1. Design of a Modular Offline Reconfigurable Unmanned Aerial
Vehicle (UAV)
Benjamin Rinauto *, Sanchit Gupta †
, Victor Maldonado‡
, Souma Chowdhury §
This paper aims to develop a computational framework to design reconfigurable unmanned aerial
vehicles (UAVs) that are inspired by modular platform planning. These reconfigurable UAVs are
unique in their ability to be assembled on-field into configurations that can perform diverse missions.
While reconfigurable UAV platforms are rare in the literature, specialized frameworks to design mod-
ular/reconfigurable UAVs are even rarer. A new design framework founded on object-oriented com-
puting is presented here. Such an approach to modular design allows flexible addition and evolution
of modules, and integration of different algorithms that interact with the module objects in estimating
the quantities of interest (e.g. aerodynamic forces). A corollary benefit is the provision for automated
batch execution of 3D CAD updates during design optimization. A case study is performed to de-
sign a set of modules that can be assembled either into a quadrotor UAV or into a fixed-wing UAV,
where their endurances are simultaneously maximized, subject to various constraints associated with
mission requirements (e.g., payload), geometry, and module interactions. Results show that the best
trade-off reconfigurable UAV designs, while expectedly compromising on endurance, provide a re-
markable 40% mass savings compared to a set of optimized dedicated quadrotor and fixed-wing
UAVs.
Nomenclature
General
QR = (as subscript) Quadrotor Configuration
FW = (as subscript) Fixed-wing Configuration
L = Lift
D = Drag
W = Total weight (including payload)
T = Thrust
P = Power
E = Endurance
C = Battery capacity (Energy)
V = Nominal Battery Operating Voltage
m = Mass
g = Acceleration due to Gravity
ρ = Air density
N = Number of components
n = Number of rotors
drotor = Position of rotor connection point
Lfuselage = Length of Fuselage
*Student, Department of Mechanical and Aerospace Engineering, University at Buffalo, AIAA Student Member
†Student, Department of Mechanical and Aerospace Engineering, University at Buffalo, AIAA Student Member
‡Assistant Professor, Department of Mechanical Engineering, The University of Texas at San Antonio, AIAA Senior member.
§Assistant Professor, Department of Mechanical and Aerospace Engineering, University at Buffalo, AIAA Senior member. Corresponding
Author. Email: soumacho@buffalo.edu
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2. Aerodynamic
CD = Coefficient of Drag
CL = Coefficient of Lift
vc = Cruise Velocity
a = Wing lift slope (Coefficient of Lift derivative w.r.t α)
a0 = Airfoil lift slope w.r.t α
α = Angle of attack
αL=0 = Angle of attack at which Lift is zero
S = Wing Planform Area
AR = Aspect Ratio
Arotor = Rotor disk area
Optimization Variables
Af = Airfoil selector
Ps = Propeller selector
Ms = Motor selector
Bs = Battery selector
ıA = Incidence Angle
λ = Taper ratio
Λ = Sweep Angle
b = Wing Span
I. Introduction: Reconfiguration in Unmanned Aerial Vehicles
Traditionally, Unmanned Aerial Vehicles or UAVs have been used for dedicated missions, with military applications
generally dominating the spectrum of UAV usage [1]. With emerging civilian applications, diversifying military
applications of UAVs and a growing marketplace for inexpensive UAVs, there is an increasing demand for UAV
platforms that offer multiple functionalities. Reconfigurable UAV platforms provide a unique solution to meet this
demand, especially for small or mini UAVs – enabling a new multifunctional or multi-ability UAV paradigm. In
general, the need for reconfiguration is driven by the need for one or more of the following three desirable properties:
1. Flexibility: Ability of the system to perform multiple dexterous functions at different times (i.e. under varying
operating conditions or to satisfy different functional requirements).
2. Modularity: Ability to readily add new functionality. This also allows quick, inexpensive maintenance and trans-
port by swapping or removing modules.
3. Robustness: Ability of the system to survive and remain operational despite failures.
In the context of the stated ”operational flexibility” property, the need for UAVs that can perform missions re-
quiring a combination of hover and efficient/rapid forward flight has sparked an interest in developing hybrid vehicle
concepts and systems. More specifically, these systems are expected to operate in either flight modes at a level of
performance approaching that of optimally designed single-mode operating systems. Conventional rotorcraft are gen-
erally most efficient in hover flight but suffer from efficiency limits to their forward flight ability due to aeroelastic and
compressible flow constraints stemming from rotor blades. For many years, attempts have been made to produce high
performance hybrid aircraft, with mixed results. Two emerging classes of hybrid aerial vehicle concepts have been
most commonly studied for combined hover and forward flight: the tilt rotor and tilt-wing-body concepts, with the
former finding the majority of practical implementations (both as full-scale and small unmanned vehicles). Examples
in the UAV domain include the Skytote developed by Aerovironment [2] and the panther fixed-wing vertical takeoff
and landing (VTOL) system developed by Israel Aerospace Industries [3]. These platforms are on the more expensive
and sophisticated end of the small UAV spectrum, thereby limiting their applicability in the civilian arena.
