ArticlePDF Available

A Multimode Two-Wheel-Legged Land-Air Locomotion Robot and Its Cooperative Control

Authors:

Abstract

In recent years, land-air locomotion robot has emerged in an endless stream. However, the increasingly complex working conditions pose higher challenges to the stability, flexibility, and other characteristics of robots. In this article, the two-wheel-legged self-balancing robot (TSR) is adopted as the crawling mechanism for the first time, and a new two-wheel-legged land-air locomotion robot (TLR for short) is designed. It has three independent modes of flight, two-wheel and four-wheel designed for various working environments. In flight mode, TLR has the fastest speed. In two-wheel mode, TSR as the crawling mechanism has the advantage of flexibly moving at high speed and being adaptive to complex terrains. The four-wheel mode provides TLR with maximum stability and load capacity. To achieve flexible mode switching and high energy utilization efficiency, we studied the cooperative control of rotor power and leg power. Two cooperative algorithms are proposed: stable cooperative algorithm with better impact resistance and stability and walking cooperative algorithm with better mobility. Both algorithms improve the stability, load capacity, and uphill ability of two-wheel mode, even breaking the constraint of the inverted pendulum, which demonstrates that TLR can balance at the specific pitch angle for completing more complex tasks.
IEEE/ASME TRANSACTIONS ON MECHATRONICS 1
A Multimode Two-Wheel-Legged Land-Air
Locomotion Robot and Its Cooperative Control
Jingsong Gao , Hongzhe Jin , Member, IEEE, Liang Gao , Jie Zhao , Member, IEEE,
Yanhe Zhu , Member, IEEE, and Hegao Cai
AbstractIn recent years, land-air locomotion robot has
emerged in an endless stream. However, the increasingly
complex working conditions pose higher challenges to
the stability, flexibility, and other characteristics of robots.
In this article, the two-wheel-legged self-balancing robot
(TSR) is adopted as the crawling mechanism for the first
time, and a new two-wheel-legged land-air locomotion robot
(TLR for short) is designed. It has three independent modes
of flight, two-wheel and four-wheel designed for various
working environments. In flight mode, TLR has the fastest
speed. In two-wheel mode, TSR as the crawling mechanism
has the advantage of flexibly moving at high speed and
being adaptive to complex terrains. The four-wheel mode
provides TLR with maximum stability and load capacity.
To achieve flexible mode switching and high energy uti-
lization efficiency, we studied the cooperative control of
rotor power and leg power. Two cooperative algorithms are
proposed: stable cooperative algorithm with better impact
resistance and stability and walking cooperative algorithm
with better mobility. Both algorithms improve the stability,
load capacity, and uphill ability of two-wheel mode, even
breaking the constraint of the inverted pendulum, which
demonstrates that TLR can balance at the specific pitch
angle for completing more complex tasks.
Index TermsCooperative control, land-air locomotion
robot, tilting quadrotor, two-wheel-legged.
I. INTRODUCTION
LAND-AIR locomotion robots have the ability to fly and
walk [1] and are widely applied in agriculture, industry,
military [2], and other fields because of their excellent adapt-
ability to the environment. Early research can be traced back to
the aircraft car developed by Tarian Vuia in 1906, namely the
Manuscript received 21 July 2023; revised 10 October 2023; accepted
8 November 2023. Recommended by Technical Editor P.-C. (TE) Lin and
Senior Editor K. J. Kyriakopoulos. This work was supported in part by
STI 2023-Major Projects under Grant 2021ZD0201400, in part by the
National Natural Science Foundation of China under Grant 62373121,
Grant 92048301, and Grant 52205012, in part by the National Outstand-
ing Youth Science Fund Project of National Natural Science Foundation
of China under Grant 52025054, and in part by the Natural Science
Foundation of Heilongjiang Province under Grant LH2023E038. (Corre-
sponding authors: Hongzhe Jin; Liang Gao.)
The authors are with the School of Mechatronics Engineering, Harbin
Institute of Technology, Harbin 150080, China (e-mail: 19b908036@hit.
edu.stu.cn; hongzhejin@hit.edu.cn; gaoliang@hit.edu.cn; jzhao@hit.
edu.cn; yhzhu@hit.edu.cn; hgcai@hope.hit.edu.cn).
Color versions of one or more figures in this article are available at
https://doi.org/10.1109/TMECH.2023.3332174.
Digital Object Identifier 10.1109/TMECH.2023.3332174
“flying car” [3]. After more than 100 years of research, many
land-air locomotion robots have been developed. Researchers
experimented with a variety of combinations of flight platforms
and crawling mechanisms to improve the robot’s performance,
adapting to various working conditions. The flight platform
mainly uses rotor and ducted fan as the power drive unit and
adopts the power configuration scheme of single engine [4],
[5], double engines [6],[7], or even multiple engines [8],[9],
[10],[11]. The crawling platform is developed under the single
ground movement mode by utilizing wheels [12],[13],crawlers
[14],legs[15],[16], etc. It is worth mentioning that there are
few researchers who designed a crawling mechanism with a
complex structure, such as the wheel-leg type robot proposed in
[17]. However, different combinations, such as wheel-legged,
encompass the high speed and efficiency of wheels with the
ground adaptability of legs. Wheel-legged robots mentioned in
[18],[19],[20], and [21] are able to pass through unstructured
terrains by walking or jumping with great ground movement
performance.
Studies also reported some development of the cooperation
between the crawling mechanism and flight platform to improve
the performance of ground movement or to complete various
tasks. For example, HyTAQ developed by the Illinois Institute
of Technology has greater operational time with the installa-
tion of a shield wrapping up the quadrotor, and the ground
movement function was realized with controlling of the rotors.
However, the ground movement operation is difficult, and the
control accuracy needs to be improved [22],[23]. Similar to
this, there is an omnidirectional robot developed by Nagoya
University of Technology in Japan [24]. Kim et al. [25] used
the rotors to assist the biped robot in walking and realized
agile movements, such as walking on loose ropes and skate-
boarding. But the independent ground movement function was
not demonstrated, and it may potentially increase the energy
consumption.
It is necessary to improve the stability, flexibility, and other
performance of land-air locomotion robots to adapt to various
working conditions and complex tasks. It means that the design
of the structure and control algorithm must be highly compatible
to reach the potential of a robot. In this article, three aspects can
be considered to tackle the challenges. First, we employed a
two-wheel-legged self-balancing robot (TSR) [26],[27],[28] as
the crawling mechanism to develop a new land-air locomotion
robot, i.e., two-wheel-legged land-air locomotion robot (TLR),
for the first time. TSR has the characteristics of being lighter
1083-4435 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
2IEEE/ASME TRANSACTIONS ON MECHATRONICS
and more flexible to reduce the load of the flight platform
and improve endurance, which are particularly suitable for a
crawling mechanism. Second, multimode can be purposely de-
signed to cater to different working environments. We designed
three motion modes: a two-wheel mode that inherits TSR’s
excellent ground mobility, a flight mode that uses a quadrotor to
achieve high-speed movement, and a four-wheel mode that has
the highest stability and load capacity. These modes can work
independently and the switching of three modes can be achieved.
Finally, the highlight of this article is the cooperation between
the rotor power and leg power. A stable cooperative algorithm
(SCA) is designed for balancing in site and vertical takeoff and
landing (VTOL) under the two-wheel mode, whereas a walking
cooperative algorithm (WCA) is designed for higher mobility,
such as the uphill process.
Based on the above-mentioned structure and the correspond-
ing control algorithms, the contributions of this work are sum-
marized as follows.
