SBlimp: Design, Model, and Translational Motion Control for a Swing-Blimp

Abstract

We present an aerial vehicle composed of a custom quadrotor with tilted rotors and a helium balloon, called SBlimp. We propose a novel control strategy that takes advantage of the natural stable attitude of the blimp to control translational motion. Different from cascade controllers in the literature that controls attitude to achieve desired translational motion, our approach directly controls the linear velocity regardless of the heading orientation of the vehicle. As a result, the vehicle swings during the translational motion. We provide a planar analysis of the dynamic model, demonstrating stability for our controller. Our design is evaluated in numerical simulations with different physical factors and validated with experiments using a real-world prototype, showing that the SBlimp is able to achieve stable translation regardless of its orientation.

Full text

SBlimp: Design, Model, and Translational Motion Control for a
Swing-Blimp
Jiawei Xu†, Diego S. D’Antonio†, Dominic J. Ammirato†, and David Saldaña†
Abstract— We present an aerial vehicle composed of a
custom quadrotor with tilted rotors and a helium balloon,
called SBlimp. We propose a novel control strategy that takes
advantage of the natural stable attitude of the blimp to control
translational motion. Different from cascade controllers in the
literature that controls attitude to achieve desired translational
motion, our approach directly controls the linear velocity
regardless of the heading orientation of the vehicle. As a
result, the vehicle swings during the translational motion. We
provide a planar analysis of the dynamic model, demonstrating
stability for our controller. Our design is evaluated in numerical
simulations with different physical factors and validated with
experiments using a real-world prototype, showing that the
SBlimp is able to achieve stable translation regardless of its
orientation.
I. INTRODUCTION
Unmanned Aerial Vehicles (UAVs) have become a great
interest for industry and academia. Some of the most popular
vehicles are multi-rotor vehicles, which use rotors to generate
thrust force to compensate for gravity and control its motion.
Multi-rotor vehicles provide unparalleled design flexibility
and aerial maneuverability. However, factors such as short
flight duration and low payload capacity constrain their real-
world applications.
To address the limitations of multi-rotor vehicles, we turn
to a well-established design in the world of aerial vehicles
and airships [1]. Non-rigid airships use large containers filled
with lighter-than-air (LTA) gas, providing a natural buoy-
ancy force that allows the vehicle to remain airborne with
minimal energy expenditure to compensate for gravity [2].
By integrating helium balloons and rotors using low-cost
components, miniature robotic blimps can be created [3].
Helium is a common gas in the universe, and when released
into the atmosphere, it has no adverse environmental impact.
Robotic blimps benefit from both the buoyancy provided
by the LTA gas and the motion capabilities of a UAV,
such as vertical takeoff and landing [4]. However, the large
size of the balloon results in a low drag-to-lift ratio, which
limits the agility of the vehicle. Researchers have developed
robotic blimps to complete tasks such as path following [5],
localization [6], air surveillance [7], turbulence detection [8],
and formation control [9]. Moreover, blimps offer a high level
of safety in cluttered environments, as the flexibility of the
The authors gratefully acknowledge the support from Office of Naval
Research Grant N00014-23-1-2535
The authors acknowledge Alex Witt at Lehigh University for his help
during the experiments.
†J. Xu, D. D’Antonio, D. Ammirato, and D. Saldaña are with
the Autonomous and Intelligent Robotics Laboratory (AIRLab), Lehigh
University, PA, USA: {jix519, diego.s.dantonio, dja223,
saldana}@lehigh.edu
Fig. 1: A flying SBlimp passing through a win-
dow. Narrated experiment videos can be found at
https://youtu.be/KN-64ZfBpFg.
balloon allows it to absorb collisions with obstacles without
incurring significant damage [10], [11].
Despite their wide range of applications, common blimp
designs are associated with several disadvantages that re-
quire reconsideration. First, most existing blimp designs
are underactuated and non-holonomic [12], [13]. Blimps
with fixed rotor directions for forwarding and levitation are
unable to translate backward without changing the heading
direction [14], [15], and those with differential models are
unable to translate sideways [16]. Second, to achieve better
actuation, the rotors typically reach out from the side of the
balloon, which weakens their safety advantage. Third, due
to the need for sufficient buoyancy, blimps tend to be large,
resulting in a high moment of inertia and vulnerability to
environmental disturbances such as wind flow [17]. Uneven
surface areas on the balloon lead to irregular swinging behav-
iors, deteriorating the quality of motion control [14]. These
factors present significant challenges to achieve effective
control of blimps. In light of these challenges, researchers
have turned to multi-rotor UAV designs for inspiration, which
have proven to offer higher motion control quality at the cost
of added complexity. For example, in [18], the blimp used
4 servo motors to change the thrusting direction of the 4
rotors, and in [19], the authors used 6 rotors to control the
motion of the blimp. Both designs achieve full actuation.
