MODELING AND VALIDATION OF AN AUTOROTATION LANDING CONTROLLER FOR REENTRY AND DESCENT APPLICATIONS

Abstract

Launch vehicles are an ever-expanding field that has gotten a lot of attention in the last years. However, what goes up must come down. Well-known approaches to the landing of spacecraft are propulsive landings, gliders and parachutes. We want to raise attention to another technology, autoro-tation. In this work, the focus lies on the simulation and control of such an autorotation lander. The analysis was part of the student project REXUS project Daedalus2. The team tested a number of approaches for axial autorotation controllers. Ranging from simple PIDs to artificial intelligence (AI) based Model Predictive Controllers (MPC). Furthermore , the flight envelope was designed to have different control regimes. Here a simple adaptive control strategy was proposed to stabilize the flight. For simulation purposes a high fidelity model was implemented. Especially important is the simulation of the rotor and fins. A wind machine 1 was used to produce axial flow through the rotor disk. The controllers were tested on a number of scenarios. This prepared the SpaceSeeds v2 of Project Daedalus 2 for further planed drop tests and ultimately the launch on REXUS29 in order to prove that autorotation is an alternative to other decelerator technologies.

Full text

MODELING AND VALIDATION OF AN AUTOROTATION LANDING CONTROLLER FOR
REENTRY AND DESCENT APPLICATIONS
Riegler C, Adler A, Appelt T, Barth´
o B, Bergmann P, Borschinsky E, B¨
os C, Dunschen F, Ettinger A,
Franssen L, Gellerman M, Klaschka P, Koch N, Mehringer J, Mutter J, Neumann T, von Pichowski J,
Reigl M, Richter L, St¨
oferle P, Werner L, Wolf J
JMU W¨
urzburg & W¨
uSpace e.V.
Informatik 8 - Space Technology
Emil-Fischerstr. 32, 97072 W¨
urzburg
ABSTRACT
Launch vehicles are an ever-expanding field that has got-
ten a lot of attention in the last years. However, what goes
up must come down. Well-known approaches to the landing
of spacecraft are propulsive landings, gliders and parachutes.
We want to raise attention to another technology, autoro-
tation. In this work, the focus lies on the simulation and
control of such an autorotation lander. The analysis was part
of the student project REXUS project Daedalus2. The team
tested a number of approaches for axial autorotation con-
trollers. Ranging from simple PIDs to artificial intelligence
(AI) based Model Predictive Controllers (MPC). Further-
more, the flight envelope was designed to have different
control regimes. Here a simple adaptive control strategy was
proposed to stabilize the flight. For simulation purposes a
high fidelity model was implemented. Especially important
is the simulation of the rotor and fins. A wind machine 1was
used to produce axial flow through the rotor disk. The con-
trollers were tested on a number of scenarios. This prepared
the SpaceSeeds v2 of Project Daedalus 2 for further planed
drop tests and ultimately the launch on REXUS29 in order to
prove that autorotation is an alternative to other decelerator
technologies.
Index Terms—Autorotation, Decelerator, Landing, Ro-
tor, EDL, Parachute
1. INTRODUCTION
This paper describes how an autorotation based landing sys-
tem for re-entry and soft landing of space vehicles can be sim-
ulated and how the simulation can be verified. The idea for
this project started in 2016 as part of the Daedalus project as
1The use of the term ”wind machine”, as compare to ”wind tunnel” is
deliberate. This device did not guarantee laminar flow, thus we restrain from
calling it a wind tunnel. However, we are very grateful that we had access
to this device owned and maintained by Chair Informatics 8 at JMU and are
confident that it improved our results.
part of the REXUS/BEXUS programme. Back then the ve-
hicle used wings that were fixedly mounted to the SpaceSeed
body. The next iteration Daedalus 2 uses a rotor head that
allows a free rotation of the rotor and an adjustable pitch. A
new simulation was needed to be able to design the controller
for the pitch. In Figure 1 a Render of the newer and improved
version is depicted.
The basic principle behind this vehicle is the same as in
a helicopter. During the different flight phases described in
chapter the SpaceSeed uses different measures to reduce its
speed and ensure a soft landing. All these phases require a
different controller due to the different control goals. A big
challenge is that the air pressure and velocity can range over
a few magnitudes during the flight. Therefor this poses a non-
linear control problem, for which different control approaches
are tested as described in chapter . Due to the many different
own simulations that are involved in this setup, the model and
the controller have to be validated and tested as described in
chapter to ensure a successful flight.
Fig. 1. Render of the SpaceSeed v2 with a rotor disk radius
of roughly 0.6m
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19 - 23 June 2022. Heilbronn, Germany

