PreprintPDF Available

A Fast and Efficient Attitude Control Algorithm of a Tilt-Rotor Aerial Platform Using Inputs Redundancies

Authors:
  • Beijing Institute for General Artificial Intelligence

Abstract and Figures

Overactuated multirotor unmanned aerial vehicles (UAVs) usually consist of multiple tiltable thrust actuators. The controllers are mostly designed by regarding the thrust forces and actuator tilting angles as inputs of outer-loop position and attitude controllers, while formulating an inner-loop controller for each actuator to track the thrust and angle as required by the outer-loop. This hierarchical control strategy separates the complicated combined dynamics into two relatively simple systems, and thus simplifies the control design. However, the interaction between the two systems is neglected and therefore the control performance will be degraded when the inner-loop dynamics are not sufficiently fast. This paper investigates the capability of a new overactuated multirotor UAV configuration, where regular quadcopters are passively hinged onto the frame as tiltable thrust actuators. Apart from the thrust force and tilting angle, each actuator has additional auxiliary torque inputs, which exhibit fast responses as they are not subject to the inner-loop actuator tilting angle dynamics. In this paper, an add-on attitude compensation control is designed exploiting the auxiliary inputs to reduce the tracking and disturbance-rejection errors from the nominal control loop. The effectiveness is demonstrated in simulation and verified by experiment.
Content may be subject to copyright.
IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED DECEMBER, 2021 1
A Fast and Efficient Attitude Control Algorithm of
a Tilt-Rotor Aerial Platform Using Inputs
Redundancies
Yao Su:, Lecheng Ruan:, Pengkang Yu:, Chen-Huan Pi, Matthew J. Gerber, and Tsu-Chin Tsao
Abstract—Overactuated multirotor unmanned aerial vehicles
(UAVs) usually consist of multiple tiltable thrust actuators. The
controllers are mostly designed by regarding the thrust forces
and actuator tilting angles as inputs of outer-loop position and
attitude controllers, while formulating an inner-loop controller
for each actuator to track the thrust and angle as required
by the outer-loop. This hierarchical control strategy separates
the complicated combined dynamics into two relatively simple
systems, and thus simplifies the control design. However, the
interaction between the two systems is neglected and therefore
the control performance will be degraded when the inner-loop
dynamics are not sufficiently fast. This paper investigates the
capability of a new overactuated multirotor UAV configuration,
where regular quadcopters are passively hinged onto the frame as
tiltable thrust actuators. Apart from the thrust force and tilting
angle, each actuator has additional auxiliary torque inputs, which
exhibit fast responses as they are not subject to the inner-loop
actuator tilting angle dynamics. In this paper, an add-on attitude
compensation control is designed exploiting the auxiliary inputs
to reduce the tracking and disturbance-rejection errors from
the nominal control loop. The effectiveness is demonstrated in
simulation and verified by experiment.
Index Terms—Overactuated multirotor, attitude control, model
mismatch, add-on compensation, input redundancy, disturbance
rejection
I. INTRODUCTION
OVERACTUATED multirotor unmanned aerial vehicles
(UAVs) are suitable for exploration and interaction ap-
plications that are challenging for traditional multirotors (e.g.
quadcopters, hexacopters), because of their advantages in
decoupling the position and attitude control compared with
collinear multirotor UAVs [1]. Different configurations of
overactuated UAV have been proposed in recent years, such as
tilt-rotor platforms [2–4], fixed tilting angle platforms [5, 6],
modular platforms [7, 8], and passive joints platforms [9–11].
To generate the thrusts and torques in arbitrary directions,
the mechanical complexity of these platforms is increased,
making it challenging to accurately model their dynamics
for controller design. The standard approach for controller
:Equal contribution.
Manuscript received: September 9, 2021; Accepted: December 7, 2021.
This paper was recommended for publication by Editor Pauline Pounds upon
evaluation of the Associate Editor and Reviewers’ comments.
Y. Su, L. Ruan, P. Yu, M.J. Gerber, and T. Tsao are with Mechanical and
Aerospace Engineering Department, University of California, Los Angeles.
e-mails: {yaosu, ruanlecheng, paulyu1994, gerber211, ttsao}@ucla.edu.
C. Pi is with the Mechanical Engineering Department, National Yang Ming
Chiao Tung University, HsinChu, and were visiting UCLA during this work.
e-mail: john40532.me00@g2.nctu.edu.tw.
Digital Object Identifier (DOI): see top of this page.
design for overactuated UAV is based on model simplification,
where the dynamics of the whole platform are separated into
two parts: the main body which is subjected to the thrust
force vectors generated by individual actuators, and low-level
actuator dynamics. The dynamics separation lends itself to the
hierarchical control structure [2]. In the outer-loop, desired
inputs of the main body from position and attitude controller
are represented by virtual force and torque commands (e.g.
6 Degree-of-freedom (DoF) wrench) based on feedback lin-
earization of the nonlinear rigid body dynamics. Then the
desired force and angle of every actuator are calculated by
an allocation mapper that accounts for redundant actuations
to meet the desired wrench [3, 12–15]. The desired force and
angle for every actuator are tracked in the inner loop by
the low-level actuator control loops. However, because the
inner-loop dynamics are neglected in the outer-loop control
design, the hierarchical controller introduces model mismatch
into the system, which will cause additional disturbances. This
uncertainty can only be compensated by adding integrators in
the outer-loop trajectory-tracking controller, which reduces the
transient performance and stability of the system and are not
able to react to fast-changing modeling errors [16].
To solve the model mismatch problem and improve the
disturbance rejection capabilities, several approaches have
been proposed. An analytical method was introduced in [17]
to compare the disturbance-rejection capability of different
overactuated UAV platforms. From this perspective, a novel
design was presented in [18] which demonstrated improved
disturbance-rejection capabilities with optimal design parame-
ters. A learning-based method was implemented in [16, 19]
to compensate for the unmodeled dynamics, and an active
disturbance rejection controller (ADRC) approach was used
in [20, 21]. However, all of these works can only compensate
for the unmodeled dynamics at the virtual wrench level, which
is generated by the inner-loop control system (normally a
second-order PID loop) and the response speed is generally
slow.
