Gait Tracking Control of Machine Leg
Based on Damping Torque Feedback Control
Pengfen Huang,* Xinghua Lu, Weipeng Huang and Ziqian Li
Huali College Guangdong U niversity of Technology
Guangzhou Zengcheng, 511325, P. R. China
Keywords: Damping torque, kinematics model,robot leg, bionics, gait tracking control.
Abstract: The machine leg is affected by the damping of the joint part when walking in the bionic gait, which leads to
the poor global stability. A gait tracking control method for machine legs based on damping torque feedback
regulation is proposed. Kinematics analysis of the kinematics equation of the machine leg is constructed by
three-axis coordinate system model. The adaptive optimization of the step sensing information of the robot
leg with the parameters of the gait motion and the damping torque as the constraint index. An inverse
stabilization control method is introduced to modify the error feedback of the gait tracking parameter of the
machine leg. The feedback adjustment of damping torque is realized by combining the nonlinear adaptive
inversion integral method, and the gait stability tracking control of the machine leg is realized. The
simulation results show that using this method to track gait control of machine legs, the walking performance
of machine legs is good, the tracking accuracy of attitude parameters is strong, and the attitude error is small.
1 INTRODUCTION
A bionic robot leg is a robot that walks by
simulating human and animal walking, as an
important application direction of AI robot, it has a
very good application value in the field of artificial
auxiliary operation, lower limb assisted
rehabilitation, detection, tracking and recognition.
The gait control of the bionic machine leg is the key
to ensure the stable walking of the machine leg. The
gait tracking control system of machine legs is a
multivariable, nonlinear and non-stationary
multivariable control system. It is necessary to
control its robustness and improve the robustness
and smoothness of bionic gait control. In order to
improve the robustness of the bionic gait control and
the stability of walking, the related control methods
are researched (LU Xing hua, 2016).
The stability control of the walking gait of the
bionic machine leg is taken based on the
measurement of the information of the physical
environment parameters of the bionic machine leg.
Inertial attitude measurement and behavior
parameter analysis of biomimetic robot legs are
carried out through sensor devices and sensing
elements (LI Ke, 2016). Combined with information
fusion and processing methods, adaptive modulation
of control parameters is realized, it can provide data
input basis for stability control of walking gait of
bionic machine legs. On the basis of sensor
information collection, the attitude parameters of the
acquired machine leg are fused and the qualitative
processing is made, combining kinematics and
mechanics analysis to realize the optimization of
control law. In traditional methods, the gait control
method of machine legs mainly adopts fuzzy control
and integral control method (GAO Shan, 2015). It is
easy to be influenced by the disturbance of machine
legs and the nonlinear disturbance of joint torque,
which leads to the poor stability of machine legs and
the low robustness of control. For example, in
reference (Guo, 2015), it has proposed an optimize
the fuzzy PID control method of the lower
extremity exoskeleton based on the design of
adaptive inversion integral controller machine legs,
but the control method of robotic leg small
disturbance rejection ability is not strong, the robotic
leg step of modeling error is big, the actual the
control effect is affected. In response to the above
problems, a gait tracking control method for
machine legs based on damping torque feedback
regulation is proposed. Kinematics analysis of the
kinematics equation of the machine leg is
constructed by three-axis coordinate system model
(ZHANG Danfeng, 2017). The adaptive
Huang, P., Lu, X., Huang, W. and Li, Z.
Gait Tracking Control of Machine Leg Based on Damping Torque Feedback Control.
In 3rd International Conference on Electromechanical Control Technology and Transportation (ICECTT 2018), pages 541-545
ISBN: 978-989-758-312-4
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
541

optimization of the step sensing information of the
robot leg with the parameters of the gait motion and
the damping torque as the constraint index. An
inverse stabilization control method is introduced to
modify the error feedback of the gait tracking
parameter of the machine leg. The feedback
adjustment of damping torque is realized by
combining the nonlinear adaptive inversion integral
method, and the gait stability tracking control of the
machine leg is realized. The simulation results show
the superiority of this method.
2 Analysis of the control principle and
kinematic model of gait tracking of
the machine leg
2.1 Control constraint parameters and
control overall structure
The bionic robot legs are affected by the key
disturbances and environmental interference of
various components during walking, and the small
disturbance and disturbance will lead to the
instability of walking posture. In order to keep the
stability of the walking posture of the bionic
machine leg in walking, stability control is required.
The realization of control law design is constructed
based on the construction of control constraint
parameters, and multi-sensor information collection
model is used for parameter acquisition of bionic
robot leg walking stability control. The sensitive
sensor uses three axis bionic robot leg walking
tracking control accelerometer, magnetic force
sensor and three-axis gyroscope to collect the
position and attitude parameter of the machine leg. A
new bionic robot leg walking posture parameter
information fusion method is established. The
gyroscope's angle estimation is taken as the process
data, and a delayed two degree of freedom control
model is applied to the external electric field
stimulation of the robot leg controller, get the
distance error function
E
V
:
sin( )