2. STATE OF THE ART
The idea of utilizing auto rotation in space applications is not
new. However, it is quite immature with only a small number
of prototypes having been built. In this section, some preced-
ing projects will be introduced shortly.
One of the first projects was implemented by Karman
Aerospace and the USAF. They built the KRC-6 and tested
the deployment of this autorotation vehicle from military air-
craft in the Mojave desert. A total of ten iteratively improved
prototypes were built which ultimately lead to a version that
was able to perform a soft landing. However, in the 1970s
when this technology was developed, it was way ahead of
its time. The vehicle was flown via remote control and mul-
tiple hundred meters away from the operator which made it
extremely hard to land. A lack of MEMS electronics also
lead to some attempts failing due to simple mechanical gyro
locks. Nevertheless, the project showed promise and proved
that autorotation landers can work. Unfortunately no follow
up projects were implemented for unknown reasons. [1]
From 2007 to 2009, ESA had two studies conducted for
autorotation landers on Mars. AMDL and ARMADA are the
names of these works. They investigated how such a vehi-
cle might work for Mars with its extremely thin atmosphere.
AMDL investigated inflatable rotors and ARMADA looked
at the approach of telescoping rotors. Both studies deemed
the technology feasible for use on Mars, however also found
that for bodies like Titan, Venus and Earth it is even more
interesting. [2, 3]
The most recent study and predecessor to this was Project
Daedalus1 [4]. Starting in 2015 a student team developed
a primitive rotor reentry vehicle that would create an under-
standing of the feasibility. This was one of the first prototypes
to be dropped from a significant altitude, roughly 75km. The
goal was to understand the flight and reentry behaviour of the
vehicles and furthermore build a baseline for future projects.
With a successful flight of the SpaceSeed v1, seen in Figure
2, in 2019 the foundation for the next iteration was created.
3. MISSION PROFILE
The mission profile also called the operating envelope is cru-
cial for the controller design so that operating areas can be
defined to adapt the controller to the respective area and opti-
mize its performance.
The SpaceSeed flight comprises several flight phases. Start-
ing with the pre-launch checks and the launch of the REXUS
rocket, where the SpaceSeeds climb to an altitude of 80 km
and are deployed. As soon as the rotor blades are unfolded
and locked in place, the Fast Descent Control starts with the
aim of reducing the rotational speed, stabilization and avoid-
ing excessive mechanical loads on the rotor blades. The con-
trol is particularly difficult because there are only a few sen-
sors available, for instance, the atmospheric pressure is too
Fig. 2. Flight hardware of the SpaceSeed v1 with a wing span
of roughly 0.8m [4]
low for pressure measurements of the barometer. Below an
altitude of 10km, the Glide Control takes over whereby a
constant rotational speed is maintained. During this period,
a hover manoeuvre (”landing simulation”) is performed at an
altitude of 2 km to demonstrate the principle of operation. At
a height of 10m, the Landing Control is triggered, which con-
trols the smooth braking and landing until touchdown.
4. MODELLING
To simulate the Mission Profile a Model is created. This
model focuses on the flight dynamics of the autorotation ve-
hicle. The goals of the modelling process are to understand
the flight and provide a tool for controller design. Beyond
aspects like gravity and atmosphere, the two key aspects will
be discussed in this section. They are the rotor model and the
fin model. Each of these models is key to understanding the
flight and creating control strategies. A total of 5 states were
propagated through the model, they are listed and explained
in Table 1 The used programming language was Matlab. To
simulate the model it was implemented in Matlab and prop-
agated via ODE-Solvers or even Euler integration since the
system was stable enough to do so.
4.1. Rotor Model
The key model to simulate the flight is the rotor dynamics
model. It is based on classic Blade Element and Momentum
Theory, commonly used for rotorcraft modelling [5, 6]. For
simplification, the model was made to be a 1D vertical model,
2nd International Conference on Flight Vehicles, Aerothermodynamics and Re-entry Missions & Engineering (FAR)
19 - 23 June 2022. Heilbronn, Germany

