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Authors:
• Shenzhen Institute of Artificial Intelligence and Robotics for Society
• The Chinese University of Hong Kong Shenzhen

## Abstract and Figures

Quadruped robots manifest great potential to traverse rough terrains with payload. Current model-based controllers, which are extensively adopted in quadruped robot locomotion control, rely on accurate estimation of parameters and will significantly deteriorate in severe disturbance, e.g., adding heavy payload. This article introduces an online identification method, which is named as adaptive control for quadruped locomotion, to address model uncertainties. Meanwhile, a concurrent adaptive controller is also indispensable to accomplish identification and locomotion. Therefore, this article presents an adaptive control algorithm based on the online payload identification for the high payload capacity (the ratio between payload and robot’s self-weight) quadruped locomotion. The newly proposed algorithm could achieve estimating and compensating the external disturbances induced by the payload online. The tracking accuracy of the robot’s center of mass and orientation trajectories for the identification task is highly improved. The locomotion task can be incorporated in inverse-dynamics-based quadratic programming, realizing a trotting gait. The proposed method is verified in a real quadruped robot platform. Experiments prove the estimation efficacy for the payload weighing from 20 to 75 $\rm kg$ and loaded at different locations of the robot’s torso.
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IEEE/ASME TRANSACTIONS ON MECHATRONICS 1
Linear Legs
Bingchen Jin , Shusheng Ye , Juntong Su , and Jianwen Luo
AbstractQuadruped robots manifest great potential to
traverse rough terrains with payload. Current model-based
robot locomotion control, rely on accurate estimation of pa-
rameters and will signiﬁcantly deteriorate in severe distur-
an online identiﬁcation method, which is named as adap-
uncertainties. Meanwhile, a concurrent adaptive controller
is also indispensable to accomplish identiﬁcation and lo-
trol algorithm based on the online payload identiﬁcation
and robot’s self-weight) quadruped locomotion. The newly
proposed algorithm could achieve estimating and compen-
sating the external disturbances induced by the payload
online. The tracking accuracy of the robot’s center of mass
and orientation trajectories for the identiﬁcation task is
highly improved. The locomotion task can be incorporated
ing a trotting gait. The proposed method is veriﬁed in a real
quadruped robot platform. Experiments prove the estima-
tion efﬁcacy for the payload weighing from 20 to 75 kg and
loaded at different locations of the robot’s torso.
robot.
I. INTRODUCTION
WHILE the humans are biologically evolved to handle a
variety of scenarios ranging from domestic service to
industrial labor, robots are usually custom-designed for particu-
lar purposes under predeﬁned engineering speciﬁcations [1]–[4].
Manuscript received January 18, 2022; revised March 25, 2022; ac-
cepted April 20, 2022. Recommended by Technical Editor D. Wollherr
and Senior Editor X. Chen. This work was supported in part by the
National Natural Science Foundation of China under Grant 51905251,
in part by Shenzhen Institute of Artiﬁcial Intelligence and Robotics for
Society under Grant AC01202101023. (Corresponding author: Jianwen
Luo.)
The authors are with the Shenzhen Institute of Artiﬁcial Intelligence
and Robotics for Society, Shenzhen 510000, China (e-mail: luojian-
wen1123@gmail.com).
https://ieeexplore.ieee.org, provided by the authors.
thors and color versions of one or more ﬁgures available at
https://doi.org/10.1109/TMECH.2022.3170548.
Digital Object Identiﬁer 10.1109/TMECH.2022.3170548
For example, the speciﬁcations for serial manipulators often aim
at dexterous object manipulation tasks, while mobile platforms
tend to overcome different terrains when carrying payloads.
Hybrid robots that combine the existing designs of two different
robots [5], i.e., a manipulator and a mobile platform, become a
convenient solution in modern applications, signiﬁcantly reduc-
ing the complexity in design and implementation but poses new
challenges in high-level control and integration [6].
Legged robots are ideal for such hybrid demand, which needs
to walk through different terrains while carrying a meaningful
one legged robot with a limited payload, one solution uses
multiple ones to effectively move a large payload, such as pulling
a truck. Many hybrid robots have been designed with updated
engineering speciﬁcations for mobile manipulation tasks to
overcome this challenge, which is usually an expensive task [8].
Another immediate solution would be directly deploying a ma-
nipulator on top of an existing legged robot. However, there
remains a limited implementation in such an effort as the payload
of most legged robots is usually limited within a relatively
small amount, leaving space for only lightweight manipulators
in practice.