In this paper, we present a novel and minimalistic design
for a robotic blimp composed of a quadrotor with tilted pro-
pellers and an LTA balloon. We highlight that the quadrotor
can fly independently [20] and the balloon can be considered
as an extension module added to the quadrotor. We name the
design SBlimp. Notably, our SBlimp leverages its pendulum-
like natural stability to achieve stable motion control solely
through translational motion control despite the heading

Fig. 2: Components of a SBlimp.
direction or the swinging behavior typically observed in
traditional blimp designs. In general, our proposed design
presents an innovative solution to the challenges posed by
traditional blimp designs.
The main contribution of this paper is threefold. First,
we propose a novel robotic blimp design composed of a
quadrotor with tilted rotors rigidly attached to a balloon.
Second, we show the stability of the blimp controlled by
the linear velocity controller in 2-D. Third, we demonstrate
a new motion behavior through numerical simulations and an
actual prototype. Compared to quadrotors, our SBlimp can
remain airborne for more than ten times longer. Compared
to other LTA airships, our SBlimp can translate without
requiring attitude control.
II. DE SIGN
The design of the SBlimp is minimalistic, composed of
two main parts (see Fig. 2):
a) Quadrotor: The vehicle is propelled by the quadro-
tor Crazyflie 2.1, an open-source software and hardware
platform. We modify the Crazyflie 2.1 design with 3D
printed motor mounts that accommodate our tilted rotor
arrangement. The design is inspired by our previous vehicle,
called 𝑇-module [20].
b) Helium Balloon: The balloon is made of Mylar
and has the shape of an ellipsoid. The total volume of the
ellipsoid is 0.125 𝑚3and is filled with industry-grade helium
with a concentration of 99% helium.
The two parts are connected using a 3D-printed support
with Formlabs Durable material. The quadrotor is centered
below the intersection of the two major axes of the ellipsoid.
The low center of mass (COM) offers a natural stability [21]
that is discussed in Sec. IV. The distance between the center
of lift (COL) of the blimp and the COM of the quadrotor,
𝐿𝑏, is measured as 0.35 𝑚. With the 1-cell (3.7𝑉)750 𝑚𝐴ℎ
battery, the SBlimp weighs 60 grams (without helium). When
the balloon is filled with helium, the negative buoyancy of
the vehicle is 5𝑔.
III. MODEL
Our objective is to design a control strategy that enables
the SBlimp vehicle to move in any direction regardless of
its orientation. This paper focuses on analyzing the planar
configuration of the vehicle. We define the world reference
frame as a fixed frame, with 𝑧-axis pointing upward, denoted
Fig. 3: The model of the SBlimp in 2-D. {𝑊}and {𝐵}
represent the world reference and the SBlimp frame, respec-
tively. 𝐿𝑏is the distance between the COL (marked with a
solid dot) and the COM (marked with a dowel pin symbol).
The pitch 𝜃describes the tilting of the blimp.
by {𝑊}. The blimp has a body frame {𝐵}with the origin
at the COM. The 𝑥-axis points toward the front of the blimp
and the 𝑧-axis points upwards, as illustrated in Fig. 3.
