# Anomalous circularly polarized light emission in organic light-emitting
diodes caused by orbital-momentum locking

Li Wan1,2,3,∗ Yizhou Liu4 Matthew J. Fuchter2,5 Binghai Yan4,†
1 Department of Physics, Imperial College London, London, SW7 2AZ, United
Kingdom
2 Centre for Processable Electronics, Imperial College London, London, SW7
2AZ, United Kingdom
3 Department of Physics, Chemistry and Biology (IFM), Linköping University,
Linköping, 58431, Sweden
4 Department of Condensed Matter Physics,Weizmann Institute of Science,
Rehovot 76100, Israel
5 Department of Chemistry, Molecular Sciences Research Hub, Imperial College
London, White City Campus, London W12 OBZ, United Kingdom

###### Abstract

Chiral circularly polarized (CP) light is central to many photonic
technologies, from optical communication of spin information to novel display
and imaging technologies. As such, there has been significant effort in the
development of chiral emissive materials that allow for the emission of
strongly dissymmetric CP light from organic light-emitting diodes (OLEDs). A
consensus for chiral emission in such devices is that the molecular chirality
of the active layer determines the favored light handedness of CP emission,
regardless of the light-emitting direction. Here, we discover that,
unconventionally, oppositely propagating CP light exhibits opposite handedness
and reversing the current-flow in OLEDs also switches the handedness of the
emitted CP light. This direction-dependent CP emission boosts the net
polarization rate by orders of magnitude by resolving an established issue in
CP-OLEDs, where the CP light reflected by the back electrode typically erodes
the measured dissymmetry. Through detailed theoretical analysis, we assign
this anomalous CP emission to a ubiquitous topological electronic property in
chiral materials, namely the orbital-momentum locking. Our work paves the way
to design new chiroptoelectronic devices and probes the close connections
between chiral materials, topological electrons, and CP light in the quantum
regime.

## Introduction

Chirality characterizes parity symmetry-breaking where a molecule cannot be
superposed on its mirror image in chemistry and biology[1, 2]. Chiral
enantiomers exhibit opposite chiroptical activity when coupling to light[3,
4]. In physics, chirality usually refers to the spin-momentum locking of
particles such as Weyl fermions[5, 6] and the circular polarized light. Chiral
organics were recently reported to exhibit a topological feature [7], in which
the electronic orbital and momentum are locked together, to rationalize the
intriguing spin selectivity in DNA-type molecules[8, 9]. Hence given the
intimate relationship between electronic states and light-matter interactions,
we were inspired to raise a question: Can topological electronic properties
(i.e., orbital-momentum locking) enhance chiroptical activity and therefore
advance the rapidly developing (chir)optoelectronic technology[10, 11]?

A future industrial application of organic chiral emissive materials is in
circularly polarized organic light-emitting diodes (CP-OLEDs)[12], which
should eliminate the $\sim$50% internal light loss caused by the contrast-
enhancing circular polarizer in OLED displays. Such efficiency gains occur via
direct circularly polarized electroluminescence (CP-EL) from the CP-OLED,
which can pass through the contrast-enhancing polarizer unhindered.[13] The
effectiveness of this strategy depends on the degree of circular polarization
of EL, where higher polarization gives better efficiency for the display in
the presence of such polarizers.[2]

Since the first CP-OLED reported in 1977[15], the circularly-polarized
electroluminescence of a material was also assumed to be identical to circular
polarization measured in absorption and in photoluminescence (cases without
current flow) from the same electronic transition . In another words, CP-EL
was considered nearly the same process as CP photoluminescence (CP-PL) [or the
inverse process of optical circular dichroism (CD)] due to a shared electronic
transition, and the magnitude of CP emission determined by the product of
electric and magnetic transition dipole moments.[16, 17] Thus most efforts in
this field were made on developing more twisted chiral emitters with stronger
magnetic transition dipoles to improve optical chirality[18, 19], without
taking current flow in an OLED device into consideration.

More importantly, in terms of device engineering, the reflective back-
electrode in an OLED device is another key issue. In all prior studies of
chiral emissive materials, CP emission is conventionally expected to exhibit
the same handedness in both emission directions (forward and back) from the
point of recombination, thus any back reflection within the device will invert
the handedness of CP emission travelling backwards and cancels out the forward
CP emission, reducing the net EL circular polarization that exits the device
through the transparent electrode[18, 20, 21, 22]. Consequently, the magnitude
of EL circular polarization from devices is much smaller than the
corresponding CP-PL measured in transmittance geometry, which does not suffer
issues of reflection[20](Fig. 1a). Even though constructing semi-transparent
OLEDs can, to some extent, mitigate the problem of reflection, such a strategy
reduces the overall the device performance in a displays, negating the
original intention of energy saving at the polarizer.[18]

Among all CP-OLEDs reported and many other chiral optoelectronic devices based
on 2D[23] and perovskite materials [24], chiral polymeric materials[2, 1, 26,
27, 28] demonstrate significant circular polarization in PL and EL, several
orders of magnitudes stronger than other chiral emissive systems[29, 18, 30,
31] (see Fig. 2a). Despite the analysis above, when constructing
optoelectronic devices from such materials, their CP-EL remains equal, or
sometimes is even enhanced compared to CP-PL or CD. Although previous
theoretical[32, 33] and experimental[2, 1, 26] work attributed the strong
optical circular dichroism to a predominately excitonic origin, these analyses
cannot account for the comparable or enhanced circular polarization in EL
devices, given the expected detrimental effect of back-electrode reflection.

In this work, we discover an anomalous light emission phenomenon from chiral
polymeric CP-OLEDs. For the chiral polymeric materials under study, CP-EL
exhibits opposite handedness in forward and backward emission directions,
counter-intuitive to what is usually expected in EL or PL (Fig. 1b). With such
direction-dependent CP emission, the back-reflected light exhibits the same
handedness as the forward emission, avoiding the polarization cancellation
which occurs in devices using other materials and boosting the net CP-EL
exiting the device[18, 20]. Furthermore, for the first time, we explain the
effect of current flow on CP-EL, where its handedness can also be switched by
reversing the current flow in an OLED. We propose that the directional CP-EL
observed is caused by the topological nature of the electronic wave functions
in chiral polymers. Because of orbital-momentum locking[7],  the current flow
induces nonequilibrium orbital polarization in electron and hole carriers.
Therefore, finite angular momentum transfers from electron/hole orbital to the
photon spin in the optical transition. When they have the same spin, the
counter-propagating CP lights exhibit opposite handedness.  This orbital
polarization effect rationalizes the fact that the handedness of CP light is
determined both by the current direction and the emission direction.
Furthermore, this model reveals an exotic CP-EL mechanism caused by current-
induced time-reversal breaking. Our work paves they way to design novel
chiroptoelectronic devices with strong circular polarization.

## Results

A chiral polymer blend consisting of an achiral light-emitting polymer (i.e.,
poly(9,9-dioctylfluorene-alt-benzothiadiazole), F8BT, Fig. 1) and a non-
emissive chiral additive (i.e., [P]-aza[6]helicene) was selected for the
investigation of CP-EL. Upon thermal annealing of spin-casted thin-films, the
chiral additive (10 wt%) induces a strong and robust chiral structure and
optical CD to the originally achiral polymer with an absorption dissymmetry
factor ($g_{abs}$) of $\sim 0.6$ (see Fig. S1)[13, 1], calculated in the
following way:

$g_{abs}=\frac{A_{L}-A_{R}}{A}=\frac{\Delta A}{A},$ (1)

where $L/R$ stands for left/right-handed CP light and $A$ refers to the
absorbance. To investigate how emission direction affects the CP-EL, CP-OLEDs
were fabricated using both conventional and inverted device structures where
the transparent electrode (i.e., Indium Tin Oxide, ITO) serves as anode and
cathode, respectively (Figs. 1c and 1d).

With a fixed current flow direction (Figs. 1c and 1d), when measuring the EL
through transparent ITO, left-handed CP light is observed in a conventional
device where the light emits in the same direction as the electron injection.
A positive EL dissymmetry factor $g_{EL}$ of +0.54 can be calculated
following:

$g_{EL}=\frac{I_{L}-I_{R}}{(I_{L}+I_{R})/2},$ (2)

where $I_{L/R}$ is the irradiance recorded from the CP-OLEDs. However, despite
a fixed absolute stereochemistry of chiral material in the emissive layer of
both devices, the sign of the CP-EL signals was found to be dependent on the
device structure. When the emission direction relative to the current
direction is switched, the inverted CP-OLED emits right-handed circularly
polarized light through ITO with a $g_{EL}$ of $?0.33$. Apart from the
emission direction-dependent CP-EL signals in conventional versus inverted
devices, we detected no evidence of erosion of $g_{EL}$ by the reflective
electrodes. Compared with other reported CP-OLEDs[29, 18, 30, 31], the
polyfluorene-based CP-OLEDs we developed exhibit one of the highest known
$g_{EL}$ values (Fig. 2a). In contrast, lanthanide complexes exhibit
intrinsically high PL dissymmetry ($g_{PL}$)[20], but the $g_{EL}$ recorded
from the transparent electrode of lanthanide-based CP-OLEDs dramatically
decreases when increasing the thickness of the reflective metal electrode.
This is similarly observed in other small molecule CP-OLEDs[29, 18, 30, 31]
(Fig. 2b).

