Variable Admittance Human-Robot Collaborative Control Based on

Motion Intention Prediction

Hao Wang, Hongjian Yu

, Zhijiang Du and Rongqiang Liu

State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Harbin, China

Keywords: Variable Admittance Control, Fuzzy Reasoning, Compliance Control.

Abstract: This paper proposes a variable compliance control method for human-robot collaborative tasks. When the

operator is towing the robot for collaborative motion, the motion trajectory of the operator's arm is unknown.

In order to meet the different motion control needs of the robot in each stage of motion, a motion intention

prediction strategy for the operator is designed, and the admittance controller is adjusted through fuzzy

reasoning. The experimental results show that this method can effectively improve the controllability and

adaptability of the robot in the process of compliant control.

INTRODUCTION

In human-robot collaborative tasks such as robot-

assisted surgery and robot-assisted assembly, the

robot needs to be used as an intelligent tool with its

movement guided by humans. This control mode

can not only give full play to the auxiliary role of the

robot, but also reflect the wisdom of humans. Robot

compliance control makes the robot dynamically

respond to the feedback information of the external

environment force through a certain control

strategy

[

Hogan N, 1984

]

. Among them, impedance control

and admittance control are widely used in

engineering compliance control strategies.

Impedance control can control the contact force

between the robot and the environment by correcting

the deviation of the end feedback position and

velocity. The admittance control makes the robot

respond to the external force information and adjust

the desired position to track the force movement.

When the operator pulls the end-effector of the

robot, the input of the control system is the

interactive force information exerted by the operator,

and the output is the expected movement of the

robot, so that the robot can follow the operator's arm

to move, the admittance control can meet this

control demand. The admittance model is shown in

Figure 1, its expression form is described as

equation (1):

00 0

()()()

MX X BX X KX X=−+−+−

   

(1)

where F is the interactive force exerted by the

operator,

M is the virtual mass coefficient, B is the

virtual damping coefficient,

K is the virtual stiffness

coefficient,





and

are the acceleration,

velocity and position of the robot in Cartesian space,





and

are the expected acceleration,

velocity and position of the robot in Cartesian space.

When the operator pulls the robot, the virtual

stiffness coefficient

K will cause the robot to

generate a certain restoring force and the end of the

robot will show a tendency to maintain the initial

position, which is not in line with the control

purpose of the robot following the interactive force.

The virtual stiffness coefficient should be set to 0.

Moreover, this motion method does not refer to the

target position, thus the expected motion state

variables (





and

) need to be ignored. In

this case, the transfer function of the admittance

controller is described in equation (2).

() 1

()

Fs Ms B

== =



(2)

Wang, H., Yu, H., Du, Z. and Liu, R.

Variable Admittance Human-Robot Collaborative Control Based on Motion Intention Prediction.

DOI: 10.5220/0012274400003807

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 2nd International Seminar on Artiﬁcial Intelligence, Networking and Information Technology (ANIT 2023), pages 80-85

ISBN: 978-989-758-677-4

Figure 1: The admittance model.

The traditional admittance control model is

preset and fixed, and the control system shows poor

adaptability when facing the changing working

environment in practical application. When the

operator pulls the end effector of the robot to

accelerate, the robot should have a certain

acceleration performance to quickly reach the

desired speed, and when the robot decelerates, it

needs better braking performance. At this time, a

single admittance model obviously cannot meet the

control requirements of each stage of the traction

robot movement. In order to improve the

performance of the control system, the control

system needs to be able to sense the external

environment and adjust the control model

autonomously. At present, many researchers have

proposed adaptive admittance control methods

(Shaodong Li - Tsumugiwa), which pay more

attention to system stability during human-robot

interaction. In order to solve the adaptability and

compliance problems in the process of human-robot

interaction, it is also necessary to enable the control

system to predict the future motion state and make

dynamic adjustments accordingly. In this paper, a

motion state perception strategy is proposed to

predict the operator's motion control intention and

adjust the control system online by fuzzy reasoning.

