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SUBMITTED MANUSCRIPT FOR PEER REVIEW 1
High-Payload Online Identification and Adaptive
Control for an Electrically-actuated Quadruped
Robot
Bingchen Jin, Shusheng Ye, Juntong Su, Chaoyang Song, Ye Zhao, Aidong Zhang, Ning Ding, Jianwen Luo∗
Abstract—Quadruped robots manifest great potential to
traverse rough terrains with payload. Numerous traditional
control methods for legged dynamic locomotion are model-
based and exhibit high sensitivity to model uncertainties
and payload variations. Therefore, high-performance model
parameter estimation becomes indispensable. However, the
inertia parameters of payload are usually unknown and
dynamically changing when the quadruped robot is deployed
in versatile tasks. To address this problem, online identification
of the inertia parameters and the Center of Mass (CoM)
position of the payload for the quadruped robots draw an
increasing interest. This study presents an adaptive controller
based on the online payload identification for the high payload
capacity (the ratio between payload and robot’s self-weight)
quadruped locomotion. We name it as Adaptive Controller for
Quadruped Locomotion (ACQL), which consists of a recursive
update law and a control law. ACQL estimates the external forces
and torques induced by the payload online. The estimation is
incorporated in inverse-dynamics-based Quadratic Programming
(QP) to realize a trotting gait. As such, the tracking accuracy
of the robot’s CoM and orientation trajectories are improved.
The proposed method, ACQL, is verified in a real quadruped
robot platform. Experiments prove the estimation efficacy for the
payload weighing from 20 kg to 75 kg and loaded at different
locations of the robot’s torso.
Index Terms—Quadruped robot, adaptive control, online
identification, payload
I. INTRODUCTION
LEGGED robots exhibit remarkable maneuvering
capability of traversing rough terrains [1], [2]. This
capability enables the legged robots to have great potential
for transportation with heavy payload in daily life. Designing
and controlling such machines has motivated considerable
research, and several quadruped platforms have been designed
and demonstrated superior topography adaptability [3].
Maximizing the legged robot’s maneuverability is one of the
most attractive research topics in the locomotion community.
The well-known MIT Cheetah robot incorporates virtual leg
compliance into its controller and realizes 2D running on the
Manuscript received: Month date, 20xx; This work was supported in part
by National Natural Science Foundation of China under Grant 51905251.
(Corresponding author: J. Luo. Email: jamesluo@cuhk.edu.cn)
B. Jin, S. Ye, J. Su, A. Zhang, N. Ding and J. Luo are with Shenzhen
Institute of Artificial Intelligence and Robotics for Society (AIRS), Shenzhen
518172, China; A. Zhang, N. Ding and J. Luo are also with Institute of
Robotics and Intelligent Manufacturing (IRIM), The Chinese University of
Hong Kong (CUHK), Shenzhen 518172, China.
C. Song is with the Southern University of Science and Technology
(SUSTech), Shenzhen 518055, China.
Y. Zhao is with the George W. Woodruff School of Mechanical Engineering,
Georgia Institute of Technology, USA.
Fig. 1. The quadruped robot with high payload capacity, Kirin, is used for the
study of the unknown payload identification and adaptive control. It is built
with prismatic legs, aiming for capacity of heavy payload carrying. There are
three degrees of freedoms (DoFs) for each leg.
treadmill up to 6 m/s with trot gait in the Sagittal plane [4].
StarlETH is another representative quadruped robot developed
by ETH Zurich, on which the hierarchical Operational Space
Control [5] is adopted to separate dynamical constraints
from trajectory tracking tasks. This enables StarlETH to trot
over rough terrains with loose and slippery obstacles [6].
Along this line of research, a Whole-Body-Control method
is integrated in the locomotion controller on ETH ANYmal,
which significantly improves the robot’s agility [7]. MIT mini
Cheetah, a lightweight version of the MIT Cheetah series, is
capable of highly dynamic gaits including 3D trotting and
galloping up to 2.5 m/s through convex model predictive
control [8]. Unitree A1 is another lightweight quadruped robot
that has performed dynamic locomotion over rough terrains
[9]. Besides agile quadruped locomotion, equipping the robot
with a payload-carrying ability is also a critical research
topic. Bigdog, the first field legged robot that leaves the
lab, is hydraulically actuated with impressive robustness to
the external disturbances. This robot weighs about 109 kg
and can carry a payload weighing more than 150 kg [10].