E
A
Vt
(1)
Wherein, A is the amplitude of the gait
oscillation of the machine leg,
2

 
f
,
f
is the
external electric field frequency applied, the
controlled constraint parameter model of the
machine leg is divided into two parts, the reference
factor and the non-reference factor, and the external
electric field current is introduced into the attitude
sensitive element of the controller:
cos( )


Em
ICA t (2)
For different sensitive characteristic parameters,
the oscillation characteristic of the step in the step of
the machine leg under the unknown disturbance has
the nonlinear characteristics, Feature sampling is
carried out according to the periodic discharge
method of the sensitive element. The chaotic
eigenvalue of the fusion parameters of the steady
state of the robot leg is extracted and the amplitude
of the stimulus is stimulated as
2.5
A
mV , applying
an external control signal
u , by analyzing the
constraint parameters of closed loop PI type iterative
learning method to realize machine leg step control,
a closed loop PI iterative learning method to realize
the constraint parameter analysis of step control of
the machine leg, the constraint parameter model of
the gait tracking control by the main HH neuron
model can be expressed as:
3
,,
4
,,
[()
()()]/
()(1 ) ()
()(1 ) ()
()(1 ) ()




   
















mEmNammmEmNa
km m Em k L m Em L m
mmm m mmm
mhm m hmm
mnm m nmm
VIgmhVVV
g
nVVVgVVVC
mVm Vm
hVh Vh
nVn Vn
(3)
Taking the sampling parameter of the sensitive
element of the input layer of HH neuron as the
research object, we amplify the amplitude of the
stimulation current by two times, and use the
damping moment as input parameter in iterative
learning:
34
,, ,
,
[()()
()]/
()(1 ) ()
()(1 ) ()
()(1 ) ()




      

 














s
Es Na s s s Es Na k s s Es k
Ls Es L m
sms s mss
shs s hss
sns s nss
VIgmhVVVgnVVV
gV V V C u
mVm Vm
hVh Vh
nVn Vn
(4)
In the process of tracking the gait of the machine
leg, the ability to follow the reference trajectory
()
d
yt
perfectly, thus improve the performance of gait
tracking control of the machine leg (XU Wei-min,
2016).
2.2 A bionic kinematic model of a
machine leg
On the basis of the constructed model of the
controlled object of the bionic machine leg, the
kinematic equation is analyzed, the kinematic
equation of the bionic machine leg is described by
using the RRT motion planning model (HE Da-kuo,
2016):
cos sin
dV
mP Xmg
dt

 
(5)
ICECTT 2018 - 3rd International Conference on Electromechanical Control Technology and Transportation
542

sin cos
d
mV P Y mg
dt


 
(6)
22
() ( )
z
z
yxyxxyy x z
d
J
JJ J M
dt

     
(7)
cos
dx
V
dt


(8)
sin
dy
V
dt


(9)
z
d
dt



(10)

  (11)
1
()
z
f
e   (12)
Wherein,

is the inclination of the bionic
machine leg centroid and the target shape vector V,

is the longitudinal inclination of the walking gait
of a bionic machine leg.
x
, y are bionic machine
leg centroid positions.
3 Optimization of gait tracking
control algorithm for machine legs
3.1 Resistance torque feedback
regulation
On the basis of above gait tracking control,
constraint parameter analysis and kinematic model
construction, gait motion mechanics and damping
moment parameters are taken as constraint indexes
to achieve adaptive optimization of stepping sensing
information of machine legs, gait tracking error
feedback control is obtained, it is assumed that the
walking motion of the bionic machine leg is a
longitudinal linear motion model, the centroid of the
bionic machine leg is the origin of the coordinate
system, and the potential error of the gait tracking is
defined as follows:

Vms
eVV (13)
According to the relationship between the
damping torque and the gait coordinated control, the
boundary coupling control integral method is
applied to the steady-state error compensation in the
synchronous control of the gait of the machine legs,
the walking tracking error of the bionic robot leg is
output in two non-coupled control integral elements:
,
x
dd
exxe


   , wherein ,
dd
x

are steady
state tracking errors of reference moment, under the
condition of limited initial integration, the adaptive
inverse integral control is adopted, and the dynamic
equation of the K iteration can be written.:
() (, (), ())
() (, ()) () ()






kkk
kk k
xt ftxtut
yt gtxt Dtut
(14)
The K tracking error is:
() () ()
kdk
et yt yt (15)
Adaptive quantization fusion processing is taken
by using closed loop PI learning method, then:
111
0
() () () ( )