1) Combining TSR with a tilting quadrotor for the first time,
a new land-air locomotion robot TLR is proposed.
2) Three independent movement modes are adaptive to vari-
ous working conditions and complex tasks. The switching
between any of the two modes can be successfully realized
with the association of two proposed algorithms.
3) Two algorithms can not only realize the coexistence of
rotor power and leg power but also improve the stabil-
ity, load capacity, and uphill ability of the two-wheel
mode, allowing TLR to break the constraint of the in-
verted pendulum and to balance at the specified pitch
angle.
The rest of this article is structured as follows. Section II
describes the structural design. Section III establishes the kine-
matics and dynamic models and introduces the rotor power
distribution method. Section IV presents the control hardware
system and corresponding algorithms. Simulations and exper-
iments of the two algorithms are presented, respectively, in
Sections Vand VI. Finally, Section VII concludes the article.
II. STRUCTURAL DESIGN OF TLR
First, TSR as the crawling mechanism is employed for the
two-wheel mode, which realizes its excellent ground mobility.
A four-wheel mode is constructed by inserting passive wheels at
the knee joint. The forward and steering actions can be realized
by the same or differential rotational speed of the hub motors.
Besides, the tilting quadrotor is chosen for the two proposed
algorithms when the net force of the rotors is toward the fuselage
at the x-direction and z-direction, as shown in Fig. 1.
Flight mode is aimed at rapid deployment and crossing huge
obstacles. The two-wheel mode can be used for flexible ground
operations. The four-wheel mode is used in the case of large
external disturbances or heavy loads. Switching between three
modes for certain purposes allows TLR to cope with more
working conditions, thus the requirements of each mode and
the mode-switching process need to be fully considered in the
structural design.
Fig. 1. Structure design. (a) Propeller. (b) Rotor motor. (c) ESC.
(d) Flight controller. (e) Leg controller. (f) Motor driver. (g) Lithium battery.
(h) Forward tilting lever. (i) Rear tilting lever. (j) Tilting servo. (k) Hip
motor. (l) Leg link. (m) Passive wheel. (n) Hub motor. (o) Tilting servo.
(p) Swing lever.
Fig. 2. (a) Leg structure design. (b) Curve is the ratio of the maximum
xand zdirections offset of the foot end to L2.
A. Skeleton Flight Platform Design
The flight platform adopts the structure of the skeleton to
reduce the mass of the body and increase the internal space. To
balance the output torque of rotor power and the compactness of
the whole structure, we set the uniaxial tension of the propeller
to 5 kg, and the blade pitch is 0.44 ×0.42 m. The front and
rear set of rotors and their electronic speed controller (ESC) are,
respectively, installed on each tilting lever. Front and rear tilting
levers are driven by the servo through a four-link mechanism.
The side plates of the skeleton utilize the structure of a V-shape
with a diversion function, reducing the resistance during the
flight and providing space for tilting rotors at the same time.
Leg links are installed outside of the skeleton to increase the
width between the two legs to improve the stability margin in
the frontal plane.
B. Structure of Legs and Centroid Design
The leg link adapts a four-link one degree of freedom struc-
ture, which realizes the leg movement only by driving the hip
joint, thus reducing the weight of the drive unit. The length of
the drive link L2is taken as the benchmark, which equals the
length of L11. The length of other leg links and the included
angle between L4and the skeleton in the x-direction are taken as
the variables. As the hip joint is the origin of the coordinate, the
impacts of different variables on the maximum deviation of the
hub motor in the xand zdirections are shown in Fig. 2. While the
hub motor’s extension in the z-direction reaches to the maximum
with the minimum deviation of hub motor in the x-direction, the
design parameters are determined.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
GAO et al.: MULTIMODE TWO-WHEEL-LEGGED LAND-AIR LOCOMOTION ROBOT AND ITS COOPERATIVE CONTROL 3
Fig. 3. Prototype of TLR.
Fig. 4. Kinematics model of TLR.
Meanwhile, the mass of the crawling mechanism is mainly
concentrated at the hub motor because of the lightweight leg
link, which minimizes the effect of leg movement toward the
centroid of the fuselage. This can minimize the target pitch
angle changing during the flight and ground mode. Ensuring the
controllers, lithium battery, and other components are inserted
very closely to the hip joint can lower the centroid of the fuselage
and improve the stability of forward flight. It is worth mentioning
that the leg links are positioned in the direction of the negative
x-axis of the hub motor, causing the centroid of the fuselage
backward slightly, which is convenient for switching the two-
wheel to four-wheel mode. Positioning the passive wheels at the
knee joint realizes four-point support, which greatly improves
the stability margin of the four-wheel mode. The setting of the
passive wheels also keeps the pitch angle of the fuselage at about
zero, further contributing to the switch between the four-wheel
and flight modes.
As shown in Fig. 3, the overall weight is 13.6 kg. The main
body is made of carbon fiber, and the rest of the fuselage is made
of aluminum alloy. The structure is verified by infinite element
software. When the legs retract the most and the fuselage is at the
lowest height, the hip motor angle is calibrated as 0 rad. The hip
motor angle ranges from 0 rad to 0.8 rad, with the corresponding
height of the fuselage from 0.41 m to 0.73 m.
III. MODELING FOR COOPERATIVE ALGORITHM
A. Kinematics Model of TLR
Assuming that the propeller rotation does not affect the
centroid of the fuselage, the skeleton and the leg link can be
considered as one simplified fuselage. The kinematics model
is established to determine the relationship between θ1and
simplified fuselage centroid position F, facilitating the dynamic
modeling and rotor power distribution, as shown in Fig. 4.
The centroid of the simplified fuselage is obtained by calcu-
lating the internal angles of the four link. The target pitch angle
Fig. 5. Whole-body dynamic model of TLR.
θs, the distance between the simplified fuselage and wheel L,the
distance between the simplified fuselage and hip joint LF, and
the inclination of simplified fuselage centroid βcan be obtained
as
θs=atan[(xFxE)/(zFzE)]
L=(xExF)2+(zEzF)2
LF=x2
F+y2
F
β=atan(zF/xF)
(1)
where
xF=mAxA+2mBxB+2mCxC+2mDxD
mA+2mB+2mC+2mD
zF=mAzA+2mBzB+2mCzC+2mDzD
mA+2mB+2mC+2mD.
Then, LFand βare variables for the rotor power distribution.
B. Dynamic Model of TLR
TLR is viewed as a two-wheeled self-balancing robot [29]
with adjustable height that is composed of the simplified fuse-
lage and two wheels. Due to the limitation of the structure, the
rotor cannot provide the y-direction force, so the force of the
four rotors can be simplified into pitch, yaw, and roll torque, and
the force that is acting on the centroid of the simplified fuselage
inxandzaxes,asshowninFig.5.
It is assumed that the wheel is not slippery. Only the forces
and torques generated by friction are considered, and the re-
sistance torque inside the motor is ignored. Newton–Euler
method is adopted for establishing the dynamic model of TLR,
and force analysis is carried out on the fuselage and wheels
as
1
2m¨xl=τl
RIω¨xl
R2Flx
1
2m¨xr=τr
RIω¨xr
R2Frx
M¨xM=Flx +Frx +Px
M¨zM=Flz +Frz +PzMg
Iθ¨
θ=(Flz +Frz)Lsin θ(Flx +Frx )Lcos θ
(τl+τr)+τθ
Iψ¨
ψ=(Flx Frx)D
2+τψ.
(2)
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
4IEEE/ASME TRANSACTIONS ON MECHATRONICS
Fig. 6. Rotor power distribution diagram.
