FLIGHT TEST AND SIMULATION RESULTS FOR AN AUTONOMOUS
AEROBATIC HELICOPTER
V. Gavrilets', I. Martino?, B. Mettler3and E. Feron', Laboratory for Information and Decision
Systems, Department of Aeronautics and Astronautics, Mfl,Cambridge, u.4
quaternion attitude representation. A magnetic
compass with reset circuit was added to provide
small heading corrections.
Introduction
In this paper we shall present the flight test and
simulation results for an X-Cell.60 helicopter,
which performs aerobatic maneuvering under
exclusive computer control. We have previously
demonstrated in flight an autonomous axial roll
maneuver [ 13. Our next goal is to demonstrate
operationally useful, and more challenging
maneuvers, namely split-S and Immelman. Both
maneuvers provide a rapid way to change direction
of flight by trading kinetic and potential energy.
Previous flight test results showed that the
engine performance was marginal at high collective
settings. In order to provide more power to the
helicopter with the avionics payload a .90-size
engine (50% larger displacement than the old .60
size) was installed, along with 700 mm instead of
690 mm blades.
During the flight tests we learned that a tight
yaw rate control by the tail rotor is necessary to
counteract large and fast changes in the collective
during some of the maneuvers. We have stiffened
the avionics box suspension system to avoid
coupling of the box and helicopter yawing
dynamics, and replaced an older Futaba S9402
analog servo on the tail rotor with a digital Futaba
S9450 to increase actuator bandwidth.
The X-Cell.60 is a model helicopter with a 5 ft
rotor diameter, designed for competition aerobatics.
Empty weight is 10 lbs, the avionics box with a
custom landing gear and a suspension system weigh
7 lbs. The avionics system features an electronic
governor, an inertial measurement unit, a single
GPS receiver, a pressure altimeter, and a magnetic
compass. The system described earlier [Z] has been
modified to enable all-attitude flight. Previously a
low-cost GPS receiver was used with one-second
latency in position and velocity updates, which
made it difficult to incorporate Kalman filter based
estimator. A set of complementary filters was used
to derive Euler attitude angles and the velocity
vector. This state estimator proved adequate for
aggressive trim trajectory tracking and for the
autonomous axial roll [l]. However, the
singularities in kinematic equations at zenith and
nadir made split-S and Immelman maneuven
impossible. We have integrated into the avionics
package the G12 receiver from Ashtech, which
features 10 Hz update rate and 50-millisecond
latency. An extended Kalman filter with bias states
for accelerometers and gyros was implemented to
provide the all attitude navigation solution using the
~~
~
An essential part of the project was the
development of an adequate nonlinear mathematical
model describing a miniature helicopter in aerobatic
flight [3]. The X-Cell helicopter features a stiff hub,
and due to its small size the dynamics are
dominated by the main rotor forces and moments.
Despite the stiff hub, the on-axes responses in the
hub are an order of magnitude higher than the offaxis responses, which makes modeling task easier
than for full scale helicopters and some small-scale
helicopters, like Yamaha R-50 [7]. The originally
developed X-Cell model [3] was refined. Instead of
linear stability derivatives describing fuselage
forces we have used effective drag areas [5]. An
engine/governor model was added to account for
the rotor speed variations during maneuvers, and for
~~
W.D. candidate,gavrick@rnit.edu
M.S.candidate, martinos@mit.edu
Post-doctoral associate, bmettler@mit.edu
Associate Professor, feron@mit.edu
.
