Proceedings of the American Control Conference Philadelphia, Pennsylvania June 1998

Aerodynamics and Flight Control Design for Hovering Micro Air Vehicles Ben Motazed, Ph.D. & David Vos, Ph.D.

Aurora Right Sciences 9950 Wak:eman Drive Manassas, VA 201 10

Mark Drela, Ph.D. Massachusetts Institute of Technology

Department of Aeronautics and Astronautics Cambridge:, MA 02139

Abstract A general overview is presented on a new area of development, namely the 15-cm and smaller Micro Air Vehicle (MAV) technology. The general set of postulated mission requirements is the driver for the design configuration and performance specifications for this class of aircraft. Low-Reynolds number and thus low- aerodynamic efficiency, power density, weight, and stability in the presence of gust are significant technical challenges for the MAV-sized class of platforms to conduct long- endurance and range missions. A 15-cm hovering MAV concept is presented, with design attributes to circumvent the stabilization and control issues associated with the conventional helicopter. Aerodynamic, stabilization, and control approaches and analysis are presented.

1. Introduction The advancement in computational power and electronic miniaturization, as well as maturation of micro- electromechanical (MEMs) sensors and actuators, have led the way to the emergence and development of a new class of micro-robotic systems, specifically micro-air-vehicles (MAVs) that will offer sufficient sensing and computational functionality to have enormous applications in many military and commercial operations. Significant potential exists for MAVs to be used by the front line warfighters as a disposable agent for look-ahead reconnaissance and surveillance for tactical and anti-terrorist operations, detection of unexplored land mines, and target identification and designation. For quick response operations, MAVs would be invaluable for the inspection and search for survivors in the interior of hazardous environments such as damaged nuclear power plants, burning structures, and earthquake stricken urban areas. MAVs, with their small size and mass would be non-intrusive and benign devices for the inspection of high-tension wires, coverage of news and sports, or in general operations that are too limiting for land based systems.

However, beyond miniaturized and power efficient electronics, serious developmental issues remain in the areas of power and propulsion for MAVs. To be of practical use, similar to their biological counterparts such as the humming- bird or the dragon-fly, MAVs have to offer unique aerodynamic efficiency and high power to weight density in order to achieve significant operational endurance. Moreover, while maximization of performance parameters are desirable attributes for most applications, range, endurance, speed, maneuverability, and hover, are elements best optimized by the mission requirements. In general, it would be a design and performance compromise for a single MAV to meet all operational requirements.

Specific to MAVs, the selection between slow-speed hover versus high-speed fixed wing configuration significantly influences the design approach. Perception of the indoor or near indoor environments for collision free navigation are more conducive to hovering MAVs high maneuverability, vertical take-off and precise landing or attachment means, versus fixed wing MAVs, that with moderate to high speed are better suited for large coverage of the outdoor environment. The focus of this paper is the aerodynamics, stabilization and flight control design for the hovering MAVs.

2. A Hovering MAV Concept Figure 1 illustrates one of Aurora's hovering 15 cm MAV concepts. The MAV's propulsion is based on two fixed pitch counter-rotating rotors, driven by a single electric motor. Counter-rotation minimizes net torque and gyroscopic effects on the MAV body. The rotors are protected by a fixed tip shroud. The shroud improves lift efficiency anid also serves as a structural member for protecting the MAV rotors and housing micro-electronic sensors and antennae. The MAV stabilization in roll and pitch and side to side translation are achieved via control vanes attached to the body within the rotorwash, and actuated by micro-brushless motors. Attitude damping is achieved by another set of fixed vanes attached to the body. Roil and pitch measurements are

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made by MEMs based accelerometers placed at the MAV center-of-gravity and rate gyros.

Figure 1. A ducted-fan hovering MAV configuration

3. Hovering MAV Aerodynamics The analytical formulation used for the design and analysis of counter-rotating rotors is based on a lifting-line representation of the rotors blade together with a general semi-free wake method used to describe the induced velocities. Simple two-dimensional profile drag characteristics are used to account for viscous losses.

Although this is a simpler model than could be constructed with a general 3-D vortex-lattice or panel method, it is more than adequate for accurate prediction of the aerodynamic performance of the rotors. Even the general 3-D formulation would have to make the same time-averaging assumptions for the unsteady counter-rotating flow as the present method, and hence would not be more sophisticated or more accurate in this regard. The chief advantage of the present method is that it is extremely fast computationally and has simple inputs, making it ideal for interactive design work.

The propeller design/analysis formulation is based on classical propeller theory [ 1,2]. The modifications made specifically for the current application were:

0 Reformulation to allow arbitrarily large induced velocities relative to the freestream velocity. This is necessary to treat the hovering case where the freestream velocity vanishes.

0 Incorporation of shrouded tip into the self-induced velocity formulation. This is necessary to treat the case of a rotor duct.

Incorporation of external velocities into the velocity triangle definition. This is necessary to represent the counter-rotating rotors and the presence of a duct.