Overactuated UAVs based on regular quadcopters and pas-
sive joints have been proposed in [10,22] for their mechanical
simplicity and inherent circumvention of disturbance torques
from propeller drag and tilting reaction torques. Compared
with other overactuated aerial platforms [2–6], this platform
has eight independent auxiliary torque inputs, which can be
set as zero for simplicity [23], or they can be utilized to
improve control performance [24]. Furthermore, these torques
are generated by the differences of the rotor speeds and as such
2 IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED DECEMBER, 2021
have faster response than the torques that would normally be
created via the inner-loop control of the actuator tilting angles
and rotor speeds.
Exploiting the unique feature of this aerial platform, this
paper extends the min-max allocation method in [23] and
introduces the fast auxiliary torque inputs to compensate for
disturbances and unmodeled dynamics. A Quadratic Program-
ming (QP) problem is formulated to find the optimal auxiliary
torque inputs at each time step. Three cases will be presented
to demonstrate the effectiveness of this add-on compensation
loop in disturbance-rejection and trajectory tracking.
The remainder of this paper is organized as follows. Sec-
tion II reviews the dynamics of the platform proposed in [10].
Section III describes the nominal controller. Section IV shows
the add-on compensation loop formulated by the auxiliary
torque inputs. The simulation and experiment setup are shown
in Section V. Both simulation and experiment results are
presented in Section VI. The conclusion is addressed in
Section VII.
II. PL ATFO RM
A. Configuration
The controller designed in this paper is based on the
platform proposed in [10, 22], where four regular quadcopters
are mounted on the UAV central frame via passive hinges (see
Fig. 1). Three coordinate systems are defined in this platform:
the world frame under North-East-Down (NED) convention
FW:tO;x
x
x, y
y
y, z
z
zu, the body frame attached to the platform
geometric center FB:tOB;x
x
xB, y
y
yB, z
z
zBu, and the quadcopter
frames on each quadcopter ias FQi:tOQi;x
x
xQi, y
y
yQi, z
z
zQiu.
The position of the central frame center is defined as ξ
ξ
ξ
rx, y, zsT,the attitude in the roll-pitch-yaw convention as
η
η
η“ rφ, θ, ψsTand the platform angular velocity in FBas
ν
ν
ν“ rp, q, rsT.
B. Actuator
In this platform, each quadcopter on the passive hinge is
regarded as a tiltable thrust actuator. For each quadcopter, the
four spinning propellers collectively generate four independent
inputs
»
Ti
Mx
i
My
i
Mz
i
»
1 1 1 1
´b´b b b
b´b´b b
cτ´cτcτ´cτ
»
ti0
ti1
ti2
ti3
,(1)
where Tiis the total thrust force provided by the quadcopter
along z
z
zQi,Mx
i,My
iand Mz
irefer to the external torques
in FQi,tij is the thrust force generated by propeller jin
quadcopter i, and it is defined by
tij KTω2
ij ,(2)
where KTis the propeller thrust constant and ωij is the
spinning speed of propeller jin quadcopter i.ba
?2,
cτKτ
KT,ais the scalar distance of each propeller to the
quadcopter center, and Kτis the propeller drag constant.
Fig. 1: The prototype and coordination systems of the overac-
tuated UAV platform. Four commercial quadcopters are passively
hinged on the central frame with equal distance to the center of the
main frame as tiltable actuators.
Furthermore, the actuator tilting angle αican be determined
through the dynamics
:
αi1
Iy
i
My
i´spπ
2iq9p´cpπ
2iq9q, (3)
where Iy
iis the inertia in y
y
yQidirection and sr¨s and cr¨s denote
sinr¨s and cosr¨s, respectively.
In addition, Mx
iand Mz
ifor each quadcopter can be directly
exerted on the platform central frame. Mz
iis generated by
propeller drag torques and usually set as zero because the
magnitude is small. Mx
iis an independent auxiliary input
of the actuator, and can be controlled directly because the
dynamics of each motor are usually sufficiently fast and
regarded as feedthrough dynamics.
C. Platform Dynamics
The platform is fully-actuated with inputs Ti,αiand Mx
i.
The translational movements can be described as
:
ξ
ξ
ξ1
m
W
BR
R
RTJ
J
JξT
T
T`G
G
G, (4)
where mrefers to the total mass of the platform, G
G
Gis the
gravitational acceleration in FW,W
BR
R
Ris the rotation matrix
from FBto FWand
J
J
Jξ»
00´20
0´103
0123
,
T
T
TT0T1T2T3T.
(5)
SU et al.: A FAST AND EFFICIENT ATTITUDE CONTROL ALGORITHM OF A TILT-ROTOR AERIAL PLATFORM USING INPUTS REDUNDANCIES 3
Fig. 2: Hierarchical control structure for the overactuated UAV platform. High-level position and attitude tracking controller outputs u
u
ud
to the allocation. This whole-body input is then allocated as the desired thrusts T
T
Tdand tilting angles α
α
αdfor each quadcopter. Each quadcopter
will regulate its tilting angle and thrust with onboard low-level controllers. Add-on attitude compensators are utilized to compensate for
modeling errors with auxiliary inputs and thus improve attitude control performance.
The rotational dynamics are
9
ν
ν
νI
I
I´1ν
ν
νˆ p
Iν
Iνq ` τ
τ
τq,(6)
where I
I
Iis the inertial matrix, and τ
τ
τPR3is the total external
torque exerted on the platform as
τ
τ
ττ
τ
τT`τ
τ
τM.(7)
Here τ
τ
τTis generated by actuator thrust forces
τ
τ
τTJ
J
JνT
T
T , (8)
where
J
J
Jνl»
´0020
010´3
0123
,(9)
and lrefers to the identical distance from FWto FQi.
τ
τ
τMis a result of the actuator auxiliary inputs Mx
ias
τ
τ
τMJ
J
JMM
M
Mx,(10)
with
J
J
JM»
´0020
010´3
0123
,(11)
M
M
MxMx
0Mx
1Mx
2Mx
3T.(12)
III. NOMINAL CONT ROLLER
A. Hierarchical Architecture
The controller of multirotor aerial platforms with tiltable
thrust actuators usually follows a hierarchical architecture, as
shown in the unshaded region of Fig. 2. This controller design
we refer to in this paper as the ”nominal controller”. The
controller uses four thrust forces and four tilting angles as
system inputs, by setting
M
M
Mx0
0
0,(13)
and rewriting the dynamics as
:
ξ
ξ
ξ
9
ν
ν
ν1
m
W
BR
R
R0
0
0
0
0
0I
I
I´1J
J
Jξ
J
J
JνT
T
T`G
G
G
0
0
0.(14)
Define two virtual inputs u
u
uξand u
u
uνfor position and attitude,
respectively. The outer-loop dynamics for six DoF can be
expressed as
:
ξ
ξ
ξ
9
ν
ν
νu
u
uξ
u
u
uν,(15)
with the feedback linearized inputs
u
u
udJ
J
Jξ
J
J
JνT
T
TF
F
Fd
τ
τ
τdmW
BR
R
RT0
0
0
0
0
0I
I
Ipu
u
uξ
u
u
uν´G
G
G
0
0
0q.(16)
The outer-loop Eq. (15) can be closed by any stabilizing
controllers. Here, we apply a LQR controller, similar to [23]
to take into consideration communication delay and improve
system robustness.