MOTION STATE PERCEPTION

STRATEGY

Dynamically adjusted admittance models generally

require known future motion instructions as a

reference. There is no track to follow when the

operator pulls the robot, and it is difficult to

establish a mathematical model by simply relying on

the operator's operation intention to generate the

motion track because it contains personal factors. In

this paper, the motion intention of the operator is

perceived by combining the traction force

information in the direction of the robot's end

motion speed and component.

2.1 Motion State Perception Strategy

In equation (2), the system gain ‘1/B’ is related to

the output amplitude of the control system, which

will directly affect the robot's motion speed and

acceleration and deceleration performance (Ikeura

R,1994). Although large virtual damping will make

the operator feel obvious resistance and limit the

acceleration ability of the robot, and damage the

smoothness and flexibility of human-robot

interaction, large virtual damping will also bring

better deceleration ability for the robot when

braking, and enable the operator to control the robot

movement more accurately. On the contrary, a small

virtual damping will make the operator feel less

resistance when pulling the end of the robot, and the

robot shows better acceleration ability during the

interaction process. The operator can make the robot

move at the expected speed with a small force, but

the reduction of virtual damping will also limit the

braking performance of the robot, resulting in the

overshoot phenomenon and reducing the stability of

the system. Therefore, after obtaining the motion

intention, the virtual damping coefficient B of the

admittance model should be adjusted so that the

robot can quickly adapt to the control demand at the

next moment.

The perception strategy is shown in Figure 2,

taking the single-degree-of-freedom motion of the

robot in Cartesian space as an example, when the

interaction force and the end velocity direction of

the robot do not reach the set threshold, the robot

maintains the current motion state without changing

the control system. When the interaction force and

velocity reach the threshold value, when the two

directions are the same, it is determined that the

operator intends to pull the robot to accelerate the

movement, and then the admittance controller is

adjusted to appropriately reduce the virtual damping

coefficient to make the robot accelerate rapidly.

When the interaction force and the velocity are

reversed, the motion is inferred as deceleration, and

the virtual damping coefficient of the admittance

controller is appropriately increased, so that the

robot speed decreases rapidly. In addition, when the

robot is moving with six degrees of freedom in

Variable Admittance Human-Robot Collaborative Control Based on Motion Intention Prediction

Cartesian space, the admittance controller should

adjust the virtual damping and virtual mass

coefficient of its six degrees of freedom direction

respectively, because the operator may decelerate

the robot in one direction and accelerate the robot in

the other direction when pulling the robot.

Figure 2: Perception strategy of the operation intention.

2.2 Variable Admittance Control

System based on Fuzzy Reasoning

Fuzzy control can only infer the possible state

according to the input and output of the controlled

object without the precise model of the object, and

then make adaptive adjustments to build a nonlinear

time-varying control system that can accurately

control the complicated and uncertain process,

which can meet the control requirements of this

paper to change the motion state according to the

operation intention. When the motion state of the

robot changes due to personal intention during the

following traction movement, the virtual damping

coefficient B can be adjusted in real time according

to the intention perception strategy in Figure 3 with

the help of the fuzzy reasoning method to adapt to

the motion demand. Compared with the discrete data

rules used by computers, the human-robot

interaction control system is described by linguistic

fuzzy variables, and the control mode of obtaining

control action set through fuzzy reasoning simplifies

the complexity of system design (

Prabhu, 1998

Therefore, a fuzzy inference system was established

in this paper to blur the interaction force exerted by

the operator, the robot's end motion speed and the

virtual damping coefficient of the admittance

controller, and adjust the virtual damping coefficient

of the system by fuzzy inference according to the

operation intention. The fuzzy system can

independently adjust the virtual damping coefficient

of the 6 degrees of freedom of the admittance

controller.

