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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.

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