The following equation can be obtained by eliminating the
terms Flx,Frx ,Flz, and Frz and the follow-up linearization:
¨x=[(IθR+MRL2+MR2L)(τl+τr)
(Mg Pz)ML2R2θ
MLR2τθ+IθR2Px/(XIθ+2MmR2L2
+2IωML2)+w1
¨
θ=[(X+MLR)(τl+τr)+(Mg Pz)XLθ +θ
+(XMR2)LPx]/[X(Iθ+ML2)M2L2R2]+w2
¨
ψ=[2R2τψ+DR(τlτr)]/(mD2R2
+IωD2+2IψR2)+w3
(3)
where X=MR2+2mR2+2Iω.w1,w2, and w3are the
unmodeled disturbance terms produced after linearization and
we assume they are bounded. There is a coupling term PzLθin
the dynamic model, but the coefficients of τθand PzLθare the
same, and the robot can still be accurately controlled after the
dynamic model is processed.
C. Rotor Power Distribution
Rotor power distribution converts forces in xand zdirections,
and pitch, yaw, and roll torque provided by the rotor into the
target tilting angle of the tilting servos αand the target speed of
the four rotors ϖi, as shown in Fig. 6.
Making the target angle of the front and rear tilting lever
always the same, so the forces in xand zdirections and pitch,
yaw, and roll torque generated by the rotors can be obtained as
Pz=CTcos α(2
1+2
2+2
3+2
4)
Px=CTsin α(2
1+2
2+2
3+2
4)
τφ=CTdsin α(2
2+2
32
12
4)
CMcos α(2
12
22
3+2
4)
τψ=CTdcos α(2
1+2
42
22
3)
CMsin α(2
22
1+2
32
4)
τθ=CT{(2
1+2
22
32
4)L5cos(θα)
+[hsin(θα)
LFcos(α+βθ)](2
1+2
2+2
3+2
4)}
(4)
where CTand CMare dimensionless force coefficient and torque
coefficient, respectively [30]. The target speed of the four rotors
ϖiand the target angle of tilting servo αcan be obtained as
Fig. 7. Leg statics model.
follows:
α= arctan(Px/Pz)
1=C1C2+C3+C42
2=C1+C2C3+C42
3=C1+C2+C3C42
4=C1C2C3C42
(5)
where
C1=Pz/cos α
C2=(τφtan ατψ)CTdcos α(tan2α1)
C3=(τφτψtan α)CMcos α(tan2α1)
C4={τθcos αPz[hsin(θα)+LFcos(α+βθ)]}
/CTL5cos(θα)cosα.
D. Statics Model of Leg Link
It shows low speed and low movement inertia of the leg link
in the process of height adjustment, the torque feedforward
compensation for the hip joint can be calculated through the
leg statics model under different z-direction force Pz,as shown
in Fig. 7.
Assuming that the pitch angle of the fuselage and the height
of the legs remain the same after self-balancing, the centroid of
the simplified fuselage is directly above the axle, and the angle
of L1link can be obtained from the angle of the drive link. The
statics model is also established by the Newton–Euler method,
and the force analysis is shown as follows:
F=Mg Pz=F12yF13y
F12x=F13x=F13ytan[θ4(θ1)+θ2(θ1)π/2]
F13xL12 tan θ4(θ1)+F13yL12 =FL
11
τL=F22yL2sin θ5F22xL2cos θ5
(6)
where θ5=θ4(θ1)+θ2(θ1)–π/2, the torque feedforward for
the hip joint is shown as follows:
τL=(Mg Pz)L2[L11 cot(θ3+θ4)tan(θ4+θ2)
L1+L12 tan θ4
×cot(θ4+θ3)]/[L11 cot(θ4+θ3)tan(θ4+θ2)].(7)
The control of the hip joint can be realized by the torque
feedforward and a PD controller.
The definition of dynamic parameters is shown in Table I.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
GAO et al.: MULTIMODE TWO-WHEEL-LEGGED LAND-AIR LOCOMOTION ROBOT AND ITS COOPERATIVE CONTROL 5
TABLE I
DEFINITION OF DYNAMIC PARAMETERS
Fig. 8. Land-air locomotion robot control system.
IV. ALGORITHM DESIGN FOR COOPERATION
Since the control of TSR is based on the inverted pendulum
model, the force or torque toward the fuselage that is produced
by the rotor will affect or even destroy TSR’s self-balancing.
Therefore, the cooperative control of rotor power and leg power
is studied in this article, so that the rotor power can not only
coexist with leg power but also improve the performance of the
two-wheel mode.
A. Hardware System Design
The hardware system consists of three parts: flight controller,
leg controller, and communication relay board, as shown in Fig.
8.
Pixhawk4 is selected as the flight controller, which is equipped
with two inertial measurement units, a magnetometer and a
barometer. An Arm Cortex M4 microcontroller is chosen to
be the leg controller, and the maximum operating frequency
can reach 168 MHz. The leg controller manipulates hip motors
and hub motors through the controller area network (CAN) and
provides feedback on the status of each motor to the flight
controller. The flight controller is responsible for collecting
attitude information and controlling the tilting servos and four
rotors through pulse width modulation signals. Meanwhile, it
accepts the control instructions of the remote control and re-
turns the robot information to the ground station for real-time
demonstration and data storage. A communication relay board
with two CAN channels is added between the two controllers
to ensure stability. The overall control frequency is above
200 Hz.
B. Control Algorithm Design
When designing the control algorithm, the original control
architecture of the two modes needs to be maintained. Thus,
this shifts to focusing on the coordination between rotor power
and leg power to facilitate the switching between flight and
two-wheel mode rather than developing an advanced algorithm.
According to (3), there is a coupling term PzLθin the whole-
body dynamic model. To achieve better control of the robot, let
τ
θ=τθPz, and the whole-body dynamics model can be
written as
¨
X=AX +BU +W(8)
where X=[x, θ , ψ],U=[τl
r
θ
ψ,P
x],W=[w1,w
2,w
3]
A=
0a12 0
0a22 0
000
,B =
b11 b12 b13 0b15
b21 b22 b23 0b25
b31 b32 0b34 0
Y=2mR2Iθ+2IθIω+MR2Iθ+2MmR2L2+2IωML2
a12 =M2gL2R2Y
a22 =MgL(2mR2+MR2+2Iω)Y
b11 =b12 =(IθR+MLR2+ML2R)Y
b13 =MLR2Y
b15 =Iθ/Y
b21 =b22 =(MRL+2mR2+2Iω+MR2)Y
b23 =(2mR2+2Iω+MR2)Y
b25 =(2mR2L+2IωL)Y
b31 =b32 =DR(2IψR2+D2mR2+IωD2)
b34 =2R2(2IψR2+D2mR2+IωD2).
According to the whole-body dynamic model, both τθand
Pxcan generate movement acceleration in the x-direction and
pitch acceleration to control the robot. But considering the
unpredictable ground effect, this article designed two cooper-
ative algorithms and compared their true effects: SCA always
maintains the rotor’s level, and the position deviation in the
x-direction is compensated by τθ, so the flow field is more stable.
WCA can tilt the propeller forward and backward according
to the calculation and uses Pxto compensate for the position
deviation, so it has a more obvious effect on position control.
As shown in Fig. 9the input of the control system includes
target position x, target velocity x, target attitude angles ψsand
φs, and target attitude angular velocities ˙
ψsand ˙
φs, given target
pitch angle θs2and target z-direction force Pz. Feedforward
torque of the hip joint is adjusted adaptively according to Pz.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
6IEEE/ASME TRANSACTIONS ON MECHATRONICS
Fig. 9. Architecture of cooperative algorithm for TLR.