The other major area of research in reconfigurable aerospace systems is reconfigurable wing shape, traditionally
referred to as morphing wings. Snyder and Weisshaar [4] give a good overview of the history of such systems, and
also design and demonstrate a method to optimize the structure of a morphing wing. Research in smart materials
has also made its way into applications in this domain. Lagoudas et. al. [5] use a coupled thermal and aerodynamic
model to modify airfoils with shape memory alloys to create wings that are efficient in both subsonic and transonic
flow regimes. Beblo et. al. [6] describe a thermally activated wing system for low-speed UAVs that are deployed from
separate high-speed vehicles. The common requirement of the morphing wing systems is the ability to fly efficiently
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3. at high and low speeds; however in this paper, we focus on a flight envelope comprising low speed forward flight and
hover
Hybrid UAV systems or UAVs that can take both hovering and fixed-wing configurations (through online or offline
transition) fill a unique niche in the Civilian UAV market for applications that require both hover and high-speed/long-
range forward flight (under different scenarios). In addition, the ability of VTOL provides an enormous advantage
over fixed-wing systems in a wide array of civilian applications, especially where a proper field site that is relatively
flat and large/long enough is not available for takeoff and landing. This eliminates the need for ground-based launch
ramp which may be impractical to setup in remote locations, disaster zones, emergency-critical solutions, or small
offshore-platforms/sea-vessels. Despite the advantages of hybrid vehicles, single-dedicated fixed-wing and rotorcraft
systems will likely continue to dominate the landscape while the state of the art in hybrid systems progresses toward
an acceptable level of maturity and mainstream adoption.
As a solution to the need for hybrid or multi-ability UAVs that could also be economical, Chowdhury et al. [7]
presented a modular UAV concept, shown in Figure 1, where UAV platforms are reconfigurable offline to provide
diverse functionality. In this concept, different UAVs can be assembled in short times and immediately prior to
a mission, from a global set of modules, where the choice of the configuration to be assembled is driven by the
mission requirements. More specifically, the authors demonstrated the applicability of this concept by designing a
set of optimum modules that can be assembled into both a quadcopter and a fixed-wing configuration (with separate
specified payload and endurance capabilities). Although the offline reconfigurable design (requiring pre-mission re-
assembly) do not provide the same degree of operational flexibility as that of a online reconfigurable hybrid UAV
(e.g., tiltrotor designs), it provides significant new opportunities for application in the civilian UAV arena, since a
set of offline-reconfigurable UAV modules is likely to be more robust in design (i.e., less prone to failure), simpler
in implementation, and significantly less expensive compared to sophisticated online reconfigurable UAV platforms.
In addition, modular UAV platforms can take full advantage of (emerging) additive manufacturing technologies to
replace or upgrade individual parts/modules onsite (in an on-demand basis), an approach that is of great interest to the
U.S. military [8] [9].
In this paper, we are adopting this offline reconfigurable UAV concept, with the aim to develop a first-of-its-kind
object oriented framework for optimal (mission-requirements-driven) design of such reconfigurable UAVs. In the
next section, the framework developed in this paper is described. The following section provides a description of
the different components of this framework. Subsequently, a case study is presented, which describes and solves the
optimization problem that enables the design of reconfigurable UAVs. This is followed by the results and discussion
sections which explore the optimal UAV designs and consider the tradeoffs involved in modular reconfigurable UAV
designs. The paper ends with concluding remarks.
a) Fixed-Wing UAV configuration b) quadrotor UAV configuration
Figure 1. 3D models of the fixed-wing and quadrotor assemblies of the reconfigurable UAV developed by Chowdhury et al. [7]
II. An Object-Oriented Design Framework
A. Design Framework Needs for Modular/Reconfigurable UAVs
The overall goal of this research effort is to lay the foundation for effective application of platform-based modular
design concepts in developing reconfigurable, multi-functional, and easy-assembly small UAVs, primarily in the small
(< 20 lb) and medium (21 − 55 lb) size groups. To that end, this paper specifically aims to construct and investigate a
specialized design framework that facilitates the following:
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4. 1. a module-based physical definition of the UAV system;
2. in-situ design and ready evolution of configurational variations that can share different sets/sub-sets of modules;
3. automated updating of the high-resolution 3D CAD models in real-time during design optimization (which
allows interactive human-in-the-loop design exploration); and
4. ready integration of multi-fidelity analysis codes to quantify various aerodynamic and basic structural properties
of interest.
It is important to note that detailed structural, control and stability factors are not explicitly considered in the first
implementation of the framework presented in this paper; however, the bounds of various module attributes are such
chosen that they mitigate the possibility of violating static stability constraints.
We seek to accomplish the above-listed (four) features and capabilities by conformal parametrization of modules
and module interactions and subsequently by taking a novel object-driven or object-orientated approach to architect
and implement the fully parameterized design framework. The framework is demonstrated by performing a case
study to design a set of modules that can be assembled into a fixed-wing UAV configuration or a quadrotor UAV
configuration, with specified payload capacities, and where the objective is to simultaneously maximize the endurance
of both configurations. In this case, (as stated before) the modular configurations and module sharing scheme are
directly motivated by the earlier optimized concept developed by Chowdhury et al. [7] − in this concept (Fig. 1), the
quadrotor UAV is comprised of modules (namely, the fuselage or central pod, and four rotor duct assemblies) that are
a subset of the fixed-wing UAV (which also contains the wing section modules). The next sub-section describes the
components of the new object-oriented framework for designing reconfigurable UAVs.
B. Components of the Framework
Figure 2. A class diagram showing the structure of parts inheriting AeroPart. All classes extending AeroPart automatically have the
functions and attributes listed, but those functions can be customized for the extending part. AeroPart provides a common interface.
In the space of UAV design, there are hardly any standards for problem representation, decomposition, and flexible
solution though computer codes. For design optimization, typically a procedural programming paradigm is used, in
which the problem is represented as a sequence of instructions and function calls. This is the case because a proce-
dural paradigm is the most well understood method for engineers who do not necessarily approach this issue from the
computing stand-point, and engineering problems are often well suited for that paradigm. The reconfigurable UAV is
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5. different in this respect. The modular nature of the project makes an object oriented approach to “system decompo-
sition” very appealing. In this paradigm, each module can be encapsulated as an object (i) with properties or module
attributes comprising geometric dimensions and discrete design choices (such as airfoil type, material selection, and
selection of off-the-shelf components), and (ii) with methods which compute derived quantities such as mass or coef-
ficients of lift and drag. Configurations can be encapsulated as combinations of modules and their relative locations,
with methods defining the physical interaction between the individual modules and their aerodynamic properties.