The helium balloon provides a buoyancy force 𝑓𝑏>0
always pointing in the direction of 𝑧𝑊, and the quadrotor
is equipped with tilted propellers. In the planar case, the
quadrotor has two rotors, tilted at angles of 𝜂1and 𝜂2with
respect to the 𝑧-axis of {𝐵}, satisfying 𝜂1= −𝜂2. The
positions of the rotors in {𝐵}are 𝒑1=𝑎𝑥, 𝑎𝑧⊤and
𝒑2=−𝑎𝑥, 𝑎𝑧⊤. Letting 𝜂=𝜂2, we characterize the blimp
with a design factor −𝜋
2< 𝜂 < 𝜋
2. We put the rotors below the
COM of the blimp so that 𝑎𝑧<0. The COL of the balloon
lies on the positive 𝑧-axis of {𝐵}, of which the distance to the
COM of the blimp is 𝐿𝑏. The position of the vehicle in {𝑊}
is denoted by 𝒓=[𝑥, 𝑧]⊤∈ℝ2. Vectors 𝒗=
𝒓and 
𝒗=
𝒓
denote linear velocity and acceleration, respectively. The
orientation of the blimp, 𝑊
𝑹
𝐵, is described by the rotation
from {𝑊}to {𝐵}. Denoting the tilting angle by the pitch
𝜃, we have 𝑊
𝑹
𝐵=Rot(𝜃)where the 2-D rotation matrix
operator Rot(𝛼) = cos 𝛼− sin 𝛼
sin 𝛼cos 𝛼. Due to the symmetric
orthogonal dynamics of the blimp in the 𝑥𝑧- and 𝑦𝑧-plane,
the analysis based on the planar model can be extrapolated
to the 3-D case.
The planar SBlimp uses two rotors to generate thrust.
We denote the thrust force by 𝑓𝑖, for 𝑖∈ {1,2}. Then
the thrust vectors in {𝐵}are 𝒇𝑖= [−𝑓𝑖sin 𝜂𝑖, 𝑓𝑖cos 𝜂𝑖]⊤.
The positions of the rotors 𝒑𝑖are the arms of the thrust
forces from the COM of the blimp. Therefore, each rotor
also applies a torque 𝜏𝑖=𝒑𝑖×𝒇𝑖on the blimp in pitch.
Thus, the total force 𝒇and torque 𝜏in {𝐵}generated by the
rotors 𝒇=𝒇1+𝒇2,and 𝜏=𝜏1+𝜏2.
Denoting 𝒖=𝑓1, 𝑓2⊤as the input vector, we can express
the force and torque applied by the rotors on the blimp in
the matrix form, 𝒇=𝑨𝒇𝒖,and 𝜏=𝑨𝜏𝒖where
𝑨𝒇=sin 𝜂− sin 𝜂
cos 𝜂cos 𝜂,and
𝑨𝜏=𝑎𝑧sin 𝜂−𝑎𝑥cos 𝜂 𝑎𝑥cos 𝜂−𝑎𝑧sin 𝜂(1)
are matrices that map the input forces into the total force
and torque in {𝐵}.

+
-
Fig. 4: The flow diagram of the SBlimp controller, where
the feedback linearization involves only the velocity.
Due to the large volume of the balloon, the blimp experi-
ences significant air drag on its surface. According to [22],
the air drag depends on the Reynold number. Under low
speed, the low Reynold number results in an air drag approxi-
mately proportional to the velocity [23]. Therefore, we incor-
porate the air drag by modeling the dissipative force as first-
order damping terms for translation 𝑫=diag 𝑑𝑥, 𝑑𝑧⊤
and rotation 𝑑𝜏>0, where 𝑑𝑥, 𝑑𝑧>0are the air drag
coefficients. The LTA helium balloon generates a buoyancy
force 𝑓𝑏at a distance 𝐿𝑏from the COM, generating a torque,
𝜏𝑏=0, 𝐿𝑏⊤×𝐵
𝑹𝑊0, 𝑓𝑏⊤= −𝑓𝑏𝐿𝑏sin 𝜃, (2)
where 𝐵
𝑹𝑊=𝑊
𝑹
⊤
𝐵. For any 𝜃≠0, the torque 𝜏𝑏≠0.
We describe the dynamics of the blimp using Newton-
Euler equations,
𝑚
𝒗= −𝑫𝒗 + (𝑓𝑏−𝑚𝑔)
𝒛+𝑊
𝑹
𝐵𝑨𝒇𝒖,(3)
𝐽𝜃
𝜃= −𝑑𝜏
𝜃+𝜏𝑏+𝑨𝜏𝒖,(4)
where the 𝑚is the mass of the blimp, 𝐽𝜃is the moment
of inertia, 𝑔is the gravitational acceleration, and 𝑓𝑏is
the buoyancy force provided by the balloon. Based on our
SBlimp model, the vehicle naturally tries to stay horizontal.
We focus on controlling its translational velocity, i.e., given
a desired velocity 𝒗𝑑, we find an input 𝒖that drives the
SBlimp to a velocity of 𝒗𝑑without controlling its attitude.