In actual controlling, the target pitch angle θsconsists of the
given target pitch angle θs2and the kinematic target pitch angle
θs1. After the speed controller calculates the target pitch angle
offset θb, the pitch angle deviation Δθcan be calculated with
the current pitch angle θ. Assume attitude angle deviations Δθ,
Δψ, and Δφ, velocity deviation Δ˙x, position deviation Δx,
and target z-direction force Pzinto the attitude controller. The
results of target output torques of left and right wheels τland
τrare sent to the drive unit of the crawling platform. The two
direction forces and pitch, yaw, and roll torque of the rotors
acting on the simplified fuselage are calculated by the attitude
controller of the flight platform. Then the target angle of tilting
servos αand the target speed of the four rotors ϖiare obtained
through the rotor power distribution. To ensure the effect of
the cooperative algorithm and facilitate the switching between
flight mode and two-wheel mode, a cascade control architecture
is adopted. The attitude controller of the crawling platform is
composed of pitch and yaw PD controllers in parallel, whereas
the attitude controller of the flight platform is composed of
four PID controllers in parallel. The difference between the two
control algorithms can be seen from the processing of the output
of the position controller. SCA takes its result as a part of the
target pitch torque τθ2and makes the x-direction force Pxto
be 0, whereas WCA takes its result as the target x-direction
force Px.
θb=k11(xxs)+k12 x˙xs)
τl=k1(θθbθs)+k2(˙
θ˙
θs)+k3(ψψs)
+k4(˙
ψ˙
ψs)
τr=k1(θθbθs)+k2(˙
θ˙
θs)k3(ψψs)
k4(˙
ψ˙
ψs)
τθ1=k5(θθbθs)k6(˙
θ˙
θs)
k7(θθs)dt PzΔθL
τψ=k8(ψψs)k9(˙
ψ˙
ψs)k10 (ψψs)dt
τθ2=k13(xxs)k14 x˙xs)k15 (xxs)dt
Px=k16(xxs)k17 x˙xs)k18 (xxs)dt.
(9)
C. Selection of Control Parameters
The cooperative algorithm aims to test the effect of rotor
power on the performance of the crawling mechanism. First,
the parameters of the flight platform and crawling mechanism
are debugged independently, and then the control parameters of
the crawling mechanism and flight platform are retained in the
cooperative control. In the debugging process of cooperative
control, the parameter of the position controller is fine-tuned
until the robot oscillates. The specific parameters of each PID
controller are debugged by the critical proportion method to
ensure the control effect. To facilitate comparison, the control
parameters, input constraints, frequency, etc., in the simulation
are consistent with the experiment.
In the whole-body dynamics model, the height of TLR is
assumed to be constant, and θs1is regarded as 0. Introduce (9)
into the whole-body dynamic model (8) and sort out
˙
Z=DSZ+W
˙
Z=DWZ+W(10)
where DSand DWrepresent the state transition matrices of SCA
and WCA, respectively. W´ is the unmodeled interference term
produced by linearization.
Z=Δxdt, Δθdt, Δψdt, Δx, Δθ, Δψ, Δ˙x, Δ˙
θ, Δ˙
ψ
W=000000w1w2w3
C1=
000
000
k15 k70
00k10
000
,C
2=
k1k11 k1k3
k1k11 k1k3
k5k11 k13 k50
00k8
000
C3=
k1k12 k2k4
k1k12 k2k4
k5k12 k14 k60
00k9
000
,C
4=
000
000
0k70
00k10
k18 00
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
GAO et al.: MULTIMODE TWO-WHEEL-LEGGED LAND-AIR LOCOMOTION ROBOT AND ITS COOPERATIVE CONTROL 7
TABLE II
COOPERATIVE ALGORITHM PARAMETERS
C5=
k1k11 k1k3
k1k11 k1k3
k5k11 k50
00k8
k16 00
,C
6=
k1k12 k2k4
k1k12 k2k4
k5k12 k60
00k9
k17 00
DS=
0E30
00E3
BC1A+BC2BC3
,
DW=
0E30
00E3
BC4A+BC5BC6
.
For the above closed-loop linear system, the stability can be
judged according to the bounded input bounded output principle
[31]. If the eigenvalues of the state transition matrix all have
negative real parts and the inputs are bounded, the outputs are
also bounded. Table II shows the parameters of the cooperative
algorithms when the hip joint angle is 0 rad.
The eigenvalues of DSand DWare solved, respectively.
The minimum eigenvalues are 164.02 and 2229.80, and the
maximum are 2.17 ×10 15 and 0.06, respectively. All
eigenvalues of the two matrices have negative real parts. When
W´ is bounded, the zero-state response of the system is also
bounded. The bounded assumption and parameter selection will
be further verified through simulations and experiments.
V. S IMULATION OF TLR
In the simulation, the lift of the rotor is simplified as a
pulling force. The rotor rotation and flow field are ignored. The
rationality of control architecture is verified.
A. Self-Balancing Simulations
After TLR is balanced at different heights, the z-direction
force Pzis gradually raised up to 5 N each time.
As shown in Fig. 10, the balanced position shows offset due
to the deviation of the kinematic target pitch angle θs1. When
the cooperative algorithm provides additional pitch torque to
the centroid of the simplified fuselage, the accuracy of position
control is significantly improved. With the increase of Pz,the
actual output torque of the hip joint τLdecreases, which proves
that the cooperative algorithm has an obvious weight reduction
effect and can improve the load capacity of TLR. Due to the
deviation of the kinematic target pitch angle θs1, the deviation
of the feedforward term in the pitch torque τ
θincreases along
Fig. 10. Simulation results of self-balance under different Pz.
Fig. 11. Simulation results of uphill.
with Pz, but the integral term of the position controller can
compensate for that.
B. Auxiliary Uphill Simulations
Take the hip joint angle of 0.5 rad as an example, TLR is
ordered to drive on slopes with different inclination angles under
different z-direction force Pz, and the changes of pitch angle and
x-direction distance xare compared.
Fig. 11 shows that there is an obvious deviation in θand x
when going uphill, and the cooperative algorithm can obviously
reduce the deviation and improve the control accuracy of attitude
and position. The deviation is descending along with the increase
of Pz. Comparing the two algorithms, the deviation under WCA
is smaller. According to the whole-body dynamics model, Pxhas
a more obvious impact on the acceleration of x, and the smaller
the position deviation, the smaller the target pitch angle offset
θbgenerated by the speed controller.
C. x-Direction Impact Resistance Simulations
After the robot is stabilized, an x-direction impact force of
20 N is applied for 1 s. The change of x-direction distance xand
pitch angle θbefore and after involving the two algorithms are
tested and compared. When the hip joint angle is 0.5 rad, the
simulation results are shown in Fig. 12.
When facing the x-direction impact force, the cooperative
algorithm can reduce the variation amplitude of θand xsig-
nificantly, which proves the role of the algorithm in improving
the anti-interference. When Pzis large, the impact resistance
of SCA is similar to that of WCA. But when Pzis small, the
pitching torque τ
θprovided by the rotor in SCA is limited and
the impact resistance is weakened.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
8IEEE/ASME TRANSACTIONS ON MECHATRONICS
Fig. 12. Simulation results of 20-N impact resistance test.
Fig. 13. Simulation results of the arbitrary pitch balancing.
D. Arbitrary Pitch Balancing Simulations
After the robot got stable, we reduced the given target pitch
angle θs2to 10°. When the robot is stable again, we restore it
to 0°. When the hip joint angle is 0.5 rad, we marked the height
as an example for comparing the effect of the two algorithms,
as shown in Fig. 13.