B. Quadcopter Control
After the required total force and torques are determined by
Eq. (16), they are allocated to real system inputs Tiand αi.
Define
F
F
FFs0Fc0. . . Fs3Fc3T,(17)
where
Fsi iTi, Fci iTi.(18)
Then
u
u
udJ
J
Jξ
J
J
JνT
T
TW
W
WF
F
F , (19)
4 IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED DECEMBER, 2021
where W
W
WPR6ˆ8is a constant allocation matrix with full
row rank. Therefore, the original inputs can be resumed with
a least-square solution [3]
F
F
FW
W
W:J
J
Jξ
J
J
JνT
T
T , (20)
and
TibF2
si `F2
ci,
αiatan2pFsi, Fci q.
(21)
For each quadcopter i, the thrust force Tican be directly
controlled, but the tilting angle αimust be controlled by
My
iunder second-order dynamics Eq. (3). A double-loop PID
controller is applied for tilt-angle tracking, as stated in [10].
The propeller thrusts can be reversely calculated as
»
ti0
ti1
ti2
ti3
»
1 1 1 1
´b´b b b
b´b´b b
cτ´cτcτ´cτ
´1»
Ti
Mx
i
My
i
Mz
i
.(22)
These thrusts are converted to PWM signals to drive the
motors.
IV. ADD -ON ATTITUDE COM PE NS ATOR W IT H AUXILIARY
INP UT S
A. Attitude Model Mismatch
As analyzed in [16, 19], there are modeling errors and un-
known disturbance in reality which will influence the control
performance. On this platform, modeling error has three main
components: (1) There is a distance between the quadcopter
center of mass (CoM) and the tilting axis. When the quad-
copter is tilted at a non-zero angle, the inertia matrix of the
entire platform changes as well. (2) The four quadcopters are
not perfectly installed at the same height (quadcopters 1and 3
are above quadcopters 0and 2with 5mm vertical distance).
(3) The low-level dynamics of regulating the tilting angle
with double loop PID control are neglected in the outer-loop
controller.
With model mismatch considered, the attitude dynamics
becomes
τ
τ
τreal τ
τ
τd`eτ
τ
τ,(23)
where τ
τ
τreal is the real achieved tilting torque, the estimation
of τ
τ
τreal is ˆ
τ
τ
τ, which can be acquired by
ˆ
τ
τ
τI
I
I
ν
ν
dt ,(24)
τ
τ
τdis the desired tilting torque calculated by the attitude
controller, eτis the additive modeling error, and it can be
estimated by
eτ
τ
τˆ
τ
τ
τ´τ
τ
τd.(25)
B. Compensation Method
As mentioned in Eq. (10), the unique dynamics of the
proposed system allow for independent auxiliary inputs M
M
Mx,
which can be utilized to improve the control specifications.
Here a separate loop is formulated, as an add-on compensator
of the nominal controller, to compensate for the unmodeled
dynamics, thus improving tracking accuracy and attenuating
unknown disturbances. Note that the add-on loop can only
compensate for the attitude controller.
The dynamics with respect to the auxiliary inputs M
M
Mxcan
be simplified as
9
ν
ν
νI
I
I´1J
J
JMM
M
Mx.(26)
A QP problem is formulated at each time step to find the
optimal auxiliary inputs M
M
Mxfor modeling error compensation.
Combining Eqs. (25) and (26), the equality constraint is
designed as
´eτ
τ
τJ
J
JMM
M
Mx`s
s
s, (27)
where s
s
sis a slack variable. And the object function is
J
J
JpM
M
Mx, s
s
sq “ M
M
MxTP
P
PM
M
Mx`s
s
sTQ
Q
Qs
s
s, (28)
where P
P
Pand Q
Q
Qare the weighting matrices.
Saturation constraints are also included as,
0ď»
1 1 1 1
´b´b b b
b´b´b b
cτ´cτcτ´cτ
´1»
Ti
Mx
i
My
i
0
ďtmax ¨1
1
1(29)
for i0,1,2,3.
In this problem, Tiand αiare known from the nominal
controller in the previous time step, My
iis sent from the
quadcopter onboard controller as feedback, and tmax refers
to the maximum thrust force that can be generated by each
propeller of the quadcopter. The control architecture related
to this part is plotted in the gray region of Fig. 2.
C. Discussion
An additional method to utilize these four auxiliary inputs
is to perform input allocation on all 12 inputs together, as
u
u
udJ
J
Jξ
J
J
JνT
T
T`J
J
JMM
M
Mx(30)
and attempt to solve for α
α
α,T
T
T, and M
M
Mxfrom the virtual input
u
u
ud. However, in this case the change of variables strategy
Eqs. (17) and (18) is not applicable to transform the nonlinear
allocation problem to a linear one because M
M
Mxis also coupled
with α
α
αthrough the multiplication with J
J
JM. In addition, this
method is still based on the simplified dynamics model to
design u
u
ud. As introduced in Section I, the unmodeled dynam-
ics are not considered in the nominal controller framework
and they can only be compensated by the integral operation
of the tracking controller. Therefore, even if additional inputs
are included or the allocation is changed to another allocation
method [13–15, 25], as long as the goal is to solve for the
control inputs from Eq. (30), the control performance will be
difficult to improve.
Based on these reasons, we decided to use the auxiliary
inputs to formulate a compensation loop. Although it has a
one-step delay, it will not affect the control allocation part
of the main controller and the unmodeled dynamics can be
directly compensated. Thus this compensation loop can work
together with any existing main controller that may have
different allocation strategies.