To overcome this challenge, a novel quadruped robot, Kirin, is
designed as shown in Fig. 1. Kirin has four proprioceptive linear
legs, driven by quasi-direct drives (QDD), making it efﬁcient in
vertical payload carrying up. At the current stage, Kirin is able
to carry up to 75 kg and walk at the speed of 0.9 m/s.The
QDD design enables the robot to have a much lighter weight
than other linear legs, achieving a decent payload capacity (PLC)
while proprioceptive during dynamic locomotion. As a potential
platform for mobile manipulation using the legged robot, it
becomes possible to integrate Kirin with the existing designs
of collaborative robots while leaving a meaningful payload for
object manipulation ranging from domestic service to industrial
algorithms during quadruped locomotion, which motivates this
article.
The robots developed by Boston dynamics provide a pool
of inspiration for modern legged robots. Moving from earlier
design with hydraulic power [9], the electrical-driven spot se-
ries feature a high power density in a lightweight form factor
with agile mobility. The engineers demonstrated an engineering
solution to overcome Spot’s drawback in absolute PLC by
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2IEEE/ASME TRANSACTIONS ON MECHATRONICS
Fig. 1. Kirin, a quadruped robot designed with proprioceptive linear
legs and high PLC. There are three joints, including hip roll, hip pitch
and knee joints. Hip roll and pitch are revolute joints while knee joint is
prismatic. (A) Kirin stands, carrying ﬁve sandbags, each of which weigh
around 25 kg. (B) Kirin identiﬁes the unknown mass and position of
payload. (C) Kirin trots in place carrying 50 kg sandbags. (D) Kirin trots
forward with around 50 kg sandbags.
using multiple robots to collectively pull a truck simultaneously.
Nevertheless, the robot still preserves a reasonable payload to
carry a manipulator as a hybrid robot, custom-designed for
in-door scenarios such as in the kitchen. However, when dealing
with industrial carrying in warehouses, the company chose a rad-
ical approach by developing a new robot, Handle, for lightweight
carrying, and another robot, Stretch, for heavy lifting. These
robots are released with limited information regarding their
technical details.
Among the research community, many quadruped robots
have been developed to demonstrate advanced locomotion, but
limited in payload carrying as a hybrid robot platform. For agile
quadruped robots, the MIT’s Cheetah [10] and ETH’s ANY-
mal [11] exhibit state-of-the-art performance in multiterrain
locomotion, but they are not able to carry heavy payload by
nature. Though, there are some novel deigns for agile robots
with lightweight robotic arms. Spova [12], an integration of spot
and a robotic arm, could realize garbing the ball. ANYmal can
be equipped with a six degrees of freedom (DOF) robotic arm
and perform objects grasping [6]. Meanwhile, some commercial
robots like Unitree’s Aliengo and DeepRobotics’ Jueying [13]
also have their speciﬁc manipulators. Despite that, their PLC is
still not enough for industrial work. On the other hand, SJTU
develops baby elephant [14] that has a parallel leg and weights
130 kg, which make it not suited for domestic service.
Besides design, the control algorithms are also critically im-
portant to deploy quadruped as the mobile platform for hybrid
robots [15]–[18]. To date, most of these advanced locomotion
controllers are developed based on accurate robot models, i.e.,
the perfect performance is greatly correlated with the accuracy
of physical parameters, including the link inertia and center-
of-mass (CoM) positions [2], [19]–[23]. In many real world
applications, e.g., carrying unknown payload, an ofﬂine sys-
tem identiﬁcation would lead to large deviations. Consequently,
the control methods that highly depend on deterministic robot
models are prone to failures.
By far, there are two main approaches have been proposed for
parameters identiﬁcation and adaptive control for robots with
payload. One is to identify the torso’s parameters online [24],
integrating the robot’s torso and the payload into a rigid body.
However, it is only conducted into the ﬁxed-base rigid body
system. An online identiﬁcation method overcomes this short-
coming and use a combination of techniques that guarantee the
robot locomotion stability [25], which was veriﬁed on HyQ in a
static walking gait. Scalf-III, a hydraulic actuated heavy-duty
quadruped robot developed by Shandong University, is con-
trolled by a CoM estimation and adaptation method in dynamic
trot gait [26].