80km
10km
Fast Descent
Control
Glide
Control
Landing
Control
10m
wind
drift
Fig. 3. Daedalus 2 Mission Profile including control zones
Table 1. Propagated States of the System
State Desc Unit
Speed Vertical velocity of the vehicle m
s
Altitude Altitude off the vehicle ASL m
Rotor rotation Rotation of the rotor blades rad
s
Body rotation Rotation of vehicle body rad
s
Induced Velocity Flow induced by the rotation m
s
as implemented by Dalamagkidis [7] and Nonami et al [8]. A
vertical model has the advantage of also being a conserva-
tive estimate because the horizontal component of autorota-
tion usually brings a significant performance gain with it.
To increase accuracy compared to other models, no im-
plicit integration was used. Blade Element theory is inte-
grated during run time for each simulation step. Furthermore,
to estimate the lift and drag, AERODAS was used [9]. AERO-
DAS is a set of equations that allows estimating L/D curves
beyond stall. This is especially important for the spin-up of
the rotor because its blades will be in stall during this phase.
Due to this design decision, another aspect could be added.
Negative rotation rates were able to be simulated. This add
on is usually not simulated as normal helicopters will never
be required to recover from such a state. However, slightly
negative rotation rates might be possible for Autorotation Ve-
hicles during spin up. Moreover, it is important to understand
how a controller copes with negative rates to add safety to the
control itself.
Another important factor is tip loss. Just like in regular
aircraft, the tip of the rotor blade induces vertices which are
reducing its effectiveness. Prantl’s Tip Loss factor approx-
imates this effect and contributes to a more realistic model
[10].
All of these effects contribute to the high fidelity, non-
linear model. It was implemented during the course of a mas-
ter thesis [11].
4.2. Fin Model
The fin model used is versatile, modular and easy to adapt to
varying circumstances. This is achieved by including many
various parameters for the simulation. The altitude of a sub-
sonic rocket is simulated with an accuracy of approximately
10–15%. Modelling of supersonic rockets is expected to be
accurate up to Mach 1.5 This model calculates the total torque
generated by the fins using the sum of the roll dampening and
roll forcing coefficients. The values of these are dependent on
the outside air temperature, the shape and number of fins (in
the current case: rectangular and 2 double fins) and whether
the speed is sub or supersonic. The exact speed of sound is
height depended, this also needs to be considered. At sub-
sonic speeds, the total force exerted on and by the fins has
to be normalised by the dynamic air pressure and the area
of attack. For supersonic speeds, the fins are divided into
streamwise strips, the normal force of which are calculated
separately and then summed. The resources upon which the
fins are modelled are reliant on works by Niskanen [12] and
Mandel et al [13].
5. CONTROL STRATEGIES
An autorotation vehicle needs to be controlled to keep it sta-
ble. The first goal was to control the rotation rate of the rotor.
It is linked to the descent rate and also prevents high rotation
rates that could damage the rotor or vehicle. The second goal
is to control the vertical velocity. This control aspect becomes
important during landing. The velocity ultimately needs to be
reduced below 1m
sto perform a smooth landing.
Due to the non-linear nature of the system, this is a chal-
lenging task. To achieve a satisfying degree of control our
team used a multilateral approach and tried a variety of con-
trollers. They are introduced in this chapter and the key ap-
proaches to their design are explained. Furthermore, other
approaches, which have not made it to the testing phase, are
outlined as well.
5.1. PID - Genetic
PID controllers are a well-known tool that solves most control
cases. Due to its simplicity and robustness, it was chosen to
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19 - 23 June 2022. Heilbronn, Germany