HyQ is another hydraulic robot developed by IIT [11]. It
weights about 80 kg and the peak torque of its hydraulic
joint is around 180 Nm which provides the robot extremely
large payload-carrying ability [12]. Different from traditional
rotation joint, baby elephant developed by Shanghai Jiaotong
arXiv:2107.12482v1 [cs.RO] 26 Jul 2021
2 SUBMITTED MANUSCRIPT FOR PEER REVIEW
University has a parallel-leg. This electric-hydraulic driven
robot weights 130 kg and can carry payload up to 100 kg
[13]. Due to the technology limitations, including the electric
motor constraints, it is yet extensively explored in the area
of the payload-carrying on the electrically-actuated quadruped
robots.
Traditional control theories are effectively deployed on
quadruped robots, which demonstrated great robustness and
agility [2], [8]. To date, most of these advanced locomotion
controllers require accurate robot models, and the predicted
control torques to drive the robot heavily rely on the
accuracy of robot models, including the link inertia and CoM
positions [5], [14], [15]. However, in the real world, the
robot may be commanded to carry unknown payload for
transporting goods. In such cases, the control methods that
highly depend on deterministic robot models are prone to
failures. Motivated by this problem, this paper explores an
adaptive controller based on online payload identification for
an electric-actuated quadruped robot to handle the unknown
payload. The contributions of this letter lie in the following
twofold:
•An online payload identification algorithm based on
a recursive formulation is devised for a high Payload
Capacity (PLC) quadruped robot. This algorithm
guarantees the fast convergence of the identification.
•An adaptive controller based on the online payload
identification is verified for PLC from 0.2to 1.5. 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.
The rest of the letter is organized as follows. The related
work is reviewed in Section II. Section III introduces the
model and dynamics control of the quadruped robot. The
payload identification and adaptive control are proposed in
Section IV. Section V shows the experimental results. This
line of research is concluded in Section VI.
II. RE LATE D WOR K
Over the last few decades, research about the robot
parameters identification and adaptive control for robots with
payload has achieved evident improvements. The inertial
parameters identification for legged locomotion has been a
critical research topic [16], [17]. These identification methods
are mostly designed offline since the robot model parameters
are usually deterministic. These methods have been verified
in several robots such as UT-µ2 [18], a small-size humanoid
robot, and the quadruped robot HyQ [19]. However, for the
robot’s torso, these methods play a limited role in identification
due to the unknown payload. By far, there are two main
approaches to solve this issue. One is to identify the torso’s
parameters online, taking the robot’s torso and the payload
as a rigid body. Research such as [20] proposes an online
inertial parameters identification for a manipulator. However, it
is only appropriate for the fixed-base rigid body system. HyQ
overcomes the shortcomings of this method and proposes a
combination of techniques that guarantee the robot locomotion
stability [21]. These methods have been verified on HyQ in
a static walking gait. Scalf-III, a hydraulic actuated heavy-
duty quadruped robot developed by Shandong University,
proposes a CoM estimation and adaptation method in dynamic
trot gait and verifies it in simulation [22]. Another approach
is to incorporate the adaptive control into the traditional
quadruped locomotion controller. A L1adaptive control theory
is proposed for legged robots and verified in simulation [23],
[24].
To our best knowledge of the existing work, the adaptive
control with online unknown payload identification is yet
fully explored for high capacity quadruped locomotion.
In this study, an adaptive control with high-payload
online identification is proposed for an electrically-actuated
quadruped robot. The robot is named Kirin as shown in Fig. 1.
The leg mechanism is designed to be prismatic so as to greatly
increase the payload capacity. Experiments are conducted on
Kirin to verify the effectiveness of ACQL.
III. DYNAM IC S CON TROL FOR QUA DRU PE D LOCOMOTION
The legged locomotion model and control relate to the
effects of the forces and the torques exerted on the robot,
which originate from the robot and payload’s gravity, and the
physical interaction with the environment. In this study, the
desired forces and torques are computed by:
Fb=Kf
p(rd
b−ra
b) + Kf
iZ(rd
b−ra
b)+
Kf
d(vd
b−va
b) + mab+Xmig+mpg
Tb=Kt
plog (qd
b·(qa
b)−1)
+Kt
iZlog (qd
b·(qa
b)−1)
+Kt
dlog (ωd
b·(ωa
b)−1)
+Xri×mig+rp×mpg
,(1)
where rd
b,vd
b,ab,qd
b,ωd
brepresent the desired position,
linear velocity, linear acceleration, rotation matrix and angular
velocity of the robot torso respectively. ra
b,va
b,qa
band ωa
b
represent the actual position, linear acceleration, rotation
matrix and angular velocity of the robot torso respectively.
migrepresents the gravitational force acting on the body i.ri
represents the corresponding position vector from the origin
of the inertial frame to the CoM of the body i.mrepresents
the total mass of the robot, which is equal to the summation
of mi.mpgis the gravity of the payload and rpmeans
the corresponding position vector of mpg. Different from
migand rithat can be generated from computer-aid design
software directly, mpgand rpare the unknown, dynamically
changing parameters that can not be ignored. K(·)
(·)represents
the diagonal gain matrices which need to be manually tuned
in the experiment. For a matrix M∈SO(3), the logarithm
operation is:
log(M) = (1
2(M−MT)d→1
arccos d(M−MT)/(2√1−d2)other ,(2)
where d= (trace(M)−1)/2.