The fuzzy reasoning system in this study is a

fuzzy system with two inputs and one output. The

system input is the interaction force F and the robot

terminal velocity V imposed by the doctor on the

robot, and the output is the virtual damping

coefficient B. Assuming that the variation ranges of

the input and output variables are

max min

FF[ ， ]

max min

VV[ ， ]

and

max min

BB[ ， ]

respectively, the

method for determining the minimum virtual

damping coefficient is as follows:

min

max

(3)

where

max

is the maximum velocity at the end of

the robot in Cartesian space, and

min

is the

minimum force that causes the velocity at the end of

the robot to reach

max

The input and output domains of fuzzy systems

are defined as F:[-3,3], V:[-3,3], B:[0,6]. Then the

fuzzy set and membership function are defined in

the input and output variable theory domain of the

fuzzy inference system. In order to take into account

the simplicity and control effect of the fuzzy

reasoning system, the fuzzy language of interaction

force F and velocity V is described as {NB (negative

big), NM (negative medium), NS (negative small), Z

(zero), PS (positive small), PM (positive medium),

PB (positive big)}. The fuzzy language of virtual

damping coefficient B is described as {ES

(extremely small), VS (very small), MS (medially

small), M (medium), MB (medially big), VB (very

big), EB (extremely big)}. All fuzzy subsets are

described by triangular membership functions, and

the membership function distribution of each fuzzy

set is shown in Figure 3.

(a) Membership function of the force.

Get the interaction force F and

velocity V

Set up the initial control system

Whether |F| and |V| are

greater than the threshold

Deceleration

motion intention

Remain unchanged

Whether F and V are

in the same direction

Accelerated motion

intention

Start

Adjust damping

model

End

ANIT 2023 - The International Seminar on Artiﬁcial Intelligence, Networking and Information Technology

(b) Membership function of the velocity.

Figure 3: Membership functions of fuzzy sets in fuzzy

inference system.

This paper adopts linguistic fuzzy rules

(Mamdani), whose expression is as follows:

11 11

,,,,

jkpq

mm mm

klpq

The

f F is D and F is D and V is E and V is E

BinsW









(4)

where



and



are the fuzzy inputs of the fuzzy

system,



is the fuzzy output of the fuzzy system,

and the a-th linguistic values of

are



and



respectively.

,,,,,jkpq



is the language value

of the



. Then the fuzzy mapping relationship of a

two-input single-output fuzzy system is established:

,, ,, ,,,,,

=( ) ( )

klpq j k p q klpq

nmmn

RDDEEW×× × ×× ×

 



(5)

The fuzzy inference rules based on the operation

intention perception strategy are shown in Table 1.

After the fuzzy inference conclusion is clarified by

the area-centric method, the fuzzy system outputs a

clear virtual damping coefficient B value. The input

and output responses of the fuzzy reasoning system

are shown in Figure 4.

Table 1: Fuzzy reasoning rules.

B V

NB NM NS Z PB PM PB

NB ES VS MS M MB VB EB

NM VS VS MS M MB VB VB

NS MS MS M MB M MB MB

Z M M MB VB MB M M

PS MB MB M MB M MS MS

PM VB VB MB M MS VS VS

PB EB VB MB M MS VS ES

Figure 4: The response diagram of the fuzzy inference

system.

According to the analysis of equation(2), when

adjusting the damping of the control system, if the

virtual mass coefficient M is kept constant and only

the virtual damping coefficient B is changed, the

system time constant M/B will be changed. The

change of the system response time will change the

dynamic characteristics of the system, and

eventually affect the smoothness and flexibility of

human-robot interaction. In order to avoid this

problem, the virtual mass coefficient M should be

adjusted synchronously with the virtual damping

coefficient B, so as to maintain the dynamic

characteristics of the control system and minimize

the impact on the operating experience.