Another approach is to incorporate the adaptive control into
control theory is proposed for legged robots and veriﬁed in sim-
ulation [27], [28]. With a hierarchical reactive control scheme,
LLAMA, a human-scale electrically driven robot can perform
efﬁcient locomotion even under variable payloads [29]. Online
learning has been performed in ﬁtting unknown dynamics and
make predictions for the future [30]. With the support of nominal
model, this method could facilitate the walking stability of
A1 under varying load conditions. Similarly, ACLF-MPC has
been developed and implemented into hardware experiments on
ANYmal [31]. With the stability guarantees provided by control
Lyapunov functions, it is able to handle external payload and
model underestimation. Furthermore, there are other studies that
where the goal is to demonstrate the robustness of controllers
based on reinforcement learning.
locomotion (ACQL) is proposed, which can be utilized in pay-
robot, Kirin, which is featured with proprioceptive linear legs
and capable of heavy payload carrying. The contributions lie in
the following twofold:
1) An online payload identiﬁcation algorithm based on a re-
cursive formulation is devised for a high PLC quadruped
robot. This algorithm guarantees the fast convergence of
the identiﬁcation.
control algorithm is veriﬁed for PLC from 0.2 to 1.5 in
quasi-static motion and trotting gait. To our best knowl-
edge, it is the ﬁrst time to deploy the adaptive control for
a wide PLC range on an electrically actuated quadruped
robot. This allows for more options of payload position
and mass. With the help of it, the quadruped robot could
expand the range of physical work to a great extent.
introduces the locomotion controller. The payload identiﬁcation
and adaptive control are proposed in Section II-B. Sections III
and IV present the experimental results and corresponding
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JIN et al.: UNKNOWN PAYLOAD ACQL WITH PROPRIOCEPTIVE LINEAR LEGS 3
II. UNKNOWN PAYL OA D ADAPTIVE CONTROL
demonstrated. In section A, the extensively adopted locomo-
tion control method, consisting of feedback, feedforward and
quadratic programming (QP) solver, is introduced. For known or
deterministic model parameters, this locomotion control method
usually works well for most legged robots [15], [33], [34]. How-
robot to greatly change the model parameters, performance is
deteriorated mainly due to the failure of feedforward and limita-
tion of feedback. In section B, ACQL is devised for identifying
the unknown payload mass and moment so as to improve the
performance of locomotion control with extra payload.
A. Locomotion Control
The DoFs and inertia distribution of Kirin are illustrated in
Fig. 1. The dynamics of Kirin is modeled as follows:
m¨ra
b=Fimigmpg
d
dt(a
b)=rbci ×Fi+rp×mpg
+ri×mig
,(1)
where mdenotes the total mass, migdenotes the gravitational
force acting on the body i.ridenotes the corresponding position
vector from the origin of the inertial frame to the CoM of the leg i.
mpgis the gravity of the payload and rpmeans the corresponding
position vector of mpg.Fidenotes the contact force of each foot
i.rbci is the position vector from base to contact foot. I∈
3×3
is the inertial of the robot. The left component of the second
equation of (1) can be extended as follows:
d
dt(a
b)=I˙ωa
b+ωa
b×(a
b).(2)
A widely used simplicity for the quadruped robot dynamics
is the precession and nutation of ωa
b×(a
b)of(2)isusually
discarded since this component contributes little to the dynamics
of the robot [16], and the second equation of (1) can be approx-
imated to be
I˙ωa
b=rbci ×Fi+rp×mpg+ri×mig. (3)
Based on (1) and (3), the feedback and feedforward control
to compute the desired force Fband moment Tbactingonthe
torso of Kirin is devised as
Fb=Kf
p(rd
bra
b)+Kf
i(rd
bra
b)dt
+Kf
d(vd
bva
b)+mab+mig+mpg
Tb=Kt
plog (qd
b·(qa
b)1)
+Kt
ilog (qd
b·(qa
b)1)dt
+Kt
dlog (ωd
b·(ωa
b)1)
+ri×mig+rp×mpg
,(4)
Fband Tbdenote the desired force and moment acting on Kirin’s
torso, respectively. rd
b,vd
b,ab,qd
b,ωd
bdenote the desired position,
linear velocity, linear acceleration, rotation matrix, and angular
velocity of the robot torso, respectively. ra
b,va
b,qa
b, and ωa
b
denote the actual position, linear acceleration, rotation matrix,
and angular velocity of the robot torso, respectively. K(·)
(·)denotes
the diagonal gain matrices, which need to be manually tuned in
the experiment. The ﬁrst three components on the right side in (4)
are the PID tracking controllers and the remaining components
are the feedforward controller.
realize the quadruped locomotion, including the trotting gait.