With the introduction of the given target pitch angle θs2,it
carries extra weight torque. Extra pitch torque can be produced
to compensate for the extra weight torque in both algorithms so
that TLR will still balance at the initial position.
E. VTOL in Two-Wheel Mode Simulations
VTOL is the key to realize flexible deployment of TLR.
The power distribution coefficient kis introduced in the VTOL
process. During the takeoff, kincreases from 0 to 1, z-direction
force Pzincreases from 0 to self-weight, and the output torque
of the wheel reduces to zero. The landing process is inverse
to the takeoff process. In addition, when the wheel touches the
ground during the landing, Pzis reduced to 80 N, and the target
pitch θsis 0°. After TLR is stable, θsis gradually changed to the
kinematic target pitch angle θs1. Then, Pzis gradually reduced
to 0 N, and TLR switches to the two-wheel mode. Take the hip
joint angle of 0.5 rad as an example, the simulation of VTOL
result is shown in Fig. 14.
TLR can also achieve the takeoff and landing while moving
in the two-wheel mode, as shown in Fig. 15.
From the above results, cooperative algorithms can improve
the stability, load capacity, and uphill ability of TLR. Based
on the arbitrary pitch balancing function, TLR can achieve the
takeoff and landing in two-wheel mode. In an ideal situation,
SCA and WCA have similar control effects. However, when
Fig. 14. Simulation of VTOL in two-wheel mode.
Fig. 15. Simulation of takeoff and landing while moving under the two-
wheel mode.
Fig. 16. Ground movement function experiment.
Pzis low, SCA is easily constrained by the lowest force limit,
affecting the control.
VI. EXPERIMENTS OF TLR
Cooperative algorithms have been examined in the actual
environment tests. The influence of rotor rotation, ground effect,
and other factors on the control effect is compared and analyzed.
First, the two-wheel mode is tested and the control parameters
are debugged. TLR can flexibly move on the ground and adapt
to uneven terrains, as shown in Fig. 16. Second, the fixed-point
hovering function is tested. The control parameters in flight
mode are debugged and TLR shows a stable flight function,
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
GAO et al.: MULTIMODE TWO-WHEEL-LEGGED LAND-AIR LOCOMOTION ROBOT AND ITS COOPERATIVE CONTROL 9
Fig. 17. Fixed-point hovering function experiment.
Fig. 18. Self-balancing experimental results. (a) Experimental effect.
(b) SCA self-balancing effect. (c) Output torque of hip joint. (d) WCA
self-balancing effect.
as shown in Fig. 17. After testing the basic movement function,
two cooperative algorithms are tested.
A. Self-Balancing Experiments
In the experiment, the throttle of 1250–1800 corresponds to
the rotor pull of 0–13.6 kg. After TLR balances at different
heights, the rotor throttle is continuously raised and the actual
output torque of the hip joint motor is read, as shown in Fig. 18.
Similar to the simulation results, the two cooperative algorithms
can balance TLR at the target position. With the increase of
throttle, the actual output torque of the hip joint decreases, which
proves that cooperative algorithms can improve the load capacity
of TLR.
The difference between the simulation and experiment is that
rotor rotation reduces the fluctuation amplitude of pitch angle θ
and the x-direction distance x, making the robot more stable. Be-
cause the ground effect produces upward force onto the fuselage,
the output torque of the hip joint is further reduced, whereas the
rotor speed under WCA is higher and the ground effect is more
obvious. Besides, the lower the height of the fuselage, the more
obvious the ground effect will be, and the greater the difference
in effort-saving between the two algorithms.
Fig. 19. Uphill results under 0.8-rad hip joint.
Fig. 20. Uphill effect comparison.
B. Auxiliary Uphill Experiments
Take the hip joint angle of 0.8 rad as an example, TLR is
driven up to a slope of about 25° at different throttles, as shown
in Fig. 19.
By comparing the pitch angle θand the x-direction distance x,
θchanges obviously and xlags significantly when TSR goes up
to the slope. The experimental results in Fig. 20 show that SCA
can guarantee the control accuracy of θand xat low throttle.
At the high throttle, SCA is too easily affected by the ground
effect for going uphill smoothly. When using WCA, the larger
the throttle, the better the compensation effect is.
The effects of the two algorithms under different heights,
throttles, and slope angles are further compared. In simulation,
the cooperative algorithms can always shorten the uphill time
tuand reduce the pitch angle variation Δθ. However, due to
the influence of the ground effect, TLR will be subjected to
resistance, resulting in poor uphill ability, or even unable to
continue going uphill. The influence of the ground effect is more
obvious at low attitude, high throttle, and high slope inclination.
On comparing the two algorithms, the flow field of SCA is more
stable, and the influence of the flow field is more obvious. WCA
can ensure TLR climbing the slope smoothly by increasing the
throttle.
C. x-Direction Impact Resistance Experiments
A push rod is used to apply the x-direction impact force to the
fuselage, and a pressure sensor is installed at the end of the push
rod to detect the impact force, which is about 15 N, as shown in
Fig. 21.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
10 IEEE/ASME TRANSACTIONS ON MECHATRONICS
Fig. 21. Impact resistance experiment of TLR.
Fig. 22. Impact resistance experiment results.
The maximum x-direction distance xmax at different heights
and throttles are shown in Fig. 22.
Same as the simulation results, when TLR is impacted in the
x-direction, the cooperative algorithms can reduce xmax obvi-
ously. With the increase of the throttle, the control of the rotor
on the fuselage is enhanced, and xmax decreases. The difference
is that the flow field generated by SCA is more stable, making
the impact resistance of SCA better than WCA. Besides, SCA
is more susceptible to the ground effect at low heights, which
leads to its insufficient adjustment. In the case of a low throttle,
SCA is also more easily limited by the lowest output throttle and
cannot provide enough pitch torque for the fuselage.
D. Arbitrary Pitch Balancing Experiments
Arbitrary pitch balancing experiments ensure TLR to balance
when the given target pitch angle θs2is ±10°, as shown in Fig.
23.
In the simulation, two cooperative algorithms can always
ensure the accuracy of attitude and position perfectly, but exper-
imental results are a little different. SCA directly compensates
the extra weight torque through τθ, whereas WCA introduces
the x-direction force Pxin the compensation process, so the
vibration of WCA is slightly greater than that of SCA. By testing
at different heights and throttles, the two cooperative algorithms
can ensure the tracking effect of θs, and then the balance effect is
compared by the maximum x-direction distance xmax,asshown
in Fig. 24.
With the increase of throttle, the force and torque of the rotors
generally increase, and xmax decreases. The greater the height,
the greater the extra weight torque and the greater the xmax.
Because SCA always keeps the rotor in a horizontal state, the
flow field formed is relatively stable, so xmax of SCA is generally
smaller than that of WCA, but its ability to adjust is smaller. At
the same time, with the low fuselage height and high throttle,
Fig. 23. Arbitrary pitch balancing.
Fig. 24. Balance effect of arbitrary pitch angle at different heights and
throttles.
SCA is more easily impacted by the ground effect, which leads
to the increase of x.
In summary, both cooperative algorithms can realize the
coexistence of rotor power and leg power in simulations and
experiments. It can not only improve the uphill ability and
impact resistance but also make the robot balance at a specified
pitch attitude. Both algorithms have their own advantages and
missions. SCA produces a more stable flow field to show its
stability, but it is also more susceptible to the ground effect.
WCA can improve the uphill ability of TLR, and it is suitable
for cooperative control of the moving process. The higher the
throttle, the better the control effect. Finally, takeoff and landing
in two-wheel mode can be realized based on the cooperative
effect. Because the actual output capacity of the flight power
system is not ideal, we choose to prove the feasibility of the
algorithm through simulation instead of experiment. This is also
the first function to be realized in future work.