When the initial parameters of the control system

increase or decrease the virtual damping, the system

response curve generated when M/B is fixed or

changed respectively is shown in Figure 5. As can

be seen from the figure, when the virtual damping

coefficient B is changed and the time constant M/B

is kept constant, the response time of the control

system is the same as that of the initial control

system under different virtual damping. However,

the response time of the output curve of the system

whose M/B changes only by changing the virtual

damping coefficient B changes to different degrees,

which indicates that it is necessary for the controller

to adjust the virtual mass synchronously to keep M/B

unchanged during the movement of the robot under

the control of variable admittance.

Variable Admittance Human-Robot Collaborative Control Based on Motion Intention Prediction

Figure 5: The response curve of a variable admittance

model.

EXPERIMENTAL

EVALUATION

In this section, the KUKA LBR iiwa robot will be

used to verify the proposed variable admittance

control algorithm. The SRI M3714A force sensor is

installed at the end of the robot to collect the force.

The operator drags the end of the robot to move

so that the acceleration and deceleration of the end

of the robot change frequently. As can be seen from

Figure 6, when the interaction force begins to

increase, the control system determines that the

operator intends to accelerate the motion according

to the interaction intention inference strategy, and

correspondingly reduces the virtual damping

coefficient of the admittance control model, so that

the end of the robot quickly reaches the expected

speed and follows the movement trend of the

operator's arm, making it easier to start. On the

contrary, when the direction of the interaction force

reverses and is opposite to the direction of motion,

the control system judges that the operator intends to

slow down, the virtual damping coefficient of the

admission control model increases, and the end of

the robot quickly brakes and changes the direction of

motion or stops under the operator's expected

posture, effectively reducing the overshoot. In

addition, the virtual mass coefficient changes in a

fixed proportion with the virtual damping

coefficient, so that the dynamic response

performance of the control system is stable under

constantly changing conditions, and the control

effect of the robot's end following the interactive

force is improved. The experimental results show

that the variable admittance compliance control

strategy based on fuzzy reasoning can dynamically

adjust the damping of the control system to quickly

respond to the operator's control intention while

maintaining the dynamic response performance of

the robot control system. This method improves the

controllability of the robot’s movement and the

ability to adapt quickly to different operator habits,

making the robot follow the operator's arm

movement more flexibly and naturally.

(a) Interaction force.

(b) The velocity at the end of the robot.

Figure 6: Variable admittance compliance control based

on fuzzy reasoning.

In order to further verify the control effect of the

dynamic adjustment admittance controller based on

fuzzy reasoning, two control methods (constant

admittance and variable admittance) are used to pull

the robot to move back and forth between two

points, as shown in Figure 7.

Figure 7: Reciprocating experiment.

ANIT 2023 - The International Seminar on Artiﬁcial Intelligence, Networking and Information Technology

The interactive force applied during the

experiment is shown in Figure 8. It can be seen that

the average and peak value of traction force applied

under variable admittance control are significantly

lower than those under constant admittance control,

which proves that this strategy can make the robot

more labor-saving and sensitive to follow the

operator's intended movement, effectively reduce the

operation intensity, and improve the human-robot

interaction experience to a certain extent.

(a) Average interaction force.

(b) Peak interaction force.

Figure 8: Comparison of two control methods for applying

interactive forces.

CONCLUSION

In this paper, a fuzzy variable admittance control

method is proposed to solve the problem of single

characteristics of the traditional admittance control

model. A dynamic adjustment admittance control

model of the fuzzy inference system is designed

based on the perception strategy of the robot's end

interaction force and velocity direction. The

experimental data show that the variable admittance

control method proposed in this paper can

significantly improve the flexibility and adaptability

of the control system when changing the robot's

motion state.

ACKNOWLEDGMENTS

This work was financially supported by Key-Area

Research and Development Program of Guangdong

Province (No.2020B0909020002) and Self-Planned

Task (No.SKLRS202211B) of State Key Laboratory

of Robotics and System (HIT).

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Variable Admittance Human-Robot Collaborative Control Based on Motion Intention Prediction