SU et al.: A FAST AND EFFICIENT ATTITUDE CONTROL ALGORITHM OF A TILT-ROTOR AERIAL PLATFORM USING INPUTS REDUNDANCIES 5
V. SIMULATION AND EXPERIMENT SETUP
A. Simulation Setup
We built a simulation in Maltab Simulink/Simscape environ-
ment to test the control performance prior to performing the
experiments. This simulator includes all the characteristics of
the real hardware system, such as physical parameters obtained
from system identification, control frequencies, measurement
noise, communication delays and noise, dynamics of propeller
motors, and thrust force saturation. Table I summarizes the
physical and software properties included in the simulation.
In this simulation, the dynamics of the entire platform
are multi-body dynamics calculated by Simscape. Therefore,
the inertia matrix of the entire platform will change when
the quadcopters are tilted at different angles, although in the
controller design process we assume that whole platform has
a constant inertia matrix. In Table I, m0and I0refer to
the mass and inertia matrix of main frame while miand Ii
refer to the mass and inertia matrix of each quadcopter with
passive hinge. It also includes the vertical distance between the
quadcopters 0,2and quadcopters 1,3. There is also a distance
between quadcopter CoM and rotation axis (drefers to this
distance), which has a pendulum effect to influence tilting
angle regulation of each quadcopter in low-level control.
TABLE I: Physical and Software Properties in Simulation
Parameter Value
m00.036 kg
mi0.031 kg
I0diagpr334.5sq kg ¨cm2
Iidiagpr0.16 0.16 0.29sq kg ¨cm2
l0.14 m
a0.032 m
d0.0144 m
tmax 0.147 N
Communication delay 0.02 sec
Host PC controller rate 100 Hz
Onboard controller rate 500 Hz
B. Experiment Setup
The platform prototype is shown in Fig. 1. The central frame
consists of two perpendicular carbon fiber tubes rigidly con-
nected at the geometric center. The quadcopters are connected
with the central frame by light-weight, 3D-printed hinges,
which have no rotation-angle limitations. We use Crazyflie
2.1 as the quadcopter module. The weight of Crazyflie 2.1 is
31 g(including passive hinge) and the maximum total payload
is 60 g(maximum thrust of 0.59 N). The total mass of the
entire platform is 160 g.
In the experiment, we use an Optitrack motion capture
system to measure the position and attitude of the central
frame. The main controller runs on a ground PC, which
communicates with the motion capture system through Eth-
ernet. The main controller calculates the desired thrust T
T
Td,
hinge angle α
α
αd, and auxiliary torque M
M
Mxd for each quadcopter
and receives the desired tilting torque M
M
Myd as feedback. The
communication between the ground PC and each quadcopter
is achieved by Crazy Radio PA antennas. Each quadcopter is
Fig. 3: Experimental communication setup. A ground PC runs
the high-level controller at 100 Hz with measurements from an
OptiTrack motion-capture system. Control signals are sent to each
quadcopter, each running a low-level controller at 500 Hz .
embedded with an onboard IMU module, and it can estimate
the hinge rotation angle knowing the attitude of central frame
η
η
η. Then, the onboard controller regulates the hinge angle and
thrust to the desired values. The measurement rate of the
Optitrack, the ground PC controller rate, and the data com-
munication rate with each quadcopter are all set to 100 Hz.
The onboard controller of the quadcopter is set to 500 Hz
to ensure fast low-level response. The software architecture is
shown in Fig. 3.
VI. SIMULATION AND EXPE RI ME NT R ES ULTS
In this section, we present the performance of the add-on
compensation loop in three cases: (1) A preliminary test with
pitch reference trajectory tracking with the other five DoFs
fixed. (2) Attitude reference trajectory tracking while hovering.
(3) Disturbance rejection while hovering. For each case, the
nominal controller was also tested for comparison. Simulation
and experiment results are provided. Each scenario is tested
multiple times, and the results are repeatable.
A. Preliminary Test
Before any experiment is conducted in air, a preliminary
experiment is designed to prove that the add-on attitude
compensation loop can improve attitude tracking performance.
In this experiment, quadcopter 0and quadcopter 2are fixed,
and the platform can only rotate around its pitch axis by the
passive hinges that pass through the geometric center, which is
shown in Fig. 4. The pitch angle of the platform is controlled to
track a sinusoidal trajectory. In this test, only quadcopter 1and
quadcopter 3are used and their desired tilting angles are zero.
Because this case does not require any tiling angle actuation
(only zero angle regulation), it should be more challenging to
improve the control performance for the add-on compensator
than the case that requires tiling angle actuation.
The experimental results are plotted in Fig. 5. From Fig. 5a
it is obvious that the implementation of add-on attitude
compensation loop can improve the trajectory tracking per-
formance. The test with the add-on attitude compensation
loop has smaller delay and overshot. The RMS error of the
pitch angle is improved from 0.173 rad to 0.110 rad (a
6 IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED DECEMBER, 2021
Fig. 4: Preliminary test setup. Five DoFs of the platform are
constrained by fixing two diagonal quadcopters. The remaining one
rotational DoF is realized by the passive hinges.
0246810
Time (s)
-1
-0.5
0
0.5
1
Orientation (rad)
pitchNpitchMx pitchref
(a) Combined Plot.
0246810
Time (s)
-0.01
-0.005
0
0.005
0.01
Mx Torques (Nm)
Mx
0Mx
1Mx
2Mx
3
(b) Mx: Mx Torques.
0246810
Time (s)
0
0.2
0.4
0.6
Thrust Forces(N)
T0T1T2T3
(c) N: Thrust Forces.
0246810
Time (s)
0
0.2
0.4
0.6
Thrust Forces(N)
T0T1T2T3
(d) Mx: Thrust Forces.
Fig. 5: Case 1: Pitch trajectory tracking performance with and without
the add-on attitude compensation loop while the other five DoFs
are fixed. (N for nominal control, Mx for with add-on attitude
compensation loop. Same notations are applied for the rest of this
paper.)
36% improvement). As shown in Figs. 5c and 5d, with the
compensation loop, the magnitude of the thrust force can be
smaller, which is helpful in avoiding the saturation of the thrust
force. This preliminary test verifies the effectiveness of the
add-on attitude compensation loop in a challenging scenario,
and gives us enough confidence to conduct the following aerial
experiments.
B. Trajectory Tracking
In this case, we compare the attitude reference trajectory
tracking performance for the nominal controller with and
without the add-on attitude compensation loop, and experiment
results are shown in Fig. 6. In Fig. 6a, it is obvious that the
nominal controller can not track the pitch reference trajectory
well due to the unmodeled dynamics. It has an obvious
overshot and cannot quickly stabilize to a steady state value.
