That interest might seem unexpected, as kites are commonly thought of as airborne playthings. But in this instance, kites are generically lifting bodies moving through flowing fluids and tethered to base stations. A kite moving in cyclic patterns perpendicular to the prevailing flow can travel much faster than the flow itself. If a turbine is attached to the kite, it can capture much more power than a stationary turbine of the same size.
The U.S. Navy in particular is interested in developing autonomous underwater vehicles (AUVs) that can support very high payloads and extended missions. These vehicles would be faced with unprecedented energy requirements, “necessitating mechanisms for harvesting a portion of the marine energy made available along the mission,” said Chris Vermillion, an associate professor of mechanical engineering at the University of Michigan in Ann Arbor who is an expert in this field.
In a scenario Vermillion sketched out, an underwater kite could be deployed from the AUV parked on the seabed. As the kite executes figure-8 orbits at speeds that are several times that of the prevailing flow, it could generate electricity to recharge the UAV’s battery.
One factor that has hampered the development of power kites up to now involved the tether, specifically the drag induced as the tether moves through the fluid. An AUV parked on relatively deep seabeds would require very long (a kilometer or more) tether to reach areas of favorable flow. And every meter of that moving tether is susceptible to drag.
To better understand the dynamics of ultralong tethers (ULTs), Vermillion and his research team at North Carolina State University (where he was an associate professor until 2024) ran a computation study that explored how to use advanced control techniques and physical morphing to overcome the drag effects of operating on a long tether.
The results of their study were published as “Drag-Mitigating Dynamic Flight Path Design and Sensitivity Analysis for an Ultra-Long Tether Underwater Kite” in the January 2025 issue of ASME Journal of Dynamic Systems, Measurement, and Control.
Tether Drag Mitigation
Vermillion conducted the computational study to determine the relationship between path shape and tether drag at varying tether lengths in order to develop meaningful insights regarding the operation of systems that require ultralong tethers to reach viable flow resources.
Tether drag mitigation is characterized through the use of a novel metric termed effective tether length, which characterizes the total length of tether engaged in drag production. The researchers also looked for ways to reduce the energy losses associated with tether drag.
All analyses were based on a flight controller that simultaneously followed an adjustable figure-8 path and limited tether tension based on structural constraints—“which is important since the required tether diameter and associated drag depend on the peak tension,” Vermillion said.
The experiments showed that tether drag is the primary loss associated with ULT applications. “We learned that, through careful flight path design, only a fraction of the tether is actually engaged in motion while the majority of the tether is approximately stationary,” he added.
For a well-designed path, the team discovered that the mean effective tether length is much less than the total tether length. A high-performance path shape can reduce the effect of tether drag by over 50 percent.
“Additionally, given the impact of tether drag on system performance, physical tether drag mitigation strategies have a large impact on system performance when applied to a relatively small portion of the tether,” Vermillion said.
Adaptive Controls
Although the initial model had an appropriate structure, several of the component models were “pretty far off” in terms of lift and drag characterizations. The kite’s fuselage and tether were large contributors to these uncertainties.
“It took a number of experimental campaigns to ultimately validate the model that we used,” Vermillion said. “Even then, our team felt that it was important that the control strategies we employed on an ULT kite be adaptive, such that the algorithm could adjust the kite’s figure-8 flight profile on the fly in order to minimize the effective tether length and maximize the power output. We ultimately settled on a variant of iterative learning control for performing this adaptation.”
One of the biggest surprises was that for kites whose tether lengths exceeded a few hundred meters, the power projections under an optimized flight path actually far exceeded the “theoretical optimum” predicted by a very simple model that has been used for decades to benchmark kite systems. This is a result of the fact that the simple benchmark model derives a theoretical optimum based on an assumption that the tether is a straight line.
Under that assumption, the entire tether is moving, with the midpoint of the tether moving at half the speed of the kite (and the quarter tether point moving at one quarter of the kite’s speed, the three-quarter point moving at three quarters of the kite’s speed, etc.). Such a “rigid” tether is actually very inefficient, since the entirety of the tether is contributing significant drag.
“By tailoring the kite’s path to keep most of the tether motionless, simulations predict that the kite’s power output can far exceed that of the straight-tether assumption—something that had not been established in the literature up to the point of our team’s study,” Vermillion said.
Mechanical engineers will be interested in the specific control strategies for UTL kites. An innovative element in this study was the use of iterative learning control (ILC) to maximize an economic objective in continuous time.
“Traditionally,” Vermillion said, “ILC has been used to improve tracking performance in manufacturing applications where a precise toolpath has been defined, and the goal is to track this path as closely as possible. However, in the kite application, the optimal flight path is in fact unknown. Indeed, the objective is no longer to track a prescribed path as quickly as possible, but to figure out the optimal path for maximizing the average power generation over a figure-8 pattern.”
The lab is focused on combining controller adaptation with physical reconfiguration and adaptation in real time.
“The reality is that a lot of performance gains can be realized through real-time controller adaptation, but some aspects of performance can only be improved with a different physical design,” Vermillion said. “By incorporating real-time physical adaptation into a system, both the control variables and physical design parameters [for example, wing geometry, rotor coning angle] can be adjusted as the operating environment changes. Of course, real-time reconfigurability comes at a cost, and our team is working to quantify the cost and benefit of this reconfigurability within an integrated multidisciplinary design optimization tool.”
Mark Crawford is a technology writer in Corrales, N.M.