We take the object oriented approach to the design framework with the following goals in mind:
Goal 1: The framework should allow itself to be readily extended to newer types of modules not yet considered (e.g.
tail sections or cargo bays).
Goal 2: The framework should be independent of the analysis that is to be done. In other words, the framework should
not be specific to a configuration, part, or design objective, thereby allowing for multidisciplinary analysis, (e.g.,
aerodynamic, structural, and control analysis).
Goal 3: The framework should be able to integrate high-fidelity geometric representations through 3D solid modeling
and performance analysis through high-fidelity simulations (e.g., CFD) as well as low-fidelity models (e.g.,
analytical or vortex lattice aerodynamic models and beam-based structural analysis).
Goal 4: The framework should be able to handle diverse assemblies and configurations of modules.
To accomplish the 4th goal, we develop a specialized architecture, which is described next. The basic interface is
an “AeroPart”, which takes as inputs references to algorithms for computing (i) mass, (ii) inertia, (iii) center of gravity,
and (iv) coefficient of drag, and which outputs those properties once they are computed. An illustration of the AeroPart
interface and its extensions (as described below) is shown in Fig. 2. An AeroPart represents a general part; inheritance
is used to make other parts such as wings, which need an analysis model to estimate coefficient of lift, and ducts,
which need analysis models that can represent power consumption as a function of the required thrust. Inheritance is
a programming method wherein the inheriting object gains all the properties and methods of the inherited object and
can be extended with new properties and methods. This extensibility specifically satisfies goals 1 and 2 – new modules
with different properties and methods can be created by extending AeroPart. A total of 6 extensions are made. Five
are for the modules: tapered wing, ducted rotor, fuselage, battery, and motor. The 6th extension is made to support
assemblies and subassemblies.
AeroPart uses the strategy pattern to determine its properties. This is why it requires models as inputs. Each model
itself is an object that acts similarly to a function handle. The strategy pattern addresses goal 3. CFD or CAD program
interfaces can be encapsulated in an algorithm object. When get mass() is called on an AeroPart, the call is passed to
the algorithm object, which would either query the relevant program for a result or compute the mass in a prescribed
way. A third option, if experimental data is available, is to encapsulate the data into an algorithm object which applies
a surrogate model to determine the desired properties. With this method, algorithm objects can be applied to new
parts, or alternatively, old parts can be ”upgraded” with new algorithms.
As a concrete example, consider the differences between the motor AeroPart extension and the wing AeroPart
extension. For mass property calculations, motors are assumed to be cylinders with uniform density. Motors contain
the properties mass, radius, and height, and the algorithm objects use these properties to compute the mass, inertia,
and center of gravity (c.g.) based on the typical equations for a cylinder. The wing extension uses a different method.
There is a CAD model available for the wing module of the reconfigurable UAV (since performance is highly sensitive
to wing geometry), so in this case the algorithm objects are written with an interface to the CAD program. The mass
properties are computed by the program on request from the algorithm object. From outside AeroPart, these details
are hidden; irrespective of the choice of algorithm, the textitget mass() method will return the mass. As an example, a
class diagram of the architecture for computing mass properties is shown in Appendix B, Fig.14 (with the TaperedWing
AeroPart shown using the CAD algorithm object).
One important advantage of the strategy pattern is the ability to develop libraries of algorithms. Once an algorithm
has been defined and encapsulated, the codes can be stored and reused without modification. Alternatively, models
can be updated during an iterative design process as more information becomes available, simply by replacing the
algorithm object in the model. Once a test is completed and data obtained, a previously approximate model for a
property can be readily replaced with empirical data or higher fidelity simulation based computations.
The architecture described so far can be used for individual parts, but cannot be used for assemblies. Two additional
objects are added to implement assemblies. First, “AssmPart” holds a reference to an AeroPart and a homogeneous
transformation matrix which describes the location and attitude of the part’s axes relative to the assembly’s axes.
This matrix is implemented with a strategy pattern as well, which allows it to be obtained through a solid modeling
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6. program or other sources. Second, the “Configuration” object holds a vector of AssmParts. A Configuration is
essentially a list of parts and their relative position in the global coordinate system. In order to add functionality
for subassemblies, Configuration implements the AeroPart interface. The algorithm objects used to compute mass
properties for configurations simply iterate through the list of “AssmParts” and combine them (in the case of mass,
it is simply a sum; for inertia, the homogeneous transformation matrix is needed). Since a Configuration is itself
an AeroPart, Configurations can be contained as an element of the part list in other Configurations; the net effect is
support for subassemblies. In essence, the architecture has an implicit tree structure: each node is a Configuration and
each leaf is an “AssmPart”. A sample Configuration is shown in Appendix B, Fig. 15. This satisfies the third goal,
that is the ability to create any configuration of modules.
Configurations still require algorithms to determine aerodynamic properties such as coefficients of lift and drag
(CD and CL). Again, the strategy pattern is used. For each Configuration, the specific CD or CL algorithm defines
the interaction between the aerodynamic properties of individual modules. First order algorithms can simply add the
drag or lift contributions of the individual parts. More advanced analysis models can account for interactive factors
such as downwash due to relative locations of parts and induced drag contributions, potentially through the (readily
integrate-able) use of CFD methods.
