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IEEE/ASME TRANSACTIONS ON MECHATRONICS 1

Unknown Payload Adaptive Control for

Quadruped Locomotion With Proprioceptive

Linear Legs

Bingchen Jin , Shusheng Ye , Juntong Su , and Jianwen Luo

Abstract—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 pa-

rameters and will signiﬁcantly deteriorate in severe distur-

bance, e.g., adding heavy payload. This article introduces

an online identiﬁcation method, which is named as adap-

tive control for quadruped locomotion, to address model

uncertainties. Meanwhile, a concurrent adaptive controller

is also indispensable to accomplish identiﬁcation and lo-

comotion. Therefore, this article presents an adaptive con-

trol 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 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

in inverse-dynamics-based quadratic programming, realiz-

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.

Index Terms—Adaptive control, payload, quadruped

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).

This article has supplementary downloadable material available at

https://ieeexplore.ieee.org, provided by the authors.

This article has supplementary material provided by the au-

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

payload, such as another manipulator [7]. Instead of using just

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

carrying. However, a research gap remains in payload adaptation

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

the traditional quadruped locomotion controller. A L1adaptive

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

refer to payload adaptation during quadruped locomotion [32],

where the goal is to demonstrate the robustness of controllers

based on reinforcement learning.

In this article, an adaptive control algorithm for quadruped

locomotion (ACQL) is proposed, which can be utilized in pay-

load adaptation The method is tested on the novel quadruped

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.

2) Based on the online payload identiﬁcation, the adaptive

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.

The rest of this article is organized as follows. Section II-A

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

discussion. Finally, Section V concludes this article.

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JIN et al.: UNKNOWN PAYLOAD ACQL WITH PROPRIOCEPTIVE LINEAR LEGS 3

II. UNKNOWN PAYL OA D ADAPTIVE CONTROL

In this section, the unknown payload adaptive control is

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-

ever, when large unknown payload is mounted on the quadruped

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=Fi−mig−mpg

d

dt(Iωa

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(Iωa

b)=I˙ωa

b+ωa

b×(Iωa

b).(2)

A widely used simplicity for the quadruped robot dynamics

is the precession and nutation of ωa

b×(Iωa

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

b−ra

b)+Kf

i(rd

b−ra

b)dt

+Kf

d(vd

b−va

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.

In this article, an inverse-dynamics-based QP is adopted to

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 ≤J−1F≤τmax

−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.

B. Payload Identiﬁcation

This section devises a method to identify the mass and mo-

ment of the unknown payload. When quadruped robots are

deployed in real world applications, e.g., carrying constant

payload, the unknown external payload would incur signiﬁcant

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

payload identiﬁcation. The ACQL identiﬁes the mass of the payload

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

payload moment concurrently.

The ﬁrst equation of (1) can be rewritten and the estimated

mass of the payload ˆmpis given by the following:

ˆmp=1

gFi−mi−m¨ra

b

g.(7)

In this article, the algorithm assumes that the motion is quasi-

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 I−1.

udenotes rbci ×Fi.kdenotes I−1ri×mig.ddenotes

I−1rp×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=x1−x1d. Therefore, ﬁrst and second derivative of the

tracking error are ˙

x=˙x1=x2and ¨

x=˙x2, 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=−B−1(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=d−ˆ

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

d−d+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

d−d+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

d−z+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,ω

a

by,ω

a

bz are the components

of angular velocity ωa

b.

JIN et al.: UNKNOWN PAYLOAD ACQL WITH PROPRIOCEPTIVE LINEAR LEGS 5

Algorithm 1: ACQL Algorithm.

Input: qd

b,ω

d

b,r

d

b,v

d

b,m

i,r

i,q

a

b,ω

a

b,q

joint ,˙qj oint,τ

joint

Output: Fd

1: Bri,Bvi,B¨ri⇐Forward kinematics (qjoint,˙qjoint )

2: Bra

b,Bva

b,B¨ra

b⇐Bri,Bvi,B¨ri

3: R⇐qd

b

4: ra

b,v

a

b,¨ra

b⇐RBra

b,R

Bva

b,R

B¨ra

b

5: Fa⇐τjoint

6: ˆmp⇐mi,¨ra

b,F

a

7: eqb ⇐log (qd

b·(qa

b)−1)

8: while eqb >e

threshold do

9: u⇐−B−1(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: Fb⇐eqr,˙eqr,m

i,ˆmp,a

b

16: Tb⇐eqb,˙eqb,r

i,m

i,u, ˆ

d

17: B⇐Fb,T

b

18: i⇐ra

b,r

i

19: Fd⇐arg 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˙

x−z(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

6IEEE/ASME TRANSACTIONS ON MECHATRONICS

Fig. 4. Mass of the payload identiﬁed in this experiment. Payload

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

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 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. 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

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. (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

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

for changing mass. In most daily tasks, payload often needs to

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

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

This article presents a method for identiﬁcation of unknown

payload within a wide range for the quadruped locomotion. Two

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

based on the online payload identiﬁcation, the adaptive control

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)

while carrying heavy payload.

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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.