To compare our results with other previously reported CP-OLEDs, we performed
CP-EL measurements on semi-transparent OLEDs in both conventional and inverted
CP-OLEDs (Fig. 2c). Surprisingly, emission direction-dependent CP-EL behavior
was observed in both device structures, where the CP-EL from forward and
backward emission (i.e., through a semi-reflective electrode) exhibit the
opposite handedness. Considering this emission direction-dependent dissymmetry
factor is only observable in EL but not for CP-PL or CD of the chiral thin
films (Fig. S2), we speculate that this behavior is associated with the flow
of charge carriers within the devices. To unambiguously describe and compare
the emission direction-dependent CP-EL signals in two device architectures, we
define the emission direction relative to the charge carrier flow direction
(See Fig. 2c). Specifically, emission from the transparent ITO in the
conventional device and the emission from semi-transparent Au in the inverted
device are defined as directionally aligned with the electron flow.
Conversely, emission from the opposite electrodes in conventional and inverted
devices is defined as directionally aligned with the hole flow. In contrast to
other chiral emitters in OLED devices[18, 20], we find $|g_{EL}|$ of net
emission from the transparent electrode increases when increasing the
thickness of the reflective electrode (Figs. 2b and 2d) for our chiral
polymeric materials. As summarized in Fig. 2d, regardless of device structure
used, F8BT:[P]-aza[6]helicene based CP-OLEDs demonstrate positive $g_{EL}$
when emission occurs along the direction of electron flow and switch to
negative $g_{EL}$ when emission occurs along the hole flow direction. This
indicates that the previously observed inversion of CP-EL sign from
conventional versus inverted devices (see Fig. 1) is due to emission
direction-dependent CP-EL relative to the electron flow direction. Given this
outcome, the reflective electrode in our system results in reflected light
with an identical sign to the forward emission, resulting in a comparable or
boosted net CP EL signal (Fig. 2b).

## Discussions

###  0.1  Experimental Summary

Our CP-EL data exhibits profound features, distinct from those obtained with
other chiral emitters in OLEDs (Fig. 2b). Besides extremely large $g_{EL}$,
the CP-EL handedness can be switched both by the current flow direction and by
the light emission direction. By carefully examining the optical elements in
our blend thin films[34], the sign inversion observed here is not caused by
linear (LD/LB) effects nor circularly polarized scattering. There are
negligible morphological change when the film is casted on the PEDOT:PSS or
ZnO layer, which suggests that the active layer morphology is identical
between conventional and inverted devices (Fig. S5). Previously, for CP-OLEDs
constructed from other materials, the position of the recombination has been
reported to effect the magnitude of the CP-EL[1, 27]. By using a TPBi electron
transport layer (LUMO $\sim$2.7 eV) in our conventional devices, we generate a
larger electron injection barrier from Ca ($\sim$2.9 eV) than would be the
case when directly depositing Ca onto F8BT (LUMO $\sim$3.3 eV). We observe
TPBi emission in our EL spectra, which indicates the recombination zone in our
conventional devices occurs at the F8BT/TPBi interface, away from the ITO
electrode. Similarly, in our inverted OLED, TCTA was used to shift the
recombination to the F8BT/TCTA interface till the observation of the interface
recombination (Fig. S6)[35]. Therefore, by careful selection of contact and
transport layers, the recombination zones in both devices were pinned
physically at the far interface of F8BT, away from ITO electrode. This ensures
the CPEL sign inversion investigated here is not caused by the previously
reported active layer thickness/recombination zone[1, 27], but instead by
current-direction (See sign-unchanged data in Fig. S7).

By ruling out other origins, we demonstrate that the CP-EL handedness
inversion is sensitive to both the current flow direction and the light
emission direction. In other words, the emitted photon seems to retain
’Circularly polarised light emitted by OLEDs exhibits opposite handedness
depending on the propagation direction of the light. Switching the current
flow in the OLED also switches the light handedness’a memory of the
propagating direction of recombining electrons and holes, despite the fact
that initial carrier velocities are usually ignored to understand the light
emission process[36]. Such an outcome indicates salient current-flow-induced
time-reversal symmetry (TRS)-breaking in the system. The exciton-coupling
model[32, 33] is based on quantum states with TRS and cannot explain such
current-direction- and emission-direction-dependent CP-EL.

###  0.2  Theoretical model

It is known that helicene additive promotes the F8BT polymer to form chiral
assemblies in solid-state thin films[32, 34]. The chiral polymer blend is the
real-space channel for both current flow and light emission. In the following,
we will discuss the light emission in the presence of TRS-breaking due to the
current flow.

We first will revisit the general theory that describes the CP emission effect
and interpret our experiments from an anomalous term. According to Fermi’s
golden rule, the emission rate of CP light is,

$I_{L/R}=\frac{2\pi}{\hbar}|\bra{0}H^{\prime}\ket{1}|^{2}\delta(\epsilon_{1}-\epsilon_{0}-\hbar\omega)$
(3)

where $\ket{0}$ ($\ket{1}$) represents the ground (excited) state with energy
$\epsilon_{0}$ ($\epsilon_{1}$), $H^{\prime}$ is the light interaction
Hamiltonian $H^{\prime}=-e\textbf{E}\cdot\textbf{r}-\textbf{m}\cdot\textbf{B}$
with m being the magnetic moment, E and B are the light electric and magnetic
fields, respectively, and $\hbar\omega$ is the photon energy. For right/left-
handed light traveling along the $z$ axis, the electric and magnetic fields
are $\textbf{E}=E_{0}(1,\pm i,0)/\sqrt{2}$ and $\textbf{B}=E_{0}/c(\mp
i,1,0)/\sqrt{2}$. Therefore, the leading term of CP light emission can be
derived as,

$I_{L}-I_{R}=-\frac{2\pi
e^{2}}{\hbar}I_{0}~{}\mathrm{Im}[x^{01}y^{10}]\delta\\\ -\frac{2\pi e}{\hbar
c}I_{0}~{}\mathrm{Im}[m_{x}^{01}x^{10}+m_{y}^{01}y^{10}]\delta$ (4)

where $x^{01}=\bra{0}x\ket{1}$ and $m_{x}^{01}=\bra{0}m_{x}\ket{1}$ represent
the electric and magnetic transition dipoles, respectively, and
$I_{0}=|E_{0}|^{2}$. We note $\textbf{m}=(m_{x},m_{y},m_{z})$,
$\textbf{r}=(x,y,z)$ and $\delta$ for the same $\delta$-function in Eq. 3.

The second term in Eq. 4 is routinely employed to understand CD, CP-PL or CP-
EL for organic/inorganic systems and has been called natural chiroptical
activity[37]. Because it corresponds to interaction with the electric and
magnetic fields of light, this term involves both electric and magnetic
transition dipoles. We call it the normal circular polarization effect (NCPE)
in the following. In chiral organic molecules, the OAM change in the
transition is zero because TRS forces the net OAM of $\ket{0,1}$ to be zero.
Due to the conservation of angular momentum, the total spin angular momenta of
all emitted photons sum to zero. Because counter-propagating photons emitted
are equal in probability, they carry opposite spins, i.e., they share the same
handedness (see illustration by Fig. 3c). Thus, the handedness of CP emission
is free from the emission direction in the case of NCPE, as observed in PL and
EL reported in other chiral emissive systems[38, 29, 18, 30, 31].

The first term in Eq. 4 corresponds to the dipole interaction with light
electric field. If $\ket{0,1}$ respect TRS, this term is exactly zero.
Additionally, a similar term corresponds to the Berry-curvature-induced[39]
anomalous Hall effect[40] in solid crystals and also vanishes if TRS appears.
Therefore, the first term was generally ignored when studying organic
molecules. It was referred to as the magnetic CD [41, 42] in absorption of
magnetic materials or in a external magnetic field. However, if electrons and
holes carry finite velocities before recombination, the first term cannot be
naively neglected. In other words, the current flow can induce magnetization,
more specifically the orbital magnetization as we will show. The
nonequilibrium phase breaks TRS in chiral molecules. We refer to the first
term as the anomalous circular polarization effect (ACPE) here. In such a
case, ACPE may contribute more to the net circular polarization than NCPE
because the electric field is much stronger than magnetic field in light.