JIN et al.: HIGH-PAYLOAD ONLINE IDENTIFICATION AND ADAPTIVE CONTROL FOR AN ELECTRICALLY-ACTUATED QUADRUPED ROBOT 3
The first three components for each equation’s right side
in (1) are the PID tracking controllers and the remaining
components represent the feedforward controller.
In this study, an inverse-dynamics-based Quadratic
Programming is adopted to realize the quadruped locomotion,
including the trotting gait. The inverse dynamics solver
outputs the desired force Fband torque Tbexerted on
the torso of the robot to track the desired motion. (1) is
formulated as a Quadratic Programming (QP) problem, by
which the contact force Fdis computed. The QP formulation
is given as:
Fd= arg min
F
(AF −B)TQ(AF −B) + FTRF
s.t.
τmin ≤J−1F≤τmax
−µFiz ≤Fix ≤µFiz
−µFiz ≤Fiy ≤µFiz
DiFi= 0
,(3)
where τmin and τmax are the robot’s minimal and maximum
joint torque. Fix, Fiy , and Fiz are the components of each
foot’s contact force vector. µis the coefficient of friction
between the contact foot and the ground. Direpresents the
matrix which selects the feet that dose not contact the ground.
ˆrbi is the skew-symmetric matrix defining the cross product of
the position vector rbci from base to contact foot. Fd∈ <3N×1
is the concatenated vector of the contact forces. Nrepresents
the number of legs that contact the ground. The diagonal
matrix Qand Rare the weight matrix which needs to be
adjusted via experiment as well. Aand Bare given as:
A="·· · I···
·· · ˆrbi ·· ·#
B="Fb
Tb#.(4)
From (1)-(4), The locomotion controller requires accurate
model parameters, especially the unknown payload
parameters. The identification of the payload will be
introduced in detail in section IV.
IV. PAYL OAD ID EN TI FIC ATION AN D ADA PTIVE CONTRO L
The high-payload identification and adaptive control for
quadruped locomotion are introduced in this section. When
quadruped robots are deployed for goods transportation, the
payload is mostly unknown and fluctuating. The variable
payload incurs significant disturbances to the robot balance.
In this study, an adaptive control for quadruped locomotion
(ACQL) is proposed to tackle this issue. For simplicity of
analysis within the scope of this study, ACQL is based on the
following assumptions:
(i) The payload effects to the robot are identified as a force
and a torque. Although the payload is always in surface contact
with the robot, only the force and moment acting on the robot
are considered in the robot’s dynamics model. Therefore, the
specific force distribution is not taken into account.
Fig. 2. Control scheme of the adaptive control with online unknown payload
identification. The Adaptive Control for Quadruped Locomotion (ACQL)
identifies the mass of the payload directly and generates an update law. The
recursive result of the update law is the moment of the payload concerning
the robot. ACQL also generates a control law by which the robot can adjust
its posture. The torques of joints are calculated via inverse dynamics based
on Quadratic Programming (QP) solver.
(ii) The force and the torque to be identified do not change
during locomotion. The identification method proposed in this
study mainly relies on the robot’s orientation error. During
the dynamic gaits, orientation errors easily bring noises in
the identification. Therefore, it is preferred to estimate these
parameters in a static pose, such as standing on the ground.
Based on the assumptions, this section introduces the
quadruped dynamics model, ACQL and demonstrates the
stability proof. ACQL is based on the quadruped dynamics
model and consists of update law and control law.
A. Quadruped Robot Model
The dynamic model of a quadruped robot is given by:
m¨ra
b=XFi−Xmig−mpg
d
dt(Iωa
b) = Xrbci ×Fi+rp×mpg
+Xri×mig
,(5)
where I∈ <3×3is the inertial of the robot. Firepresents the
contact force of each foot i. The left component of the second
equation of (5) can be extended as:
d
dt(Iωa
b) = I˙ωa
b+ωa
b×(Iωa
b).(6)
With the aforementioned assumption (ii), when the robot
stands on the ground with all four legs, the robot’s angular
velocity is small, and the precession and nutation of ωa
b×(Iωa
b)
of (6) contribute little to the dynamics of the robot. Thus, this
component can be discarded, and the second equation of (5)
can be changed to be:
I˙ωa
b=Xrbci ×Fi+rp×mpg+Xri×mig. (7)
B. Identification of Payload Mass and Moment
The scheme of ACQL for the identification of the payload’s
mass and moment is shown in Fig. 2. In the proposed ACQL,
the payload’s estimated mass is given by an analytical solution
which is computationally efficient. A control law is proposed
4 SUBMITTED MANUSCRIPT FOR PEER REVIEW
to adjust the robot’s posture while an update law is used to
identify the moment of the payload concurrently.