The inverse dynamics solver computes the desired force Fband
torque Tbacting on the torso of the robot to track the desired
motion. (4) is formulated as a QP problem, by which the contact
force Fdis computed. The QP formulation is given as follows:
Fd=argmin
F
(AF B)TQ(AF B)+FTRF
s.t.
τmin J1Fτmax
μFiz Fix μFiz
μFiz Fiy μFiz
DiFi=0
,(5)
where τmin and τmax are the robot’s minimal and maximum joint
torque. Fix,F
iy, and Fiz are the components of each foot’s
contact force vector. μis the coefﬁcient of friction between the
contact foot and the ground. Jdenotes the Jacobian matrix of the
robot. Didenotes the matrix which selects the feet that does not
contact the ground. ˆrbi is the skew-symmetric matrix deﬁning
the cross product of rbci.Fd∈
3N×1is the concatenated vector
of the contact forces. Ndenotes the number of legs that contact
the ground. The diagonal matrix Qand Rare the weight matrix
and needs to be adjusted via experiment as well. Aand Bare
given as follows:
A=··· I···
··· ˆrbi ···
,B =Fb
Tb.(6)
From (4) to (6), The locomotion controller requires accurate
model parameters, which would be impaired by large distur-
bance. Therefore, the identiﬁcation of the payload will be de-
tailed in the next section.
This section devises a method to identify the mass and mo-
deployed in real world applications, e.g., carrying constant
disturbances to the mobile platform. This study proposes an
ACQL to tackle this issue. For analysis simplicity, within the
scope of this study, ACQL is based on the assumption that the
disturbance by payload are composed of an external force and
the corresponding torque. Only the force and torque exerted
on the robot base are taken into consideration, which is also
reasonable. Based on the assumption, the quadruped dynamics
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4IEEE/ASME TRANSACTIONS ON MECHATRONICS
Fig. 2. Control scheme of the adaptive control with online unknown
directly and generates an update law. The recursive result of the update
law is the payload moment around the robot. ACQL also uses an aux-
iliary input to demonstrate the posture of robot and help to derive the
update law. The torques of joints are calculated via inverse dynamics
based on QP solver.
model for ACQL is presented. The proposed ACQL consists of
an auxiliary input and a corresponding update law.
The scheme of ACQL is shown in Fig. 2. In ACQL, the pay-
load’s estimated mass is given by an analytical solution, which
is computationally efﬁcient. An auxiliary input is proposed to
adjust the robot’s posture while an update law identiﬁes the
The ﬁrst equation of (1) can be rewritten and the estimated
mass of the payload ˆmpis given by the following:
ˆmp=1
gFimim¨ra
b
g.(7)
static. Therefore, the acceleration-dependent term could be
omitted. Meanwhile, when relatively minor payload is imposed
during locomotion, we propose to use the current estimation
of mto compute the acceleration-dependent term. Though it
tends to overestimate the mass of the payload at ﬁrst, ˆmpcould
be corrected via seven approximately. To estimate the payload
moment, (3) is reformulated in a standard state-space form
˙x1=x2
˙x2=Bu +d+k
˙
ˆ
d=φ
(8)
where x1denotes the robot orientation. Though there exists a
projection matrix from the time derivatives of Euler angles to
angular velocity, it is approximated as the identity matrix, since
the Euler angles are actually near to zero in the experiments.
x2denotes the angular velocity of the robot. Bdenotes I1.
udenotes rbci ×Fi.kdenotes I1ri×mig.ddenotes
I1rp×mpgwhich is the parameter to be identiﬁed. ˆ
ddenotes
the estimated value of d.φdenotes the update law ˙
ˆ
d.
There are multiple options for tracking the balance of a
quadruped robot, such as base orientation, angular velocity of
torso, and rotation matrix. In this study, the base orientation
error is selected as the tracking object, which could be deﬁned
as x=x1x1d. Therefore, ﬁrst and second derivative of the
tracking error are ˙
xx1=x2and ¨
xx2, respectively. Con-
sider the function
s=˙
x+λx(9)
where λis a positive deﬁnite matrix. Combined with (8), the
derivative of sis given by the following:
˙s=¨
x+λ˙
x
x2+λx2
=Bu +d+k+λx2.(10)
Based on the derivation, the auxiliary input is devised as
follows:
u=B1(ˆ
d+k+cs +λx2)(11)
where cis a positive deﬁnite matrix. Put (11) in (10), we are left
with
˙s=cs +
d(12)
where
d=dˆ
d. From (12), it can be concluded that ˙swill
asymptotically converge to zero if
dasymptotically converges
to zero, with the property that swill be equal to zero. The update
law ˙
ˆ
dis devised based on uand the aforementioned assumptions.