The next section describes the application of this framework to the optimization of a modular UAV concept that
can take fixed-wing and quadrotor configurations. The problem formulation including the design vector, constraints,
and optimization method is explained here.
III. Case Study: Reconfigurable UAV
A. Problem Formulation
In order to demonstrate the first implementation of this new object-oriented computing framework for system decom-
position and design of reconfigurable UAVs, we perform a case study based on the modular UAV concept presented
by Chowdhury et. al [7], namely RECU (Reconfigurable UAV). The UAV involves two different configurations: a
quadrotor and a flying wing style fixed-wing. The configurations share multiple modules, e.g. the ducts and central
pod. In the earlier work, an optimal conceptual design was obtained with respect to different performance parameters
including weight and cost, accomplished by altering attributes of modules such as the wing, fuselage, and ducts. The
resulting design from that work is shown in Fig.1.
In our case study, three module types are explicitly considered: fuselage, wing, and (four identical) ducts. Except
the wing, all modules are shared by the two configurations. The goal of the optimization process presented here is
to simultaneously maximize the endurance of both configurations by adjusting the module design variables, that are
described in the next section.
There is also a need for a reference design to gauge the performance of the optimal modular UAV designs. In order
to provide a basis for comparison, the same method should be used to compute endurance in the reference design. In
this case, even though estimated endurances may be optimistic (given the possibility of the low-fidelity aerodynamic
models over-estimating the performance), a comparison between the optimized design and the reference design (both
evaluated using the same models) is expected to provide realistic insights. To create these reference designs, the same
framework and aerodynamic models are thus used, while the constraints on module sharing are removed to create
zero-commonality fixed-wing (FW) and quadrotor (QR) designs – i.e. unique configurations dedicated to separate
mission requirements.
The next subsection describes the module attributes (which serve as design variables) that are considered in the
optimization of the modular UAV.
B. Design vector
The modules are defined here in terms of parameters or module attributes. A block diagram illustrating the modules
and their variables (attributes), the operational variables, and the information flow from variables to objective functions
is shown in Fig. 3.
The motor and battery are modeled as (categorical variables treated as) as discrete variables with linked properties
for geometry, mass, and power, where both of these variables are selected from a data-base of off-the-shelf alternatives.
The battery and motor properties are listed in Tables 4 and 7 in Appendix A. The fuselage and rotor are parameterized
in terms of geometric variables. The rotor is defined by only one variable: propeller size. The propeller size is derived
from the selection of the propeller, where propeller choice is itself a discrete variable; the choice is made from a list
of four off-the-shelf propellers, listed in Table 5 in Appendix A. The fuselage attributes are automatically derived
from the following equality constraints – length was set equal to either wing root chord or 1.2 times the battery length
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7. Figure 3. Information flow in the reconfigurable UAV design framework.
(whichever is larger), and its width is chosen to fit the selected battery and a Pixhawk autopilot with 2cm of extra space.
This “automatic” sizing is done to reduce the number of variables and constraints. The tapered wing is comprised of
the following variables: span, root chord length, taper ratio, sweep angle, angle of incidence, and airfoil type. The
airfoil type is selected from a list of 3 candidates, listed in Table 6 in Appendix A; hence it is also a categorical
variable that is treated as a discrete variable. In total, there are 9 module attributes (serving as design variables) with
their bounds given in Table 1.
Table 1. VARIABLE BOUNDS
Variable Lower Bound Upper Bound
Airfoil Type 1 3
Span(m) 0.36 2.0
Root Chord (m) 0.1 1.0
Taper Ratio 0.1 1.0
Sweep Angle (deg) 0 45
Incidence Angle (deg) -8 12
Propeller Selector 1 5
Motor Selector 1 4
Battery Selector 1 8
In order to determine aerodynamic performance, first order models are used for the wing and rotor. The wing
lift coefficient (CL) is determined from Kuchemann’s modification of Prandtl lifting line theory [10], assuming level
cruise flight. This is shown in Eq. (1),(2) and (3). The rotor power (P) to thrust (T) relationship is determined by
the Rankine-Froude momentum theory [11], assuming a hovering quadrotor as shown in Eq. (4). These theories are
encapsulated in the computational framework as a Lift Coefficient algorithm object and a Power-to-Thrust algorithm
object respectively.
CL = a(α − αL=0) (1)
a =
a0cosΛ
1 + [a0cosΛ/(πAR)]2 + (a0cosΛ/(πAR))
(2)
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8. AR =
b2
S
(3)
P =
nT3/2
2ρArotor
(4)
In order to demonstrate the flexibility of the framework, a CAD interface has been included in the loop. The wing,
fuselage, and duct mass properties are all determined from a simplified CAD model (using a CAD Mass Property
algorithm object). In contrast, the motor and battery pack are assumed to be simple solids with uniform density (with
properties computed by Cylinder and Rectangular Prism Mass Property algorithm objects, respectively). These are
illustrated in Fig. 14, which shows different implementations of the mass properties interface (Appendix B). For the
purpose of defining the configuration, the motor is taken to be at the center of the duct, and the battery is taken to be
in the center of the fuselage – the homogeneous transformations of the battery and the motor are linked to the CAD
models of the fuselage and rotor.
C. Objective function
The endurance (EFW) of the fixed-wing configuration is determined using the following expression (Eq. 5).
EFW =
CV
PFW
(5)
where C is the capacity of the battery, V is its nominal operating voltage, and PFW is the total power required to
maintain level cruise flight of the fixed-wing UAV. This clearly depends on the total weight of the configuration and
the lift available from the wing. The power is determined from the thrust-power relationship given by Rankine-
Froude momentum theory (Eq. 4). The required Thrust is estimated by determining the total drag on the fixed-wing
configuration. For the wing, profile and induced drag are considered. For the fuselage and rotors, constant drag
coefficients are chosen based on their shape. The battery and motor are assumed to have zero contribution to drag.
