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Autonomous Guidane of a Circular Parachute Using Descent Rate Control
Article in Journal of Guidance Control and Dynamics · July 2012
DOI: 10.2514/1.55919
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Autonomous Guidance of a Circular Parachute
Using Descent Rate Control
Travis D. Fields,1 Jerey C. LaCombe2 and Eric L. Wang3
University of Nevada, Reno, Nevada, 89557, USA
This paper describes a novel method for control of the landing location of a descent
vehicle using a variable-drag circular parachute. Wind data is collected prior to deployment, ideally from a dropsonde, and used to predict the descent path using a 3degree
of freedom model to land at a line segment target on the ground. Guidance is achieved
by controlling only the descent rate via the drag area of the parachute. Simulations
using experimental wind data are presented to demonstrate the feasibility and value
of the approach. Results show that when accurate wind data is available, the performance of this simple scheme is signicantly better than an uncontrolled parachute.
The results demonstrate the potential for using simple and inexpensive onboard ight
hardware to autonomously guide a descent vehicle to a linear target on the ground.
1
2
3
Graduate Research Assistant, Mechanical Engineering, 1664 N Virginia St. MS 312, Reno, NV, and AIAA Student
Member.
Associate Professor, Chemical and Materials Engineering, 1664 N Virginia St.
MS 388, Reno, NV, and AIAA
Member.
Associate Professor, Mechanical Engineering, 1664 N Virginia St. MS 312, Reno, NV.
1
Nomenclature
Cd A
= Drag area, product of parachute's drag coecient, Cd , and reference area, A
P, P̂
= Actual and predicted descent paths, P, P̂ ∈ (x, y, z)
d¯C , d¯U
= Mean distance from landing target for controlled and uncontrolled simulations
m
= Total mass of descent vehicle
p, p̂
= Actual and predicted descent paths projected onto ground, p, p̂ ∈ (x, y)
r
= Range vector projected onto ground r ∈ (x, y) with magnitude r = |r|
z(t), ẑ(t) = Actual (measured) and predicted descent proles
zn
= Altitude at nth time step
ż, z̈
= Vertical components of speed (descent rate) and acceleration
σU , σC
= Standard deviations of landing distances from target dC , dU for
uncontrolled and controlled simulations
ρ
= Air density (varies with altitude)
θ
= Bearing from current location to landing location
I.
Introduction
The objective of this study is to investigate the potential of reaching a targeted landing location
by autonomously controlling the descent rate of a circular parachute. This work contributes to a
growing area of interest in accurate cargo deliveries from high altitudes. Several approaches have
been proposed, including autonomous circular parachutes controlled via pneumatic actuators [13].
Such systems actively steer the parachute using pneumatics capable of altering the parachute shape
with a limited number of actuations. Autonomous parafoil descent vehicles (example: [46]) are
also reported, and use steerable ram air parachutes, controlled via manipulation of control lines.
These can be very complex, requiring extensive modeling and control systems, but are capable of
high accuracy. The approach developed here instead uses a simple control scheme of altering the
descent rate (detailed below) to control the landing location.
The approach described herein contrasts with the other approaches discussed above in two
important ways. First, the wind provides the sole means of lateral translation, with guidance of
the vehicle achieved by changing the drag area, Cd A, which aects the extent of downwind drift
2
during the descent. Second, the system makes use of detailed wind data to both predict the landing
location and make periodic corrections for errors in the trajectory. The end result is a system in
which the horizontal distance traveled during descent can be benecially controlled for purposes
such as delivering payloads to an extended linear target such as a road or valley, independent of the
release point. The specic point
along
the linear target cannot, however, be controlled using this
approach, and the extent of control authority is determined by wind conditions. This is the tradeo
for the simplicity of the system, but in comparison with an uncontrolled parachute, the accuracy
will be shown below to be signicantly enhanced. Key to this approach is the use of detailed wind
data to plan the trajectory and to make adjustments during descent. Whereas the actual mechanics
for adjusting the drag area are beyond the scope of this work, we note that continuous control of
the descent rate can be accomplished by changing the drag area through reversible reeng of the
parachute or by venting the parachute.
The proposed system consists of an adjustable parachute, detailed wind data, and a control
system that periodically adjusts the parachute's drag area, Cd A, to govern the horizontal distance
traveled during the descent. The predictive capability of the system permits it to deliver the descent
vehicle close to a desired target "nish line" (Figure 1). Foreknowledge of both the wind speed and
direction at each altitude is thus critical for the performance of the control system. Wind data is
envisioned to be collected using either a dropsonde or radiosonde that is released both temporally
and spatially close to the descent [7, 8].
II.
A.
