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

Authors:
  • Beijing Institute for General Artificial Intelligence

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 letter investigates the capability of a new overactuated multi-rotor 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 letter, 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.
1214 IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 7, NO. 2, APRIL 2022
A Fast and Efficient Attitude Control Algorithm of a
Tilt-Rotor Aerial Platform Using
Inputs Redundancies
Yao Su , Lecheng Ruan , Pengkang Yu , Graduate Student Member, IEEE, Chen-Huan Pi, Member, IEEE,
Matthew J. Gerber , and Tsu-Chin Tsao , Senior Member, IEEE
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 letter investigates the capability of a new overactuated multi-
rotor 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 letter, 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 demon-
strated 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 decou-
pling the position and attitude control compared with collinear
multirotor UAVs [1]. Different configurations of overactuated
Manuscript received September 9, 2021; accepted December 6, 2021. Date
of publication December 28, 2021; date of current version January 5, 2022.
This letter was recommended for publication by Associate Editor Santhakumar
Mohan and Editor Pauline Pounds upon evaluation of the reviewers’ comments.
(Yao Su, Lecheng Ruan, and Pengkang Yu contributed equally to this work.)
(Corresponding author: Yao Su.)
Yao Su, Lecheng Ruan, Pengkang Yu, Matthew J. Gerber, and
Tsu-Chin Tsao are with the Mechanical and Aerospace Engineering
Department, University of California, LA CA 90095 USA (e-mail:
yaosu@g.ucla.edu; ruanlecheng@gmail.com; paulyu1994@g.ucla.edu; ger-
ber211@ucla.edu; ttsao@ucla.edu).
Chen-Huan Pi is with the Mechanical Engineering Department, National Yang
Ming Chiao Tung University, HsinChu 300093, Taiwan (e-mail: john40532.
me00@g2.nctu.edu.tw).
This letter has supplementary downloadable material available at
https://doi.org/10.1109/LRA.2021.3138806, provided by the authors.
Digital Object Identifier 10.1109/LRA.2021.3138806
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 design for overactu-
ated 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 struc-
ture [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 linearization 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 dis-
turbance rejection capabilities, several approaches have been
proposed. An analytical method was introduced in [17] to
compare the disturbance-rejection capability of different over-
actuated UAV platforms. From this perspective, a novel de-
sign was presented in [18] which demonstrated improved
disturbance-rejection capabilities with optimal design param-
eters. A learning-based method was implemented in [16], [19]
to compensate for the unmodeled dynamics, and an active distur-
bance 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 gener-
ated 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 passive
joints have been proposed in [10], [22] for their mechanical
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SU et al.: FAST AND EFFICIENT ATTITUDE CONTROL ALGORITHM OF A TILT-ROTOR AERIAL PLATFORM USING INPUTS REDUNDANCIES 1215
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 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 letter
extends the min-max allocation method in [23] and introduces
the fast auxiliary torque inputs to compensate for disturbances
and unmodeled dynamics. A Quadratic Programming (QP)
problem is formulated to find the optimal auxiliary torque inputs
at each time step. Three cases will be presented to demon-
strate the effectiveness of this add-on compensation loop in
disturbance-rejection and trajectory tracking.
The remainder of this letter is organized as follows. Section II
reviews the dynamics of the platform proposed in [10]. Sec-
tion 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 Sec-
tion V. Both simulation and experiment results are presented in
Section VI. The conclusion is addressed in Section VII.
II. PLATFORM
A. Configuration
The controller designed in this letter is based on the plat-
form 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:{O;x
x
x, y
y
y,z
z
z}, the body frame attached to the platform
geometric center FB:{OB;x
x
xB,y
y
yB,z
z
zB}, and the quadcopter
frames on each quadcopter ias FQi:{OQi;x
x
xQi,y
y
yQi,z
z
zQi}.The
position of the central frame center is defined as ξ
ξ
ξ=[x, y, z]T,
the attitude in the roll-pitch-yaw convention as η
η
η=[φ, θ, ψ]T
and the platform angular velocity in FBas ν
ν
ν=[p, q, r]T.
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
=
1111
bbb b
bbbb
cτcτcτcτ
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)
Fig. 1. The prototype and coordination systems of the overactuated 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.
where KTis the propeller thrust constant and ωij is the spinning
speed of propeller jin quadcopter i.b=a
2,cτ=Kτ
KT,ais the
scalar distance of each propeller to the quadcopter center, and
Kτis the propeller drag constant.