These types of drag are all encoded in CD Algorithm objects and applied to the appropriate AeroParts. No aerodynamic
interaction between the parts is considered here.
The endurance (EQR) of the quadrotor configuration is determined using the following expression (Eq. 6).
EQR =
CV
PQR
(6)
Where, again, C is the capacity of the battery, V is the operating voltage, and PQR is the total power required to keep
the quadrotor in level hover. This power requirement is determined from the thrust to power relationship (Eq. 4) and
by assuming thrust equal to total weight.
The total weight of both configurations is determined from the CAD model and payload operational variables. The
target payload weight for the quadrotor configuration is set at 0.5 kg and that for the fixed-wing configuration is set to
2.0 kg. A mass buffer of 0.25 kg is included in each configuration to allow for the weight of small components like
connectors and wires. The total weight is then given by the following expression (Eq. 7).
W = g(mparts + mpayload + mbuf fer) (7)
D. Constraints
A total of nine constraints are considered here. Four constraints are applied to power. First, the power required for
the FW and QR configurations need to be less than the motor maximum steady power, where the latter is the power at
which the motor can run for a long period of time without overheating. For motor candidates where this property isn’t
readily available (in their web listing), we conservatively assume it to be equal to half of (rated) peak motor power. In
practice, we found this constraint to rarely be active.
With considerations of general mission requirements, the cruise velocity is constrained to the following lower and
upper bounds: 16 m/s and 32 m/s.
Three additional geometric constraints are considered. The rotors are “programmed” in CAD to be non-interfering,
and are constrained to ensure that they remain attached to the wing (in the fixed-wing configuration) and fuselage
(in the quadrotor configuration). This resulted in two constraints: that the span-wise position of the outer rotors’
attachment points in the fixed-wing configuration is less than half of the span (i.e. on the wing), and that the lengthwise
positions of the rotors’ attachment points in the quadrotor configuration are less than half of the fuselage length from
the center (i.e. they stay on the fuselage).
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9. Two additional constraints are associated with the net mass of the UAV configurations. The empty mass (excluding
the payload, e.g. mparts + mbuf fer ) of the fixed-wing configuration is constrained to be less than 2.5 kg. The empty
mass of the quadrotor configuration is constrained to be less than 1.5 kg. The problem formulation is shown in below
(Eq. 8).
max f1(x) = EFW
max f2(x) = EQR
s.t. PFW, PQR < Pmotor
mFW < 2.5kg
mQR < 1.5kg
16m/s < vc < 32m/s
AR > 4
drotor,FW < (Lfuselage − .01m)/2
drotor,QR < (b − .01m)/2
x = {Af , b, cr, λ, Λ, iA, Ps, Ms, Bs}
(8)
where Pmotor is the maximum allowable motor power, drotor is the position of the connection point of the rotors, and
Lfuselage is the length of the fuselage. Note that the .01m appearing in the last two constraints is there to allow a small
gap between the rotor ducts.
E. Zero-Commonality Optimizations
The reference designs are created with the same framework and models, where the constraints on module sharing are
removed. This yields the following two problem formulations.
The design vector for the dedicated quadrotor configuration consists of only three variables: propeller, motor, and
battery selectors. The limits for these are the same as in the general formulation. Only three constraints are required
in this formulation. The problem formulation for the dedicated quadrotor optimization is given below (Eq. 9).
max f1(x) = EQR
s.t. PQR < Pmotor
mQR < 1.5kg
dduct,QR < (b − .01m)/2
x = {Ps, Ms, Bs}
(9)
The design vector for the fixed-wing optimization is the same as that for the modular UAV. Only the constraints are
changed. In this case, the fixed-wing is relieved of the constraints associated with sharing modules with the quadrotor
(those listed in Eq. (9)), but is still subjected to the remaining constraints from Eq. (8). The problem definition for the
dedicated fixed-wing optimization is given below (Eq. 10).
max f1(x) = EFW
s.t. PFW < Pmotor
mFW < 2.5kg
16m/s < vc < 32m/s
AR > 4
dduct,FW < (Lfuselage − .01m)/2
x = {Af , b, cr, λ, Λ, iA, Ps, Ms, Bs}
(10)
F. Optimization Methods
The zero-commonality optimizations are both single objective nonlinear problems. The quadrotor optimization in-
volves only discrete variables. Since the total number of combinations of discrete variables is relatively small (260)
in this case, and the criteria functions are not expensive to evaluate, an exhaustive search is used to identify the
optimum dedicated quadrotor configuration. Every combination of the three discrete variables is checked. The ded-
icated/reference fixed-wing optimization is a constrained nonlinear mixed-integer problem, and is solved using the
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10. mixed-discrete Particle Swarm Optimization algorithm deveoped by Chowdhury et. al, MDPSO [12]. MDPSO is a
particle swarm algorithm for mixed-integer non-linear constrained optimization problems. A population size of 120
was used for 50 generations, and typical values for the inertial, local, and global coefficients were chosen (0.5, 1.4,
and 1.4, respectively).