Methods
Model Description
The complexities of controlling a descent vehicle are welldocumented [9]. However, one advantage of the present system is the ability to use a relatively simple 3degree of freedom (DOF)
model of the descent vehicle, coupled with a 1DOF control scheme where Cd A is the only control
parameter. Figure 1 depicts the projection of the descent path onto the ground, p, in relation to
the targeted "nish line", which takes the form of a line between two points. The descent path
projection p originates at the projected release point (x0 , y0 ), and terminates at (xf , yf ), dening
3
12
Landing
(xf , yf)
Target
"Finish Line"
10
Y-Distance (km)
CdA = 0.91 m2
8
CdA = 1.18 m2
CdA = 1.42 m2
CdA = 1.60 m2
Alternate
Landing
Locations
6
r
4
2
Release
(x0, y0)
θ
0
0
Projection of
descent path, p
1
2
3
4
5
X-Distance (km)
Fig. 1: Projection of descent path, p, from release point (x0 , y0 ) to landing point
(xf , yf ). Adjustments to the descent rate will scale p and r , but will not aect θ . The
solution technique adjusts Cd A so that xf , yf , falls along the nish line segment. In
this example, this results from a drag area of Cd A = 1.18m2
the range vector r , at a bearing angle θ from the release point.
The control scheme comprises of a descent path prediction algorithm and a drag area control
algorithm. Both were developed for implementation on a microcontroller. For this study, the drag
area control algorithm behaves as if there will be only a single actuation for the remainder of the
descent; however, the prediction is periodically updated to correct for errors in wind data. This
approach avoids the necessity to incorporate schedules of future actuations in the prediction, but
neither does it attempt to take advantage of "favorable" winds to be encountered later in the descent.
4
1.
Descent Path Prediction
If it is assumed that all drag forces are in the vertical direction, the acceleration in the vertical
direction can be expressed in terms of gravitational and drag forces acting on the parachute:
z̈ =
ρ (Cd A) ż 2
− g,
2m
(1)
where both ρ and Cd A are functions of altitude, z , and therefore a closedform solution to z(t) using
Equation (1) is not readily expressed. However, by assuming the vehicle is at terminal velocity at
all times, the velocity at each time step can be calculated using Equation (1) with z̈ = 0, and a
suciently small time step. The terminal velocity assumption was validated through simulations
run using a full RungaKutta solution approach. Note that terminal velocity varies due to changing
air density during descent. For the nth time step, the descent rate takes the form
s
żn =
2mg
.
ρ (Cd A)
(2)
The predicted descent prole, ẑ(t), is generated by estimating the terminal velocity at each
time step, and using this to determine the change in altitude using the zeroacceleration kinematics
equation for the descent prole,
ẑn = ẑn−1 + żn−1 ∆t.
(3)
Combining with the measured wind data yields a 3-D kinematic prediction of the descent path,
P̂ (x, y, z, t), that factors in lateral wind drift in a similar manner to Equation (3). By varying
the parachute drag area, Cd A, the attainable landing locations can be identied. This process is
depicted visually in Figure 1, where four dierent values of Cd A were considered to identify the
solution of 1.18 m2 which produced the desired range value of r = 10.3 km that reached the target.
2.
Drag Area Controller
To determine the optimal drag area setting, three candidate drag areas are selected within the
range of the hardware limits: (Cd A)max , (Cd A)min , and (Cd A)nominal . The corresponding predicted
landing ranges are t to a parabola, which is then used to quickly determine the optimal value of
5
Cd A that places the landing location along the target line (Figure 1). The quick determination of
the optimal drag area is possible if it is assumed that Cd A remains constant for the remainder of
descent. In this case, θ is independent of descent rate because all lateral motions are scaled equally
by the duration spent within each altitude's wind.
If the wind data used by the descent prole predictor is accurate, then no further action would
be required. However, as is discussed below, inaccuracies in the wind data can signicantly impact
the overall performance of the system. By periodically recalculating the optimal drag area, the
system can compensate for errors in the wind data. Note that with each recalculaton of the optimal
drag area, θ may change.
It is important to note that if the target line is determined to be unreachable based on the wind
and canopy characteristics, it will attempt to get as close as possible. Additionally, if the wind data
is not available for some segment of the descent phase, the algorithm will extrapolate or interpolate
available wind data.
B.
Impact of Errors in Wind Data
With the simplied 1DOF control approach employed here, the main challenges result from
imperfect knowledge of the wind speeds and directions throughout the air column. For many
geographical areas, wind data is periodically measured at various locations using sounding balloons
(radiosondes) or acoustic soundings (echosondes). However, use of such data can be detrimentally
inaccurate if the descent vehicle is deployed at a dierent time and/or location than the wind
data was collected. Inaccurate wind data will result in improper parachute trim commands being
issued by the control algorithm. An alternative is to make direct measurements of the wind eld
immediately prior to deployment of the descent vehicle using a sounding balloon or a suitable
dropsonde, deployed from an aircraft [7].