The first equation of (5) can be rewritten and the estimated
mass of the payload ˆmpis given by:
ˆmp=1
gXFi−Xmi−m¨ra
b
g.(8)
To estimate the moment of the payload, (7) can be
rewritten with some substitution and the robot dynamics can
be formulated in a standard state-space form:
˙x1=x2
˙x2=Bu +d+k
˙
ˆ
d=w
,(9)
where x1represents the robot orientation. x2represents the
angular velocity of the robot. Brepresents I−1.urepresents
Prbci ×Fi.krepresents Pri×mig.drepresents I−1rp×
mpgwhich is the parameter to be identified. ˆ
drepresents the
estimated value of d.wrepresents the update law ˙
ˆ
d.
In the quadruped robot system, there are multiple variables
that can be used as the observed quantity such as orientation,
angular velocity of torso and rotation matrix. In this study,
the robot orientation is selected as the tracking object. The
tracking error can be written as ex=x1−x1dand the first and
second derivative of the tracking error are ˙
ex= ˙x1=x2and
¨
ex= ˙x2respectively. Consider the function:
s=˙
ex+λex, (10)
where λis a positive definite matrix. Combined with (9), the
derivative of sis given by:
˙s=¨
ex+λ˙
ex
= ˙x2+λx2
=Bu +d+k+λx2.
(11)
Based on the derivation, the control law is devised as:
u=−B−1(ˆ
d+k+cs +λx2),(12)
where cis a positive definite matrix. Put (12) in (11) we have:
˙s=−cs +e
d, (13)
where e
d=d−ˆ
d. From (13), it can be concluded that ˙swill
asymptotically converge to zero if e
dasymptotically converges
to zero, and in this case s= 0. The proof of this conclusion
will be demonstrated in the next subsection.
The update law ˙
ˆ
dis devised based on the control law and
the aforementioned assumptions. Consider the manifold:
M={(x1, x2, d)∈ <3×3|ˆ
d−d+β(x1, x2)=0},(14)
where β(x1, x2)is the estimation error function to be
designed. As such, the problem is reformulated into the design
of an appropriate function β(x1, x2)to ensure the manifold to
be invariant and attractive. Define the manifold as:
z=ˆ
d−d+β(x1, x2).(15)
Algorithm 1 ACQL algorithm
Input: qd
b, ωd
b, rd
b, vd
b, mi, ri, qa
b, ωa
b, qjoint ,˙qjoint , τjoint
Output: Fd
1: Bri,Bvi,B¨ri⇐Forward kinematics (qjoint ,˙qj oint)
2: Bra
b,Bva
b,B¨ra
b⇐Bri,Bvi,B¨ri
3: R⇐qd
b
4: ra
b, va
b,¨ra
b⇐RBra
b, RBva
b, RB¨ra
b
5: Fa⇐τjoint
6: ˆmp⇐mi,¨ra
b, Fa
7: eqb ⇐log (qd
b·(qa
b)−1)
8: while eqb > ethreshold do
9: u⇐ −B−1(ˆ
d+k+cs +λx2)(control law)
10: ˙
d⇐ −M(Bu +ˆ
d+β(x1, x2) + k)(update law)
11: ˆ
dk+1 =˙
d∆t+ˆ
dk
12: Tb⇐Iu
13: Fb⇐mi,ˆmP,¨ra
b
14: end while
15: eqr ⇐ra
b, rd
b
16: ˙eq r ⇐va
b, vd
b
17: ˙eq b ⇐log (ωd
b·(ωa
b)−1)
18: Fb⇐eqr ,˙eqr , mi,ˆmp, ab
19: Tb⇐eqb,˙eqb , ri, mi, rp,ˆmp
20: B⇐Fb, Tb
21: i⇐ra
b, ri
22: Fd⇐arg min
F
(AF −B)TQ(AF −B) + FTRF
The derivative of zis:
˙z=˙
ˆ
d+˙
β(x1, x2).(16)
Substitute the robot dynamic system (9) into (16):
˙z=w+∂β
∂x1
x2+∂β
∂x2
˙x2
=w+∂β
∂x1
x2+∂β
∂x2
(Bu +d+k)
=w+∂β
∂x1
x2+∂β
∂x2
(Bu +ˆ
d−z+β(x1, x2) + k).
