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I have been working on a guidance and control scheme for a fixed wing aircraft that enables autonomous aerobatics on commanded path. The developed method utilizes the nonlinear path-following guidance law in the outer-loop, which creates an acceleration command for a given desired path, current position and velocity of the vehicle. The scheme considers the gravity outside the inner-loop, in that gravitational acceleration is subtracted from the acceleration command to form the specific force acceleration command. With the gravity term removed, the specific force acceleration is more easily controlled in the inner-loop compared to the total acceleration. For an aircraft with sufficient side-force authority a roll attitude is not constrained but can be selected. As a result a roll-to-inverted flight and active sideslip maneuvers such as knife-edge and slow roll are accomplished. Applications to a series of standard aerobatic maneuvers were demonstrated through flight tests to show the performance of the this method.
Guidance and Control
- First, the acceleration command is created by the nonlinear path-following guidance method
- Next, the command for specific force acceleration is computed by subtracting the gravitational acceleration from the total acceleration command
- The specific force acceleration command is decomposed into the aircraft body axis x,y,z components. Among them, the y and z components become the reference values for the inner-loop controllers to follow in the pitch and yaw directions using the elevator and rudder, respectively.
<Conversion from total acceleration command to specific force acceleration command >
One of the interesting features of this guidance/control method is that the roll attitude is not necessarily a constraint in following a given trajectory. The roll can be controlled in conjunction with the y -axis component of the specific force acceleration which is induced by sideslip. In one case, roll may be manipulated in such a way as to minimize the y -axis component of the specific force acceleration (or f tilde in the diagram) in order to minimize the use of sideslip. In this case, for example, a coordinated turn can be performed. Alternatively, if the flight speed is high enough and/or the side area of the aircraft is sufficiently large, the roll attitude does not have to be aligned to minimize sideslip. Instead, the roll can be chosen, by manipulating f tilde angle, as a way to actively use the y -axis component of the specific force acceleration. In this case, sideslip maneuvers such as slow-roll and knife-edge can be performed.
Test bed UAV
The test bed UAV has a total mass of 2.95 kg, a wing span of 1.54 m, and is equipped with a 0.3 kg of avionics. The avionics includes a GPS, inertial sensors, pitot-static tube, and a flight control computer with the guidance and control algorithms implemented. The aerodynamic coefficients were mainly obtained using a vortex lattice method.
<Test bed UAV >
Flight Test Results
The guidance and control scheme has been implemented in the test bed aircraft. Some of the standard aerobatic maneuvers were performed. The results are presented below.
In what follows the trajectory command is indicated by a dotted line in the figure. The trace of the vehicle position and attitude from the recorded flight data is depicted by the series of aircraft snap-shots displayed at one second intervals along with the other dotted line that passes through them.
Link to Flight Test Movie
In this test the aircraft was commanded to follow a straight line while making a 360-degree turn about a roll axis. The average roll rate during the slow roll maneuver was 25 deg/sec. The altitude dropped by 2.52 meters when the roll angle was near 90 degrees. The standard deviation of the overall cross-track error was found to be 2.21 meters.
In this test the aircraft rolled by 180 degrees to configure an inverted attitude while following a short straight line, and then it followed the figure-8 path command, which is composed of two circular segments with a radius of 100 meters and two other straight lines that join the arcs. The standard deviation of the cross-track error was 3.75 meters, and the maximum error was found to be 6.99 meters in this test.
The aircraft initially made a 180-degree turn with a radius of 100 meters. After the first turn, the aircraft was commanded to follow a straight line segment while increasing the roll angle from 0 to 90 degrees. Then, the aircraft was commanded to follow the second circular segment while maintaining the knife-edge configuration. After the second turn the aircraft followed the last straight segment where the roll angle was released back to zero. The flight data indicated approximately 25 degrees of pitch attitude when the roll is under the knife-edge configuration. The required rudder deflection to maintain the associated sideslip was approximately 12 degrees.
Knife-Edge on Figure-8
The aircraft started from a steady level condition in the middle of the graph. The roll angle changed by -90 degrees to configure a left-wing down knife-edge attitude. Then it followed a figure-eight path while holding the roll angle at -90 degrees.
<Knife-Edge on Figure-8 path>
This maneuver is known to be an efficient way to quickly reverse flight course while minimizing the extra load to the aircraft. A speed increase is also gained at the end of the maneuver. Initially, the aircraft follows a straight line segment. During this time the roll angle increases from 0 to 180 degrees. Thus at the end of the first segment, the aircraft is configured for an inverted-flight. Then, it is commanded to follow a half circle of 50 meter radius in order to reverse the flight course. Once the aircraft exits the circular segment it follows another straight line in the other direction to finish the maneuver. The maximum load factor was marked 2.3 g when the aircraft was near the end of the circular segment.
As suggested by some of the above flight test results the roll attitude can be “chosen” independently regardless of the flight path to a certain degree. One of the extreme examples of such a case is illustrated here. In this flight test, except for the beginning and ending of the flight path, the flight course is a circle with a radius of 100 meters in a horizontal plane in the counter-clockwise direction. In nominal cases, the aircraft typically maintains a left-wing down roll attitude in order to follow the circle. But in this flight test the roll angle was commanded to keep changing at approximately -45 deg/sec in order to perform what is known as a “rolling-circle”. The flight result indicates that the aircraft keeps changing the roll attitude while tracking the commanded circular path pretty well with a standard deviation of the cross-track error of 4.58 meters. Of course, the required lift to maintain the vehicle weight and the centripetal force to follow the circular path are all generated by the proper combination of the main wing lift and the sideslip induced side-force depending on the aircraft attitude.
A flight trajectory command was constructed with several circular segments to lead the aircraft to a series of wingovers. This type of maneuver is often called a lazy eight. The associated altitude change was more than 60 meters. The maximum pitch attitude was approximately 70 degrees, and the maximum roll angle was near 80 degrees when the aircraft was passing by the peak height.
Here is a flight test data from a loop maneuver. Starting from a level flight, the aircraft followed a circular path with a radius of 50 meters on a vertical plane. This maneuver is quite dynamic in a sense that the speed during the loop changes dramatically. The maximum load factor of almost 3g was recorded when the aircraft was near the end of the circular segment.
In Cuban-8 maneuver the aircraft makes a figure-eight path which lies on a vertical plane. Also, the plane has to make a 180-degree roll turn on each straight line segment in the middle that joins the two circular arcs.
- The contributions by Lee, Sang-Hyup and Jeong, Min-Jeong in the hardware in-the-loop simulation and the flight tests are greatly appreciated
- This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2011-0014057)
Last Update - December 1, 2011