###  0.3  Orbital-momentum locking in chiral molecules

We discuss the TRS-breaking of $\ket{0,1}$ in the presence of current flow.
Although the average momentum is zero for electrons in a molecule, the
simultaneous momentum ($k$) can be significant. For example, we can
approximate the molecule as a box confining electrons inside (see Figs. 3a-b
). Electrons move back-and-forth due to boundary scattering and form a
standing wave $\ket{\psi}$. The standing wave is a superposition of a forward-
moving state $\ket{\psi^{\pm}}$ and a backward-moving state $\ket{\psi^{-}}$,
where we choose $\ket{\psi^{+}}=\ket{\psi^{-}}^{*}$ because TRS allows
$\ket{\psi}$ to be real valued. If an electron picks up a velocity along $\pm
z$ caused by the current flow, its wave function reduces from $\ket{\psi}$ to
$\ket{\psi^{\pm}}$. We point out that $\ket{\psi^{\pm}}$ themselves violate
TRS, although $\ket{\psi}$ does not.

Next, $\ket{\psi^{\pm}}$ carry opposite OAM ($\pm l$) in a chiral molecule
[7]. As illustrated in Fig. 3b, electrons that travel along a chiral pathway
pick up a self-rotation, i.e., the OAM, in analogue to the spinning bullet out
of a rifled barrel. Mathematically, we can generally describe a positive-
moving plane wave by $\ket{\psi^{+}}=A(\rho,z)e^{il\phi+ikz}$, where
$A(\rho,z)$ is a general coefficient depending on $z$ and the radial distance
$\rho$, $k$ is the momentum, and $l=0,\pm 1,\pm 2?$ represents OAM.
$\ket{\psi^{+}}$ is a chiral plane wave if $l\neq 0$ and reduces to a normal
plane wave for $l=0$. Because both the inversion symmetry and mirror symmetry,
either of which forces $l=0$, are broken $l\neq 0$ generically holds in a
chiral system. It is obvious that $\ket{\psi^{-}}$ with $-k$ carries opposite
OAM $-l$ because $\ket{\psi^{+}}=\ket{\psi^{-}}^{*}$. Such
orbital($l$)-momentum($k$) locking represents the wave function topology, in
which the parallel or antiparallel $l-k$ relation depends on the molecular
chirality and chemical potential. It is similar to the monopole-like spin-
momentum locking in the topological Weyl fermion [5, 6].

###  0.4  Angular momentum transfer from electrons to light

The injected electrons and holes carry finite OAM because of the polymer
chirality in the OLED. Given the low mobility in the organic semiconductor,
the linear momentum is quickly relaxed, for instance, by interface scattering
between neighboring aggregate clusters. But the OAM relaxation time should be
much longer than the momentum relaxation time because neighboring clusters
share the same chirality. Due to the same chirality protection, we also expect
that OAM is robust against electron-electron interactions. Therefore,
electrons and holes can preserve the OAM polarization when they form excitons
for light emission. In the following, we discuss the OAM transfer from
carriers to CPL in the electron-hole recombination.

The ACPE term in Eq. 4 is equivalent to the OAM shift in the optical
transition[43, 41, 42]

$\Delta l=\braket{\hat{L}_{z}}_{0\rightarrow
1}=x^{01}p_{y}^{10}-y^{01}p_{x}^{10},$ (5)

where $\hat{L}_{z}=xp_{y}-yp_{x}$ is the OAM operator (see more information in
Supplementary Information). In the presence of current along $-z$, we need
replace $\ket{0^{+}}$ ($\ket{1^{+}}$) for $\ket{0}$ ($\ket{1}$) to evaluate
the ACPE in Eq. 4. In this case, $\Delta l$ is nonzero in the optical
transition from $\ket{1^{+}}$ to $\ket{0^{+}}$, both of which carry finite
OAM, as illustrated in Fig. 3d. In addition, reversing current leads to
$-\Delta l$ (Fig. 3e). We note that $\Delta l$ is gauge invariant although $l$
of a given band depends on the specific gauge.

For a photon with a positive spin angular momentum , it is defined as right-
handed CP light if it travels along $+z$ and as the left-handed CP light if
along $-z$. Therefore, the finite angular momentum , which is transferred from
OAM of electrons/holes to spin of photons ($S=+\Delta l$), forces that the
handedness of CP light relies on the emission direction. Overall, the orbital-
momentum locking eventually leads to the current direction- and emission-
direction dependencies of CP-EL, fully consistent with our experiments.

To summarize the ACPE mechanism, it includes two parts. (i) In a chiral
molecule/chiral aggregate, the OAM is parallelly or anti-parallelly locked to
the intrinsic momentum (see more discussions on its difference from the
mobility-related drift velocity in SI). Opposite momenta with opposite OAM
coexist and cancel each other at equilibrium. (ii) When the current flows, one
momentum is enhanced while the opposite one is suppressed, so as the OAM.
Therefore, conducting electrons/holes are OAM polarized in the nonequilibrium
phase. Direct electron-hole recombination leads to finite OAM transfer from
charge carriers to CPL, leading to the ACPE.

###  0.5  Ab initio calculations

Furthermore, we quantitatively estimate the ACPE and NCPE for the chiral F8BT
polymer assembly by ab initio calculations. It is challenging to refine the
accurate atomic structure of such chiral aggregates. Without losing
generality, we simulate chiral stacking of F8BT molecules and focus on the
intermolecular chirality that is associated with the dominant charge transport
direction along the layered packing structure (noted as $z$ axis here)[44].
Although $\ket{0,1}$ can be generally many-body wave functions, we use the
highest occupied molecule orbital (HOMO) and lowest unoccupied molecule
orbital (LUMO) to represent $\ket{0}$ and $\ket{1}$, respectively, by ignoring
higher-order corrections (like the distortion in excited states) in the
calculations. As shown in Fig. 4, two layer stacking with a counter-clockwise
twisting angle 30∘ reshapes HOMO and LUMO wave functions dramatically compared
to a single layer of molecule. By calculating the ACPE involving the $+z$
moving HOMO and LUMO, we obtain a large dissymmetry factor $|g_{EL}|=0.48$
($0.44$) for two (three) layer stacking, which is in the same order of
magnitude as experimental $g_{EL}$. The OAM can be evaluated from the phase
winding number in the $xy$ plane (see Fig. 4c and the Methods section),
verifying the orbital-momentum locking in $\ket{0^{\pm}}$ and $\ket{1^{\pm}}$.
Because $\ket{0,1}$ is usually composed by many plane waves, the total value
of $l$ is unnecessarily an integer. Better knowledge on the molecular
arrangement of chiral polymer assemblies will help improve the prediction
power of calculations in the future work.

Additionally, the current-induced magnetization in our experiments is relevant
to the orbital rather than spin of electronic states. If electron-spin
polarization matters, it would require substantial spin-orbit coupling (SOC)
in the device. We know that these organic polymers made of light elements
exhibit negligible SOC. Despite that metal electrodes may include heavy
elements, the circular polarization rate remains the same for Al, Ag and Au
electrodes with largely varied SOC (Fig. S8). Thus, the role of electron spin
may be negligible in ACPE although ACPE may also appear in systems with strong
SOC. The ACPE is caused by the chirality-induced orbital polarization,
different from the chirality-induced spin selectivity effect discussed in
literature[8]. Our experiment demonstrates a significant consequence of the
electron orbital effect in chiral materials. Here, the electron OAM is
indicated by the the handedness flip of CP light (spin flip of light) as
reversing the current flow (e.g., see Figs. 1c-d).

## Summary

In summary, we report an anomalous phenomenon where the handedness of CP light
emission depends on the emission direction. This effect enables us to design
unconventional CP-OLED devices with large $g_{EL}$ and without errosion from
the back-electrode reflection. We highlight that the orbit-momentum locking
causing ACPE is strongly associated with the charge transport mode in the
polymer systems and therefore suggest the following design principles for
further development of CP-OLEDs with strong CP-EL. To ensure the entire stack
of molecular assemblies exhibit strong ACPE, it is necessary that the emissive
sites should strongly couple with chiral transport sites or ideally within the
same sites as in our polymer systems, to induce strong orbital-momentum
locking in conduction electrons. If charge carriers are independently
transported, such as in host materials, then they get scattered to random
adjacent chiral emissive sites, the net momentum and OAM will be quenched and
only NCPE will appear. In this case, CP-EL can no longer be considered as the
same origin as CP-PL and circular dichroism where no charge transport and
current flows exist.

We propose an ACPE that involves finite angular momentum transfer in the
optical transition. Because ACPE and NCPE come from the first and second-order
optical transitions in Eq. 4, ACPE is often much larger than NCPE when TRS is
broken. We highlight that the unusual TRS-breaking in ACPE is driven by the
nonequilibrium orbital magnetization, which originates in the chiral orbital
nature in wave functions. In CP-OLED, such orbital magnetization is caused by
the current flow (rather than static magnetization or magnetic field), the
impact of which was rarely recognized in previous studies on chiral
materials[45]. Our work reveals an intriguing unification of chirality in
seemingly unrelated aspects: structure geometry, electronic topology, and the
light handedness. The chirality information can be transferred from the
material geometry to electronic wave function and further to the spin of
light.