(17)
The update law ˙
ˆ
dand manifold zcan thus be designed as:
(˙
ˆ
d=−∂β
∂x1x2−∂ β
∂x2(Bu +ˆ
d+β(x1, x2) + k)
˙z=−∂β
∂x2z.(18)
In order to make sure the system zis Lyapunov stable
and reduce the computation complexity, the estimation error
function β(x1, x2)is designed as:
β(x1, x2) =
k1ωa
bx
k2ωa
by
k3ωa
bz
,(19)
where k1, k2, k3are all greater then zero. ωa
bx, ωa
by, ω a
bz are the
components of vector ωa
b.
The update law ˙
ˆ
dand the function zcan thus be written as:
(˙
ˆ
d=−M(Bu +ˆ
d+β(x1, x2) + k)
˙z=−M z ,(20)
JIN et al.: HIGH-PAYLOAD ONLINE IDENTIFICATION AND ADAPTIVE CONTROL FOR AN ELECTRICALLY-ACTUATED QUADRUPED ROBOT 5
where Mis given as:
M=
k10 0
0k20
0 0 k3
.(21)
The ACQL algorithm is shown in Algorithm 1. In terms
of Lyapunov’s second method for stability, it proves that (20)
asymptotically converges to zero. The moment of the payload
concerning the robot can be identified with (12) and (20). It
is noteworthy that the control law of (12) is the aggregate
moment of all four foot-end forces. This value is redistributed
to each foot with the QP solver.
C. Stability Proof of ACQL
The proof of the convergence of sin the identification of the
payload moment section is shown in this subsection. Firstly,
it is proven that there exists s= 0. Substitute (12) into (20):
˙
ˆ
d=−M(−cs −λx2+β)
=M[c(˙
ex+λex) + λx2−M x2]
=M[cλ(x1−x1d)+(c+λ−M)M x2].
(22)
It can be summarized by (22) that the update law ˙
ˆ
ddepends
on the robot orientation error and its angular velocity. By
choosing appropriate positive definite matrices of c, λ, and
M, the robot is able to adjust its orientation until its error
approaches zero, which implies the function swill eventually
approach zero.
Secondly, it is proved that (13) asymptotically converge to
zero. since e
dis designed to asymptotically converge to zero as
described above, only ˙s=−cs needs to be considered. Define
the Lyapunov function as:
V(s) = 1
2s2.(23)
It can be seen in (23) that V= 0 if and only if s= 0 and
V > 0when s6= 0. The derivative of Vis:
˙
V(s) = s˙s=−cs2≤0.(24)
According to the second method of Lyapunov, the system
as described in (13) is proven to asymptotically converges to
zero. Therefore, ACQL is proven to be Lyapunov stable.
V. EX PE RI ME NT
A. Experiment Platform
The experiments to verify the verification of the
effectiveness of the proposed method are conducted on the
quadruped robot, Kirin. The Kirin is an electrically actuated
quadruped robot developed for high payload capacity. Kirin
has one hip roll joint, one hip pitch joint, and one knee joint
on each leg (as shown in Fig. 3). The total weight of Kirin
is around 50 kg and payload capacity can reach up to 2.0
(with at least 100 kg payload). The hip roll and pitch joints
are revolute joints, while the knee joint is designed as the
prismatic joint. The controller of Kirin consists of Nvidia TX2,
on which RT-Linux is installed. The high-level forward and
inverse dynamics, online payload identification, and adaptive
control algorithms are running on RT-Linux. The size of Kirin
Fig. 3. The quadruped robot for high payload capacity locomotion. It is an
electrically-actuated quadruped robot with 12 degrees-of-freedom (DoFs) and
is named as Kirin. The knee joint is designed to be prismatic to enhance the
payload-carrying capacity in dynamic locomotion.
TABLE I
SPE CIFI CATI ONS O F TH E QUADR UPE D ROB OT KIRIN
Property Parameters
Dimensions (L×W×H) (mm) 700 × 240 × 600
Active DoF number 12
Total weight (kg) 50
Maximum payload *(kg) 100+
Motion range of hip roll joint (◦) 280
Motion range of hip pitch (◦) 360
Motion range of knee joint (mm) 300
Electric actuator Customized QDD
Computing board Nvidia Jetson TX2
Joint peak torque (Nm) 200
Joint peak speed (rpm) 150
Motor driver G-SOLWH120/100EES
*Due to the safety consideration, 100kg is the experiment result at the
current stage. More payload is to be tested.
is 700 mm ×240 mm ×600 mm. The peak joint torque and
velocity are around 200 Nm and 150 rpm respectively. The
actuator specifications of all the joints are uniform due to the
commercial constraints. The joint power and the mechanism
design are capable of supporting the heavy payload carrying
and dynamic gait. The specifications of the quadruped robot
Kirin are listed in Table. I.