To determine the impact of inaccurate wind data on the performance of the system, two types of
errors in the wind data were investigated using simulations: 1) Type A errors caused by large spatial
and/or temporal dierences between the predicted and actually experienced winds, and 2) Type B
errors caused by measurement precision limitations or inaccuracies and/or small-scale variations in
6
the wind. For all of the results presented, the simulated deployment altitudes were 10 km and the
drag area controller calculated a new optimal drag area every ten meters of descent.
To investigate the Type A errors, simulations were run where the control algorithm used "inaccurate" wind data for the control decisions, while the vehicle was subjected to "true" wind in
the kinematic motion simulation. Eleven matched pairs of GPS-derived wind data were experimentally obtained from dierent (but nearby) locations using sounding balloons for the "inaccurate"
and dropsondes for the "true" wind data. The pairs of data sets were representative of real-world
inaccuracies in wind data due to realistic dierences in both location (20-70 km) and time (30-80
mins). With these data, descent simulations were performed using both controlled and uncontrolled
descent schemes to permit baseline comparisons with an uncontrolled parachute.
To investigate the Type B wind errors, Monte Carlo simulations were performed with Gaussian
noise (2 m/s standard deviation) superimposed onto a single experimentally-measured "true" wind
data set (GPS-derived) for use in the algorithm's path planning calculations. The noise-free data
was used in the calculations of the actual motion. The noise amplitude was estimated using shortterm variations in experimentally measured wind data, consistent with other reported approaches
[10]. 250 simulated descents were performed with the target at the origin, and the release point at
(x0 , y0 , z0 ) = (-5.3, 12.0, 10.0) km. The target line was chosen to be approximately perpendicular
to the dominant wind direction to simulate a worst-case scenario in changing wind magnitudes, as
the nite control authority of the vehicle can potentially render the vehicle incapable of reaching the
landing target, depending on the magnitude of the noise. Additionally, noise in the wind direction
will produce scattering laterally along the target line. These simulations represent the case where
a dropsonde or radiosonde is released nearby, immediately prior to the deployment of the descent
vehicle, and the applied noise represents typical measurement precision and scatter levels in the
wind data.
III.
Results and Discussion
The simulation results for Type A wind errors (large scale) are shown in Figure 2a. The mean
distance to the target line for the uncontrolled parachutes was d¯U = 622.7 m (σU = 478.7 m). The
7
controlled descent vehicles faired only slightly better with a mean distance to the target line of
d¯C = 409.4 m (σC = 245.1 m). A paired, 2-sided t-test (t = 1.93, p = 0.08) indicates that at a 95%
condence level, there is no signicant dierence in the accuracies of the controlled and uncontrolled
systems. This highlights the fact that the performance of the system is predicated on the availability
of good quality wind data. If the wind data are not accurate enough (i.e., current and local), the
control system's eectiveness is hampered by using invalid wind data in making corrections, and
performs no better than an uncontrolled system.
4000
b)
North/South Distance [m]
North/South Distance [m]
a)
Target
Line
2000
0
–2000
–2000
Uncontrolled
Parachute
Controlled
Parachute
0
2000
4000
East/West Distance [m]
200
0
Target
Line
Uncontrolled
Parachute
Controlled
Parachute
–200
–200
0
200
East/West Distance [m]
Fig. 2: a) Type A wind errors (large scale) showing landing location errors for
controlled and uncontrolled descent vehicle simulations. The mean landing error
(distance from the target) for the uncontrolled and controlled simulations were
indistinguishable. b) For the simulated Type B wind errors, the mean landing error
of the uncontrolled system was over three times larger than for the controlled system.
For the simulations of Type B wind errors (Figure 2b), the landing locations are normally
distributed about the target due to the Gaussian nature of the superimposed noise. However, unlike
the previous scenario, the controlled parachutes (d¯C = 14.2 m, σC = 17.3m) performed much
better than the uncontrolled parachutes (d¯U = 54.0 m, σU = 41.2 m), with the controlled system
producing only one third the error of the uncontrolled system. A paired, 2-sided t-test (t = 14.38,
p 0.000) conrms that at a 95% condence level, there is clearly a dierence in the accuracies
of the controlled and uncontrolled systems. Errors in the wind data at the scale of instrument
8
precisions can accumulate to produce signicant errors in the landing location, but the control
scheme can counteract this greatly, provided high-quality (e.g. dropsonde) wind data is available.
As a nal validation, a xed drag area (uncontrolled) descent vehicle was experimentally deployed from an altitude of 10 km. The parachute's descent path and landing location were recorded
with a GPS. So that variations in the wind could be studied, a dropsonde was released 4 minutes
prior from the same location, and a radiosonde was launched ∼ 30 mins prior from ∼ 10 km upwind
of the deployment location.