Acknowledgements: Dedication: To the memory of Professor Alasdair James
Campbell (1961-2021). L.W. would like to thank Prof. Alasdair Campbell and
Prof. Jenny Nelson for useful discussions at Imperial College London. L.W.
would like to thank Mr. Kim Stjerne (Biolab A/S, Denmark) and Dr. Theis Brock-
Nannestad (University of Copenhagen, Denmark) for the access to CPL-300
spectrometer. L.W. would like to thank Dr. Rui Zhang (Linköping University)
for the help of processing GIWAXS data. B.Y. acknowledges the financial
support by the MINERVA Stiftung with the funds from the BMBF of the Federal
Republic of Germany and the European Research Council (ERC Consolidator Grant
“NonlinearTopo”, No. 815869). L.W. and M.J.F. would like to thank Cambridge
Display Technology Limited (company number 02672530) for providing the F8BT
polymers. L.W. and M.J.F. would like to acknowledge EPSRC research grants
EP/P000525/1, EP/L016702/1 and EP/R00188X/1. For the purpose of open access,
the author has applied a Creative Commons Attribution (CC BY) licence to any
Author Accepted Manuscript version arising
Competing Interests: The authors declare the following competing financial
interest(s): M.J.F. is an inventor on a patent concerning chiral blend
materials (WO2014016611). The remaining authors declare no competing
interests.

Figure 1: Device-structure dependent circular polarized (CP)
Electroluminescence (EL) . (a) Normal circular polarization effect where CP-EL
is emission direction-independent. (b) Anomalous circular polarization effect
where CP-EL is emission direction-dependent. $I_{L}$ and $I_{R}$ represent
light intensity of Left- (red arrows) and Right-handed (blue arrows)
circularly polarised emission. Device structures of (c) conventional and (d)
inverted CP-OLEDs. EL of F8BT:[P]-aza[6] helicene-based CP-OLEDs recorded from
(e) conventional and (f) inverted CP-OLEDs. Inset: Molecular structure of F8BT
and [P]-aza[6]helicene. Figure 2: Emission-direction-dependent CP emissions
relative to charge carrier flow directions.  (a) Summary of reported CP-OLEDs
using different types of chiral emitters including polyfluorene, lanthanide
complex, thermally assisted delayed fluorescent emitter (TADF), and
phosphorescent emitters. Detailed information on molecular structures and
corresponding citations can be found in Table S1 and Scheme S1. $|g_{PL}|$ and
$|g_{EL}|$ represent photo- and electro-luminescence dissymmetry factors. (b)
Comparison of $|g_{EL}|$ values reported from polyfluorene (inverted device in
this work), lanthanide complex (data points from Ref.zinna2017design), and
phosphorescent emitter (data points from Ref.yan2019configurationally) as a
function of reflective electrode thickness. The trends are represented as the
solid lines. (c) Schematic diagram of semi-transparent conventional (top) and
inverted (bottom) CP-OLEDs based on F8BT:[P]-aza[6]helicene. Red arrows stand
for the EL emitted along the electron flow direction and blue arrows stand for
the EL emitted along the hole flow direction. Interlayers are removed for
clarity. (d) Summary of $g_{EL}$ measured from both sides of the semi-
transparent CP-OLEDs. Detailed spectra for data point in b and d can be found
in Figs. S3 and S4. Figure 3: Illustration of orbital-momentum locking and
anomalous circular polarization effect. (a) The wave function ($\ket{\psi}$)
of The electron confined in an achiral box can be regarded a superposition of
counter-propagating plane waves,$\ket{\psi^{\pm}}\sim e^{\pm ikz}$. (b) The
wave function in a chiral box can be regarded a superposition of counter-
propagating chiral plane waves, $\ket{\psi^{\pm}}\sim e^{\pm ikz}e^{\pm
l\phi}$. $\ket{\psi^{\pm}}$ carry opposite orbital angular momenta (OAM) ($\pm
l$), i.e. $\ket{\psi^{\pm}}$ share the same electronic chirality induced by
the box chirality. The black arrow represents the propagating direction ($k$)
and the helix-like trajectory indicates $l$. (c) Normal circular polarized
emission from the excited state $\ket{1}$ to ground state $\ket{0}$, where
$\ket{0,1}$ carry zero OAM. The angular momentum transfer in the transition
$\Delta l=0$. So the zero net spin of light leads to the same handedness in
emitted lights along two directions. “e” and “h” represent electron and hole,
respectively. (d) Anomalous circular polarized emission from $\ket{1^{+}}$ to
$\ket{0^{+}}$, where $\ket{0^{+},1^{+}}$ carry finite OAM. Because $\Delta l$
is finite, oppositely emitted lights carry the same spin and exhibit opposite
handedness. (e) Reversing the current-flow with respect to (d) switches the
CPL handedness.  Figure 4: The chirality and circular polarized emission for
stacking two F8BT molecules with a twisted angle. (a) The total charge density
distribution for the HOMO ($\ket{0}$) and LUMO ($\ket{1}$) states calculated
by density functional theory. (b) Schematics of transition from $\ket{1^{+}}$
to $\ket{0^{+}}$. (c) The phase distribution $\varphi(\mathbf{r})=l\phi$ in
the $xy$ plane for a vortex-like plane wave $e^{i(l\phi\pm kz)}$ (left). The
$l$ is deduced from the phase winding number of $\varphi(\mathbf{r})$ (right)
counterclockwise along the dashed circle path $C$. $\ket{0^{+}}$
($\ket{1^{+}}$) with $+k$ exhibits $l=3$ ($2$) while $\ket{0^{-}}$
($\ket{1^{-}}$) with $-k$ exhibits $l=-3$ ($-2$), demonstrating the orbital-
momentum locking ($l||k$).

## References

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## Methods

Samples: [P]-aza[6]helicene was synthesized as previously reported[1] and
separated using preparative chiral HPLC.

Thin-film and device fabrication: The cleaning process for all substrates
(fused silica and prepatterned ITO glass, Thin Film Devices Inc., 20 ohms/sq)
involved rinsing in an ultrasonic bath with acetone, isopropyl alcohol (IPA),
Hellmanex III (Sigma-Aldrich), and deionized water for 30 min. These were
transferred to a plasma asher for 3 min at 80 W and 50 W before spin-coating
for fused silica and prepatterned ITO, respectively. F8BT and aza[6]helicene
were dissolved in toluene to a concentration of 30 mg/mL and blended to form a
10% aza[6]helicene solution. About 130 nm thick emissive layer can be achieved
by dynamically spin-coating at 2300 rpms for 1 min. Chiral samples were
annealed for 10 min in a nitrogen atmosphere (glovebox, $<0.1$ ppm of H2O,
$<0.1$ ppm of O2). Dynamic coating ensures strong chiroptical activity is
achieved without giving too thick films, compared to previous studies[1, 2].
Organic film thicknesses was monitored using a Dektak 150 surface profiler and
the metal thickness was used as displayed from QCM monitor.

Photophysical characterization: Circular dichroism measurements were performed
using a Chirascan (Applied Photophysics) spectrophotometer. CP-PL was measured
in a transmittance geometry using a CPL-300 JASCO spectrometer. GIWAXS data
was measured in ALBA beamline (Spain). The incidence angles of the X-ray beam
were set to be 0.2 for all films. The GIWAXS patterns were recorded with a 2D
CCD detector and an X-ray irradiation time 10-20s, dependent on the saturation
level of the detector.

CP-EL: Left-handed and right-handed CP emission spectra were collected using a
combination of linear polarizer and zero-order quarter-wave plate (546 nm,
Thorlabs) placed before detectors. The device is driven by a constant current
of 1 mA (pixel area = 0.045 cm2). The dissymmetry factor $g$ in the EL spectra
was calculated from the equation $g=2(I_{L}?I_{R})/(I_{L}+I_{R}),|g|\leq 2$.
Here, $I_{L}$ and $I_{R}$ are the left-handed and right-handed emission
intensities. EL spectra from the PLED were recorded using an Ocean Optics USB
2000 charge-coupled spectrophotometer. All CP-EL measurements are carried out
after measuring with only a linear polarizer to ensure negligible linear
polarization or random polarization, which should be considered in all CP
emission measurements.

Conventional devices: Poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate)
(PEDOT:PSS) (H.C. Starck GmbH) (55 nm) was dynamically spin-coated on cleaned
ITO substrate with a spin speed of 2500 rpms for 1 min. [P]-aza[6]helicene-
blended F8BT deposition was the same as for the thin film studies, followed by
the thermal evaporation of a 10 nm TPBi (Sigma-Aldrich), 10 nm Ca layer
(Sigma-Aldrich), capped by an Al (99.99%, Kurt J. Lesker Company Ltd.) layer
up to 100 nm on the organic layer under a vacuum level of $1\times 10^{?7}$
mbar. Conventional device structure: ITO/PEDOT:PSS/TFB/
F8BT:[P]-aza[6]helicen/TPBi/Ca/Al.