After combining with the add-on attitude compensation loop,
the trajectory tracking performance improves significantly. As
shown in Fig. 6b, it has a smaller overshot and shorter response
time. The RMS error along the entire trajectory is improved
0 5 10 15
Time (s)
-0.4
-0.2
0
0.2
0.4
Orientation (rad)
roll pitch yaw
(a) N: Attitude.
0 5 10 15
Time (s)
-0.4
-0.2
0
0.2
0.4
Orientation (rad)
roll pitch yaw
(b) Mx: Attitude.
0 5 10 15
Time (s)
0
0.02
0.04
0.06
0.08
0.1
RMS Error
Position RMS Error(m)
Attitude RMS Error(rad)
(c) N: RMS Error.
0 5 10 15
Time (s)
0
0.02
0.04
0.06
0.08
0.1
RMS Error
Position RMS Error(m)
Attitude RMS Error(rad)
(d) Mx: RMS Error.
0 5 10 15
Time (s)
0.2
0.3
0.4
0.5
0.6
Thrust Forces(N)
T0T1T2T3
(e) N: Thrust Forces.
0 5 10 15
Time (s)
0.2
0.3
0.4
0.5
0.6
Thrust Forces(N)
T0T1T2T3
(f) Mx: Thrust Forces.
0 5 10 15
Time (s)
-1
-0.5
0
0.5
1
Tilting Angles (rad)
0 1 2 3
(g) N: Tilting Angles.
0 5 10 15
Time (s)
-1
-0.5
0
0.5
1
Tilting Angles (rad)
0 1 2 3
(h) Mx: Tilting Angles.
0 5 10 15
Time (s)
-0.01
-0.005
0
0.005
0.01
Mx Torques (Nm)
Mx
0Mx
1Mx
2Mx
3
(i) N: Mx Torques.
0 5 10 15
Time (s)
-0.01
-0.005
0
0.005
0.01
Mx Torques (Nm)
Mx
0Mx
1Mx
2Mx
3
(j) Mx: Mx Torques.
Fig. 6: Case 2: Trajectory tracking performance with and without
add-on attitude compensation loop.
from 0.04 rad to 0.02 rad (50% improvement) (Figs. 6c
and 6d).
TABLE II: Accumulated RMS Errors for Three Cases
x(mm) y(mm) z(mm) roll(rad) pitch(rad) yaw(rad)
Case1:N (Exp) - - - - 0.173 -
Case1:Mx(Exp) - - - - 0.110 -
Case2:N (Exp) 10.8 14.4 12.8 0.012 0.045 0.011
Case2:Mx(Exp) 11.4 9.9 9.1 0.013 0.018 0.011
Case3:N (Sim) 7.4 5.0 19.0 0.013 0.066 0.026
Case3:Mx(Sim) 3.7 2.9 14.7 0.007 0.050 0.010
Case3:N (Exp) 10.3 5.1 20.5 0.017 0.110 0.011
Case3:Mx(Exp) 9.4 4.0 11.2 0.011 0.087 0.011
C. Disturbance Rejection
In this case, we compare the disturbance rejection per-
formance of the nominal controller with and without the
add-on attitude compensation loop while hovering. Both the
simulation and the experimental results are shown in Fig. 7.
The disturbance used in this experiment is manually created
SU et al.: A FAST AND EFFICIENT ATTITUDE CONTROL ALGORITHM OF A TILT-ROTOR AERIAL PLATFORM USING INPUTS REDUNDANCIES 7
0 2 4 6 8 10
Time (s)
-0.2
0
0.2
0.4
Orientation (rad)
roll pitch yaw
(a) S(N): Attitude.
0 2 4 6 8 10
Time (s)
-0.2
0
0.2
0.4
Orientation (rad)
roll pitch yaw
(b) S(Mx): Attitude.
0 2 4 6 8 10
Time (s)
-0.2
0
0.2
0.4
Orientation (rad)
roll pitch yaw
(c) E(N): Attitude.
0 2 4 6 8 10
Time (s)
-0.2
0
0.2
0.4
Orientation (rad)
roll pitch yaw
(d) E(Mx): Attitude.
0 2 4 6 8 10
Time (s)
0
0.05
0.1
0.15
0.2
RMS Error
Position RMS Error(m)
Attitude RMS Error(rad)
(e) S(N): RMS Error.
0 2 4 6 8 10
Time (s)
0
0.05
0.1
0.15
0.2
RMS Error
Position RMS Error(m)
Attitude RMS Error(rad)
(f) S(Mx): RMS Error.
0 2 4 6 8 10
Time (s)
0
0.05
0.1
0.15
0.2
RMS Error
Position RMS Error(m)
Attitude RMS Error(rad)
(g) E(N): RMS Error.
0 2 4 6 8 10
Time (s)
0
0.05
0.1
0.15
0.2
RMS Error
Position RMS Error(m)
Attitude RMS Error(rad)
(h) E(Mx): RMS Error.
0246810
Time (s)
0.2
0.3
0.4
0.5
0.6
Thrust Forces(N)
T0T1T2T3
(i) S(N): Thrust Forces.
0246810
Time (s)
0.2
0.3
0.4
0.5
0.6
Thrust Forces(N)
T0T1T2T3
(j) S(Mx): Thrust Forces.
0246810
Time (s)
0.2
0.3
0.4
0.5
0.6
Thrust Forces(N)
T0T1T2T3
(k) E(N): Thrust Forces.
0246810
Time (s)
0.2
0.3
0.4
0.5
0.6
Thrust Forces(N)
T0T1T2T3
(l) E(Mx): Thrust Forces.
0 2 4 6 8 10
Time (s)
-1.5
-1
-0.5
0
0.5
1
1.5
Tilting Angles (rad)
0 1 2 3
(m) S(N): Tilting Angles.
0 2 4 6 8 10
Time (s)
-1.5
-1
-0.5
0
0.5
1
1.5
Tilting Angles (rad)
0 1 2 3
(n) S(Mx): Tilting Angles.
0 2 4 6 8 10
Time (s)
-1.5
-1
-0.5
0
0.5
1
1.5
Tilting Angles (rad)
0 1 2 3
(o) E(N): Tilting Angles.
