Over the centuries, humanity has created ever more ingenious systems to traverse the oceans and skies of our planet. Modern ships and planes operate with powerful engines that require substantial amounts of fuel, leading to high operating costs. However, this approach becomes impractical for applications that require extended periods of autonomous operation without the possibility of refueling. This dissertation starts with the idea of operating systems by going with the flow: harnessing the wind and ocean currents by letting the system drift in favorable directions and strategically using a low-power engine to change flows when this is beneficial. As the power to counteract drag forces scales cubically with the relative velocity of the system, this new paradigm reduces the power required for operation by 2-3 orders of magnitude, thereby significantly reducing the system and operating costs. This could enable a host of novel applications that require low-cost and long-term operations, such as active environmental monitoring of the oceans and atmosphere or floating solar platforms. The primary case study used throughout this work is autonomous seaweed farms that roam the oceans while rapidly growing biomass for biofuel, bioplastic, or to sink it for carbon removal.

In this dissertation, we systematically develop control techniques to tackle the four key challenges of operating by going with the flow: First, the system is severely underactuated with its own propulsion often being less than 1/10th of the magnitude of the surrounding flows. Second, to make strategic control decisions when to change flows, only coarse, deterministic forecasts are available. Third, the forecasts have a limited time horizon of 5-10 days, but realistic control objectives extend over weeks to months. Lastly, the forecast error defined as the difference between the forecasted and the true flows often exceeds the propulsion capabilities of the system, hence robust control is infeasible.

We start by introducing techniques for continuous-time optimal control when the complex flows are known. We use dynamic programming for the objectives of navigation and maximizing seaweed growth. Next, we turn towards the challenge of operating with imperfect and short-term forecasts. Our insight is that the value functions obtained by the previously developed optimal control methods can be used as closed-loop control policies, which are equivalent to replanning on the forecast at every step. Through extensive simulation studies in realistic ocean conditions, we demonstrate that such frequent replanning allows for reliable operation despite significant forecast errors. To enable reasoning beyond the forecast horizon, we derive a discounted optimal control formulation and demonstrate how the value function can be extended by estimating the cost-to-go using historical flow averages. In the last part of this dissertation, we focus on how to handle constraints in these challenging environments. For that, we integrate time-varying obstacles into our value function and show empirically that this almost eliminates the risk of stranding. Moreover, we develop a hierarchical control approach to operate a fleet of underactuated autonomous systems while avoiding collisions and ensuring connectivity across the fleet.

At the end of this dissertation, we summarize our techniques for operating by going with the flow which could enable a host of new applications of low-power autonomous systems in the oceans and skies. We also discuss promising ongoing and future research directions towards further improving the performance of underactuated robotic systems operating in flows.