IV. CONTROL DESIGN
We design a velocity controller for the SBlimp using its
inherent rotational stability. An overview of our controller
is illustrated in Fig. 4. The objective of our controller is to
drive the blimp to a desired velocity, 
𝒓𝑑.
When the blimp is not actuated, i.e.,𝒖=𝟎, the system
in (4) is reduced to 𝐽𝜃
𝜃= −𝑑𝜏
𝜃+𝜏𝑏. Substituting the buoy-
ancy torque 𝜏𝑏from (2), the differential equation describes a
behavior that is similar to a damped pendulum model [24],
which is stable for any initial 𝜃.
A. Feedback Linearization
We use the quadrotor to control the translational motion
of the blimp. With tilted rotors, i.e.,0< 𝜂 < 𝜋
2,𝐵
𝑹𝑖≠𝑰, the
allocation matrix 𝑨𝒇is full-rank and invertible, allowing the
vehicle to generate forces in any direction within the rotor
constraints. We will use this property to achieve the control
objective. Since the rotation matrix 𝑊
𝑹
𝐵is observable and
invertible, we apply feedback linearization on 3. Ignoring the
damping force, we can choose the input
𝒖=𝑚𝑨𝒇
−1 𝐵
𝑹𝑊𝑔−𝑓𝑏
𝑚
𝒛+𝒘,(5)
where 𝐵
𝑹𝑊=𝑊
𝑹−1
𝐵=𝑊
𝑹⊤
𝐵, and 𝒘=
𝒗is the additional
input, which shows that the system is linearized via static
feedback. We apply a proportional control on the velocity,
𝒘=𝑲𝒗𝒗𝑑−𝒗,(6)
where 𝑲𝒗=Diag 𝑘𝑥, 𝑘 𝑧 ⊤is the positive-definite gain
matrix.
B. Stability analysis
We first show the stability in velocity tracking of the blimp
with our controller. Inserting (5) and (6) into (3), we obtain
the closed-loop velocity dynamics,
𝑚
𝒗=𝑲𝒗𝒗𝑑−𝒗−𝑫𝒗.(7)
which takes the form of a first-order linear differential equa-
tion. Solving the equation using the integrating factor method
for 𝒗gives the linear velocity response of the controlled
SBlimp,
𝒗=
𝑘𝑥
𝑘𝑥 +𝑑𝑥
0
0𝑘𝑧
𝑘𝑧 +𝑑𝑧
𝒗𝑑+𝑒−𝑘𝑥 +𝑑𝑥
𝑚𝑡0
0𝑒−𝑘𝑧 +𝑑𝑧
𝑚𝑡𝒗0,(8)
where 𝒗0is the initial velocity of the blimp, and 𝑡is the time.
With sufficiently large gains 𝑘𝑥 ≫ 𝑑𝑥, 𝑘 𝑧 ≫ 𝑑𝑧the velocity
in 𝑥𝑧-plane exponentially converges to the desired value as
𝑡→∞up to an arbitrary precision depending on the gains,
showing the exponential stability of the closed-loop velocity
dynamics of the SBlimp.
Even though the linear and angular accelerations are
coupled, we can show that the system is stable around 𝜃= 0.
Proposition 1 (The pitch angle is asymptotically stable
around 𝜃= 0).If the additional input 𝒘=𝑲𝒗𝒗𝒅−𝒗
only takes feedback on velocity, the pitch 𝜃in (4) can still
converge to 0asymptotically.
Proof. Inserting (5) and (6) into (4), we obtain the closed-
loop angular dynamics,
𝐽𝜃
𝜃= −𝑑𝜏
𝜃+𝜏𝑏+𝑨𝜏𝑨𝒇
−1 𝐵
𝑹𝑊𝑚𝑔 −𝑓𝑏
𝒛+𝑚𝒘.(9)
Notably, the allocation matrices 𝑨𝜏and 𝑨𝒇are not linearly
independent for a SBlimp. The coupling relationship is de-
scribed as 𝑨𝜏=[𝑐0]𝑨𝒇, where the coefficient 𝑐=𝑎𝑧−𝑎𝑥
tan 𝜂
depends on 𝜂,𝑎𝑥, and 𝑎𝑧. Therefore, (9) is simplified to
𝐽𝜃
𝜃=𝑐cos 𝜃
sin 𝜃⊤𝑚𝑔 −𝑓𝑏
𝒛+𝑚𝒘− (𝑑𝜏
𝜃+𝑓𝑏𝐿𝑏sin 𝜃).