0 2 4 6 8 10
Time (s)
-1.5
-1
-0.5
0
0.5
1
1.5
Tilting Angles (rad)
0 1 2 3
(p) E(Mx): Tilting Angles.
0 2 4 6 8 10
Time (s)
-0.01
-0.005
0
0.005
0.01
Mx Torques (Nm)
Mx
0Mx
1Mx
2Mx
3
(q) S(N): Mx Torques.
0 2 4 6 8 10
Time (s)
-0.01
-0.005
0
0.005
0.01
Mx Torques (Nm)
Mx
0Mx
1Mx
2Mx
3
(r) S(Mx): Mx Torques.
0 2 4 6 8 10
Time (s)
-0.01
-0.005
0
0.005
0.01
Mx Torques (Nm)
Mx
0Mx
1Mx
2Mx
3
(s) E(N): Mx Torques.
0 2 4 6 8 10
Time (s)
-0.01
-0.005
0
0.005
0.01
Mx Torques (Nm)
Mx
0Mx
1Mx
2Mx
3
(t) E(Mx): Mx Torques.
0 2 4 6 8 10
Time (s)
-0.1
-0.05
0
0.05
0.1
Disturbance (N)
T0
dist T1
dist T2
dist T3
dist
(u) Disturbance Forces. (v) Video clips of disturbance rejection experiments
Fig. 7: Case 3: Disturbance rejection performance with and without the add-on attitude compensation loop. (S for simulation, E for experiment)
by adding a disturbance thrust-force signal (Fig. 7u) onto the
desired thrust force commands T
T
Td. This disturbance signal
begins at 3sand lasts for 0.6s.
In Figs. 7c and 7d, the nominal controller requires larger
movement to attenuate this disturbance comparing with the
one with the add-on attitude compensation loop. Their position
and attitude RMS errors are plotted in Figs. 7g and 7h, which
shows that with the add-on attitude compensation loop, the
attitude RMS error is improved from 0.11 rad to 0.087 rad
(20.6% improvement). Similar to the result of Section VI-A,
the magnitude of the desired thrust forces are smaller with
the add-on attitude compensation loop, as shown on Figs. 7k
and 7l. In Fig. 7l, the thrust force command T0is close
to the maximum value (0.59 N), meaning its margin for
stabilization is small. If the disturbance is larger, this platform
is likely to become unstable. But in Fig. 7k, we notice that
the maximum thrust force is only 0.52 N, implying that with
the compensation loop, the platform can maintain its stability
even under larger disturbance torques. We can find similar
results in Figs. 7o and 7p, where the required tilting angles
can be smaller when the add-on attitude compensation loop is
implemented. Some video snapshots for this experiment are
shown in Fig. 7v.
In simulation, we can also find similar results, namely
that when the compensation loop is implemented, the attitude
RMS error is improved from 0.07 rad to 0.05 rad (28%
improvement) under the same disturbance (Figs. 7e and 7f),
and the magnitude of desired thrust force (Figs. 7i and 7j)
8 IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED DECEMBER, 2021
and tilting angles (Figs. 7m and 7n) is smaller which will be
helpful to prevent saturation.
D. Discussion
In these three experiments we have proven that with the
add-on attitude compensation loop, the attitude control per-
formance of our customized overactuated UAV platform with
quadcopters and passive hinges can be dramatically improved.
The reason for this improvement is twofold. First, when the
add-on attitude compensation loop is implemented, each quad-
copter has one additional control input in the control system,
which can be used to compensate for modeling mismatch. In
other words, the number of total inputs is increased from 8
to 12 by adding this compensation loop. Second, inside the
add-on attitude compensation loop, the unmodeled dynam-
ics are estimated as torque commands, which are directly
compensated by the auxiliary torque inputs via control of
the rotor speeds. In contrast, the nominal controller does
not take the unmodeled dynamics into consideration and it
can only be compensated by the integrator of a tracking
controller. Furthermore, this compensation must pass through
inner-loop dynamics, where the actuator angle responses are
slower than the rotor speed responses with one extra relative
degree of the plant dynamics. Therefore, with the add-on
attitude compensation loop, the control system can achieve
faster response speeds compared with the nominal controller.
VII. CONCLUSION
We have proposed a fast and efficient attitude control
strategy for the tilt-rotor aerial platform with passive hinges
and quadcopters. Compared with other tiltable actuator aerial
platforms, the auxiliary torque inputs of each quadcopter are
unique on this platform and they are utilized to formulate
an add-on compensation loop to dynamically compensate
the estimated unmodeled dynamics. This approach is shown
to exhibit superior performance compared with the nominal
controller where the compensation of the unmodeled dynamics
purely relies on the slower response integral action of an
attitude controller and the inner-loop tilting-angle control loop.
The simulation and real-world experimental results from the
three cases have clearly demonstrated the effectiveness of the
proposed method.
ACK NOW LE DG EM EN T
The authors would like to thank Dr. Hangxin Liu, Mr.
Wenzhong Yan and Dr. Ankur Mehta for the access and
technical assistance in the motion capture system.
REFERENCES
[1] M. Furci, C. Nainer, L. Zaccarian, and A. Franchi, “Input allocation for
the propeller-based overactuated platform rospo,IEEE Transactions on
Control Systems Technology, vol. 28, no. 6, pp. 2720–2727, 2019.
[2] M. Ryll, H. H. B¨
ulthoff, and P. R. Giordano, “A novel overactuated
quadrotor unmanned aerial vehicle: Modeling, control, and experimental
validation,IEEE Transactions on Control Systems Technology, vol. 23,
no. 2, pp. 540–556, 2014.
[3] M. Kamel, S. Verling, O. Elkhatib, C. Sprecher, P. Wulkop, Z. Taylor,
R. Siegwart, and I. Gilitschenski, “The voliro omniorientational hexa-
copter: An agile and maneuverable tiltable-rotor aerial vehicle,IEEE
Robotics and Automation Magazine, vol. 25, no. 4, pp. 34–44, 2018.
[4] M. J. Gerber and T.-C. Tsao, “Twisting and tilting rotors for high-
efficiency, thrust-vectored quadrotors,” Journal of Mechanisms and
Robotics, vol. 10, no. 6, p. 061013, 2018.
[5] M. Ryll, G. Muscio, F. Pierri, E. Cataldi, G. Antonelli, F. Caccavale, and
A. Franchi, “6d physical interaction with a fully actuated aerial robot,”
in Proceedings of International Conference on Robotics and Automation
(ICRA), IEEE, 2017.