Furthermore, the actuator tilting angle αican be determined
through the dynamics
¨αi=1
Iy
i
My
isπ
2i˙pcπ
2i˙q, (3)
where Iy
iis the inertia in y
y
yQidirection and s[·]and c[·]denote
sin[·]and cos[·], respectively.
In addition, Mx
iand Mz
ifor each quadcopter can be directly
exerted on the platform central frame. Mz
iis generated by pro-
peller 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
ξ=1
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
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1216 IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 7, NO. 2, APRIL 2022
Fig. 2. Hierarchical control structure for the overactuated UAV platform. High-level position and attitude tracking controller outputs u
u
udto 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.
FBto FWand
J
J
Jξ=
0020
0103
0123
,
T
T
T=T0T1T2T3T
.(5)
The rotational dynamics are
˙
ν
ν
ν=I
I
I1(ν
ν
ν×(
)+τ
τ
τ),(6)
where I
I
Iis the inertial matrix, and τ
τ
τR3is the total external
torque exerted on the platform as
τ
τ
τ=τ
τ
τT+τ
τ
τM.(7)
Here τ
τ
τTis generated by actuator thrust forces
τ
τ
τT=J
J
JνT
T
T, (8)
where
J
J
Jν=l
0020
0103
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
τM=J
J
JMM
M
Mx,(10)
with
J
J
JM=
0020
0103
0123
,(11)
M
M
Mx=Mx
0Mx
1Mx
2Mx
3T
.(12)
III. NOMINAL CONTROLLER
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 letter as the “nominal controller”. The controller
uses four thrust forces and four tilting angles as system inputs,
by setting
M
M
Mx=0
0
0,(13)
and rewriting the dynamics as
¨
ξ
ξ
ξ
˙
ν
ν
ν=1
m
W
BR
R
R0
0
0
0
0
0I
I
I1J
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 ex-
pressed as
¨
ξ
ξ
ξ
˙
ν
ν
ν=u
u
uξ
u
u
uν,(15)
with the feedback linearized inputs
u
u
ud=J
J
Jξ
J
J
JνT
T
T=F
F
Fd
τ
τ
τd=mW
BR
R
RT0
0
0
0
0
0I
I
Iu
u
uξ
u
u
uνG
G
G
0
0
0.
(16)
The outer-loop (15) can be closed by any stabilizing con-
trollers. Here, we apply a LQR controller, similar to [23] to take
into consideration communication delay and improve system
robustness.
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SU et al.: FAST AND EFFICIENT ATTITUDE CONTROL ALGORITHM OF A TILT-ROTOR AERIAL PLATFORM USING INPUTS REDUNDANCIES 1217
B. Quadcopter Control
After the required total force and torques are determined by
(16), they are allocated to real system inputs Tiand αi. Define
F
F
F=Fs0Fc0... F
s3Fc3T
,(17)
where
Fsi =iTi,F
ci =iTi.(18)
Then
u
u
ud=J
J
Jξ
J
J
JνT
T
T=W
W
WF
F
F, (19)
where W
W
WR6×8is a constant allocation matrix with full row
rank. Therefore, the original inputs can be resumed with a least-
square solution [3]
F
F
F=W
W
WJ
J
Jξ
J
J
JνT
T
T, (20)
and
Ti=F2
si +F2
ci,
αi=atan2(Fsi,F
ci).(21)
For each quadcopter i, the thrust force Tican be directly
controlled, but the tilting angle αimust be controlled by My
i
under second-order dynamics (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
=
1111
bbb b
bbbb
cτcτcτcτ
1
Ti
Mx
i
My
i
Mz
i
.(22)
These thrusts are converted to PWM signals to drive the motors.
IV. ADD-ON ATTITUDE COMPENSATOR
WITH AUXILIARY INPUTS
A. Attitude Model Mismatch
As analyzed in [16], [19], there are modeling errors and
unknown 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 quadcopter
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 1 and 3 are
above quadcopters 0 and 2 with 5 mm 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 be-
comes
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
τ=I
I
I
ν
ν
dt ,(24)
τ
τ
τdis the desired tilting torque calculated by the attitude con-
troller, eτis the additive modeling error, and it can be estimated
by
eτ
τ
τ=ˆ
τ
τ
ττ
τ
τd.(25)
B. Compensation Method
As mentioned in (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 distur-
bances. 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
˙
ν
ν
ν=I
I
I1J
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 (25), and (26), the equality constraint is designed as
eτ
τ
τ=J
J
JMM
M
Mx+s
s
s, (27)
where s
s
sis a slack variable. And the object function is
J
J
J(M
M
Mx,s
s
s)=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,
0
1111
bbb b
bbbb
cτcτcτcτ
1
Ti
Mx
i
My
i
0
tmax ·1
1
1(29)
for i=0,1,2,3.