Based on the aerodynamic analysis results, one-sided aluminum molds were precision machined directly from airfoil CAD model descriptions. The MAV rotors and duct were then manufactured from laying up thin sheets of carbon-fiber cloth and epoxy resin onto these molds, and cured under vacuum and heat.

4. Hovering MAV stabilization

4.1 Passive Stabilization

In terms of power consumption and weight savings, a passive stabilization scheme would be more attractive over active servo control of the vanes to keep the hovering MAV stable and level in flight. A pendulous based stabilization mechanism as sown in figure 2 was conceived and investigated.

Vector \Omst

,,I-

,,* a=m a. ,/, . , K m / n

Figure 2. Vane actuation via pendulum motion

The investigation concluded that the concept would not work. The fundamental result is that the pendulum follows the local acceleration vector with bandwidth of the pendulum natural frequency, namely (g/L)OS rad/% The pendulum thus aligns itself with the vehicle thrust axis with this bandwidth, and cannot provide any attitude information at frequencies below this bandwidth, i.e. the angle between the vehicle and the pendulum sensing axis approaches zero for frequencies approaching DC, below the pendulum natural frequency. These observations were verified experimentally by analyzing high speed video footage of a 15 cm MAV in flight which incorporated the pendulous mechanism shown in figure 2. More formally, referring to figure 2, the transfer function from vehicle attitude (@, measured from vertical), to the angle between the pendulum

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attitude with respect to vertical (ap) and @, namely &QP, can be written as

This transfer function represents the relative angles between the pendulum and the vehicle frame, which could then ostensibly be used for feedback to the attitude control fins. The implication is, however, that for frequencies below the pendulum natural frequency, there is effectively no signal to feedback, i.e. the pendulum tracks the vehicle attitude such that there is no difference between vehicle and pendulum angles. The solution would be to have a very long pendulum, such that the pendulum is effectively static in inertial space, but that is not practical and introduces further complication in that the low frequency (frequencies approaching DC) behavior will be unstable. Note that this signal could theoretically be used in an active controller, but again, the pragmatic issue of attaching an extremely long pendulum to the vehicle precludes this option.

4.2 Active Stabilization

Active proportional control of the vanes is an alternate method to MAV attitude and translation control. Vane angular motion is proportional to accelerometer measurements which are closely placed to the vehicle mass center with the sensing axes in the horizontal plane (two orthogonal axes, i.e. fore-aft, and lateral). Attitude control can also be accomplished with MEMs based solid-state gyros, however gyro drift has to be compensated for by augmenting accelerometer data in the formulation. From the equations of motion derivation, the acceleration measured at the mass center is given by

Clearly, a large component of the accelerometer signal will be the first term, which for hovering flight (T = Mg), becomes ga). This is in effect a tilt sensor. A typical sensor which has noise floor of 500pg / Hz'.~, implies that signals down to about 5 milli-g can be resolved over wide bandwidth of 100 Hz, which in the tilt sensing application means 5 milli-radian (0.29 degrees) angular resolution. This is adequate for attitude control. Shown in figure 3, are the accelerometer signal measured with the rotors rotating at 4000 rpm. The signal is shown filtered in one case by a low pass filter of corner frequency 80 rads, and in the other case low pass filter corner frequency of 20 rad/s. The signal to be measured is the large amplitude semi-sinusoid of frequency approximately 1 Hz (-6 rads), which would be about 6 times faster than the 1.2 rad/s desired closed loop attitude dynamics bandwidth. The phase lag even through the 20

~

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rads filter is tolerable, and the signal quality is good with good resolution, indicating that this sensor is an appropriate choice for this application.

With 0.005 radians noise floor on the sensor, we expect to see lateral acceleration deadband in the control of about g@=0.049 m.s.*. A very rough first order estimate of the horizontal translational velocity and position error due to this deadband and the closed loop attitude control having a time constant of about U1.2 seconds is obtained by integrating appropriately over the period of one time constant. The velocity excursions estimated in this way will thus be approximately 0.04 m / s and the position excursions might be approximately 0.017m (17 mm).

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l ime [s)

Figure 3. Two filtered roll and pitch accelerometer signals.

5. Conclusions This work set the initial ground work for investigating the aerodynamic and stabilization issues of 15-cm and smaller hovering air vehicles. It was determined that using a pendulum device for passive stabilization of hovering MAVs is not a feasible method. Active stability control indicates sufficient bandwidth and signal-to-noise ratio in the presence of vibrational disturbance from the propulsion module. Active vane control flight tests will be available by mid- summer 1998.

6. Acknowledgments This work was performed at Aurora Flight Sciences as part of the DARPA Phase I SBIR contract DAAH01-96-C-R40.

7. References [l] A. Betz. Airscrews with minimum energy loss. Report, Kaiser Wilhelm Institute for Flow Research, 1919.

[2] H. Glauert. Elements of Ai@oil and Airscrew Theory, Cambridge University Press, Cambridge, 1937.