Post-mission, two simulations were performed using these experimentally-measured wind data
sets. In both simulations, the actual landing point was used as the target (with the target line
approximately perpendicular to the dominant wind direction), and the actual wind, logged during
the descent, was used for the "true" wind that dictated the kinematic motion of the simulated
vehicles. However, the two simulations respectively used the radiosonde and dropsonde data in
their control decisions, simulating two types of "inaccurate" wind data. Both of these simulated
descents' landing locations were then compared with the actual experimentally-deployed vehicle's
descent. The results were that the actual (experimental) uncontrolled descent vehicle travelled
approximately 23 km downrange. The simulated landing location of the controlled descent vehicle
using the dropsonde data was only 42 m further downrange. Contrasting, the simulated landing
location using the radiosonde data was ∼ 1800 m further downrange than the actual landing location,
demonstrating that local, current dropsonde data is critical to the system's performance.
IV.
Conclusions
A technique was developed to autonomously navigate a descent vehicle towards a target line
using a variable-drag parachute. The method was designed with a simple and inexpensive implementation in mind, such as using a microcontroller with a single actuator to trim the canopy. A
3DOF model predicts the descent path of the parachute and a simple, single-parameter control
algorithm adjusts the descent rate to guide the vehicle to a linear landing target.
The results indicate that the approach is eective, but is highly dependent on the accuracy of
the wind data used. When there are large dierences between the expected wind used in the control
9
algorithm and the actual wind encountered by the descent vehicle, a controlled parachute performs
no better than an uncontrolled, xed drag area parachute on average. It was demonstrated that
such "large" discrepancies between the expected and actual wind data can arise from spatial and
temporal dierences typically associated with radiosonde data. However, when accurate wind data
is available, such as that from a dropsonde deployed immediately prior to release of the controlled
parachute, it performs signicantly better than an uncontrolled parachute, even though the system
is inherently simple compared to other reported approaches.
Acknowledgement
Funding provided by the Nevada NASA Space Grant Consortium through NASA grant number
NNX10AJ82H. The authors also wish to express thanks to O.A. Yakimenko and N. Slegers for many
fruitful discussions and encouragements in this new line of research for our team.
References
[1] Yakimenko, O. A., Dobrokhodov, V. N., and Kaminer, I. I., Synthesis of Optimal Control and Flight
Testing of an Autonomous Circular Parachute, Journal of Guidance, Control, and Dynamics , Vol. 27,
No. 1, 2004, pp. 2940.
[2] Brown, G., Haggard, R., Almassy, R., Benney, R., and Dellicker, S., The Aordable Guided Airdrop
System (AGAS), 15th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar ,
June 8-11, 1999, Toulouse, France.
[3] Gilles, B., Hickey, M., and Krainski, W., Flight Testing of a Low-Cost Precision Aerial Delivery
System, 18th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar , May 2326, 2005, Munich, Germany.
[4] Slegers, N. and Costello, M., Aspects of Control for a Parafoil and Payload System, Journal of
Guidance, Control, and Dynamics , Vol. 26, No. 6, 2003, pp. 898905.
[5] Slegers, N., Beyer, E., and Costello, M., Use of Variable Incidence Angle for Glide Slope Control of
Autonomous Parafoils, Journal of Guidance, Control and Dynamics , Vol. 31, No. 3, 2008, pp. 585596.
[6] Slegers, N., Eects of Canopy-Payload Relative Motion on Control of Autonomous Parafoils, Journal
of Guidance, Control, and Dynamics , Vol. 33, No. 1, 2010, pp. 116125.
[7] Kelly, K. and Pena, B., Wind Study and GPS Dropsonde Applicability to Airdrop Testing, 16th AIAA
Aerodynamic Decelerator Systems Technology Conference and Seminar , May 21-24, 2001, Boston, MA.
10
[8] Benjamin, S. S., Jamison, B. D., Moninger, W. R., Schwartz, B., and Schlatter, T. W., Relative
forecast impact form aircraft, proler, rawinsonde, VAD, GPSPW, METAR and mesonet observations
for hourly assimilation in the RUC, 12th Conference on IOAS-AOLS, American Meteorological Society ,
20-24 January 2008, New Orleans, LA.
[9] Yakimenko, O., On the Development of a Scalable 8-DoF Model for a Generic Parafoil-Payload Delivery
System, 18th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar , May 2326, 2005, Munich, Germany.
[10] Quadrelli, M. B., Cameron, J. M., and Kerzhanovich, V., Modeling, Simulation, and Control of
Parachute/Balloon Flight Systems for Mars Exploration, 16th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar , 21-24 May 2001, Boston, MA.
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