A 2009 study by Campbell and Maciejowski demonstrated model predictive control (MPC) of a highly flexible micro air vehicle (MAV) whose wings are mounted on springs, comparing a passive-spring configuration with an active-articulated one in which the MPC commands the wing spring mounting angles. The study closed with three unresolved issues that remain open: no means has been shown to be best for improving lateral-directional maneuverability while retaining the flexible wing's passive gust rejection (candidates include scheduling spring mounting angles, dynamically adjusting wing damping, or applying a direct wing moment from a fuselage-mounted actuator); the MPC-controlled MAV has not been evaluated over a full flight envelope (steady climbs, steady turns, descending turns); and real-time feasibility on embedded hardware is unproven, since the worst-case optimization time (0.139 s) exceeded the 0.1 s sampling period. The coupled objective — an agile, gust-robust, full-envelope, real-time MPC design for this class of highly flexible MAV — is not known to have been achieved.

Background

Micro air vehicles (MAVs) are small unmanned aircraft, typically with spans of a few tens of centimeters or less, flown at low airspeeds where the Reynolds number (the ratio of inertial to viscous forces in the airflow, here on the order of a hundred thousand or below) makes the aerodynamics unsteady and hard to model. Many successful MAV designs use highly flexible wings: a compliant carbon-fiber skeleton covered by a membrane skin, with the wing in some designs attached to the fuselage through springs. Compliance gives passive gust rejection — when a gust strikes, the wing twists and changes camber in a way that partially sheds the load before it reaches the airframe, so the vehicle's attitude and any onboard imaging are disturbed far less than for a rigid wing of the same size. The price is that the rigid-body flight dynamics become coupled to the wing's structural dynamics (aeroelasticity), and control authority — especially in the lateral-directional channel, meaning roll, yaw, and sideslip motion — is weak and strongly dependent on the wing-fuselage mounting.

This tradeoff was established by the University of Florida and US Air Force Research Laboratory flexible-wing MAV programs. Early flight tests (Ifju, Waszak, and Jenkins, 2001) characterized how wing flexibility changes the stability and control properties of a fixed-wing MAV; in-flight shaping of the membrane wing was shown to alter flight characteristics (Abdulrahim, Garcia, and Lind, 2005); and actuating the membrane skin was proposed specifically as a roll-control device (Stanford, Abdulrahim, Lind, and Ifju, 2007). Gust-resistant flexible-wing MAV design was analyzed by Galiński (2006), and the Air Force Research Laboratory defined a flexible-wing MAV research configuration for this class of studies (Stewart, Wagener, Abate, and Salichon, 2007).

Campbell and Maciejowski (2009) asked whether model predictive control could exploit, rather than fight, this aeroelastic coupling. MPC is a feedback law in which, at every sampling instant, a finite-horizon constrained optimization of the predicted plant trajectory is solved to select the control input; the standard stability and optimality framework is due to Mayne, Rawlings, Rao, and Scokaert (2000). They used a simulation model of a highly flexible MAV whose wings are mounted on springs, with the rigid-body flight states augmented by aeroelastic wing states, and compared two configurations: a passive one with fixed spring mountings, and an active-articulated one in which the MPC commands the wing spring mounting angles. Active articulation improved the MAV's maneuverability, but at a computational price: the worst-case optimization solve time, 0.139 s, exceeded the 0.1 s sampling period, so the control loop could not be guaranteed to run in real time on embedded-class MAV hardware. Approximation techniques for accelerating MPC (Wang and Boyd, 2008) were identified as a partial remedy.