VII. CONCLUSION
In this article, TSR and tilting quadrotor are combined to
build a new land-air locomotion robot TLR. Two cooperative
algorithms are designed and verified through simulations and
experiments. The main conclusions are as follows. First, TSR
as the crawling mechanism is first used for TLR to achieve
excellent ground mobility. Three movement modes enable TLR
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
GAO et al.: MULTIMODE TWO-WHEEL-LEGGED LAND-AIR LOCOMOTION ROBOT AND ITS COOPERATIVE CONTROL 11
to adapt to many different environments. Second, two cooper-
ative algorithms are proposed and compared for achieving the
coordination of rotor power and leg power. The algorithms are
proven to improve load capacity, impact resistance, and uphill
ability of TLR, and even to balance at specified pitch attitude,
further achieving VTOL in two-wheel mode. SCA generates a
more stable flow field and is suitable for balancing in the site.
WCA shows stronger adjustment ability and is less affected
by ground effect and the lowest power output, so it is more
suitable for cooperative control in the moving process. In the
future, TLR will be further developed based on the result of this
article. In addition to the functions mentioned in this article, the
main direction is to realize control under more complex scenar-
ios, such as VTOL on uneven terrains and cooperative control
on slippery roads. Furthermore, an intelligent decision-making
algorithm based on multimode and task-oriented requirements
will be developed.
REFERENCES
[1] Z. Guo, T. Li, and M. Wang, “A survey on amphibious robots, in Proc.
IEEE 37th Chin. Control Conf., Jul. 2018, pp. 5299–5304.
[2] Y. Mulgaonkar et al., “The flying monkey: A mesoscale robot that can
run, fly, and grasp, in Proc. IEEE Int. Conf. Robot. Autom., 2016,
pp. 4672–4679.
[3] L. Filimon, “Traian Vuia the Romanian inventor who first flew a powered
airplane in 1906,” Incas Bull., vol. 3, no. 3, pp. 147–150, 2011.
[4] A. Kossett, R. D’Sa, J. Purvey, and N. Papanikolopoulos, “Design of an
improved land/air miniature robot, in Proc. IEEE Int. Conf. Robot. Autom.,
2010, pp. 632–637.
[5] A. Kossett and N. Papanikolopoulos, “A robust miniature robot design for
land/air hybrid locomotion,” in Proc. IEEE Int. Conf. Robot. Autom., 2011,
pp. 4595–4600.
[6] R. S. Adarsh and M. M. Dharmana, “Multi-terrain multi-utility robot,
Procedia Comput. Sci., vol. 133, pp. 651–659, 2018.
[7] J. Yang, Y. Zhu, L. Zhang, Y. Dong, and Y. Ding, “SytaB: A class of
smooth-transition hybrid terrestrial/aerial bicopters,” IEEE Robot. Autom.
Lett., vol. 7, no. 4, pp. 9199–9206, Oct. 2022.
[8] Z. Liu and Y. Liu, “Switching decision of air-ground amphibious robot
using neural network-based reinforcement learning,” in Proc. IEEE 9th
Int. Conf. CYBER Technol. Autom., Control Intell. Syst., Jul, 2019,
pp. 883–888.
[9] J. Guo, K. Zhang, S. Guo, C. Li, and X. Yang, “Design of a new type
of tri-habitat robot,” in Proc. IEEE Int. Conf. Mechatron. Autom., 2019,
pp. 1508–1513.
[10] J. Colmenares-Vazquez, N. Marchand, P. Castillo, J. E. Gomez-Balderas,
J. U. Alvarez-Munoz, and J. J. Tellez-Guzman, “Integral backstepping
control for trajectory tracking of a hybrid vehicle,” in Proc. Int. Conf.
Unmanned Aircr. Syst., Jun. 2015, pp. 209–217.
[11] Q. Tan, X. Zhang, H. Liu, S. Jiao, M. Zhou, and J. Li, “Multimodal dy-
namics analysis and control for amphibious fly-drive vehicle, IEEE/ASME
Trans. Mechatron., vol. 26, no. 2, pp. 621–632, Apr. 2021.
[12] F. Chen, R. Jiang, K. Zhang, B. Jiang, and G. Tao, “Robust backstepping
sliding-mode control and observer-based fault estimation for a quadro-
tor UAV,” IEEE Trans. Ind. Electron., vol. 63, no. 8, pp. 5044–5056,
Aug. 2016.
[13] N. Takahashi, S. Yamashita, Y. Sato, Y. Kutsuna, and M. Yamada, “All-
round two-wheeled quadrotor helicopters with protect-frames for air–
land–sea vehicle (controller design and automatic charging equipment),
Adv. Robot., vol. 29, no. 1, pp. 69–87, 2015.
[14] A.-M.R. McGowan et al., “Recent results from NASA’s morphing project,
in Proc. SPIE, 2002, pp. 97–111.
[15] H. Shan, G. Chen, S. Shi, Z. Wang, M. Qin, and W. Dong, “Dragon rider -
An integrated unmanned quadruped-hexarotor system for flight-impeded
area exploration,” in Proc. 27th Int. Conf. Mechatron. Mach. Vis. Pract.,
Nov. 2021, pp. 411–416.
[16] R. J. Bachmann, F. J. Boria, R. Vaidyanathan, P. G. Ifju, and R. D. Quinn,
“A biologically inspired micro-vehicle capable of aerial and terrestrial
locomotion,” Mechanism Math. Theory, vol. 44, no. 3, pp. 513–526, 2009.
[17] E. Zhang, R. Sun, Z. Pang, and S. Liu, “Obstacle capability of an air-
ground amphibious reconnaissance robot with a planetary wheel-leg type
structure,” Appl. Bionics Biomech., vol. 2021, 2021, Art. no. 7925707.
[18] S.Wang, Z. Chen, J. Li, J. Wang,J. Li, and J. Zhao, “Flexible motion frame-
work of the six wheel-legged robot: Experimental results,” IEEE/ASME
Trans. Mechatron., vol. 27, no. 4, pp. 2246–2257, Aug. 2022.
[19] Z. Chen, J. Li, J. Wang, S. Wang, J. Zhao, and J. Li, “Towards hybrid gait
obstacle avoidance for a six wheel-legged robot with payload transporta-
tion,” J. Intell. Robot. Syst., vol. 102, no. 60, 2021, Art. no. 60.
[20] Z. Chen, J. Li, S. Wang, J. Wang, and L. Ma, “Flexible gait transition for
six wheel-legged robot with unstructured terrains,” Robot. Auton. Syst.,
vol. 150, 2022, Art. no. 103989.
[21] H. Peng, J. Wang, W. Shen, D. Shi, and D. Liu, “Coordinated motion
control for a wheel-leg robot with speed consensus strategy, IEEE/ASME
Trans. Mechatron., vol. 25, no. 3, pp. 1366–1376, Jun. 2020.
[22] A. Kalantari and M. Spenko, “Modeling and performance assessment of
the HyTAQ, a hybrid terrestrial/aerial quadrotor,” IEEE Trans. Robot.,
vol. 30, no. 5, pp. 1278–1285, Oct. 2014.
[23] A. Kalantari and M. Spenko, “Design and experimental validation of
HyTAQ, a hybrid terrestrial and aerial quadrotor,” in Proc. IEEE Int. Conf.
Robot. Autom., 2013, pp. 4445–4450.