[6] R. Rashad, F. Califano, and S. Stramigioli, “Port-hamiltonian passivity-
based control on se (3) of a fully actuated uav for aerial physical in-
teraction near-hovering,IEEE Robotics and Automation Letters, vol. 4,
no. 4, pp. 4378–4385, 2019.
[7] M. Zhao, T. Anzai, F. Shi, X. Chen, K. Okada, and M. Inaba, “De-
sign, modeling, and control of an aerial robot dragon: A dual-rotor-
embedded multilink robot with the ability of multi-degree-of-freedom
aerial transformation,” IEEE Robotics and Automation Letters, vol. 3,
no. 2, pp. 1176–1183, 2018.
[8] J. Xu, D. S. D’Antonio, and D. Salda˜
na, “H-modquad: Modu-
lar multi-rotors with 4, 5, and 6 controllable dof,” arXiv preprint
arXiv:2106.04048, 2021.
[9] H.-N. Nguyen, S. Park, J. Park, and D. Lee, “A novel robotic platform
for aerial manipulation using quadrotors as rotating thrust generators,”
IEEE Transactions on Robotics, vol. 34, no. 2, pp. 353–369, 2018.
[10] C. Pi, L. Ruan, P. Yu, Y. Su, S. Cheng, and T. Tsao, “A simple six
degree-of-freedom aerial vehicle built on quadcopters,” in Proceedings
of IEEE Conference on Control Technology Applications (CCTA), 2021.
[11] P. Yu, Y. Su, M. J. Gerber, L. Ruan, and T.-C. Tsao, “An over-actuated
multi-rotor aerial vehicle with unconstrained attitude angles and high
thrust efficiencies,IEEE Robotics and Automation Letters, vol. 6, no. 4,
pp. 6828–6835, 2021.
[12] A. F. S¸ enkul and E. Altu ˘
g, “System design of a novel tilt-roll rotor
quadrotor uav,Journal of Intelligent & Robotic Systems, vol. 84, no. 1,
pp. 575–599, 2016.
[13] Y. Su, P. Yu, M. Gerber, L. Ruan, and T.-C. Tsao, “Nullspace-based
control allocation of overactuated uav platforms,IEEE Robotics and
Automation Letters, vol. 6, no. 4, pp. 8094–8101, 2021.
[14] M. Zhao, K. Okada, and M. Inaba, “Enhanced modeling and control for
multilinked aerial robot with two dof force vectoring apparatus,IEEE
Robotics and Automation Letters, vol. 6, no. 1, pp. 135–142, 2020.
[15] M. Santos, L. Hon´
orio, A. Moreira, M. Silva, and V. Vidal, “Fast real-
time control allocation applied to over-actuated quadrotor tilt-rotor,
Journal of Intelligent & Robotic Systems, vol. 102, no. 3, pp. 1–20,
2021.
[16] W. Zhang, M. Brunner, L. Ott, M. Kamel, R. Siegwart, and J. Nieto,
“Learning dynamics for improving control of overactuated flying sys-
tems,” IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 5283–
5290, 2020.
[17] Z. J. Chen, J. X. Bannwarth, K. A. Stol, and P. J. Richards, “Analysis
of a multirotor uav with tilted-rotors for the purposes of disturbance
rejection,” in International Conference on Unmanned Aircraft Systems
(ICUAS), IEEE, 2018.
[18] Z. Chen, K. Stol, and P. Richards, “Preliminary design of multirotor
uavs with tilted-rotors for improved disturbance rejection capability,”
Aerospace Science and Technology, vol. 92, pp. 635–643, 2019.
[19] R. Yang, L. Zheng, J. Pan, and H. Cheng, “Learning-based predictive
path following control for nonlinear systems under uncertain distur-
bances,” IEEE Robotics and Automation Letters, vol. 6, no. 2, pp. 2854–
2861, 2021.
[20] Z. Wang, Z. Gong, Y. Chen, M. Sun, and J. Xu, “Practical control
implementation of tri-tiltrotor flying wing unmanned aerial vehicles
based upon active disturbance rejection control,Proceedings of the
Institution of Mechanical Engineers, Part G: Journal of Aerospace
Engineering, vol. 234, no. 4, pp. 943–960, 2020.
[21] Z. Wang, J. Li, and D. Duan, “Manipulation strategy of tilt quad
rotor based on active disturbance rejection control,Proceedings of
the Institution of Mechanical Engineers, Part G: Journal of Aerospace
Engineering, vol. 234, no. 3, pp. 573–584, 2020.
[22] L. Ruan, Independent position and attitude control on multirotor aerial
platforms. PhD thesis, University of California, Los Angeles, 2020.
[23] L. Ruan, C. Pi, Y. Su, P. Yu, S. Cheng, and T. Tsao, “Control and exper-
iments of a novel tiltable-rotor aerial platform comprising quadcopters
and passive hinges,Mechatronics(submitted), Elsevier, 2021.
[24] Y. Su, Compensation and Control Allocation with Input Saturation Lim-
its and Rotor Faults for Multi-Rotor Copters with Redundant Actuations.
PhD thesis, University of California, Los Angeles, 2021.
[25] M. Santos, L. Hon´
orio, A. Moreira, P. Garcia, M. Silva, and V. Vidal,
“Analysis of a fast control allocation approach for nonlinear over-
actuated systems,” ISA Transactions, 2021.
ResearchGate has not been able to resolve any citations for this publication.
Thesis
Full-text available
Multirotor copters with full six DoF maneuvering are often overactuated with redundancy. By having redundant actuation, the multirotors can have better fault-tolerance, energy-efficiency, and payload carrying capability. And they can have an infinite number of solutions when doing control allocation due to their redundancy. However, how to take full advantage of input redundancy to improve control performance of overactuated UAV under some constraints is still an open problem. And insufficient usage of input redundancy may dramatically influence the control performance of overactuated UAV in some cases. For example, (i) on tilt-rotor quadcopter platform, the maximum range of attitude is limited caused by input saturation. (ii) the twist and tilt rotor quadcopter platform cannot track a vertical rotation trajectory due to kinematic-singularity. The contributions of this dissertation are addressing the important issues in the copter's redundant actuator control: Firstly, an add-on controller is designed which utilizes the auxiliary inputs at low-level control to do dynamic compensation, thus it can attenuate unknown disturbance and track the reference trajectory with faster response and better performance. Secondly, a novel nullspace based allocation framework is proposed in high-level control, which can take input constraints and explore the nullspace of the allocation matrix to find exact solutions. It is also very robust about controller sampling frequency and measurement noise. Lastly, a fault-tolerant control (FTC) is designed which takes advantage of input redundancy in both high-level and low-level control, and can maintain the stability of whole platform under propeller failure. All these works are validated in both simulation and real-world experiment.