The reconfigurable UAV optimization is a constrained nonliner mixed-discrete multiobjective optimization. A
Matlab implementation of the non-dominated sorting genetic algorithm (NSGA-II) [13], called NPGM [14] is used
to solve this multi-objective optimization. NSGA-II is a genetic algorithm that is generally well-suited to solve such
multi-objective mixed-discrete optimization problems. Here, a population size of 180 is used, and a total of 70 gen-
erations is allowed. Linear crossover and Gaussian mutation methods are employed. NSGA-II is run multiple times
to verify the results. To check and potentially improve the quality of best tradeoff designs provided by NSGA-II, a
follow-up optimization is performed. For every feasible quadrotor design, obtained by constraint filtering the results
of the exhaustive search, a single objective optimization was performed on the wing module variables using MDPSO
(which is also used for the zero-commonality optimizations). The multiple optimal designs obtained via this method,
which we call iterative MDPSO implementation, are subjected to a Pareto filter to yield the best tradeoff designs. The
results from the direct multiobjective optimization (using NSGA-II) and multiple/iterative single objective optimiza-
tions (using MDPSO) are compared in the next section.
IV. Results
The best zero-commonality designs obtained by MDPSO are shown in Fig. 4 and Fig. 5. The estimated maximum
endurance for the zero-commonality fixed-wing is 202 minutes (range of 334 km). The estimated maximum endurance
for the zero-commonality quadrotor is 10.2 minutes. Their combined mass is 3.98 kg. Preliminary investigation
shows that the quadrotor design appears reasonable; however, the fixed-wing design requires further consideration.
Since no explicit structural considerations are made in this analysis, the optimization yielded the design with the most
aerodynamically and energy efficient characteristics. This produced large rotors and a high aspect-ratio wing, which
might cause structural issues. However, since the purpose of the zero-commonality optimal designs is to obtain a
performance upper bound or reference with which we can compare our optimal reconfigurable UAV designs, these
results were considered to be useful. The performance of the zero-commonality UAV considerations, as well as the
results from the optimization of the reconfigurable UAV, are summarized in Table 2.
Figure 4. The optimal zero-commonality fixed-wing design (12 in / 31 cm ruler for scale).
Figure 5. The optimal zero-commonality quadrotor design (12 in / 31 cm ruler for scale).
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11. For the reconfigurable UAV, NSGA-II and the iterative MDPSO optimizations over the feasible quadrotor designs
produce different results. The first method produces the Pareto front shown in Fig. 6. Examination of the scale of the
y-axis reveals that there is not a practical tradeoff – the amount of variation in quadrotor endurance across the Pareto
solutions is only a few milliseconds. This suggests that either there are no tradeoffs or that the solver has converged
prematurely. To resolve these very questions, we employ the iterative MDPSO method, which produces the results
shown in Fig. 7.
60 80 100 120 140 160
Fixed Wing Endurance (min)
8.950
8.955
8.960
QuadrotorEndurance(min)
Run 1
Run 2
Combined Pareto Solutions
Figure 6. The Pareto solutions yielded by the two runs of NSGA-II for the reconfigurable UAV optimization.
20 40 60 80 100
Fixed Wing Endurance (min)
5
6
7
8
9
10
11
QuadrotorEndurance(min)
Best Designs from iter. MDPSO
Filtered Pareto Solutions
Figure 7. The optimal solutions and the resulting (filtered) Pareto solutions yielded by the iterative MDPSO optimizations over the feasible
quadrotor designs.
The iterative MDPSO method did not find a fixed-wing design with an endurance as great as that of some of the
best tradeoff designs obtained by NSGA-II. However, the iterative MDPSO approach succeeded in finding a quadrotor
design that significantly exceeds the range of solutions produced by NSGA-II. The results of the two methods are
combined in Fig. 8, which indicates that there are essentially two useful best tradeoff (BTO) solutions (designated as
BTO 1 and BTO2 in Fig. 8, marked with circles). Since the tradeoff between BTO2 and the other points produced
by NSGA-II is trivial, and because there is only one other significant tradeoff (BTO1), only those two solutions or
optimal designs are considered for further discussion. The UAV design at BTO1 has a fixed-wing endurance of 95.6
minutes (range of 130 km) and a quadrotor endurance of 10.1 minutes; their 3D CAD models are shown in Fig. 9 and
Fig. 10. The design at BTO2 has a fixed-wing endurance of 152 minutes ( 160 km) and a quadrotor endurance of 8.95
minutes, and their 3D CAD models are shown in Fig. 11 and Fig. 12. The results are summarized in Table 2.
We arrived at the following explanation for the best tradeoffs through careful exploration and with the assistance
of the following observations. First, BTO1 has larger, more efficient rotors, and BTO2 has a more efficient wing; this
is what directly creates the difference in endurances, as seen in Fig. 8. Second, BTO1 has nearly reached the mass
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12. constraint for the fixed-wing configuration, while BTO2 has nearly reached the span (i.e. wing size) constraint, as is
evident from Table 2. The larger rotors on BTO1 demand a larger fuselage so that the rotors do not intersect in the
quadrotor configuration. Since the fuselage length is equal to the the root chord of the wing, larger rotors can only
exist with a larger root chord. Efficient wings generally involve large aspect ratios, but for BTO2 this is hindered by
the existence of the combination of a large root chord and mass constraint. Instead, once the propellers are chosen,
the most efficient wing that can be allowed under the given constraints becomes itself constrained. This suggests that
the relaxing the equality constraint between the length of the fuselage and the wing root chord could improve the
endurance of the fixed-wing configuration.
The scarcity of Pareto solutions can be explained by the type of variables in each configuration. Since the quadrotor
relies only on discrete variables, its performance effectively falls into discrete bins. The NSGA-II results found only
one of the possible bins, which resulted in all the solutions having a quadrotor endurance of approximately 8.95
minutes. The fixed-wing configuration, on the other hand, involves a majority of continuous variables. As a result,
a wide spread of possible solutions are observed. If NSGA-II had found the feasible quadrotor design that gave a
quadrotor endurance of about 10.1 minutes, we might see a stratum of fixed-wing solutions in that bin as well.