(10)
We linearize the angular dynamics around 𝜃= 0 by taking
the Taylor expansion of cos 𝜃and sin 𝜃. As 𝜃→0,cos 𝜃=
∞
𝑛(−1)𝑛𝜃2𝑛
(2𝑛)!
→1, and sin 𝜃=∞
𝑛(−1)𝑛𝜃2𝑛+1
(2𝑛+1)!
→𝜃,
considering 𝑛= 0 and discarding all higher order terms.
Therefore, (10) becomes
𝐽𝜃
𝜃=𝑐1𝜃𝑲𝒗𝒗𝒅−𝒗− (𝑑𝜏
𝜃+𝑓𝑏𝐿𝑏𝜃),(11)
which depends on the velocity tracking error of the blimp.
By replacing 𝒗with the general solution of the closed-loop

velocity response (8), we obtain the second-order differential
equation of 𝜃. The general solution to the non-homogeneous
differential equation is in the form of the multiplication
of Bessel functions [25] and negative-exponent exponential
functions of 𝑡. The Bessel function highlights the vibration
behavior of 𝜃near 𝜃= 0, which results in the swinging of our
SBlimp. The exponential components describe the dissipated
kinetic energy as 𝑡→∞regardless of the initial value of 𝜃,
which shows the asymptotic stability of the pitch 𝜃around
its natural equilibrium 𝜃= 0.
Numerical approximations of the non-linearized angular
dynamics as described in (10) also show the convergence of
𝜃to 0as 𝑡→∞, which further demonstrates the damped
pendulum-like stability of the pitch angle.
V. EVALUATION
To evaluate the performance and limits of our design and
control, we conduct experiments in simulations and with
physical robots1. We build a prototype SBlimp as described
in Section II and test its ability to follow increasingly
complex trajectories, validating the effectiveness of the con-
troller and demonstrating the blimp’s significantly elongated
hovering time. In simulation, we focus on metrics of velocity
error and pitch swinging angle, while in experiments, we use
position error as our primary evaluation metric.
A. Simulation
We implement a 2-D numerical simulator using Python.
We leverage the convenience of manipulating various phys-
ical factors that influence the performance of the blimp,
which would otherwise be time-consuming to investigate on
a physical prototype, including the distance between the COL
and COM 𝐿𝑏, the mass 𝑚, and the target speed. In each set
of tests, the blimp follows a circular path of 1-meter radius
for 100 seconds while recording velocity and angular errors.
The maximum and minimum rotor power of each of the two
rotors are set at 0.15 𝑁and 0respectively. We refer to a
rotor as “saturated” when the required force output from the
controller goes beyond these limits.
1) Distance 𝐿𝑏:We evaluate the effect of 𝐿𝑏in the
performance, the distance between the COM and the COL
of the blimp. During the early prototyping stage, the test
flights indicated that 𝐿𝑏affects i) whether the rotors can
obtain enough airflow to generate the target thrust; and ii)
the frequency and amplitude of the pendulum behavior of the
SBlimp. Although the simulator is not capable of simulating
the aerodynamics of the system, we consider the pendulum
behavior a key factor to the stability of the SBlimp. We
increase the length 𝐿𝑏from 0.01 𝑚to 1.0𝑚subsequently and
keep all other factors identical throughout the tests, including
the target circular trajectory at a speed of 0.1𝑚∕𝑠. The mass
of the blimp is 𝑚= 0.06 𝑘𝑔, and the buoyancy provided
by the balloon is 𝑓𝑏= 0.55 𝑁. Our simulations reveal that
larger values of 𝐿𝑏result in lower maximum and average
angular errors, while the maximum velocity error remains
1The source code of our simulation and experiments can be found at
https://github.com/swarmslab/OpenBlimp
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
0.0
2.5
5.0
7.5
Angular Errors (degrees)
avg angular error
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Speed (m/s)
0
20
40
60
Velocity Errors (m/s)
avg velocity error
Fig. 5: The average tracking errors of the SBlimp as the
target speed increases with their maximum and minimum
range. The maximum and average errors increase linearly as
the target speed increases until the rotor saturation at the
target speed of 0.6𝑚∕𝑠.
below 0.01 𝑚∕𝑠. However, beyond 𝐿𝑏= 0.3𝑚, the angular
error reduction becomes marginal, as the maximum angular
error is below 0.02◦. The result suggests that we are able
to reduce the swinging behavior by increasing the length of
the support. However, such design benefits may be offset
by practical concerns such as reduced support rigidity and
increased weight and inertia. We, therefore, conclude that
𝐿𝑏= 0.3𝑚is an appropriate choice for balancing between
performance and practical considerations in the following
simulations.