Article
Full-text available
Multirotor copters with full six Degree of Free-dom(DoF) maneuvering are often overactuated. The control allocation of overactuated UAV platforms can have an infinite number of solutions due to their redundancy. The most common allocation framework is based on Force Decomposition(FD), which provides a robust least-square solution and is easy to implement, but it does not account for input constraints. A control allocation framework based on Quadratic Programming (QP) can take input constraints; however, it will introduce linear approximation error and it has not been formulated and implemented on physical systems. In this paper, we propose a nullspace-based allocation framework for overactuated UAV platforms that combines the advantages of the FD-based framework and QP-based framework. Our proposed nullspace-based framework can take input constraints while eliminating the linear approximation error in the control allocation. It is also robust against controller sampling frequency and measurement noise. These three allocation frameworks are implemented and compared on our novel overactuated UAV platform in simulation to evaluate the robustness of the proposed method and in experiment for a vertical rotation trajectory to demonstrate its performance.
Article
Full-text available
Fully-actuated multi-rotor aerial platforms are receiving increasing research interests for the capability of six degree-of-freedom (DOF) motions such as hovering at non-horizontal attitude angles. Existing real world hardware and experiments have demonstrated such capability for a limited range of angles. This paper presents an aerial platform that achieves maneuvering at arbitrary attitudes with uniformly high thrust efficiency over its achievable configuration space. We propose a novel vectoring thrust force actuator by mounting a regular quadcopter on a passive mechanical gimbal mechanism. The UAV platform achieves full six-DOF motion with redundancies from four of these vectoring thrust actuators. We present the hierarchical controller that generates the high level virtual wrench command allocated to each gimbal actuator and the low-level actuator control to track the commanded wrench. We demonstrate the first real-world experiments of any pose maneuver over 360 degrees without requiring unwrapping rotations.
Article
Full-text available
This paper presents a novel light-weighted Unmanned Aerial Vehicle (UAV), an over-actuated tilt-rotor quadrotor with an innovative control allocation technique, named as Fast Control Allocation (FCA). In this arrangement, every motor has its own independent tilting command angle. By using this novel approach, the aircraft enhances its yawing capability and increases one more actuation domain: forward/backward velocity. However, this approach generates a control allocation matrix with non-unique solutions, breaking the effectiveness matrix into two parts. The first one is created considering the yawing torque and forward/backward velocity, and the second one considers all aircraft dynamics, running iteratively until the convergence criteria are reached. The results showed a well designed UAV where the FCA convergence and robustness was visible, allowing reliable and safe flight conditions with low computational effort control boards.
Article
Full-text available
The multilinked or modular structure is one of the state-of-the-art topics in aerial robot field. One type of the multilinked aerial robot called DRAGON containing a two degree-of-freedom (DoF) force vectoring apparatus in each link has been developed in our previous work to augment both maneuvering and manipulation ability. However, several types of invalid robot poses, which are due to the mechanical structure, the previous control method and the interrotor aerodynamic interference, significantly reduce the region of deformation. Thus, enhanced modeling and control methods are necessary to overcome these problems. In this letter, we first develop an integrated thrust and vectoring control method with a rigorous allocation to solve the control singularity. Second, we present a vectoring configuration planning method, which solves the mechanical singularity by locking one of the axes in the two DoF vectoring apparatus. Finally, we propose an estimation method and an active compensation control regarding the aerodynamic interference to improve the flight stability. In the end, simulation studies and experiments involving the hovering and deformation along a vertical plane are performed to evaluate the whole modeling and control framework.
Article
This paper presents the control and experiments of a novel multirotor aerial platform, which is capable of full actuation for six Degree of Freedom (DoF) motions. The platform is actuated by a number of tilting-thrust modules, each consisting of a regular quadcopter and a mechanically passive hinge. The platform in this paper has four such actuator modules, making an over-actuated system that requires input allocations in the feedback control. In addition to the common least-square method that minimizes the sum of squares of the thrusts, we propose a control allocation that minimizes the maximum thrust in a closed-form analytical solution for efficient real time computation. This allocation can achieve larger inclination angles than that by the least-square method, when thrust forces are insufficient to overcome the gravity for all poses. Simulation and real world experiments are presented to demonstrate the control of the aerial platform for six DoF motion tracking and disturbance rejection.
Article
Autonomous Robots with multiple directional thrusters are normally over-actuated systems that require nonlinear control allocation methods to map the forces that drive the robot’s dynamics and act as virtual control variables to the actuators. This process demands computational efforts that, sometimes, are not available in small robotic platforms. The present paper introduces a new control allocation approach with fast convergence, high accuracy, and dealing with complex nonlinear problems, especially in embedded systems. The adopted approach divides the desired nonlinear system into coupled linear problems. For that purpose, the Real Actions (RAs) and Virtual Control Variables (VCVs) are broke in two or more sets each. While the RA subsets are designed to linearize the system according to different input subspaces, the VCV is designed to be partially coupled to overlap the output subspaces. This approach generates smaller linear systems with fast and robust convergence used sequentially to solve nonlinear allocation problems. This methodology is assessed in mathematical tutorial cases and over-actuated UAV simulations.
Article
Accurate path following is challenging for autonomous robots operating in uncertain environments. Adaptive and predictive control strategies are crucial for a nonlinear robotic system to achieve high-performance path following control. In this letter, we propose a novel learning-based predictive control scheme that couples a high-level model predictive path following controller (MPFC) with a low-level learning-based feedback linearization controller (LB-FBLC) for nonlinear systems under uncertain disturbances. The low-level LB-FBLC utilizes Gaussian Processes to learn the uncertain environmental disturbances online and tracks the reference state accurately with a probabilistic stability guarantee. Meanwhile, the high-level MPFC exploits the linearized system model augmented with a virtual linear path dynamics model to optimize the evolution of path reference targets, and provides the reference states and controls for the low-level LB-FBLC. Simulation results illustrate the effectiveness of the proposed control strategy on a quadrotor path following task under unknown wind disturbances.