Table 2. Results
Quantity/Attribute ZC FW ZC QR RECU BTO1 RECU BTO2
FW Endurance (min) 202 - 95.6 152
QR Endurance (min) - 10.2 10.1 8.95
Empty Mass (kg) 2.50 1.48 2.48 (FW), 1.49 (QR) 2.41 (FW), 1.37 (QR)
Cruise Velocity (m/s) 27.6 - 22.6 17.6
Payload (kg) 2.0 0.5 2.0 (FW), 0.5 (QR) 2.0 (FW), 0.5 (QR)
Range of FW (km) 334 - 130 160
Airfoil* 1 - 1 1
Span (m) 1.83 - 1.45 1.99
Root Chord (m) 0.105 - 0.269 0.215
Taper Ratio 0.76 - 0.252 0.205
Sweep Angle (deg) 12.5 - 12.58 0.032
Incidence Angle (deg) 11.5 - 6.53 4.01
Propeller Selector* 2 2 2 1
Motor Selector* 4 3 3 3
Battery Selector* 7 4 4 4
(ZC: Zero-commonality, RECU: Reconfigurable UAV, BTO: Best trade off)
*See Appendix A.
90 100 110 120 130 140 150 160
Fixed Wing Endurance (min)
8.5
9.0
9.5
10.0
10.5
QuadrotorEndurance(min)
Soln. from Iter. MDPSO
Soln. from NSGA-II
BTO1
BTO2
Figure 8. The final Pareto solutions obtained by combining all reconfigurable UAV optimizations. The effective best tradeoff (BTO)
solutions are marked by circles.
The optimum reconfigurable UAV designs BTO1 and BTO2 expectedly offer lower endurance than the zero-
commonality designs. For BTO1, the QR endurance is lower 1%, while the FW endurance is lower by 52.5%, both
compared to the respective optimal zero-commonality (dedicated) designs. For BTO2, the quadrotor endurance ex-
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13. Figure 9. The fixed-wing configuration for BTO1.
Figure 10. The quadrotor configuration for BTO1.
Figure 11. The fixed-wing configuration for BTO2.
Figure 12. The quadrotor configuration for BTO2.
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14. hibits a 13.3% reduction, and for the fixed-wing, 24.8%. In order to address all missions that the reconfigurable UAV
can perform, a user would have required both of the dedicated zero-commonality fixed-wing and quadrotor UAVs.
Compared to this alternative, the reconfigurable UAV designs offer a significant mass savings of about 40%, which
is in addition to the other benefits generally associated with shared modular platform-based systems. Comparisons of
the quantities of interest between the optimized zero-commonality and reconfigurable UAV configurations are given
in Table 3.
Table 3. Reduction in endurance and mass of the two selected best tradeoff reconfigurable UAV designs w.r.t. the optimized zero-
commonality designs.
Property BTO1 BTO2
FW Endurance Reduction 52.5% 24.8%
QR Endurance Reduction 1.0% 13.3%
Mass Reduction 37.7% 39.5%
A broad goal of this research is to maximize the mission space coverage and minimize the mass of a family of
modular UAVs. In contrast with the case study presented here, the mission space coverage goal would explore adding
extra modules to the UAV in order to expand its functional capabilities. For instance, the addition of a second set of
rotor modules would add mass to the (combined) system, but would decouple much of the design and allow better
endurance for both configurations, or introduce a second fixed-wing configuration. In general, the performance of
such a system (with multiple options for each module) could be measured by mission space coverage. Each candidate
design would contain a large number of configurations (resulting from the enormous combinatorial possibilities of
having multiple options for each module), and in turn, each configuration would have a curve describing payload to
endurance trade-offs for either hover or forward flight modes. Those curves, when plotted together, illustrate the range
of possible missions requirements that could be satisfied by the different combinations of modules; this is what we
refer to as mission space coverage, a representative example of which is shown in Fig. 13. Maximizing mission space
coverage would further demonstrate the flexibility of a modular reconfigurable UAV platform. The computational
framework outlined here represents an important step towards that goal.
0 0.5 1.0 1.5 2.0 2.5 3.0
Payload (kg)
0
100
200
300
400
Endurance(min)
Config. 1 mission space
Config. 2 mission space
Combined mission space
Figure 13. A sample mission space (for illustration only). The shaded area shows mission space coverage.
V. Concluding Remarks
Emerging civilian application of UAVs create a need for small and medium UAVs (i.e., in the <55 lb size) that can
perform diverse missions and provide multiple functionalities (seen in military UAVs, but rare among existing com-
mercial platforms), while also providing an attractive cost point and convenience of usage and assembly (rare among
sophisticated military platforms). As a broad (long-term) goal of the research presented in this paper, we explore the
hypothesis that the challenging combination of the above-stated (desirable) features can be accomplished by UAVs
that are reconfigurable − where reconfigurability is enabled by a modular design platform, allowing multiple UAV
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15. assemblies to share an optimal set of modules.
In this paper, we take an important step towards exploring this hypothesis by laying the foundation of a new design
framework that allows methodical design and evolution of reconfigurable UAVs. This design framework is built around
conformal parameterization of the UAV modules and an object-driven design/computing platform that can integrate
module interactions and various analysis codes (that quantify quantities of interest, e.g. mass and aerodynamic forces).
Important components of this framework (e.g., AeroPart, employing the strategy pattern, and AssmPart) are introduced
in this paper, and their integrative implementation is demonstrated by performing a design case study.