2) Mass: We test how the increased mass of the quadrotor
𝑚can affect the performance as if the SBlimp is carrying
heavier equipment and batteries. We increase 𝑚from 0.05 𝑘𝑔
to 0.1𝑘𝑔 subsequently and keep other factors constant,
i.e.,𝐿𝑏= 0.3𝑚,𝑓𝑏= 0.55 𝑁, and the target speed of
0.1𝑚∕𝑠. The simulations show that when the rotors are not
saturated, the angular and velocity errors remain close to 0
as 𝑚increases. An increased mass only results in increased
rotor force. When the gravity of the blimp is less than
the buoyancy or the maximum thrust combined with the
buoyancy cannot compensate for the gravity, the blimp loses
control over its height.
3) Speed: We evaluate the effect of varying speeds on
the performance. Because of its low lift-to-drag ratio, the
blimp experiences an increasing difficulty following higher
velocity commands. Therefore, we would like to know the
theoretical limits of the speed for the blimp to maintain a
high tracking quality. We test target speeds from 0.01 𝑚∕𝑠
to 2.0𝑚∕𝑠with an increment of 0.01 𝑚∕𝑠. As expected, the
results of this simulation show that the maximum and average
error increases almost linearly against the target speed until
the rotor saturation, where the target speed is 0.6𝑚∕𝑠. As
shown in Fig. 5, when the target speed reaches 0.6𝑚∕𝑠, the
swinging in pitch worsens dramatically. As the target speed
exceeds 0.8𝑚∕𝑠, the controller loses stability in velocity
tracking.

0.08 0.1 0.16 0.31
Speed(m/s)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Position error
Fig. 6: The position error magnitudes of the SBlimp follow-
ing the circular trajectory at different speeds. The Average
and maximum errors increase as the speed increases.
B. Experiments with a prototype
We build a prototype of the SBlimp with 𝐿𝑏= 0.35 𝑚,
𝑚= 0.06 𝑘𝑔, and 𝑓𝑏= 0.55 𝑁. The localization of the
vehicle is realized using a motion capture system (Optitrack)
operating at 120 Hz. The angular velocity and linear accel-
eration are measured directly from Crazyflie 2.1’s integrated
IMU sensor. These two data sources are merged through
Crazyflie’s onboard Extended Kalman filter [26]. We use
the crazyswarm framework [27] to communicate the desired
linear velocity and yaw angle to the robot via the crazyradio
communication protocol [28]. During the experiments, we
send desired positions and velocities along a trajectory to
the Crazyflie. With the prototype, we evaluate the errors in
position when following trajectories of different target speeds
and complexities.
1) Experiment - Hovering: We evaluate the blimp’s ability
to hover at a fixed position. The average magnitude of the
position error during hovering was 0.01 𝑚. Our experiments
showed that the robot can hover for 1 hour and 15
minutes, which is more than ten times longer than the
airborne duration achieved by the quadrotor alone.
2) Experiment - Tracking a circular trajectory: To
demonstrate the independence of blimp translation on its
heading direction, we conduct experiments in which the
SBlimp follows a circular trajectory in the 𝑥𝑦-plane without
rotation. The trajectory is a circle with a radius of 1𝑚
and a fixed yaw of 0degrees, described by linear velocities
𝑥 = − sin 2𝜋
𝑣𝑡and 𝑦 = cos 2𝜋
𝑣𝑡, where 𝑣is the constant
target speed and 𝑡is the time from the beginning of the
experiment. We change 𝑣between experiments to evaluate
the speed limit of our system. The results are shown in
Fig. 6. Since the actuation in the 𝑥- and 𝑦- coordinates are
coupled with the pitch and roll, the vehicle exhibits swinging
behaviors. We observe that a higher target speed result in
larger position errors. At 𝑣= 0.1𝑚∕𝑠, the average error is
0.05 𝑚, which is higher than hovering. At 𝑣= 0.31 𝑚∕𝑠,
the average error is around 0.1𝑚. The increased error
indicates that the rotors experience saturation when trying
to achieve the required speed during swinging. Overall, our
experiment successfully demonstrates that the SBlimp can
control translational motion despite the swinging behavior.