Consider the manifold
M={(x1,x
2,d)∈
3×3|ˆ
dd+β(x1,x
2)=0},(13)
where β(x1,x
2)is the estimation error function to be designed.
As such, the problem is reformulated into the design of an
appropriate function β(x1,x
2)to ensure the manifold to be
invariant and attractive. Deﬁne the manifold as
z=ˆ
dd+β(x1,x
2).(14)
The derivative of zis
˙z=˙
ˆ
d+˙
β(x1,x
2).(15)
Substitute the robot dynamic system (8) into (15)
˙z=φ+∂β
∂x1
x2+∂β
∂x2
˙x2
=φ+∂β
∂x1
x2+∂β
∂x2
(Bu +ˆ
dz+β(x1,x
2)+k).(16)
Thus, the update law ˙
ˆ
dand manifold zcan be designed as
˙
ˆ
d=∂β
∂x1x2∂β
∂x2(Bu +ˆ
d+β(x1,x
2)+k)
˙z=∂β
∂x2z. .(17)
In order to make sure the system zis Lyapunov stable and re-
duce the computation complexity, the estimation error function
β(x1,x
2)is designed as
β(x1,x
2)=[k1ωa
bx,k
2ωa
by,k
3ωa
bz]T(18)
where k1,k
2,k
3are positive. ωa
bx
a
by
a
bz are the components
of angular velocity ωa
b.
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JIN et al.: UNKNOWN PAYLOAD ACQL WITH PROPRIOCEPTIVE LINEAR LEGS 5
Algorithm 1: ACQL Algorithm.
Input: qd
b
d
b,r
d
b,v
d
b,m
i,r
i,q
a
b
a
b,q
joint ,˙qj oint
joint
Output: Fd
1: Bri,Bvi,B¨riForward kinematics (qjoint,˙qjoint )
2: Bra
b,Bva
b,B¨ra
bBri,Bvi,B¨ri
3: Rqd
b
4: ra
b,v
a
b,¨ra
bRBra
b,R
Bva
b,R
B¨ra
b
5: Faτjoint
6: ˆmpmi,¨ra
b,F
a
7: eqb log (qd
b·(qa
b)1)
8: while eqb >e
threshold do
9: u⇐−B1(ˆ
d+k+cs +λx2)(auxiliary input)
10: ˙
d⇐−M(Bu +ˆ
d+β(x1,x
2)+k)(update law)
11: ˆ
dk+1=˙
dΔt+ˆ
dk
12: eqr ra
b,r
d
b
13: ˙eqr va
b,v
d
b
14: ˙eqb log (ωd
b·(ωa
b)1)
15: Fbeqr,˙eqr,m
i,ˆmp,a
b
16: Tbeqb,˙eqb,r
i,m
i,u, ˆ
d
17: BFb,T
b
18: ira
b,r
i
19: Fdarg minF(AF B)TQ(AF B)+FTRF
20: end while
Thus, the update law ˙
ˆ
dand zcan be written as
˙
ˆ
d=M(Bu +ˆ
d+β(x1,x
2)+k)
˙z=Mz
(19)
where M=diag(k1,k
2,k
3).
Meanwhile, the convergence analysis of the estimation error
could be derived via (20), which is obtained by incorporating
(14) and (18)
d=M˙
xz(20)
Since Mis a positive deﬁnite matrix, the second row of
(19) indicates that zwould exponentially decay and converge
to zero. On the other hand, with the support of (4) and (5)
in which the feedback components could keep the posture of
robot’s base under perturbation, the angular velocity ˙
x=x2
tends to converge to zero. Therefore, (20) suggests that
dis able
to converge, resulting in that ˆ
dwill converge to the true value
of d.
The ACQL algorithm is shown in Algorithm 1. In terms
of Lyapunov’s second method for stability, it proves that (19)
asymptotically converges to zero. The payload moment around
the robot can be identiﬁed with (11) and (19). It is noteworthy
that the auxiliary input in (11) is the aggregate moment of all
four foot-end forces.