0-7803-7367-7/02/$17.00 0 2002 IEEE
8.C.3-1
linearized lateral-directional dynamics of the
helicopter is well described by a 5* order model,
with the state vector containing side velocity, lateral
flapping angle of the main rotor, roll rate, yaw rate
and bank angle [ 1,3,9]. Similarly, linearized
longitudinal-vertical dynamics is described by a 5*
order model with the states being body axis forward
and vertical velocities, longitudinal flapping angle,
pitch rate and pitch angle. All states except the
flapping angles can be accurately measured or
estimated. The flapping angles participate in the
lightly damped fuselage-rotor modes, which are
characteristic of small-scale helicopters with
stabilizer bars [lo]. We have applied notch filters
on cyclic inputs to suppress the modes, and used the
rigid body approximations to the notched plants for
the LQ design [l, 91. The controller gains were
scheduled with the forward speed. The lateral
directional controller gains were switched discretely
with the hysteresis logic; this prevented undesirable
rolling and yawing during fast transitions between
hover and forward flight. The bumpless transition
between the gain sets is ensured by a proper
initialization of the integrator states to keep surface
commands continuous.
the delay in the transmission of the main rotor
torque to the fuselage through the engine. The
engine was modeled as a first order lag, and the
governor as a gain. The resulting transfer function
from the rotor speed command to the rotor speed is
well-damped second order; its damping ratio and
natural frequency were derived from timefrequency decomposition of the engine sound
recordings during commanded rotor speed
transitions [2]. The model of the suspension system
for the avionics box was added to account for its
lightly damped modes and a possible effect on the
gain margin.
The next section summarizes our approach to
implementing aerobatic maneuvers autonomously.
Subsequent sections of the paper will describe
implementation of the axial roll maneuver, and
simulation studies for the Immelman and split-S
maneuvers.
An Approach To Aggressive
Maneuvering
Control laws for unmanned helicopters can be
broken down into two categories: trim trajectory
tracking controllers, and those for implementing
extremely agile, or aerobatic maneuvers. To
implement an autonomous aerobatic maneuver we
used both kinds in different phases of the flight. A
velocityheading rate/altitude tracking controller
was used for the entry and recovery phases (trim
trajectory controller), while an angular rate tracking
controller with predefined commanded trajectories
was used for the maneuver itself.
Other approaches to tracking trim trajectories
and non-aggressive transitions between trim
trajectories have been suggested in the literature on
small-scale helicopters. La Civita et al. have tested
H-infinity loop shaping controller on a Yamaha R50 helicopter. In this approach, frequency weights
are used to perform loop shaping and alleviate the
lightly damped fiselage-rotor flapping mode.
Johnson and Kannan [ 121 implemented neural
network based adaptive controller on an improved
version of R-50,the Yamaha RMAX helicopter.
The Yamaha helicopters are an order of magnitude
heavier than the X-Cell, feature a relatively flexible
hub and were not designed for aerobatics.
Trim Trajectoy Controller
The trim trajectory controller has to feature
both high bandwidth and good stability to guarantee
fast recovery from an aerobatic maneuver. We have
developed a state-feedback linear quadratic (LQ)
controller [8] with integrators appended on tracking
variables, which proved adequate for the task [l].
We used an analytical linearization of the full
nonlinear model at different forward speed settings
to obtain state transition and input matrices for the
LQ design. For X-Cell the coupling between the
lateral-directional and the longitudinal-vertical
dynamics is negligible, except for the variations of
the main rotor torque due to collective changes. The
Human-CenteredApproach ToAutonomous
Aerobatics
In the beginning of the program we have
performed a number of manual flights with an
instrumented X-Cell60 helicopter [4, 131. The tests
showed that the maneuvers performed by an expert
pilot are repeatable; the pilot actions can be well
approximated by piece-wise linear or piece-wise
constant commands; and switching between the
8.C.3-2
commands occurs upon reaching specific attitude
angles. Simulation studies [4] have also shown that
some degree of continuous feedback is desirable for
repeatable autonomous execution of maneuvers.