B. ACQL Test with Varied Payload
In this section, several experiments were carried out with
the Kirin that verifies the efficacy of the proposed ACQL
Fig. 4. The experiment scenario of the payload mass identification. (a) is
the initial posture of the robot. (b) is the posture of the robot when the
identification ends.
6 SUBMITTED MANUSCRIPT FOR PEER REVIEW
Fig. 5. The mass of the payload identified in this experiment. Payload varies
from 20kg to 75kg. Payload varies from 20kg to 75kg, which corresponds
to PLC (Payload Capacity) from 0.4 to 1.5. The identification starts from 6
s(red region) and ends at around 6.5 s(blue region)
Fig. 6. The estimated dand the estimated moment of payload. Since the
inertial matrix of the robot is a diagonal matrix, the estimated dand the
estimated moment of payload have the same shape with the different values.
The recursive process undergoes in the red region and converges in the blue
region.
Fig. 7. The norm of the robot position error and orientation error. Each
corresponds to the payload arrangements in Fig. 8(a) and (b) respectively.
The recursive process undergoes in the red region and converges in the blue
region.
algorithm. As shown in Fig. 4, the robot initially stands
on the 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. Then, the robot will not stop
the identification of the mass and the moment concerning the
robot generated by the payload and adjusting its posture using
the adaptive control proposed above 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
Fig. 8. The top view of the quadruped robot in the experiment of identifying
the moment with respect to the robot induced by payload. The payload is
two sandbags, each of which weighs about 25 kg. They are placed on the
different location on the robot’s back.
Fig. 9. The experiment scenario of different PLC. Payload of different mass
are placed in the front on the robot back. Each sandbag weights 25kg while
each dumbbell weights 5kg.
c, λ, and Min ACQL are set to 0.7I, 0.7I, and 1.3I
respectively. These parameters govern the recursive rate of the
payload moment identification.
The results of the payload mass identification are shown in
Fig. 5. In the experiment, payload varies from 20 kg to 75 kg,
which implies that PLC varies from 0.4 to 1.5. Benefiting from
our previous work [25] and ACQL, the maximum estimated
error of the payload mass is about 3 kg, which accounts for
only 6%of the robot’s mass. The error has little influence on
the robot dynamic locomotion.
The results of the moment concerning the robot generated
by the payload are depicted as shown in Fig. 6 to Fig. 7. As
shown in Fig. 8 (a), two sandbags (each weighs around 25 kg)
are loaded on the back of Kirin. These two sandbags are placed
in the front and left part on the back of Kirin, away from the
robot’s original CoM, to verify the effectiveness of ACQL. The
result of the derivative of dis shown in Fig. 6. These values
converge to less than 0.005 Nm/(kg ·m3·s)within 2 swhen
the orientation error reduces below the threshold. The result
of the estimated dand the moment of the payload are shown
in Fig. 6. 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
JIN et al.: HIGH-PAYLOAD ONLINE IDENTIFICATION AND ADAPTIVE CONTROL FOR AN ELECTRICALLY-ACTUATED QUADRUPED ROBOT 7
Fig. 10. The experiment screenshots of Kirin trotting with payload weighing around 50kg. Two sandbags are placed on the back of Kirin, each of which
weighs around 25kg.
Fig. 11. The 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.
different values. With the measured mass of the payload and
the dimensions of the robot depicted in table I, it can be proved
that the estimated moment of the payload is close to its true
value. The norm of the robot position and orientation tracking
errors is shown in Fig. 7, which are usually used to illustrate
the identification performance [26]. As shown in Fig. 7, after
the payload identification, the robot adjusts its body with the
position and orientation tracking error at around 3 mm and
0.008 rad respectively. To furtherly verify the effectiveness
of ACQL, both two sandbags (50 kg) are placed in the front
of the robot as shown in Fig. 8 (b). The robot has the same
tracking performance as shown in the right subfigure of Fig.
7.
The convergence time of the proposed ACQL is tested on
Kirin with a wide range of PLC. Payload varies from 20 kg to
75 kg which represents PLC from 0.4 to 1.5 as shown in Fig.
9. These payloads are placed at the same place, in the front of
the robot, which will generate moment along the pitch axis.
Each test for a PLC is repeated five times. The experiment
results are depicted as shown in Fig. 11. As shown in the
figure, 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 on the robot. Even
with the open-loop force control method, the robot can achieve
satisfactory performance. However, given a large PLC, which
is yet fully tested on electrically-actuated quadruped robots,
Fig. 12. The robot position and orientation in the world coordinate during
trotting with the payload.
Fig. 13. The information of the right front leg of the robot. The left figure
is the actual joint position and the right figure is the actual joint torque.
the influence of the payload on the robot can not be ignored.
It will take a few seconds before the identification converges.