[24] K. Kawasaki, M. Zhao, K. Okada, and I. Masayuki, “MUWA: Multi-field
universal wheel for air-land vehicle with quad variable-pitch propellers,”
in Proc. IEEE Int. Conf. Intell. Robot. Syst., Nov. 2013, pp. 1880–1885.
[25] K. Kim, P. Spieler, E. S. Lupu, A. Ramezani, and S. J. Chung, “A bipedal
walking robot that can fly, slackline, and skateboard, Sci. Robot.,vol.6,
no. 59, 2021, Art. no. eabf8136.
[26] V. Klemm et al., “Ascento: A two-wheeled jumping robot,” in Proc. IEEE
Int. Conf. Robot. Autom., 2019, pp. 7515–7521.
[27] V. Klemm et al., “LQR-assisted whole-body control of a wheeled bipedal
robot with kinematic loops,” IEEE Robot. Autom. Lett., vol. 5, no. 2,
pp. 3745–3752, Apr. 2020.
[28] L. Cui et al., “Learning-based balance control of wheel-legged robots,
IEEE Robot. Autom. Lett., vol. 6, no. 4, pp. 7667–7674, Oct. 2021.
[29] L. Guo, S. Rizvi, and Z. Lin, “Optimal control of a two-wheeled self-
balancing robot by reinforcement Q-learning,” Int. J. Robust Nonlinear
Control, vol. 31, no. 6, pp. 1885–1904, 2021.
[30] D. Chen, K. Qian, C. Liu, and Y. Zhu, “Research on attitude control system
of four-rotor UAV based on two ring control,” in Proc. IEEE Inf. Technol.
Mechatron. Eng. Conf., 2020, pp. 249–253.
[31] S. Eshaghi and M. S. Tavazoei, “Finiteness conditions for performance
indices in generalized fractional-order systems defined based on the reg-
ularized Prabhakar derivative, Commun. Nonlinear Sci. Numer. Simul.,
vol. 117, 2023, Art. no. 106979.
Jingsong Gao received the B.S. degree in me-
chanical design and manufacture and automa-
tion and the M.S. degree in mechanical engi-
neering, in 2017 and 2019, respectively, from
Harbin Institute of Technology, Harbin, China,
where he is currently working toward the Ph.D.
degree in mechatronics engineering with the
State Key Laboratory of Robotics and System,
HIT.
His research interests include amphibious
robots and robotic control.
Hongzhe Jin (Member, IEEE) received the
B.S. degree in instrument science and technol-
ogy from Harbin Institute of Technology (HIT),
Harbin, China, in 1999, and the Ph.D. degree
in electronic engineering from Pusan National
University, Busan, South Korea, in 2009.
He is currently an Associate Professor with
the School of Mechatronics Engineering, HIT.
His research interests include modeling, con-
trol, and identification of complex systems and
robotics.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
12 IEEE/ASME TRANSACTIONS ON MECHATRONICS
Liang Gao received the B.S. and Ph.D. degrees
in mechatronics engineering from Harbin Insti-
tute of Technology (HIT), Harbin, China, in 2011
and 2020, respectively.
He is currently a postdoctoral researcher
with the School of Mechatronics Engineering,
HIT. His research interests include amphibious
robots and morphing flying robots.
Jie Zhao (Member, IEEE) received the B.S.
and Ph.D. degrees in mechatronics engineer-
ing from Harbin Institute of Technology (HIT),
Harbin, China, in 1990 and 1996, respectively.
He is currently a Professor with the School
of Mechatronics Engineering, HIT, where he is
also the Director of the State Key Laboratory
of Robotics and System. He is the Leader of
the Subject Matter Expert Group of Intelligent
Robots in the National 863 Program supervised
by the Ministry of Science and Technology of
China. His research interests include industrial robots and bionic robots.
Yanhe Zhu (Member, IEEE) received the B.S.
and Ph.D. degrees in mechatronics engineer-
ing from Harbin Institute of Technology (HIT),
Harbin, China, in 1998 and 2004, respectively.
He is currently a Professor with the School
of Mechatronics Engineering, HIT. His research
interests include exoskeleton robots, modular
self-reconfigurable robots, and supernumerary
robotic limbs.
Hegao Cai received the B.S. degree in mecha-
tronics engineering from Harbin Institute of
Technology (HIT), Harbin, China, in 1958.
He is currently an Academician with the Chi-
nese Academy of Engineering and a Profes-
sor with the School of Mechatronics Engineer-
ing, HIT. He authored or coauthored more than
200 articles published in journals and confer-
ence proceedings in his field. His current re-
search interests include the design, control, and
application of industrial robots.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on March 14,2024 at 09:19:22 UTC from IEEE Xplore. Restrictions apply.
... However, the parallel mechanism limits the workspace of the base links, e.g., operational height and base pitch angle. On the contrary, WBRs with planar two-link serial legs [5]- [8], shown in Fig. 2b, have larger workspace. A serial design usually has the knee motor aligned with the hip joint and connected to the knee by a parallel four-bar linkage to reduce the leg inertia. ...
... It approximates the WBR dynamics by a body-fixed inverted pendulum with wheels. The WIP is integrated with PID controllers [1], [2], whole body controllers (WBC) [5], [8], [10], and model predictive controllers (MPC) [6], [7] for various scenarios and applications. However, to simultaneously control the height and orientation of WBRs with 2-DoF legs, the assumption of fixed body will be inevitably violated. ...
Preprint
Full-text available
Wheeled bipedal robots (WBRs) have the capability to execute agile and versatile locomotion tasks. This paper focuses on improving the dynamic performance of WBRs through innovations in both hardware and software development. Inspired by the human barbell squat, a bionic mechanical design is proposed and implemented as shown in Fig. 1. It distributes the weight onto its hip and knee joints to improve the effectiveness of joint motors while maintaining a relatively large workspace of the base link. Meanwhile, a novel model-based controller is devised, synthesizing height-variable wheeled linear inverted pendulum (HV-wLIP) model, Control Lyapunov Function (CLF) and whole-body dynamics for theoretically guaranteed stability and efficient computation. Compared with other alternatives, as a more accurate approximation of the WBR dynamics, the HV-wLIP can enable more agile response and provide theory basis for WBR controller design. Experimental results demonstrate that the robot could perform human-like deep squat, and is capable of maintaining tracking CoM velocity while manipulating base states. Furthermore, it exhibited robustness against external disturbances and unknown terrains even in the wild.
... For the multimodal quadrotor [10], the quadrotor can perform different tasks by presetting several variation modes, and switching among them during flight to meet the multitasking requirements. To this end, for each variation mode, a corresponding control law is predesigned [11], [12]. For the foldable quadrotor [13], the quadrotor modifies its size by actively changing the mechanical structure to enhance its passability (e.g., passing narrow channels). ...
Preprint
Full-text available
In comparison to common quadrotors, the shape change of morphing quadrotors endows it with a more better flight performance but also results in more complex flight dynamics. Generally, it is extremely difficult or even impossible for morphing quadrotors to establish an accurate mathematical model describing their complex flight dynamics. To figure out the issue of flight control design for morphing quadrotors, this paper resorts to a combination of model-free control techniques (e.g., deep reinforcement learning, DRL) and convex combination (CC) technique, and proposes a convex-combined-DRL (cc-DRL) flight control algorithm for position and attitude of a class of morphing quadrotors, where the shape change is realized by the length variation of four arm rods. In the proposed cc-DRL flight control algorithm, proximal policy optimization algorithm that is a model-free DRL algorithm is utilized to off-line train the corresponding optimal flight control laws for some selected representative arm length modes and hereby a cc-DRL flight control scheme is constructed by the convex combination technique. Finally, simulation results are presented to show the effectiveness and merit of the proposed flight control algorithm.