We have designed decoupled body-axis
angular rate tracking controllers. All controllers are
constant gain proportional-integral with crossover
frequencies above 5 radsec for all speeds from
hover to 15 d s e c . We have applied notch filters on
cyclics to suppress the lightly damped fbselagerotor flapping modes [9]. The pilot has flown a
number of maneuvers (axial roll, loop, 180 and 540
hammerheads, split S and Immelman) with the rate
tracking controllers and an open loop collective
command. Recorded inputs and state trajectories
were analyzed to create angular rate reference
trajectories and execution strategies for various
maneuvers. The attitude angles for the switching of
the rate commands were determined. We have also
observed that the collective command used by the
pilot during the maneuvers is roughly proportional
to cosine of the angle between the local vertical and
the helicopter Z-axis. This allows the pilot to keep
the thrust pointing up in all attitudes to reduce
altitude loss, and close to zero when the rotor disk
is close to being perpendicular to the ground (which
reduces unwanted deviations from the flight path).
setpoint for the altitude hold, and resumes tracking
the speed setpoint.
Experimental Axial Roll Maneuver
During the axial roll maneuver the pitch and
yaw rate commands are zero. The collective is
varied proportionally to cosine of the bank angle.
The roll rate trajectory, given in Figure 1, consists
of four phases.
-
Roll rate command, deglsec
1.5
2
2.5
3
time, sec
Figure 1. Roll Rate Reference Trajectory
First, a linear ramp up to the maximum
commanded rate is performed in a given time (0.3
seconds). Next, the roll rate command is kept at the
maximum until an integrated roll rate (pseudoroll
angle) reaches a specific value, determined from the
pilot’s execution of the maneuvers with the rate
tracking control augmentation system (3 10
degrees). At this point the roll rate command is
linearly ramped down in a specific time (0.2
seconds). The last phase is a predefined settling
period (0.2 seconds) with the zero roll rate
command to arrest the roll rate and achieve a 360
degree revolution. The maneuver is exited upon
reaching a 360 degree roll as determined by the
integrated roll rate, or upon completion of the
sequence described above.
A safe set of states for the maneuver entry was
determined with simulations. This imposes limits
on the initial attitude angles, as well as the
minimum entry speed and altitude. The exit
condition from the maneuver is determined by
either reaching a certain attitude or expiration of the
time allocated for the maneuver. To guarantee a
bumpless transition between the maneuver
controller and the trim trajectory-tracking controller
we initialize the integrator states such that the
control surface commands are continuous.
Prior to the maneuver the pilot brings the
helicopter to the maneuver speed and altitude using
the trim trajectory-tracking controllers, and chooses
the direction of flight with a heading rate command.
Before the maneuver, the helicopter is leveled by
commanding a zero heading rate, whereas the
forward speed and the altitude are maintained by
the trim trajectory controller. The fully automatic
maneuver sequence is engaged by a switch on the
R/Ctransmitter. Upon the exit from the maneuver
the helicopter accepts the exit altitude as a new
More than 6 autonomous axial rolls have been
executed in flight, and the state trajectories proved
to be repeatable, and predicted well by the
simulation [l]. The flight data for one of the
autonomous rolls is given in Figure 2.
8.C.3-3
maneuver, which reduces the natural tendency of
the helicopter to weathervane. At the end of the
maneuver the pilot rapidly increased collective
angle, which led to significant unwanted yawing
immediately after the maneuver completion. This
problem is commonly alleviated by WC pilots by
using yaw rate control augmentation devices (hobby
gyros) with PI controllers. Tight feedback gain on
the integral of yaw rate error is necessary to
alleviate collective-yaw coupling at low speed.
Figure 4 shows cyclic and collective commands
during the maneuver, the yaw rate command was
not used by the pilot during the maneuver. We can
see that commands are mainly piece-wise linear or
piece-wise constant.
20 -
lime, sec
Figure 2. State Trajectories During An
Autonomous Axial Roll.
Simulated Immelman Maneuver
An Immelman maneuver starts in a steady
level forward flight (above 25 knots speed) and
consists of half a loop (1 80 degrees in pitch)
followed by half a roll. The maneuver provides a
fast way of changing the direction of flight in a
confined environment, e.g. between buildings in a
city.