Inverted devices: The ZnO is deposited on the cleaned ITO by a sol?gel method
which has been described elsewhere followed by a PEIE (30 wt % in water,
Sigma-Aldrich) rinsing step. Then, [P]-aza[6]helicene-blended F8BT was
dynamically spin-coated onto ZnO/PEIE. Afterward, 25 nm TCTA (97% Sigma-
Aldrich), MoOx (99.97%, Sigma-Aldrich) and Au (99.99%, Kurt J. Lesker Company
Ltd.) up to 120 nm were thermally evaporated onto the organic layer under
vacuum level of $1\times 10^{?7}$ mbar.Inverted device structure:
ITO/ZnO/PEIE/ F8BT:[P]-aza[6]helicene/TCTA/MoOx/Au.

Ab inito calculations: The electronic wave functions and charge densities of
F8BT chiral assemblies were calculated by the density-functional theory (DFT)
implemented in the Vienna ab initio Simulation Package (VASP).[3] The
generalized gradient approximation (GGA) was used for the exchange-correlation
functionals.[4] F8BT molecules were stacked along the $z$ axis in a twisted
manner. The molecular cluster model included at least 10 $\AA$ vacuum
distances along all directions. An energy cutoff of 400 eV was used for the
plane wave basis. The total number of plane waves is about 4$\times 10^{5}$.
We note the plane wave by wave vector $\mathbf{G}=(G_{x},G_{y},G_{z})$. In the
plane wave basis, for example, the wave function of HOMO, $\ket{0}$, can be
expressed as:

$\begin{split}\ket{0}&=\sum_{G_{z}}\phi_{0}(G_{z})e^{iG_{z}z},\\\
\ket{0^{\pm}}&=\sum_{G_{z}>0/G_{z}<0}\phi_{0}(G_{z})e^{iG_{z}z},\end{split}$
(6)

where
$\phi_{0}(G_{z})=\sum_{G_{x},G_{y}}c^{0}_{\mathbf{G}}e^{i(G_{x}x+G_{y}y)}$ and
$c^{0}_{\mathbf{G}}$ is the plane wave coefficient extracted directly from DFT
wave functions. The charge density is $\rho_{0}=|\ket{0}|^{2}$. Besides
$G_{z}z$, the phase of the $G_{z}$ propagating wave in Fig. 4 is
arg$\phi_{0}(G_{z})$. Under electrical current along $-z$, the CP electric
dipole transition amplitudes are calculated as:

$\begin{split}I_{R/L}(\omega)&\propto\left|\langle 0^{+}|x\pm
iy|1^{+}\rangle\right|^{2}\delta(\epsilon_{1}-\epsilon_{0}-\hbar\omega)\\\
&=\left|\int
d\boldsymbol{r}~{}\sum_{G^{\prime}_{z}>0}\sum_{G_{z}>0}\phi^{*}_{0}(G^{\prime}_{z})(x\pm
iy)\phi_{1}(G_{z})e^{i(G_{z}-G^{\prime}_{z})z}\right|^{2}\delta(\varepsilon_{1}-\varepsilon_{0}-\hbar\omega)\\\
&=\left|\sum_{G_{x}}\sum_{G_{y}}\sum_{G_{z}>0}c^{1}_{\mathbf{G}}\left(\frac{\partial
c^{0}_{\mathbf{G}}}{\partial G_{x}}\mp i\frac{\partial
c^{0}_{\mathbf{G}}}{\partial
G_{y}}\right)^{*}\right|^{2}\delta(\varepsilon_{1}-\varepsilon_{0}-\hbar\omega),\end{split}$
(7)

where ∗ represents taking complex conjugate. One can analyze the symmetry
constrain on CP emission from Eq. (7). If inversion symmetry is present, then
$c^{0,1}_{\mathbf{G}}=p_{0,1}c^{0,1}_{-\mathbf{G}}$ with $p_{0,1}=\pm 1$
refers to the parity eigenvalue of $\ket{0}$ or $\ket{1}$. On the other hand
the time-reversal symmetry requires that
$c^{0,1}_{\mathbf{G}}=(c^{0,1}_{-\mathbf{G}})^{*}$. Thus, if inversion and
time-reversal symmetries exist simultaneously, the coefficient
$c^{0,1}_{\mathbf{G}}$ is purely real (imaginary) for the parity even (odd)
state. Therefore, $I_{R}=I_{L}$ always holds according to Eq. (7). When
inversion is broken, the circular polarization ($I_{R}\neq I_{L}$) can appear.

OAM and winding number: The OAM $l$ is a topological number charactering the
phase winding of the wave function in real space, which is defined as [5]:

$l=\frac{1}{2\pi}\oint_{C}d\varphi=\frac{1}{2\pi}\oint_{C}d\boldsymbol{r}\cdot\boldsymbol{\nabla_{r}}\varphi(\boldsymbol{r}),$
(8)

where $\varphi(\boldsymbol{r})$ is the real-space distribution of wave
function phase, and $C$ refers to the integration contour (dashed circle in
Fig. 4c). $l$ represents the total phase change (in multiples of $2\pi$) after
circulating the contour $C$. Generally, a nonzero winding number indicates a
topological defect inside the contour $C$ which cannot be removed by
continuously varying the wave function without creating or annihilating
another topological defect.

## Data and code availability:

All data needed to evaluate the conclusions in the paper are present in the
paper and/or the Supplementary Materials. Additional data related to this
paper can be requested from the authors. Source data are provided.
∗Email of<EMAIL_ADDRESS>
† Email of correspondence<EMAIL_ADDRESS>
## Method-only references:

## References

  * [1] Wan, L. _et al._ Inverting the handedness of circularly polarized luminescence from light-emitting polymers using film thickness.  _ACS nano_ 13, 8099–8105 (2019).
  * [2] Wan, L. _et al._ Highly efficient inverted circularly polarized organic light-emitting diodes.  _ACS Applied Materials & Interfaces_ 12, 39471–39478 (2020).  URL ttps://doi.org/10.1021/acsami.0c09139.  PMID: 32805911.
  * [3] Kresse, G. & Furthmueller, J.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set.  _Phys. Rev. B_ 54, 11169–11186 (1996).  URL https://link.aps.org/doi/10.1103/PhysRevB.54.11169.
  * [4] Perdew, J. P., Burke, K. & Ernzerhof, M.  Generalized gradient approximation made simple.  _Physical Review Letters_ 77, 3865 (1996).
  * [5] Nakahara, M.  _Geometry, Topology and Physics_ (Taylor & Francis, Andover, England, UK, 2017).


# AOSoar: Autonomous Orographic Soaring of a Micro Air Vehicle

Sunyou Hwang1, and Bart D. W. Remes1, Guido C. H. E. de Croon1 1 All authors
are with the MAVLab, Department of Control and Operations, Faculty of
Aerospace Engineering, Delft University of Technology, 2629HS Delft, the
Netherlands (email<EMAIL_ADDRESS><EMAIL_ADDRESS>G.C.H.E.deCroon@tudelft.nl)This paper has a supplementary video of flight
tests and a replay of the flight log available at http://ieeexplore.ieee.org,
provided by the authors.

###### Abstract

Utilizing wind hovering techniques of soaring birds can save energy
expenditure and improve the flight endurance of micro air vehicles (MAVs).
Here, we present a novel method for fully autonomous orographic soaring
without a priori knowledge of the wind field. Specifically, we devise an
Incremental Nonlinear Dynamic Inversion (INDI) controller with control
allocation, adapting it for autonomous soaring. This allows for both soaring
and the use of the throttle if necessary, without changing any gain or
parameter during the flight. Furthermore, we propose a simulated-annealing-
based optimization method to search for soaring positions. This enables for
the first time an MAV to autonomously find a feasible soaring position while
minimizing throttle usage and other control efforts. Autonomous orographic
soaring was performed in the wind tunnel. The wind speed and incline of a ramp
were changed during the soaring flight. The MAV was able to perform autonomous
orographic soaring for flight times of up to 30 minutes. The mean throttle
usage was only 0.25% for the entire soaring flight, whereas normal powered
flight requires 38%. Also, it was shown that the MAV can find a new soaring
spot when the wind field changes during the flight.

##  I INTRODUCTION

Flight endurance is one of the major factors holding back the real-world
application of micro air vehicles (MAVs). For low size, weight, and power
(SWaP) MAVs, flight endurance mainly depends on the power density of the
battery, which is limited [1, 2], without fundamental progress on the horizon.
One way to improve flight endurance is to exploit energy from the environment.
Birds like albatrosses, vultures, ospreys, and kestrels are well known for
their ability to actively use the wind to minimize their energy expenditure to
fly longer distances or time [3, 4, 5]. For example, vultures utilize energy
from rising air columns created by uneven ground heating, called thermals [6].
Thermal soaring of unmanned aerial vehicles (UAVs) has been studied in various
aspects, not only through manually developed guidance and control strategies
[7, 8] but also through reinforcement learning of detecting and exploiting
thermals [9, 10].