As shown in Fig. 11, for different PLC, the convergence time
is consistently around 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.
8 SUBMITTED MANUSCRIPT FOR PEER REVIEW
C. Payload-carrying Trotting Test with ACQL
In this subsection, the robot is designed to trot with a
payload of 50 kg, as heavy as the robot’s own weight. The
experiment screenshots is shown in Fig. 10. The predefined
time of the swing phase and the stance phase are both 0.5 s.
The results of the experiment are shown in Fig. 12 and Fig
.13. The robot is designed to trot in place at a desired robot
CoM position (0, 0, 0.41) with the desired orientation (3.25,
-0.01, 0), representing the yaw, pitch, and roll. As shown in
Fig. 12, the robot trotting with the position deviation around
0.01 min each direction and the orientation less than 0.03 rad
in each axis. It can be derived that the robot is able to trot with
the desired position and orientation even with the payload as
heavy as itself. The locomotion performance is not discounted
by the payload. Usually, the torque of the knee joint will be
two times that of the hip pitch joint if all the robot joints
are designed as the articulated ones [27]. Benefiting from the
prismatic knee joint in our quadruped robot Kirin, the actual
torque of the knee joint is similar to that of the hip pitch joint
as shown in Fig. 13. This means that, with the prismatic knee
joint instead of the traditional rotation joint, the robot’s ability
of payload-carrying is greatly improved.
VI. CONCLUSION
This letter presents an online high-payload identification
and adaptive control for an electrically-actuated quadruped
robot. By the aid of the identified mass and moment of
the unknown payload, the quadruped locomotion is able to
adapt to the dynamically changing high-payload. In this study,
an electrically-actuated quadruped robot for heavy payload-
carrying, Kirin, is used the support the tests to verify the
effectiveness of the proposed method, ACQL. ACQL is
validated for a wide range of PLC from 0.2 to 1.5. The
effectiveness of ACQL is also verified in the trotting gait
with a payload as heavy as the robot itself. Statistic results
show that ACQL is able to converge fast and run efficiently
online, which demonstrates that the proposed method is valid
for the payload with no matter unknown weight or unknown
location. However, at the current stage, ACQL is still limited
for the payload with static weight. Therefore, the future
work will include dynamic quadruped locomotion control with
dynamically changing payload.
REFERENCES
[1] J. Lee, J. Hwangbo, L. Wellhausen, V. Koltun, and M. Hutter, “Learning
quadrupedal locomotion over challenging terrain,” Science robotics,
vol. 5, no. 47, 2020.
[2] D. Kim, S. J. Jorgensen, J. Lee, J. Ahn, J. Luo, and L. Sentis,
“Dynamic locomotion for passive-ankle biped robots and humanoids
using whole-body locomotion control,” The International Journal of
Robotics Research, vol. 39, no. 8, pp. 936–956, 2020.
[3] G. Bledt and S. Kim, “Extracting legged locomotion heuristics with
regularized predictive control,” in 2020 IEEE International Conference
on Robotics and Automation (ICRA). IEEE, 2020, pp. 406–412.
[4] D. J. Hyun, S. Seok, J. Lee, and S. Kim, “High speed trot-
running: Implementation of a hierarchical controller using proprioceptive
impedance control on the mit cheetah,” The International Journal of
Robotics Research, vol. 33, no. 11, pp. 1417–1445, 2014.
[5] M. Hutter, H. Sommer, C. Gehring, M. Hoepflinger, M. Bloesch, and
R. Siegwart, “Quadrupedal locomotion using hierarchical operational
space control,” The International Journal of Robotics Research, vol. 33,
no. 8, pp. 1047–1062, 2014.
[6] M. Hutter, C. Gehring, M. A. H ¨
opflinger, M. Bl¨
osch, and R. Siegwart,
“Toward combining speed, efficiency, versatility, and robustness in an
autonomous quadruped,” IEEE Transactions on Robotics, vol. 30, no. 6,
pp. 1427–1440, 2014.
[7] C. Gehring, C. Dario Bellicoso, P. Fankhauser, S. Coros, and M. Hutter,
“Quadrupedal locomotion using trajectory optimization and hierarchical
whole body control,” in 2017 IEEE International Conference on
Robotics and Automation (ICRA), 2017, pp. 4788–4794.
[8] G. Bledt and S. Kim, “Implementing regularized predictive control for
simultaneous real-time footstep and ground reaction force optimization,”
in 2019 IEEE/RSJ International Conference on Intelligent Robots and
Systems (IROS). IEEE, 2019, pp. 6316–6323.
[9] A. Kumar, Z. Fu, D. Pathak, and J. Malik, “Rma: Rapid motor adaptation
for legged robots,” arXiv preprint arXiv:2107.04034, 2021.