be investigated. Nonami et al [8] already showed that PID
control for autorotation of model helicopters is viable. They
utilized hand-tuned controllers which they also applied to real
RC helicopters and found good results. We went one step
further and decided to investigate tuning methods to solve this
problem.
The chosen method was the Genetic Algorithm (GA) [14].
GAs simulate evolution where Generations with individual
Specimens are formed. They compete amongst each other
and the one that performs best will be used to create a new
generation. Mutation is another important aspect introduced
to avoid local minima.
A native implementation of Matlab (R2019b) for the GA
was used to optimize the PID sets. As cost function, a simple
LQR cost function was used to validate the performance. To
control the flight of the vehicle a controller was tuned on rota-
tion rate as the key state. For the landing controller, a velocity
ramp function was used. The ramp was created to reduce the
speed linearly until 0mabove ground to 0m
s.
The GA converged comparatively quickly when provided
with a hand-tuned estimate. The final optimization runs 30
Generations with 24 specimens each were chosen. 2Opti-
mized controllers showed good performance in the simula-
tion and were then moved forward to wind tunnel testing. It
should be noted that the PID controllers usually were reduced
to PI controllers. The GA optimizer almost always reduced
the D term to nearly zero, which is not unheard of for PIDs
controlling non-linear systems.
For testing, we used Adaptive and Static controllers to un-
derstand which would perform better compared to the imple-
mentation effort and risk.
5.2. NMPC
The Idea of NMPC control was derived by approaches of
Dalamgkidis [7] and Nonami et al [8]. They tried different ap-
proaches for Model Predictive Controllers, mainly driven by
AI. All approaches demanded significant calculation power
beyond an embedded system. Therefore, a different approach
had to be made for the SpaceSeed v2. A reduced model
was made that incorporated some simplifications and thus al-
lowed for faster calculations of each step. Furthermore, the
integrated NMPC function of Matlab was used to model the
controller. The prediction and control horizons were kept be-
tween 5 and 10 with a stepsize of 0.1s. Ultimately there was
still a demand for significant calculation power, thus initial
tests were done as hardware in the loop tests with a laptop
executing the controller at a 10Hz frequency.
2This number was chosen as a multiple of 12 which is the core count of
the used CPU. Parallel Processing was activated thus multiples of 12 yielded
the best performance per time.
5.3. Other Concepts
Besides the already addressed control strategies, additional
concepts were selected, implemented and evaluated to gain
more experience in controller design and finally to design a
more powerful controller whose robustness is comparable to
that of the classical PID.
In further developing the NMPC towards an LMPC, new
methods were investigated to obtain an improved linearized
model for the Seed autorotation from simulation results and
wind tunnel test data. To ensure a fast realization, we decided
to follow a state-space model approach using Matlab’s Sys-
tem Identification Toolbox, which can be deployed directly
on the embedded system, instead of using machine learning
approaches. For stable system identification and generation
of a linearized model, we first generated test data by simu-
lation using domain randomization to account for different
initial conditions and environmental parameters. For the wind
tunnel test, altitude and speed were kept constant during sim-
ulation. Finally, the linearized model was validated using
wind tunnel test data estimating the Seed state with respect to
the pitch angle input with an accuracy of more than 85%.
In addition to this concept, a neural network-based controller
was developed, which has not been tested yet.
6. VALIDATION & TESTING
It is of other most importance to Validate and Test what was
created. Validation & Testing were done in two steps. First,
the model was validated with other comparable models. This
was done before controller tuning to make sure the controllers
are tuned on a validated baseline. Second, the SpaceSeed v2
was taken to wind machine tests, here the controllers were
tested. This is another important step to be sure that the con-
trollers act as they should.
These Tests are explained in the following sections. This
includes the setup of the tests, especially for the wind ma-
chine. Their most important results are shown and discussed.
6.1. Model Validation
Model Validation, before controller tuning, was the first big
step to confirming the validity of the system. Validation of the
Model was part of a master thesis that accompanied the whole
project [11]. This was done by comparison with the model of
Dalamagkidis [7]. Their work had a simplified model, how-
ever, was expected to yield comparable results. The most sig-
nificant expected difference was spin up behaviour. Dalam-
agkidis assumed linear lift for all pitch angles, thus overes-
timating lift and torque in stall. Therefore, we expected to
show noticeable lower spin-up times. Furthermore, the model
developed in our work took into account several factors that
were expected to slightly alter the glide behaviour. Thus,
we expected slightly different descent speeds to be simulated
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within 10% of each other. This will also lead to slightly dif-
ferent pitch angles being simulated.
0 10 20 30
Time [s]
-20
-15
-10
-5
0
5
10
15 Alpha [DEG]
0 10 20 30
Time [s]
0
50
100
150
200
250
300 Height [m]
0 10 20 30
Time [s]
800
1000
1200
1400
1600
1800
2000
2200
2400
2600 Rotorrotationspeed [rpm]
0 10 20 30
Time [s]
-16
-14
-12
-10
-8
-6
-4
-2
0Verticalspeed [m/s]
0 10 20 30
Time [s]
1
2
3
4
5
6
7
8
9Induced velocity [m/s]
Riegler
Dalamagkidis
Fig. 4. Comparison of the developed models versus the verti-
cal autorotation model of Dalamagkidis [11]
Numerous different comparison runs were done to under-
stand how the models compare. A very typical run was a
spin-up from a lower rotation rate which then translated into
a glide and finally performed landing. The run of these simu-
lations can be seen in Figure 4. The graphs show very similar
behaviour and are also showing the previously expected ef-
fects. After all runs, no major inconsistencies between the
models were found. Thus, the model was considered valid
for controller tuning and further analysis.
6.2. Wind Machine Testing Results
The student team of Daedalus 2 had access to a wind machine.
With the SpaceSeed v2 mounted in front of the turbines of this
device, it was possible to create axial flow. The setup during
testing can be seen in Figure 5 during operation. Wind speeds
were able to be set between 6 m
sand 18 m
s. This is within
the range of the expected steady-state descent, also shown in
Figure 4.
During testing, different test profiles were performed. The
most important will be listed here:
• Spin up and hold rotation rate
• Spin up and hold rotation rate for a long time (20min)
• Spin up and switch between different rotation rates and
controllers (Adaptive PID approach)
• Spin up to low rotation rates, below 100 RPM.
Fig. 5. Wind Machine testing setup during a rotation test of
the SpaceSeed v2
Fig. 6. Rotation Rate and Pitch Angle during D2 wind ma-
chine test with PID control
A scenario where rotation rates and PID sets were changed
can be seen in Figure 6. The output is spot on what we wanted
to achieve. Only during the last step, we can see 0.2°jitter in
the pitch angle. This was due to a rotor configuration which
had mechanical jitter. While this was fixed, it gave us even
more confidence in the robustness of the control strategies
that were chosen. Adaptive controllers showed good results,
but not significantly better than static PID values, thus these
were chosen furthermore.
Moreover, we also tested the NMPC implementation. A
representative test run can be seen in Figure 7. This con-
troller failed to achieve its goal of spinning up to and hold-
ing a steady rotation rate (not multiple as demonstrated in the
PID example). The NMPC is a comparably slow controller
because it has to predict a preset number of possible scenar-
ios for a certain time horizon. In this scenario, the controller
was running at 10Hz, as compared to the PID which was run
at 100Hz and could have been run at even higher frequencies.
While initially the NMPC shows a good rise behaviour and
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19 - 23 June 2022. Heilbronn, Germany