III. EXPERIMENTS
In this section, experiment results are demonstrated to verify
the effectiveness of the proposed method in this study. The
experiment setup is introduced in section A. Unknown payload
Fig. 3. (a) The electrically actuated quadruped robot, Kirin, for high
PLC locomotion with linearly driven QDD legs. (b) and (c) present the
experiment scenario of the payload mass identiﬁcation. (b) is the initial
posture of the robot. (c) is the posture of the robot when the identiﬁcation
ends.
TABLE I
SPECIFICATIONS OF THE QUADRUPED ROBOT KIRIN
Due to the safety consideration, 75 kg is the experiment result at the current stage.
More payload is to be tested.
with different mass and location in Kirin’s quasi-static motion is
tested using proposed ACQL in section B. The results of trotting
control depending on the identiﬁed extra mass is presented in
section C.
A. Experiment Setup
To verify the proposed method, experiments are conducted
on Kirin, which is an electrically actuated quadruped robot
developed for high PLC. Kirin has one revolute hip roll joint,
one revolute hip pitch joint, and one prismatic knee joint on each
leg (as shown in Fig. 3). The total weight of Kirin is around 50
kg and PLC can reach up to 1.5 (with at least 75 kg payload).
The prismatic joint is driven by QDD with 20:1 gear ratio. QDD
is a solution to realize a proprioceptive joint so as to mitigate
impact and achieve high-bandwidth physical interaction [35].
The speciﬁcations of the quadruped robot Kirin are listed in
Table I.
B. ACQL Test for Varied Payload in Quasi-Static Motion
In this section, several experiments are carried out with the
Kirin that verify the efﬁcacy of the proposed ACQL algorithm.
As shown in Fig. 3(b) and (c), the robot initially stands on the
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6IEEE/ASME TRANSACTIONS ON MECHATRONICS
varies from 20 to 75 kg. Payload varies from 20 to 75 kg, which cor-
responds to PLC from 0.4 to 1.5. The identiﬁcation starts from 6 s(red
region) and ends at around 6.5 s(blue region). The red lines represent
the reference lines.
Fig. 5. Left subﬁgure shows the results of the moment of payload
identiﬁcation. dis the moment indicator. τis the estimated moment of
payload which equals to the inertial matrix multiplied by d.dhas the
same shape as τbecause the inertial matrix of the robot is a diagonal
matrix. The right subﬁgure shows the recursive and converges process.
˙
dis recursive rate of d.
ground and carries unknown payloads (sandbags). A predeﬁned
control torques are applied to drive the robot to reach the desired
height with four legs on the ground supporting the main body.
Inﬂuenced by the unknown payloads, there are both signiﬁcant
errors in the position and orientation of the robot’s torso at the
beginning. Then, the robot begins the identiﬁcation of the mass
and the moment around the robot generated by the payload and
until the errors of the robot’s orientation reduce to the predeﬁned
thresholds. In the experiments, the thresholds for the orientation
convergence are set to 0.01 rad in each rotational direction. The
parameters c,λ, and Min ACQL are set to 0.7I,0.7I, and 1.3I,
respectively. These parameters govern the recursive rate of the
The results of the payload mass identiﬁcation are shown in
Fig. 4. In the experiment, payload varies from 20 to 75 kg, which
implies that PLC varies from 0.4 to 1.5. With the time horizon
of 0.5 s, no matter the mass of payload, the estimation converges
to an acceptable threshold quickly, no more than 3 kg.
The results of the moment concerning the robot generated by
the payload are depicted in Fig. 5.Fig. 6 shows the performance
Fig. 6. Norm of the robot position error and orientation error. Each cor-
responds to the payload arrangements in Fig. 7(a) and (b) respectively.
The recursive process undergoes in the red region and converges in the
blue region.
Fig. 7. (a) and (b) are the top views of the quadruped robot in the
experiment of identifying the moment with respect to the robot induced
25 kg. They are placed on the different location on the robot’s back. (c)
The experiment scenario of different PLC. Payload of different mass are
placed in the front on the robot back. Each sandbag weights 25 kg while
each dumbbell weights 5 kg.
of the robot position and orientation tracking. As visualized in
Fig. 7(a), two sandbags (each weighs around 25 kg) are loaded
on the back of Kirin. In order to verify the effectiveness of
ACQL, these two sandbags are placed in the front and left part
on the back of Kirin, away from the robot’s original CoM. The
result in Fig. 5 demonstrates that the derivative of dis able to
converge to less than 0.005 N·m/(kg ·m3·s) within 2 swhen
the orientation error reduces below the threshold. The result
of the estimated dand the payload moment are displayed in
Fig. 5. Since the inertial matrix of the robot, generated from
CAD, is a diagonal matrix, the estimated dand the estimated
moment of payload have the same structure yet with different
values. The norm of the robot position and orientation tracking
errors is shown in Fig. 6, which can be used to illustrate the
identiﬁcation performance [36]. As shown in Fig. 6, the position
and orientation tracking errors reduce to around 3 mm and 0.008
rad, respectively. To further verify the effectiveness of ACQL,
two sandbags (50 kg) are placed in the front of the robot as
shown in Fig. 7(b). The robot has the same tracking performance
as shown in the right subﬁgure of Fig. 6.
