equivariant-Decentralized-Controllers.

Collaborative robotics is a new and challenging field in the realm of motion control and human-robot interaction. The safety measures needed for a reliable interaction between the robot and its environment hinder the use of classical control methods, pushing researchers to try new techniques such as machine learning (ML). In this context, reinforcement learning has been adopted as the primary way to create intelligent controllers for collaborative robots, however supervised learning shows great promise in the hope of developing data-driven model based ML controllers in a faster and safer way. In this work we study several aspects of the methodology needed to create a dataset to be used to learn the dynamics of a robot. For this we tune several PD controllers to several trajectories, using a multi-objective genetic algorithm (GA) which takes into account not only their accuracy, but also their safety. We demonstrate the need to tune the controllers individually to each trajectory and empirically explore the best population size for the GA and how the speed of the trajectory affects the tuning and the dynamics of the robot.