[10] M. Raibert, K. Blankespoor, G. Nelson, and R. Playter, “Bigdog, the
rough-terrain quadruped robot,” IFAC Proceedings Volumes, vol. 41,
no. 2, pp. 10 822–10 825, 2008, 17th IFAC World Congress.
[11] C. Semini, N. G. Tsagarakis, E. Guglielmino, M. Focchi, F. Cannella,
and D. G. Caldwell, “Design of hyq – a hydraulically and electrically
actuated quadruped robot,” Proceedings of the Institution of Mechanical
Engineers, Part I: Journal of Systems and Control Engineering, vol.
225, no. 6, pp. 831–849, 2011.
[12] C. Semini, V. Barasuol, J. Goldsmith, M. Frigerio, M. Focchi, Y. Gao,
and D. G. Caldwell, “Design of the hydraulically actuated, torque-
controlled quadruped robot hyq2max,” IEEE/ASME Transactions on
Mechatronics, vol. 22, no. 2, pp. 635–646, 2017.
[13] J. Zhang, F. Gao, X. Han, X. Chen, and X. Han, “Trot gait design
and cpg method for a quadruped robot,” Journal of Bionic Engineering,
vol. 11, no. 1, pp. 18–25, 2014.
[14] J. Luo, Y. Fu, and S. Wang, “3d stable biped walking control and
implementation on real robot,” Advanced Robotics, pp. 634–649, 2017.
[15] J. Luo, Y. Su, L. Ruan, Y. Zhao, D. Kim, L. Sentis, and C. Fu, “Robust
bipedal locomotion based on a hierarchical control structure,” Robotica,
vol. 37, no. 10, pp. 1750–1767, 2019.
[16] M. Mistry, S. Schaal, and K. Yamane, “Inertial parameter estimation
of floating base humanoid systems using partial force sensing,” in 2009
9th IEEE-RAS International Conference on Humanoid Robots, 2009, pp.
492–497.
[17] J. Luo, Y. Zhao, L. Ruan, S. Mao, and C. Fu, “Estimation of com and cop
trajectories during human walking based on a wearable visual odometry
device,” IEEE Transactions on Automation Science and Engineering,
2020.
[18] T. Sugihara, K. Yamamoto, and Y. Nakamura, “Architectural design
of miniature anthropomorphic robots towards high-mobility,” in 2005
IEEE/RSJ International Conference on Intelligent Robots and Systems,
2005, pp. 2869–2874.
[19] S. Fahmi, C. Mastalli, M. Focchi, and C. Semini, “Passive whole-body
control for quadruped robots: Experimental validation over challenging
terrain,” IEEE Robotics and Automation Letters, vol. 4, no. 3, pp. 2553–
2560, 2019.
[20] J.-J. E. Slotine and W. Li, “On the adaptive control of robot
manipulators,” The international journal of robotics research, vol. 6,
no. 3, pp. 49–59, 1987.
[21] G. Tournois, M. Focchi, A. Del Prete, R. Orsolino, D. G. Caldwell, and
C. Semini, “Online payload identification for quadruped robots,” in 2017
IEEE/RSJ International Conference on Intelligent Robots and Systems
(IROS), 2017, pp. 4889–4896.
[22] C. Ding, L. Zhou, Y. Li, and X. Rong, “Locomotion control of quadruped
robots with online center of mass adaptation and payload identification,”
IEEE Access, vol. 8, pp. 224 578–224 587, 2020.
[23] Q. Nguyen and K. Sreenath, “L 1 adaptive control for bipedal robots with
control lyapunov function based quadratic programs,” in 2015 American
Control Conference (ACC). IEEE, 2015, pp. 862–867.
[24] M. Sombolestan, Y. Chen, and Q. Nguyen, “Adaptive force-based control
for legged robots,” arXiv preprint arXiv:2011.06236, 2020.
[25] B. Jin, C. Sun, A. Zhang, N. Ding, J. Lin, G. Deng, Z. Zhu, and
Z. Sun, “Joint torque estimation toward dynamic and compliant control
for gear-driven torque sensorless quadruped robot,” in 2019 IEEE/RSJ
International Conference on Intelligent Robots and Systems (IROS).
IEEE, 2019, pp. 4630–4637.
[26] T. F. Nygaard, C. P. Martin, J. Torresen, and K. Glette, “Self-modifying
morphology experiments with dyret: Dynamic robot for embodied
testing,” in 2019 International Conference on Robotics and Automation
(ICRA), 2019, pp. 9446–9452.
[27] D. Kim, J. Di Carlo, B. Katz, G. Bledt, and S. Kim, “Highly dynamic
quadruped locomotion via whole-body impulse control and model
predictive control,” arXiv preprint arXiv:1909.06586, 2019.