Article
Aiming at the problem that the two‐wheeled mobile self‐balancing robot (TWMSR) is challenging to control balance when TWMSR drives on uneven surface road, this study adds a DNN‐compensator specially used to curb the TWMSR's toppling based on the traditional PID motion balance control system. A coupling function couples the control value between the PD‐controller and the DNN‐compensator. Its effect is that when the PD‐controller's output value is insufficient to maintain the TWMSR's balance, the DNN‐compensator will compensate the PD‐controller's output. The experimental results show that using our DNN‐compensator coupling PD‐controller balance control strategy to control the TWMSR movement on uneven surface road can maintain the TWMSR drive stability; compared to traditional PD‐controller, our control strategy braking performance is better, and the pitch angle () fluctuation range is smaller, TWMSR topple over is difficult.
Article
Full-text available
According to the requirements of the reconnaissance robot for the ability to adapt to a complex environment and the in-depth study of the obstacle climbing mechanisms, a planetary wheel-leg-combined mechanism capable of adapting to complex terrains is proposed. According to the proposed planetary wheel-leg-combined mechanism, the land part of the air-ground amphibious reconnaissance robot is designed. Considering the obstacle and fast marching performance, four groups of combined wheel-leg mechanisms are adopted in the land bank. Under the action of three kinds of obstacles, the stability and the movement ability of the robot are analyzed by using the static method. The parameter model of the reconnaissance robot is built by a virtual prototype dynamics software MSC.ADMAS. The kinematic characteristic curves of each component and the whole prototype are obtained, which provides a theoretical basis for the design and numerical calculation of the robot structure. Finally, the climbing ability tests of the reconnaissance robot prototype verify the reliability and practicability of the body structure of the reconnaissance robot.
Article
Full-text available
This paper studies the adaptive optimal control problem for a wheel-legged robot in the absence of an accurate dynamic model. A crucial strategy is to exploit recent advances in reinforcement learning and adaptive dynamic programming (ADP) to derive a learning-based solution to adaptive optimal control. It is shown that suboptimal controllers can be learned directly from input-state data collected along the trajectories of the robot. Rigorous proofs for the convergence of the novel data-driven value iteration (VI) algorithm and the stability of the closed-loop robot system are provided. Experiments are conducted to demonstrate the efficiency of the novel adaptive suboptimal controller derived from the data-driven VI algorithm in balancing the wheel-legged robot to the equilibrium.
Article
Full-text available
With the increasing requirements for vehicle mobility and transport efficiency, the amphibious fly-drive vehicle has attracted more widespread attention. This paper presents a novel fly-drive vehicle driven by rotor-wing in the air and Ackerman chassis on the road. The vehicle is designed to achieve continuous air-land motion. To describe the multimodal motion, an integrated dynamic model is proposed, mainly combining the rotor-wing model, tire model, chassis two-track model, and suspension model. Based on the coupling dynamic analysis of the landing process, the rotor-wing is designed as an active regulator to compensate for the suspension vibration after the tire crashing to the ground. The controller is achieved by combining the model predictive controller (MPC) and control allocation under a two-layer structure. The integrated model is implemented in MATLAB, and the landing motion results caused by different parameters show a reasonable varying trend. Compared with a normal landing process, the proposed rotor-wing controller is verified with hardware-in-the-loop simulation (HIL) to be efficient in enhancing the landing stability of the fly-drive vehicle.
Article
In the present paper, we introduce the generalized fractional-order control systems with the regularized Prabhakar fractional derivative and investigate the BIBO stability for this kind of systems. For such kind of systems with step functions at their inputs, we establish some conditions imposed on the parameters of the corresponding fractional-order transfer functions under which the steady state error is zero and the performance indices are finite. Further, in order to examine the analytical obtained results, several generalized fractional-order transfer functions are considered. Then, we show that the parameters of the regularized Prabhakar fractional derivative play significant roles in finiteness of the performance indices in the systems.
Article
This work details the design, modeling and control of SytaB, a vehicle capable of hybrid terrestrial/aerial mobility with smooth transition, where the structure embedding a bicopter is adopted for the first time. In contrast to previous hybrid terrestrial/aerial vehicles with a quadrotor embedded, SytaB not only requires less energy for the same takeoff weight, but also regulates its attitude less frequently to restrain the vibration of sensors. Three modes, the terrestrial/aerial/transitional modes, are considered for the vehicle , and the dynamics modeling and controller design of each mode are carried out . The transition between terrestrial and aerial locomotions is smooth compared with the case of non-inclusion of transitional mode such that the bounce and shake of the vehicle are alleviated. The energy efficiency is compared between the terrestrial and aerial modes, and between the energy-saving and high-maneuverability paradigms (a choice enabled in the terrestrial mode of SytaB). Experimental results are presented to demonstrate the potential of SytaB, the effectiveness of the designed controllers, and the necessity of considering the transition process.
Article
The flexibility of gait and trajectory planning with heavy payload are the main challenges for legged stable walking of hexapod robots in unstructured terrain, especially in time-varying and local terrain mutation conditions. To guarantee adaptability in unstructured terrain environment, the factors, including the obstacle height, terrain depth, and secure foothold as well as stability state, should be considered in the gait and trajectory planning. In this article, a novel gait transition hierarchical control framework based on a flexible gait planner (FGP), and gait feedback regulator (GFR) with behavior rules is proposed for the developed hexapod wheel-legged robot (BIT-6NAZA). The core of this gait planner is to select the optimal footholds and change gait types according to secure foothold and stability margin and kinematic margin of legs, and the GFR is applied to modify the foot-end trajectory of the selected gait according to the terrain feedback information to adapt to unstructured terrain. Finally, taking BIT-6NAZA robot as an example, the simulation and experiment are carried out under the proposed control framework. The co-simulation and experimental results show that the robot can modify the foot-end trajectory in dynamic unstructured terrain and obtain elastic gait in obstacle avoidance.
Article
Numerous mobile robots in various forms specialize in either ground or aerial locomotion, whereas very few robots can perform complex locomotion tasks beyond simple walking and flying. We present the design and control of a multimodal locomotion robotic platform called LEONARDO, which bridges the gap between two different locomotion regimes of flying and walking using synchronized control of distributed electric thrusters and a pair of multijoint legs. By combining two distinct locomotion mechanisms, LEONARDO achieves complex maneuvers that require delicate balancing, such as walking on a slackline and skateboarding, which are challenging for existing bipedal robots. LEONARDO also demonstrates agile walking motions, interlaced with flying maneuvers to overcome obstacles using synchronized control of propellers and leg joints. The mechanical design and synchronized control strategy achieve a unique multimodal locomotion capability that could potentially enable robotic missions and operations that would be difficult for single-modal locomotion robots.
Article
This article concerns optimal control of the linear motion, tilt motion, and yaw motion of a two‐wheeled self‐balancing robot (TWSBR). Traditional optimal control methods for the TWSBR usually require a precise model of the system, and other control methods exist that achieve stabilization in the face of parameter uncertainties. In practical applications, it is often desirable to realize optimal control in the absence of the precise knowledge of the system parameters. This article proposes to use a new feedback‐based reinforcement learning method to solve the linear quadratic regulation (LQR) control problem for the TWSBR. The proposed control scheme is completely online and does not require any knowledge of the system parameters. The proposed input decoupling mechanism and pre‐feedback law overcome the commonly encountered computational difficulties in implementing the learning algorithms. Both state feedback optimal control and output feedback optimal control are presented. Numerical simulation shows that the proposed optimal control scheme is capable of stabilizing the system and converging to the LQR solution obtained through solving the algebraic Riccati equation.