In this case study, a fixed-wing UAV and a quadrotor UAV (where the latter comprises a sub-set of modules of
the fixed-wing UAV) are designed to satisfy specified payload capacities and offer maximal endurance. A multi-
objective Genetic Algorithm followed by an iterative implementation of a single objective mixed-discrete PSO is used
for optimization (the framework however facilitates the use of other suitable non-linear optimization techniques). The
results show that among the best trade-off solutions, the fixed-wing configuration spans a wide range of endurances,
while the quadrotor configuration spans a much smaller range of endurances. This observation can be attributed to the
high-sensitivity of the latter to the discrete set of choices of off-the-shelf battery, motor, and propeller components;
the wing design is on the other hand highly flexible, owing to its continuous geometric variables, allowing greater
performance variation in best trade-off fixed-wing configurations. The design optimization yielded effectively two
best tradeoff solutions. Dedicated or zero-commonality fixed-wing and quadrotor configurations are also designed
(optimized) to serve as references with which the optimized reconfigurable designs are compared. While compro-
mising on endurance (w.r.t the optimal dedicated/zero-commonality designs – particularly the dedicated fixed-wing
UAV), the reconfigurable UAV designs provided a remarkable 40% mass savings, in addition to the other well-known
practical benefits of modular systems such as cost-savings, ease of maintenance, transportability, and design evolution.
Immediate future work would seek to include control and stability analysis, allowing the setting of pertinent stability
constraints. Exploration of the flexibility to design more than two configurations (producing a family of macro-scale
reconfigurable UAVs) in the future would further establish the exceptional potential of this new reconfigurable UAV
design framework.
References
[1] Gertler, J., “U.S. Unmanned Aerial Systems,” www.fas.org, 2012.
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[4] Snyder, M. P. and Weisshaar, T. A., “Simultaneous Configuration Optimization of Multistate Reconfigurable Aerostructures,”
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[5] Lagoudas, D. C., Strelec, J. K., Yen, J., and Khan, M. A., “Intelligent Design Optimization of a Shape Memory Alloy Actuated
Reconfigurable Wing,” Smart Structures and Materials 2000: Mathematics and Control in Smart Structures,
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[6] Beblo, R., Joo, J., Smyers, B., and Reich, G., “Design, modeling, and optimization of a thermally activated reconfigurable
wing system,” Journal of Intelligent Material Systems and Structures, Vol. 23, No. 17, 2012, p. 19872002,
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[7] Chowdhury, S., Maldonado, V., and Patel, R., “Conceptual Design of a Multi-Ability Reconfigurable Unmanned Aerial
Vehicle (UAV) through a Synergy of 3D CAD and Modular Platform Planning,” 15th AIAA/ISSMO Multidisciplinary Analysis
and Optimization Conference,
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[8] Locascio, D., Ramee, C., Schaus, E., Cooksey, K. D., Spero, E., and Mavris, D. N., “A Framework for Integrated Analysis,
Design, and Rapid Prototyping of Small Unmanned Airplanes,” , 2016,
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[9] Mangum, P., Fisher, Z., Cooksey, K. D., Mavris, D., Spero, E., and Gerdes, J. W., “An Automated Approach to the Design of
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[10] Anderson, J. D., Fundamentals of aerodynamics, McGraw-Hill, 2001.
[11] Leishman, J. G., Principles of helicopter aerodynamics, Cambridge University Press, 2006.
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Preservation,” Structural and Multidisciplinary Optimization, Vol. 47, No. 3, 2013, pp. 367–388.
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16. [13] Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T., “A Fast and Elitist Multi-objective Genetic Algorithm: NSGA-II,” IEEE
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17. Appendix A: Discrete Variable Design Choices
Table 4. Battery Choices, obtained from MaxAmps.com
Battery Capacity (Ah) Voltage (V) Mass (kg) Length (m) Width (m) Height (m)
1 1.3 14.8 0.13 0.064 0.035 0.029
2 1.8 14.8 0.165 0.067 0.034 0.035
3 2.25 11.1 0.17 0.1 0.035 0.024
4 2.8 11.1 0.188 0.108 0.037 0.022
5 3.25 11.1 0.249 0.138 0.045 0.018
6 4 11.1 0.294 0.137 0.045 0.022
7 5.45 11.1 0.354 0.137 0.045 0.027
8 6 14.8 0.57 0.162 0.045 0.036
Table 5. Propeller Choices, obtained from quadrocopter.com
Propeller Radius (m)
1 0.08255
2 0.1016
3 0.127
4 0.1778
5 0.2032
Table 6. Airfoil Choices, data was obtained from Airfoiltools.com.
Airfoil Selection Airfoil type
1 Eppler 422
2 Eppler 393
3 NACA 4412
Table 7. Motor, obtained from various hobby websites
Motor Weight (kg) Radius (m) Length (m) Cruise Power (W)
1 0.114 0.025 0.031 209
2 0.065 0.014 0.03 150
3 0.05 0.014 0.03 102.5
4 0.015 0.0105 0.016 24.5
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18. Appendix B: Object Diagrams
Figure 14. The strategy pattern. MassPropertiesAlgorithm is another interface. Three extensions are shown: CAD, Cylinder, and Rect-
angular Prism. The CAD module is defined to interface with Solidworks. The TaperedWing AeroPart uses this algorithm to determine its
mass properties. When get mass() is called in TaperedWing, the call is routed through the CAD Mass Properties algorithm.
Figure 15. Left: The structure of a configuration (i.e. an assembly). Note that Configuration inherits AeroPart, and thus a Configuration
can be stored in an AssmPart. Right: the specific structures used for the quadrotor and fixed-wing configurations in this paper. The
fixed-wing structure takes advantage of the ability to nest configurations.
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