0 50 100 150 200 250
Time in seconds
0
500
1000
1500
2000
2500
Rotation Speed in RPM
Rotation Speed of the Rotor
Raw
0 50 100 150 200 250
Time in seconds
-10
-8
-6
-4
-2
0
Collecitve Pitch in DEG
Fig. 7. Rotation Rate and Pitch Angle during D2 wind ma-
chine test with NMPC control. An unstable behaviour is ob-
served. The NMPC was tasked to achieve and hold only one
control goal.
can even hold the rotation rate for a certain amount of time,
it then diverges and loses the rotation completely. Higher fre-
quencies might have solved this issue, but that was not pos-
sible at all with the used embedded computer. Authors like
Dalamgkidis [7] and Nonami et al [8] who used the model
predictive approach before, was mostly assumed to have sig-
nificant calculation power available. For normal-sized heli-
copters, this should be easily achievable, but for an autoro-
tation vehicle with a total mass of 2.1kg, this was not realis-
tic. Thus, the NMPC was ditched and not considered further,
however, it could be done for other vehicles in the future and
should definitely be taken into account as an option.
7. DISCUSSION & FUTURE WORK
Overall the results are encouraging. Controller tuning, while
comparably unconventional in its approach, was successfully
validated on the wind machine. Furthermore, only a hand-
ful of re-runs had to be made until the tuning was on point.
The scheduled suborbital test flight in March 2023 promises
to yield the first flight data of a controlled autorotation vehicle
in recent times. Since this project is just a student project the
data yield and sophisticatedness of the system are expected to
be lower than usual. Previous studies and the Daedalus stud-
ies all suggest that this technology is promising. Ultimately, a
continuation of this work as a research project would be ben-
eficial for its advancement. Currently, a PhD Thesis is con-
ducted that shall create an understanding of the utilization of
autorotation on other planets. During or after this, it is aimed
to acquire funding to continue this work as a sophisticated
research project.
We want to thank all our Sponsors of Project Daedalus 2.
Please find this ever-growing list on www.wuespace.de. Fur-
thermore, we want to thank our endorsing professors, Prof.
Hakan Kayal and Prof. Sergio Montenegro for their help.
Without support from the Chair of Informatics 8 at JMU
W¨
urzburg, our projects would not be possible.
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19 - 23 June 2022. Heilbronn, Germany

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2nd International Conference on Flight Vehicles, Aerothermodynamics and Re-entry Missions & Engineering (FAR)
19 - 23 June 2022. Heilbronn, Germany