In this problem, Tiand αiare known from the nominal
controller in the previous time step, My
iis sent from the quad-
copter 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
ud=J
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 (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
α
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1218 IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 7, NO. 2, APRIL 2022
TAB L E I
PHYSICAL AND SOFTWARE PROPERTIES IN SIMULATION
TAB L E II
ACCUMULATED RMS ERRORS FOR THREE CASES
through 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 dynamics 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
(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 com-
pensated. Thus this compensation loop can work together with
any existing main controller that may have different allocation
strategies.
V. S IMULATION 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 quad-
copters are tilted at different angles, although in the controller
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.
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 Iirefer to the mass and
inertia matrix of each quadcopter with passive hinge. It also
includes the vertical distance between the quadcopters 0,2 and
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.
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 Ethernet. 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 tilt-
ing 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 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 communication 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 EXPERIMENT RESULTS
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
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SU et al.: FAST AND EFFICIENT ATTITUDE CONTROL ALGORITHM OF A TILT-ROTOR AERIAL PLATFORM USING INPUTS REDUNDANCIES 1219
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.
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 letter.)
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. The related errors
are shown in Table II.
A. Preliminary Test
Before any experiment is conducted in air, a preliminary
experiment is designed to prove that the add-on attitude com-
pensation loop can improve attitude tracking performance. In
this experiment, quadcopter 0 and quadcopter 2 are 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 1 and
quadcopter 3 are 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. 5(a) it
is obvious that the implementation of add-on attitude compen-
sation loop can improve the trajectory tracking performance.
Fig. 6. Case 2: Trajectory tracking performance with and without add-on
attitude compensation loop.
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 rd to 0.110 rd (a 36% improvement). As shown in
Figs. 5(c) and (d) 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 with-
out the add-on attitude compensation loop, and experiment
results are shown in Fig. 6. In Fig. 6(a), it is obvious that
the nominal controller can not track the pitch reference trajec-
tory 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. 6(b), it has a smaller overshot and shorter response
time. The RMS error along the entire trajectory is improved from
0.04 rd to 0.02 rd (50% improvement) (Figs. 6(c) and (d)).
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1220 IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 7, NO. 2, APRIL 2022
Fig. 7. Case 3: Disturbance rejection performance with and without the add-on attitude compensation loop. (S for simulation, E for experiment).
C. Disturbance Rejection
In this case, we compare the disturbance rejection perfor-
mance 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 distur-
bance used in this experiment is manually created by adding a
disturbance thrust-force signal (Fig. 7(u)) onto the desired thrust
force commands T
T
Td. This disturbance signal begins at 3 sand
lasts for 0.6 s.
In Figs. 7(c) and (d) 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. 7(g) and (h) which shows
that with the add-on attitude compensation loop, the attitude
RMS error is improved from 0.11 rd to 0.087 rd (20.6% im-
provement). 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. 7(k) and (l). In Fig. 7(l),
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. 7(k), 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. 7(o) and (p), 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. 7(v).
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 rd to 0.05 rd (28% improvement)
under the same disturbance (Figs. 7(e) and (f)), and the
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SU et al.: FAST AND EFFICIENT ATTITUDE CONTROL ALGORITHM OF A TILT-ROTOR AERIAL PLATFORM USING INPUTS REDUNDANCIES 1221
magnitude of desired thrust force (Figs. 7(i) and (j)) and tilting
angles (Figs. 7(m) and (n)) 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 performance
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 quadcopter 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 compen-
sation loop, the unmodeled dynamics 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 re-
sponses 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 strat-
egy for the tilt-rotor aerial platform with passive hinges and
quadcopters. Compared with other tiltable actuator aerial plat-
forms, 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.
ACKNOWLEDGMENT
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.
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... This is called the fast auxiliary input as it has much faster dynamics (zero's order for any given , feedthrough) compared with the in (5) (second order dynamics as need to be controlled by (8) to generate desired ). This property has been found of great significance in our following works for the tracking of highly-dynamic reference signals [32] and flight recovery under certain actuator failures [33,34]. On the other hand, C1 does not have auxiliary inputs according to (9) and (10). ...
... On the other hand, C1 does not have auxiliary inputs according to (9) and (10). C2 only have , but the magnitude (therefore the control effort) is much smaller than , and is usually not sufficient to handle the tracking or failure recovery tasks in [32,33]. ...
... One unique functionality of the presented configuration is the fast auxiliary input, which has been proved to be effective on improving the tracking performance of high-bandwidth Refs. [32] and recovering from actuator failure [33]. ...
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