The study's own conclusions pose the three unresolved issues that define this problem: the best means of improving lateral-directional maneuverability while retaining passive gust rejection has not been identified (the options named are control of the spring mounting angles, dynamically adjusting the wing damping coefficient, or exerting a moment directly on the wing with an actuator inside the fuselage); the MPC-controlled MAV has not been evaluated in steady climbs, steady turns, and descending turns, so its full-flight-envelope behavior is unknown; and the computation time of the MPC optimization must be reduced to guarantee real-time feasibility on limited embedded hardware. These three issues are facets of a single engineering objective: a highly flexible MAV that is simultaneously agile in the lateral-directional channel, gust-robust, controllable across its entire envelope, and computable in real time on flight-worthy hardware.

Problem Statement

For a highly flexible micro air vehicle of the spring-mounted-wing class studied by Campbell and Maciejowski (2009), determine and demonstrate a control solution that jointly achieves the three objectives left open by that study:

  1. Lateral-directional maneuverability with retained passive gust rejection. Identify the best means of improving lateral-directional maneuverability relative to the passive-spring configuration while retaining the flexible wing's passive gust rejection, comparing at least the options the source study named — control of the wing spring mounting angles, dynamic adjustment of the wing damping coefficient, and a moment applied directly to the wing by an actuator inside the fuselage — or establishing that some alternative dominates them. The comparison must quantify both maneuverability (lateral-directional command tracking and response) and gust rejection (closed-loop disturbance response to characterized gusts) against the passive baseline.

  2. Full-envelope operation. Evaluate and achieve closed-loop MPC-controlled flight over the flight-envelope segments the source study did not cover — steady climbs, steady turns, and descending turns — with one vehicle and controller design spanning these regimes rather than isolated point designs.

  3. Real-time feasibility. Ensure the MPC optimization meets the real-time constraint of the flight control computer: worst-case solve time within the controller sampling period (0.1 s in the source study), on embedded-class hardware representative of MAV payloads.

An admissible answer provides quantified evidence — from flight test, wind tunnel, validated simulation, or a combination — for all three objectives on a common vehicle model and controller, so that the maneuverability gain, the gust-rejection retention, the envelope coverage, and the computation-time bound are demonstrated together rather than separately.

References

  1. Christopher Campbell and Jan Maciejowski, "Control and Guidance of a Highly-Flexible Micro Air Vehicle Using Model Predictive Control", AIAA Guidance, Navigation, and Control Conference, Chicago, Illinois, 2009. DOI: 10.2514/6.2009-5874. https://doi.org/10.2514/6.2009-5874
  2. Kelly Stewart, Jeffrey Wagener, Gregg Abate, and Max Salichon, "Design of the Air Force Research Laboratory Micro Aerial Vehicle Research Configuration", 45th AIAA Aerospace Sciences Meeting and Exhibit, 2007. DOI: 10.2514/6.2007-667. https://doi.org/10.2514/6.2007-667
  3. Peter Ifju, Martin Waszak, and Luther Jenkins, "Stability and control properties of an aeroelastic fixed wing micro aerial vehicle", AIAA Atmospheric Flight Mechanics Conference and Exhibit, 2001. DOI: 10.2514/6.2001-4005. https://doi.org/10.2514/6.2001-4005
  4. Cezary Galiński, "Gust Resistant Fixed Wing Micro Air Vehicle", Journal of Aircraft 43(5):1586-1588, 2006. DOI: 10.2514/1.23373. https://doi.org/10.2514/1.23373
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  6. Bret Stanford, Mujahid Abdulrahim, Rick Lind, and Peter Ifju, "Investigation of Membrane Actuation for Roll Control of a Micro Air Vehicle", Journal of Aircraft 44(3):741-749, 2007. DOI: 10.2514/1.25356. https://doi.org/10.2514/1.25356
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  12. Jonathan B. Walters, Katie A. Evans, Animesh Chakravarthy, and Lisa M. Kuhn, "A comparison of morphing control strategies for a flexible wing micro air vehicle model incorporating Spatial Hysteresis damping", 53rd IEEE Conference on Decision and Control (CDC), pp. 583-588, 2014. DOI: 10.1109/CDC.2014.7039444. https://doi.org/10.1109/CDC.2014.7039444
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