The convergence time of the proposed ACQL is tested on
Kirin with a wide range of PLC. Payload varies from 20 to 75
kg which represents PLC from 0.4 to 1.5 as shown in Fig. 7(c).
These payloads are placed at the same place, in the front of the
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JIN et al.: UNKNOWN PAYLOAD ACQL WITH PROPRIOCEPTIVE LINEAR LEGS 7
Fig. 8. Convergence time and the RMSE of the tracking errors for a
series of PLCs with ACQL. ACQL is veriﬁed to converge within a wide
range of payload with PLC up to 1.5.
Fig. 9. Experiment screenshots of Kirin trotting with payload weighing
around 50 kg. Two sandbags are placed on the back of Kirin, each of
which weighs around 25 kg. (a) shows the screenshots of trotting in
place. (b) shows the screenshots of trotting forward with the speed of
0.2 m/s. The yellow arrow represents the trotting direction. The time
interval is 0.25 sfor each screenshot.
robot. Each test for a PLC is repeated ﬁve times. The experiment
results are depicted as shown in Fig. 8.
C. ACQL Test for Payload Carrying During Trotting
Motion
In this section, the robot is designed to trot in place and
forward with the speed of 0.2 m/swith a payload of 50 kg,
respectively. The experiment screenshots and results are shown
in Figs. 9 and 10, respectively. For the trotting test, Kirin identi-
ﬁes the payload in quasi-static motion and then trot in place and
forward with the updated mass parameters.
In the experiment of trotting in place, the robot is controlled to
trot in place at a desired height of 0.41 mw.r.t. the ground. The
desired orientation (3.25, -0.01, 0) represents the yaw, pitch,
and roll. As shown in Fig. 10(a), during trotting in place, the
robot trots with the position deviation being around 0.01 min
each direction and the orientation deviation less than 0.03 rad
along each axis. In the forward trotting experiment, as shown
in Fig. 10(b), the desired orientation is (2.4, -0.01, 0) and the
desired height is 0.45 m. The position and orientation deviation
of the robot are around 0.02 mand 0.05 rad, respectively.
To investigate the performance of changing mass during the
dynamic locomotion, 5 kg payload is put on the back of Kirin
during locomotion. The identiﬁcation result is shown in Fig. 11.
Fig. 10. Experiment results of the trotting with payloads. (a) shows the
results of body position, body orientation and the joint torques during
the trotting in place. (b) presents the results of body position, body
orientation and the joint torques during the trotting forward with the
speed of 0.2 m/s.ω, θ, ϕ and τrepresent the roll, pitch, yaw angular
of the robot and the torque of the robot joints, respectively.
Fig. 11. Changing mass identiﬁcation during locomotion. 5 kg payload
is put on Kirin’s back during locomotion at around 5.5 s. The blue line
denotes 5 kg as the true value of the added mass. Orange line denotes
the identiﬁed changed mass, which converges to around 7.7 kg.
Orange lines denotes the identiﬁed changed mass, which con-
verges to 7.6 with 2.6 kg errors.
IV. DISCUSSION
Using the proposed ACQL in this study, the maximum esti-
mated error of the payload mass is about 3 kg, which accounts
for only 6%of the robot’s mass. In terms of mass and moment
identiﬁcation within a wide PLC range, ACQL improves the
locomotion control through providing a satisfactory estimation
of unknown payload. To further investigate the performance
of ACQL for the changing mass during dynamic locomotion,
5kg mass is put on the back of Kirin when it moves. The
identiﬁed changed mass is around 7.6 kg. Due to the safety
consideration, heavier payload is not tested. The experiment
results demonstrates that ACQL beneﬁts the locomotion control
be put on the carrying platform, such as Kirin. The platform is
usually static or quasi-static. Therefore, it is believed that this
study is meaningful for this potential application.
