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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

−b−bb b

b−b−bb

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)

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

i−sπ

2i˙p−cπ

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=⎡

⎢

⎣

sα00−sα20

0−sα10sα3

cα0cα1cα2cα3

⎤

⎥

⎦,

T

T

T=T0T1T2T3T

.(5)

The rotational dynamics are

˙

ν

ν

ν=I

I

I−1(−ν

ν

ν×(Iν

Iν

Iν)+τ

τ

τ),(6)

where I

I

Iis the inertial matrix, and τ

τ

τ∈R3is 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⎡

⎢

⎣

−cα00cα20

0cα10−cα3

sα0sα1sα2sα3

⎤

⎥

⎦,(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=⎡

⎢

⎣

−cα00cα20

0cα10−cα3

sα0sα1sα2sα3

⎤

⎥

⎦,(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

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 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

Iu

u

uξ

u

u

uν−G

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 =sαiTi,F

ci =cαiTi.(18)

Then

u

u

ud=J

J

Jξ

J

J

JνT

T

T=W

W

WF

F

F, (19)

where W

W

W∈R6×8is 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

W†J

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

−b−bb b

b−b−bb

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 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

Idν

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

τ−τ

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

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 (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

−b−bb b

b−b−bb

cτ−cτcτ−cτ

⎤

⎥

⎥

⎥

⎦

−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

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

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)).

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

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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