Another type of soaring is orographic soaring. Kestrels are often observed
hovering at a position over a dune without flapping their wings, which is
called wind-hovering [11]. This is a good example of the orographic soaring,
using the updraft generated by obstacles such as hills, mountains, and
buildings when the wind hits the obstacle. Wind-hovering can be useful for
remaining in a single place for observation, but also for prolonging the
flight range. For example, gulls appear to plan their path to exploit
orographic soaring on the way to their destination to save energy [12, 13]. In
this paper, we solely focus on orographic soaring.

Figure 1: Autonomous orographic soaring of a micro air vehicle. Without a
priori knowledge of the wind field, the MAV successfully performs autonomous
soaring in the wind tunnel using little to zero throttle throughout the
flight. The MAV can find a new position to soar when environmental conditions
vary without any human intervention or manual parameter changes. In this
picture, the increasing slope angle changes the wind field, and the MAV
autonomously finds a new soaring position. It moves to the front and downward
because of the combination of changes in the updraft and the MAV’s sink rate.

Wind fields around obstacles and flight conditions for orographic soaring were
analyzed using simulations and measurement data [14, 15, 16, 17]. These
studies introduced unique opportunities and possibilities for exploiting
orographic updrafts using MAVs. The feasibility and strategies of orographic
soaring were also discussed. However, there was no actual flight demonstration
performed in these studies.

Orographic soaring of MAVs in a real-world environment has been demonstrated
in only a few studies [18, 19]. However, the method in [18] was based on a
priori knowledge of the entire wind field to generate a pre-defined trajectory
to the soaring spot, while the method in [19] required manually positioning
the MAV at a precise initial soaring position before switching on the
autonomous soaring controller. To achieve a fully autonomous soaring,
considerable challenges remain. In practice, accurately predicting or
measuring the wind field is not feasible. Moreover, the MAV has to be able to
explore and look for a feasible soaring position autonomously.

In this paper, we demonstrate for the first time the autonomous orographic
soaring of an MAV without a priori knowledge of the wind field nor precise
initial positioning of the MAV by a human pilot. To achieve this, we present
(1) a local search algorithm to find a soaring position and (2) an INDI
controller with control allocation that enables the MAV to use the same
controller setting during the entire flight. An important advantage of the
proposed control method is that the MAV does not need to switch controllers
between soaring and navigation and can use the throttle whenever necessary. We
demonstrate the proposed method with a real-world flight in a wind tunnel.
Moreover, we validate the versatility of the proposed methods by changing the
wind speed and updraft during the autonomous soaring flight.

The paper is structured as follows: In section II, an INDI-based soaring
controller and searching method are presented. In section III, we introduce
the MAV and the wind tunnel test setups. In section IV, the results from an
autonomous soaring flight in the wind tunnel are presented. We discuss the
flight test in section V. Finally, we draw conclusions and suggest future
research directions in section VI.

##  II Methods

There are many challenges for autonomous orographic soaring. In this article,
we focused on two main aspects.

The first one is the controller. There is a unique challenge for orographic
soaring because the aim is to maintain the position without using the
throttle. Also, it is only feasible in a small updraft region of the wind
field with high wind speed. Previous studies used a glider plane without a
motor or changed controller or gains when the MAV enters the soaring mode.
However, for sake of control fluidity, it would be desirable to use a single
controller. We adopted INDI with control allocation to enable using a single
controller during the whole flight, regardless of navigation or soaring. We
present our control method in section II-A.

The second aspect is to find feasible soaring positions. For fully autonomous
flight, the MAV should be able to find where it can soar. In previous studies,
it was determined either from a priori knowledge of the wind field or by a
human pilot. We present a method for the MAV to autonomously find feasible
soaring positions based on simulated annealing in section II-B.

###  II-A INDI controller with allocation

Traditional PID controllers were used in most previous research, however, many
of the authors have mentioned the need for a more advanced controller,
especially for gust rejection. Therefore, we adopted an INDI controller for
soaring flights. INDI is good at disturbance rejection and requires little
model information [20, 21, 22]. INDI is an incremental form of nonlinear
dynamic inversion. It controls angular acceleration $\dot{\omega}$ in an
incremental way. The only required knowledge is the control effectiveness $G$,
mapping an increment in the control input $u$ to a resulting rotational
acceleration increment $\dot{\omega}-\dot{\omega_{0}}$ :

$\displaystyle\dot{\omega}=\dot{\omega_{0}}+G(u-u_{0})$ (1) $\displaystyle
u=u_{0}+G^{-1}(\nu-\dot{\omega_{0}})$

Where $\nu$ is the virtual control vector, and subscript 0 indicates a time in
the past. The control effectiveness depends on the inertia of the vehicle.
However, directly measuring the inertia can be challenging. Alternatively, it
can be estimated from flight test data with actuator inputs with angular
acceleration. Using the flight test data, the control effectiveness matrix(G)
can be estimated by dividing angular acceleration by a control input
vector($u$). Practically, we conducted several manual outdoor flight tests to
log radio control input commands and angular accelerations by post-processing
the inertial measurement units reacting to the radio input. The control
effectiveness was calculated by dividing the change of angular acceleration by
the change of input commands from radio control, for each pitch, roll, and yaw
axis at various airspeeds. After that, the effectiveness values were fitted as
a quadratic function and scheduled by airspeed measurement, because the
effectiveness of control surfaces depends on the dynamic pressure
$q=\frac{1}{2}\rho V^{2}$.

Figure 2: A schematic overview of the soaring controller. $\xi$ is the
position, $\eta$ is the attitude, $\omega$ is the angular rate, $\psi$ is the
yaw angle, $T$ is the thrust, and $u$ is actuator commands. Subscript $ref$
means reference, and subscript $f$ is for filtered signals.

Figure 2 shows the overview of the soaring controller. An INDI controller is
used for both the inner loop and the outer loop. For the outer loop, linear
acceleration error is calculated from position error and fed into the INDI
outer loop.

The MAV’s position($\xi$), velocity($\dot{\xi}$), and a reference position are
passed to a PD controller, and a linear acceleration
reference($\ddot{\xi}_{ref}$) goes into the INDI outer loop [22]. Then, pitch,
roll references, and thrust increment are calculated from the outer loop.
$K_{\xi}$ and $K_{\dot{\xi}}$ are the gains for position error and velocity
error, respectively.

$\ddot{\xi}_{ref}=K_{\dot{\xi}}(K_{\xi}(\xi_{ref}-\xi)-\dot{\xi})$ (2)

To keep the heading towards the wind, we calculate a yaw($\psi$) reference. We
set a virtual waypoint at 15 meters into the center of the cross-section of
the wind tunnel. The yaw reference is calculated based on the error between
the MAV’s position and the virtual waypoint. Let $x_{ref},y_{ref}$ be the x
and y position of the virtual waypoint, and $x,y$ the longitudinal and lateral
position of the MAV. Then the yaw reference is determined by the following
equation:

$\psi_{ref}=\mathrm{atan}(\frac{y_{ref}-y}{x_{ref}-x})$ (3)

The attitude reference($\eta_{ref}$ = $[$$\phi_{ref}$ $\theta_{ref}$
$\psi_{ref}$$]^{T}$) is passed to an inner loop PD controller. Then, the
angular acceleration reference($\dot{\omega}_{ref}$) calculated from the PD
controller and the thrust increment are passed into the inner loop INDI
controller.

$\dot{\omega}_{ref}=K_{\omega}(K_{\eta}(\eta_{ref}-\eta)-\omega)$ (4)

The throttle is useful to navigate to the soaring region or to deal with a
strong gust. It is also necessary to use throttle when the MAV cannot fly
without power due to the wind conditions. However, changing gains or switching
the controller from one to another in flight to enable or disable the throttle
is not desirable. We utilized control allocation to cope with this problem. An
INDI controller with control allocation allows the MAV to use the same
controller and parameters throughout the flight, but seamlessly cut off or
increase the throttle when desired. In particular, this makes it unnecessary
to change anything when switching between navigating, searching for a soaring
spot, and soaring flight.

Control allocation of INDI was originally developed to prevent actuator
saturation for over-actuated vehicles, because of aggressive yaw control
behaviour. The weighted least square (WLS) algorithm was integrated with the
INDI controller for inner loop control allocation in a paper by Smeur et al.
[23]. Here, we use control allocation for achieving as still soaring as
possible. This implies a preference for reducing throttle and minimizing
accelerations. This leads to the following control allocation cost function:

$\displaystyle C_{alloc}(u_{wls})=\lVert W_{u}(u_{wls}-u_{p,wls})\rVert^{2}+$
(5) $\displaystyle\gamma\lVert W_{v}(G_{o}u_{wls}-v_{wls})\rVert^{2}$

Where $u_{wls}$ is a control increment vector, $W_{u}$ is a weighting matrix
for the control inputs, $W_{v}$ is a weighting matrix for the control
objective, $G_{o}$ is the control effectiveness matrix for the outer loop,
$v_{wls}$ is the virtual control increment command for the outer loop, $u_{p}$
is the preferred control increment vector, and $\gamma$ is a scale factor.