3) Experiment - Tracking a helix trajectory: This exper-
iment demonstrates motion in all three axes following the
shape of a helix with a radius of 1𝑚, starting from a height
x(m)
1.0 0.5 0.0 0.5 1.0
y(m)
1.0
0.5
0.0
0.5
1.0
z(m)
0.3
0.4
0.5
0.6
0.7
0.8
x
xd
(a) 3D desired helix trajectory denoted as 𝑥𝑑and
the blimp’s real path denoted as 𝑥.
2.5
0.0
x(m)
x xd
0.0
2.5
y(m)
02468
Time(min)
0.5
1.0
z(m)
(b) Helix trajectory in 𝑥-, 𝑦-, and 𝑧- axes vs time.
Fig. 7: The helix trajectory, and the blimp’s position readings
against the reference. The magnitude of the translational error
remains less than 0.25 𝑚and achieves an average of 0.04 𝑚.
of 0.35 𝑚and ending at 1.0𝑚. The ascending speed in 𝑧-
axis remains constant at 0.002 𝑚∕𝑠and the speed in the 𝑥𝑦-
plane increases from 0.06 𝑚∕𝑠to 0.35 𝑚∕𝑠. The trajectory
is described by linear velocities 𝑥 = − sin 2𝜋
𝑣(𝑡)𝑡,𝑦 = cos 2𝜋
𝑣(𝑡)𝑡,
and 𝑧 = 0.002 where 𝑣(𝑡) = 0.06+0.000537𝑡is the increasing
target speed. The results of this experiment are shown in
Fig. 7, with two plots showing the blimp’s position relative
to the desired. The blimp manages to keep the magnitude
of its position error at an average of 0.04 𝑚. As the target
speed increases, the error remains under 0.25 𝑚before losing
stability in the trajectory tracking. In the orange region of
Fig.7b, as the target speed in the 𝑥𝑦-plane exceeds 0.35 𝑚∕𝑠,
the rotors of the blimp saturates while trying to drive the
blimp to follow the desired speed. The combined disturbance
caused by the air drag and the input mismaatch between the
model and the reality causes the blimp to lose stability.
4) Experiment - Colliding with obstacles: We demon-
strate the collision-tolerant capabilities of the SBlimp plat-
form. Although the collision recovery is not a focus of this
work, the excessive dimensions of the balloon offers the
blimp with resilience to collision as the it prevents a direct
contact between the actuators and the external object. We
direct the blimp towards a window where its path intersected
with the frame. The experimental results are presented in
Fig. 8, which shows that in the orange region of the plot, the
SBlimp collided with the window at a speed of 0.25 𝑚∕𝑠and
recovered its trajectory within 30 𝑠. Despite the collision, the
SBlimp could recover and continue its intended trajectory.

2.5
0.0
x(m)
x xd
0
1
y(m)
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Time(min)
0.50
0.75
1.00
z(m)
Fig. 8: The blimp’s position readings against the reference
while following a path and colliding with an obstacle.
VI. CONCLUSION AND FUTURE WORK
In this paper, we proposed the design of the SBlimp and
presented the planar dynamic model of the blimp. Utilizing
the natural pendulum-like stability, we developed a transla-
tional motion controller for the miniature robotic blimp and
proved its stability in 2-D. The controller allows it to translate
regardless of its orientation. We implemented a numerical
simulator for the SBlimp in 2-D and constructed a prototype
in real-world based on a Crazyflie 2.1 quadrotor. Through
simulation, we evaluated factors that affect the performance
of the blimp. Finally, we demonstrated the effectiveness
of our design and the controller in experiments using a
real-world prototype, where the blimp follows a series of
trajectories of different complexities. The blimp’s design and
control demonstrated a low tracking error and an extended
flight time, making it a promising platform for long-term
traversal tasks. In future work, we would like to experiment
with different shapes of blimps and conduct a deeper study
on the effect of the air drag on the blimp’s surface to improve
its performance at higher speeds.
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