0
,
-5
0
1
.J
2
3
4
5
6
1
8
- colieotb. deg
Figure 3 shows an Immelman maneuver
performed by an expert pilot on the instrumented XCell helicopter.
-10
0
1
2
3
4
time. sec
5
6
7
8
Figure 4. Pilot Inputs During Manual Immelman
Maneuver.
;P
1
0
-Fvd
-2oa';
2
Y
3
4
5
6
7
8
1
5
6
7
8
We have designed reference trajectories for the
pitch rate during the pull-up half-loop, and for the
roll rate during the following half roll. The
trajectories contain the same four phases as the roll
rate trajectory for axial roll given in Figure 1. The
attitude values for initializing the ramp-down were
determined in simulation. To increase maneuver
exit velocity the pitch rate trajectory was selected
such that the helicopter ends up in slightly nose
down attitude (more than 180 degree loop). The
collective was varied proportionally to cosine of the
angle between local vertical and helicopter Z-axis.
The time histories for the simulated Immelman are
given in Figure 5.
,m1sec
3
'
llma, sec
Figure 3. State Time Histories During Manual
Immelman Maneuver.
A proportional yaw rate feedback to the tail
rotor pitch was used. As can be seen, the helicopter
slows down to a zero forward speed during the
8.C.3-4
the helicopter spends longer time facing down; this
will improve weathervaning.
20
-20
An
3
1
2
3
4
5
---
50
3
4
6
7
6
7
- Altihde. rn I
5
I
- Fwd Speed, mlm
0
-I,
I
1
2
3
4
5
6
?
8
'I
2
3
4
5
6
7
8
1
2
3
4
time. 88c
5
6
7
8
80'
/
1
2
a
3
4
time, sec
5
6
7
t
2@
{ - Altitude, rn 1
I
15
Figure 5. State Time Histories For Simulated
Automatic Immelman Maneuver
10
0
The helicopter consistently exits the maneuver
with the attitude very close to the desired: heading
180 degrees different from original, roll angle close
to zero, pitch angle around 10 degrees nose down.
However, after the exit from the maneuver and reengagement of the trim trajectory-tracking
controllers the altitude hold increases collective,
which leads to about 25 degree heading change.
Much higher heading change was also observed in
flight during manually executed Immelman
maneuvers. This deficiency can be corrected by
tighter turn rate tracking in the trim trajectory
controller, or by making a wider loop to retain
higher airspeed after the exit from the maneuver.
An autonomous aerobatic maneuver was
executed on a miniature model helicopter.
Maneuver execution strategies were inspired by
human pilots [ 1,4, 131. Operationally useful
Immelman and split-S maneuvers were
demonstrated in the simulation, and will be
executed in flight tests to validate the suggested
general approach to autonomous aggressive
maneuvering.
Simulated Split-S Maneuver
Acknowledgements
The split-S maneuver is an Immelman in
reverse: starting from a steady level forward flight
the helicopter performs half a roll, then half a loop.
The maneuver provides a very quick way of
reversing flight direction without losing speed by
tradiig potential energy €or kinetic energy. It can be
used in a tight environment given sufficient altitude.
MIT students Kara Sprague, Rodin Lyasoff,
Chris Sae-Hoo and Allen Wu have helped
implement the avionics upgrade. Partial funding for
this research was provided by the office of Naval
Research under a Young Investigator Award and by
the NASA grants NAG2- 144 1, NAG2-1522.
Similarly to other maneuvers, the reference
trajectories for roll and pitch rates were designed
with fixed ramp up time, maximum command until
preset pseudo-attitude is reached, fixed ramp down
and settling times. Figure 6 shows the state vector
time histories during the simulated split-S
maneuver. A significant collective increase upon
the exit from the maneuver led to unwanted yawing.
Higher airspeed upon maneuver can be retained if
References
Figure 6. State Time Histories For Simulated
Automatic Split S Maneuver
Conclusion
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