Underactuated control and distribution of multi-agent systems in stratified flow environments

The present paper shows how vertical actuation alone may be used to effectively control the spatial distribution of mobile vehicles (“balloons” in air, or “drifters” in water) in vertically-stratified background flows. Applying iterative, adjoint-based, model predictive control (MPC) techniques coupled with linear quadratic regular (LQR) feedback, agent trajectories and feedback control strategies are determined to ensure the desired terminal-time spacing of multiple agents. Variations in both starting locations and disturbances are considered to illustrate the significant control authority in this agent separation problem in both laminar and turbulent background flows, despite the fact that linear controllability is lost in certain limiting cases. The paper thus demonstrates a novel application of feedback control theory to an emerging real-world application in multi-agent systems. The results lay the groundwork for future applications in Lagrangian sampling of underwater ecosystems as well as the efficient sampling of hurricanes for the purpose of forecasting their development.