As visualized in Fig. 8, when PLC is low, less than 0.4 in
this experiment, the identiﬁcation is able to converge fast. In
fact, due to the robot’s inertia, the payload has limited inﬂuence
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8IEEE/ASME TRANSACTIONS ON MECHATRONICS
on the robot. However, given a large PLC, which is yet fully
tested on electrically actuated quadruped robots, the inﬂuence
of the payload on the robot can not be ignored. It will take a few
seconds before the identiﬁcation converges. For different PLC,
the convergence time is consistently within 2 s. The convergence
rate can be faster by manually tuning c,λ, and M. In this study,
the performance is constrained within a safe range, i.e. 2 s,
to prevent possible overshooting for each robot joint and the
potential overturning for the robot.
V. C ONCLUSION
contributions are highlighted. One is that an online payload iden-
tiﬁcation algorithm is devised for a high PLC quadruped robot.
The algorithm is named as ACQL, which guarantees the fast
convergence of the identiﬁcation. The second highlight is that
algorithm is veriﬁed for PLC from 0.2 to 1.5 in quasi-static
motion and also validated in trotting gait with a payload as
heavy as the robot itself. To our best knowledge, it is the ﬁrst
time to deploy the adaptive control for a wide PLC range on
an electrically actuated quadruped robot. With the help of it,
the quadruped robot has the potential to expand the range of
physical work to a great extent.
To test ACQL for a large PLC, a novel quadruped robot, Kirin,
is utilized for the purpose of high payload carrying. Kirin is
designed with proprioceptive linear legs, which are capable of
heavy payload supporting. Experiments demonstrate that such a
design is able to achieve dynamic locomotion (such as trotting)
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Bingchen Jin received the B.S. degree in me-
chanical engineering from Jiangsu University,
Zhenjiang, China, in 2015, and the M.S. degree
in mechatronics engineering from Harbin Insti-
tute of Technology, Harbin, China, in 2018.
He is currently a Research Assistant with
Shenzhen Institute of Artiﬁcial Intelligence and
Robotics for Society (AIRS), Shenzhen, China.
His research interests include quadruped loco-
motion and joint torque estimation.
Shusheng Ye received the B.S. degree in me-
chanical engineering from Beijing Jiaotong Uni-
versity Haibin College, Cangzhou, China, in
2019.
He is currently an Assistant Engineer with
Shenzhen Institute of Artiﬁcial Intelligence and
Robotics for Society (AIRS), Shenzhen, China.
Juntong Su received the B.S. degree in me-
chanical engineering from Wuhan University
of Science and Technology, Wuhan, China, in
2012.
He is currently an Engineer with Shenzhen
Institute of Artiﬁcial Intelligence and Robotics for
Society (AIRS), Shenzhen, China.
Jianwen Luo received B.S. degree in mechani-
cal engineering from Honor School, Harbin In-
stitute of Technology, Harbin, China, in 2012,
the M.S. and Ph.D. degrees in mechatronics
engineering from State Laboratory of Robotics
and System, Harbin Institute of Technology, in
2014 and 2018, respectively.
Since Sep. 2010 through Jan. 2011, he vis-
ited, Mechanical Engineering Department, The
University of Hong Kong, Hong Kong, as an
Exchange Student. Since Mar. 2016 through
Apr. 2018, he worked with Stanford Robotics Lab, Stanford University,
Stanford, CA, USA, as a joint PhD student. Since Feb. 2017 through
May 2017, he worked with University of Texas at Austin, Austin, TX,
USA, as a Visit Scholar. Since 2019 through 2021, he is PostDoc with
University of Science and Technology of China. Since Jun 2020 through
Dec 2020, he is selected as PostDoc with Massachusetts Institute of
Technology, Cambridge, MA, USA. He is currently a Research Associate
with The Chinese University of Hong Kong, Hong Kong. He is also the
PI of legged robot project group with Shenzhen Institute of Artiﬁcial
Intelligence and Robotics for Society (AIRS), Shenzhen, China. His main
research interests focus on legged locomotion, dynamics control, whole
body control, robotic system design.
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... and are the position vectors of and the payload w.r.t. the CoM, respectively. The details about the estimation of can be seen in [28]. is the robot's position. ...
... The results of the unknown payload identification are shown in Fig. 8. The details of experiments are seen in [28]. In the experiment, the payload is changed from 20 kg to 75 kg, with the corresponding PLC varying from 0.4 to 1.5. ...
... =̇is the update law [28].the main scope of this paper and page limitation, more details about the estimation results are introduced in[28]. ...
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