In this study, control allocation is used to prioritize the controls to
minimize thrust for the outer loop controller. We set a higher priority to
control pitch than the thrust by adjusting weight for the WLS optimization.
Therefore, for $W_{v}$, we choose the weights to be 1, 100, 1 for roll($rad$),
pitch($rad$), and thrust in a range of [0, 9600] respectively. For $W_{u}$, we
choose 1 for all axes, $\gamma$ is $10^{6}$, and $u_{p}$ is a zero vector.

###  II-B AOSearch: Autonomous Orographic Search for a soaring location

To exploit updrafts, MAVs have to find feasible soaring locations
autonomously. If the environment is static and a prior knowledge of the wind
field is provided, it can be calculated from the MAV model and wind speed by
finding an equilibrium. However, in the real world, it is difficult to measure
the entire wind field. Furthermore, the wind speed may change during the
flight. Thus, we developed an algorithm to find the soaring location which is
applicable in a non-static environment, without any prior knowledge of the
wind field.

Simulated annealing is a local meta-heuristic search technique [24, 25]. It
attempts to minimize a cost function by taking steps to neighboring positions
in the search space. It either accepts or rejects the solution based on an
acceptance probability which usually decreases to zero as the ”temperature”
decreases. Initially, steps that increase the cost are allowed, but
eventually, simulated annealing becomes a greedy algorithm.

Based on simulated annealing, we implemented _AOSearch_ : Autonomous
Orographic Search algorithm. In our case, there could be environmental changes
at any time during the flight, regardless of the progress of the search. For
example, wind speed can be changed over time. Therefore, the temperature does
not decrease at each step. The temperature is set to zero, so the search
algorithm only accepts better solutions. When the MAV finds a position at
which it can soar, the search is finished. Hence, we implemented a threshold
cost. If the value of the cost function is lower than the threshold at a
certain position, it is considered converged and does not move to a new
neighbour. When the value of the cost function exceeds the threshold because
of an environmental change, the MAV restarts the search until it finds a new
position that satisfies the threshold condition.

We want to minimize energy expenditure as well as stay in the same position as
much as possible just like kestrels hovering without moving its head for
observation. In our case, thrust is the primary source of energy consumption
to minimize. Pitch rate is also contributing because controlling the elevator
spends energy. Furthermore, we aim for wind-hovering, which means that the MAV
maintains its position. So, we want to minimize both horizontal and vertical
speed. The cost function($C_{search}$) captures all requirements for still,
orographic soaring, with the MAV able to keep its downward view as static as
possible with minimum throttle usage, also meaning minimal position and pitch
changes. Hence, it is a function of thrust($T$$[\%]$), horizontal and vertical
ground speed($\dot{x}$, $\dot{z}$$[m/s]$), and pitch
rate($\dot{\theta}$$[rad/s]$) with a gain for each parameters.

$C_{search}=k_{1}T+k_{2}|\dot{x}|+k_{3}|\dot{z}|+k_{4}|\dot{\theta}|$ (6)

The gains were $k_{1}$=9.6, $k_{2}$=1.6, $k_{3}$=1.0, and $k_{4}$=10. The
threshold value was set to 43. The gains and threshold value were determined
empirically, by observing the values when the MAV was soaring in a stable
manner.

_AOSearch_ : the autonomous orographic search method is described in algorithm
1. First, calculate the cost function. Based on the value of the cost
function, a step size($S$) is selected. If the value is lower than the
threshold, the MAV stays at the current position($Pos(s_{new})$). If the value
of the cost function has increased compared to the previous
position($Pos(s)$), go back to the previous position. If the value has
decreased, keep the same direction. If it has just come back from a previous
position, pick a new random neighbour. To get a random neighbour $s_{new}$,
pick a random direction($Dir(s_{new})$) among four direction vectors of [x,
z]: forward[1, 0], backward[-1, 0], up[0, 1], down[0, -1]. Then, a new soaring
position is: $Pos(s_{new})$ $=$ $Pos(s)$ $+$ $Dir(s_{new})$ $\times$ $S$.
Repeat the process until the cost function value becomes less than the
threshold.

The step size (S) is set to four steps depending on the value of the cost
function. As the value gets lower, the step size decreases from 0.3 $m$ to
0.05 $m$. The logic behind this is that the MAV takes a bigger step to explore
the wind field when the energy consumption at the current position is high.
When the value of the cost function is low at the current position, the MAV
tries to fine-tune its position.

$\small{S=\begin{cases}0.3,&\text{for $C\geq 3\times threshold$}\\\
0.2,&\text{for $3\times threshold>C\geq 2\times threshold$}\\\ 0.1,&\text{for
$2\times threshold>C\geq 1.5\times threshold$}\\\
0.05,&\text{otherwise}\end{cases}}$

Algorithm 1 AOSearch

1:$C(s_{new})$ $\leftarrow$
$k_{1}T+k_{2}|\dot{x}|+k_{3}|\dot{z}|+k_{4}|\dot{\theta}|$ $\triangleright$
Calculate cost function

2:S $\leftarrow$ Calculate a step size

3:if $C(s_{new})<threshold$ then

4: Stay at the current position

5:else

6: if $C(s_{new})<C(s)$ then

7: if returned $is$ True then

8: $Dir(s_{new})\leftarrow random$ $\triangleright$ pick a random direction

9: $returned\leftarrow False$

10: else

11: $Dir(s_{new})\leftarrow Dir(s)$ $\triangleright$ keep the same direction

12: end if

13: else

14: $Dir(s_{new})\leftarrow-Dir(s)$ $\triangleright$ go back to the previous
position

15: $returned\leftarrow True$

16: end if

17: $Pos(s_{new})$ $=$ $Pos(s)$ $+$ $Dir(s_{new})$ $\times$ $S$

18: Move to a new soaring position $Pos(s_{new})$

19:end if

##  III Hardware and test setup

###  III-A Eclipson model C 3d-printed model plane

An Eclipson model C [26] airplane was used for the flight tests. It is a
3d-printed plane, which makes it easy to replace parts in case of a crash. It
was printed with lightweight polylactic acid (LW-PLA) to reduce weight and
increase aerodynamic performance. Unlike other studies that used a glider or a
flying wing with flaps, we chose a 5-channel model plane to have more control.
It has four servos for control surfaces (elevator, left aileron, right
aileron, and rudder) and an electric motor at the front. Especially the rudder
is useful to keep its heading toward the wind while maintaining its lateral
position to stay in a small updraft region. The throttle is also necessary to
navigate and fly safely in case of a strong gust or sudden environmental
changes.

The MAV is shown in Figure 3. It has a wingspan of 1100$mm$, 18$dm^{2}$ wing
surface area, and an aspect ratio of 6.9. A Pixhawk 4 with Paparazzi autopilot
open-source software [27] was used. Pixhawk 4 board has a processor and an
inertial measurement unit. A GPS module and opti-track markers were used for
outdoor and indoor localization, respectively. An airspeed sensor was mounted
under the wing and calibrated in the wind tunnel. The weight of the aircraft
with electronics was 595 grams excluding battery, and a total of 716 grams
including a 1.5$A$ Lithium-Polymer battery.

###  III-B Wind tunnel test setup

The TU Delft open jet facility (OJF) is a wind tunnel with a $2.85m\times
2.85m$ cross-section. We installed a ramp in front of the wind outlet to
generate an orographic updraft. The OJF and the slope are shown in Fig. 4. The
slope angle and wind speed were adjustable during the flight. For safety
reasons, a rope system was attached to the ceiling. An Opti-track system
installed in the wind tunnel was calibrated before the flight test. In order
to get insight into the wind field with this setup, a computational fluid
dynamics (CFD) simulation was performed using ANSYS fluent [28]. The contours
of horizontal and vertical wind speeds are shown in Fig.5. The strongest
updraft occurs close to the end of the slope, and the wind speed decreases
near the slope because of the boundary friction.

Figure 3: Eclipson model C 3D-printed airplane. It has 1.1$m$ wingspan and a
weight of 716$g$ including a 1.5$A$ Li-Po battery. Pixhawk4 is equipped with
Paparazzi open-source autopilot software. An airspeed sensor is mounted under
the wing. GPS sensor and opti-track markers are used for localization. Figure
4: TU Delft OJF and the slope setting for generating orographic updraft. The
cross-section of the wind tunnel is $2.85m\times 2.85m$. A wooden plate
($2.44m\times 2.44m$) was used for the slope. The slope was placed in front of
the outlet of the wind tunnel.

###  III-C Glide polar

To measure the sink rate, a series of outdoor flight tests was performed. The
MAV had the same hardware and weight setting with the indoor tests for
consistency. We flew the MAV manually on a calm day, and retrieved sink rate
and airspeed data from flight logs during parts of the flight where the motor
was turned off. The data points and the glide polar are shown in Fig. 6. The
data was divided into two sections and fitted with a fourth-order polynomial
function. The sink rate sharply increases around 9.8 m/s of airspeed. This is
because the propeller started windmilling at that airspeed, generating
additional drag.

Figure 5: Contours of horizontal and vertical wind speed over a slope in the
wind tunnel. The slope angle was set to 23.2 degrees and the wind speed from
the OJF was set to 8.5 m/s.

##  IV Test results

Figure 6: Glide polar of the Eclipson model C airplane. The data was divided
into two sections and fitted with a fourth-order polynomial. Additional drag
was generated at around 9.8 m/s of the airspeed because of the propeller
windmilling. Figure 7: Horizontal and vertical position, and throttle usage of
the MAV during the flight according to the change of the wind speed from the
wind tunnel. Figure 8: Flight trajectory during the autonomous search, from
352 to 537 seconds in case 1. The MAV started searching at the standby
position (STDBY), marked as a black dot. It found a good soaring location and
achieved zero throttle in 185 seconds. Figure 9: Horizontal and vertical
position, and throttle usage of the MAV during the flight according to the
change of the slope angle.

###  IV-A Autonomous Soaring

Indoor flight tests were performed to demonstrate autonomous soaring using the
proposed methods in this paper. We first started the flight in manual mode for
safety reasons until the nominal wind speed reached 8.0 $m/s$. Once the wind
speed was stabilized, we switched on the autonomous flight mode. The MAV was
fully autonomous from that point. It first hovered at a standby position and
stabilized itself. Then it started the local search and autonomously moved its
target soaring position until it converged according to algorithm 1. The
standby position was set where requires approximately 20% of the throttle for
hover. During the flight, we changed the environmental conditions, either the
wind speed or the slope angle. Everything was running onboard, except position
measurements from the opti-track. Data from onboard sensors was written on an
SD card using a high speed flight logger and retrieved after the flight.

There were two experimental cases: one in which we changed the wind speed with
a fixed slope angle, and another in which we changed the slope angle with a
fixed wind speed. In both cases, the MAV was able to successfully soar using
very little energy without any prior knowledge of the wind field. Furthermore,
it was shown that autonomous soaring in a changing environment is possible by
using the proposed methods.

####  IV-A1 Changing nominal wind speed

The first case is to change the wind speed during soaring. We started
autonomous soaring at a wind speed of 8.5 m/s, and then slowly increased it to
9.8 m/s, and decreased it again. When the wind speed changes, the MAV either
stays at the same position if possible, or tries to find another position. If
the current position becomes not feasible for soaring due to the change of the
wind field, it restarts searching for a new feasible soaring position.

Figure 7 shows the wind speed, horizontal and vertical position, and throttle
usage during the flight. Figure 8 shows the trajectory during the autonomous
search from an initial position at 8.5 $m/s$ wind speed. The throttle started
of at 20%, but after the autonomous search for a soaring location turned on at
352 seconds, the MAV found a good soaring location in 185 seconds, achieving
zero throttle at 537 seconds. From that time on, the throttle usage was very
low. At 2244 seconds, we retook manual control to make the MAV land. Manual
control is shown by the shaded regions. The wind speed was changed over time,
which led to changes in position. There is no clear proportional relationship
between wind speed and the positions. We will analyze the chosen soaring
positions further in the next section. The flight time was a total of 30
minutes excluding a short manual flight after launch and landing. During the
soaring, the mean throttle usage was 0.25 %. Note that it is a significant
decrease in throttle usage compared to non-soaring flights. 38% of the
throttle was required for the MAV to hover in the wind tunnel without a ramp
at 8.5 m/s wind speed, and 30 to 50% of the throttle was normally used during
outdoor flights.

####  IV-A2 Varying slope angle

In the second case we changed the slope angle during soaring. The procedure
remained the same as the first case, but instead of changing the wind speed,
we changed the slope inclination while the nominal wind speed was fixed at 8.5
m/s. The slope angle, the MAV’s horizontal and vertical position, and the
throttle usage are shown in figure 9. The slope angle was set from 22.1
degrees to 25.2 degrees. The step size of the slope angle was not consistent
because of the practical difficulty of moving the ramp precisely during the
flight. The throttle usage was 25% at the start. We started the autonomous
search at 1440 seconds. The MAV achieved zero throttle flight at 1572 seconds,
132 seconds after starting the search. At 2950 seconds, we retook manual
control for landing. With a slope angle of 22.1 degrees, the inclination was
small, so less updraft was generated than other conditions. Because of that,
the combination of the horizontal and vertical wind was not favorable to hover
stationary. Nevertheless, it was still able to soar using zero throttle at
22.1 degrees slope angle, allowing some movement. The soaring position moved
frontward when the slope inclination increased, and it moved backward again
when the slope angle decreased. This is because the feasible soaring region
pushed forward as the slope angle increased. We will analyze the change of the
wind field and chosen positions in the next section. The soaring flight time
was a total of 25 minutes, excluding short manual flights after launch and
before landing. During the soaring, the mean throttle usage was 0.25 %. Note
that in both test cases, the flight was stopped before using up all the
battery because of the size of the flight log file and limited onboard memory.

##  V Analysis and Discussion

For further analysis, we ran a CFD simulation for each combination of wind
speed and slope angle. Based on the wind field calculated by the CFD
simulation and the MAV’s sink rate, a feasible soaring region can be
determined. The MAV can soar where the updraft and sink rate are balanced
(i.e. excess updraft = updraft - sink rate = 0), which is a white region in
figures 10 and 11. The trajectory shows that the MAV mostly stayed in the
region where the updraft and sink rate is balanced. The plots show that the
MAV generally resides inside or very close to the white areas, in which the
predicted excess updraft is zero. The MAV does occasionally fly in slight non-
zero excess updraft locations, which we expect to be due to imperfections in
the predictions. These imperfections can have various sources: differences
between the CFD simulation and the real world, imperfect sink rate measurement
and fitting, airspeed sensor measurement, and the wind speed controller of the
OJF also had steady-state errors within 0.1 m/s range.

Figure 10: Case 1: autonomous soaring in changing wind speed from 8.5 to 9.8
m/s. Contours of excess updraft and the MAV trajectory are shown for each
nominal wind speed. In the last plot, the range of sink rate for each case is
shown on the glide polar. Figure 11: Case 2: autonomous soaring at varying
slope angles from 22.1 to 25.2 degrees. The contours of excess updraft and the
MAV trajectory for each slope angle are shown. On the last plot, glide polar
with the range of the sink rate for each case is presented. The sink rates
stayed in similar ranges because the nominal wind speed was fixed at 8.5 m/s
in this case.

One thing we noticed is that the vertical position of the MAV went down as the
wind speed increased. Although this may seem counter-intuitive, the glide
polar explains the behavior. The minimum sink rate of the MAV occurs at around
9.1 m/s of airspeed. When the airspeed gets higher than that, the sink rate
significantly increased. As a result, more updraft is required for the MAV to
stay aloft, and the MAV lowers its altitude to find a stronger updraft. In
case of a varying slope angle, the position of the MAV moved forward as the
inclination increased. It is because more updraft is generated with a larger
slope angle, thus the position that balances the sink rate and the updraft
moved forward.

In both cases, the throttle usage and energy consumption decreased
significantly after switching on the soaring mode. We set a position where the
MAV can hover using approximately 20% of the throttle as a standby. During the
soaring flight, the throttle usage dropped and remained at close to 0% for
almost all the time. The mean throttle usage of the entire soaring flight was
0.25% for both cases, compared to 38% for a nominal flight. There were a few
moments that the MAV used throttle because it was necessary to avoid a stall
or recover the position. Note that the size of the feasible soaring region is
only 10 to 20 cm vertically, which is very small to maintain the position
within the region even for a human pilot. Also, we changed the wind field
during the flight so sometimes the MAV had to overcome a sudden change using
the throttle.

##  VI Conclusion

In this paper, we demonstrated the first autonomous orographic soaring in the
real-world environment without a priori knowledge of the wind field, pre-
defined trajectory planning, or manual initialization by a human pilot. A
fully autonomous orographic soaring was performed in the wind tunnel with
changing environment settings. With a combination of the local search
algorithm and the INDI controller with control allocation, the MAV was able to
soar autonomously with almost zero throttle in the updraft for over 25 minutes
of flight time. Furthermore, we verified that the MAV can find a new soaring
position when the updraft changes by using the proposed search method.

For future work, performing an outdoor flight test will be the next step. The
proposed methods in this paper are applicable to outdoor flights because they
do not depend on any pre-measured environmental condition. However, the MAV
will have to be more aware of its environment, as the wind may change
direction and it will have to sense and avoid obstacles during the search.
Using additional sensors can be helpful for recognizing the surroundings.

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