 

t
kkpkik
ututketkesds (16)
With the above process, the damping torque
parameter is taken as the constraint index to
optimize the stepping sensor information of the
robot legs, so as to achieve feedback regulation of
the torque and improve the tracking stability of the
robot legs.
3.2 Optimization of gait tracking
control law for machine legs
Combined with nonlinear adaptive inversion integral
method, the feedback regulation of damping torque
is realized, and the optimal control of robot leg gait
tracking control is achieved. The output leg number
of robot leg gait tracking control structure is m,
performance index function of robot leg step sensing
information optimization is:
22
1111
()
QQ
mN
T
qq kq i
qqki
F
xee e v

 

 
(17)
The e
q
is the desired output attitude parameter of
the q samples and the error of the inertial fusion
parameter, the parameter correction vector of the
gait tracking of the leg is obtained by using the
inverse stabilization control method:
11 11
[,,,]
T
tn mt
x
wwzz ，
，
(18)
According to the nonlinear adaptive inversion
integral method, the Jacobi matrix can be written as
a quantitative fusion of the attitude parameters of the
machine gait tracking:
11 11 11
11 12
21 21 21
11 12
11 12
()
mt
mt
mQ mQ mQ
mt
ee e
ww z
ee e
ww z
Jx
ee e
ww z
 


 


 

 




 


 





(19)
The general term is:
1
()
'( )
dq dq dq
kj kj kj
t
dj jq
j
dq
kj
eYgo
zz z
za
go
z

 

 







(20)
Gait Tracking Control of Machine Leg Based on Damping Torque Feedback Control
543

The steady state of the walking attitude of the
machine leg is the constraint condition of the
independent variable control, set:
.
sin ,| |
2
,| |
,| |
i
ii
i
e
e
e
e



















(

>0 (21)
According to the normal correlation between the
steady state disturbance
)(kw and the acceleration
measurement matrix
)(k
i
u
based on the walking
posture of the robot leg, the information state of the
walking posture of the machine leg is updated:









)()()()|,1()|,(
)()()()|,1(
ˆ
)|,(
ˆ
1
1
kkkkkjkkj
kkkkkjkkj
jj
T
j
jj
T
j
HRHYY
MRHyy



(22)
Wherein,
)1|(
ˆ
)|,0(
ˆ
 kkkk yy
,
)1|()|,0(  kkkk YY
, and:
)()()()1|(
)()()()1|(
)|,()|(
1
1
1
kkkkk
kkkkk
kkNkk
T
N
j
jj
T
j
HRHY
HRHY
YY









(23)
In a comprehensive analysis, the gait stability
tracking control of the machine leg is realized
through the feedback adjustment of the damping
torque.
4 Simulation experiment
In order to test the application performance of this
method in the implementation of the bionic robot leg
walking stability control, the simulation experiment
is carried out, the experiment is designed by Matlab,
using digital magnetometer, accelerometer and gait
parameters of three axis gyroscopes. The
measurement error of the acquisition of the original
attitude parameter of the machine leg by three kinds
of sensitive elements is set respectively. 2mm,
1.2mm and 1.2mm. The initial position of the
machine leg is

T
01
0
x
,







1.00
01
0
p
, adaptive
control parameters are:
121 2
1, 1, 2, 2cc  ,
the intensity of the error disturbance
25.0)(

kQ ,
the system equation parameters of the gait tracking
control model of the machine leg are set as follows:
0.0508N.m/V
m
K 
s
0.5732V /rad
e
K  ,
10.6
04 0.5.





A
,
1
1




B
,


11C
,
0.1D
,
1
0.02 0.01
Δ
0.02 0.12








A
,
1
Δ0B
,
2
0.804(1 0.5)
p
J
kg m

, according to the above
simulation environment and parameter setting, the
robot leg gait tracking control simulation is carried
out, and the speed, acceleration, displacement and
damping force of the machine legs are obtained. The
results are shown in Figure 1.
0 100 200 300 400
0
50
100
t(ms)
V(mV)
0 50 100
0
0.5
1
V(mV)
m
0 100 200 300 400
0
50
100
t(ms)
V(mV)
0 50 100
0
0.2
0.4
0.6
0.8
1
V(mV)
m
A
B
C
D
Fig.1 Parameter acquisition of robot leg gait
tracking
Taking the gait parameter collected from
machine legs collected from Figure 1 as input data,
gait tracking, stability control and simulation test are
carried out, and the predicted output and expected
output of gait tracking function in two groups of test
environment are obtained, as shown in Figure 2.
(a) Curved gait tracking environment
(b) Linear gait tracking environment
Fig.2 Output of tracking function of machine leg gait in
different environments
Figure 2 analysis showed that in two different
ICECTT 2018 - 3rd International Conference on Electromechanical Control Technology and Transportation
544

test conditions, this method of robotic leg gait
tracking accuracy is higher, which in a straight-line
walking condition, stability better track machine leg
gait, walking in curved environment, this paper
through the method of feedback correction and error
adjustment of damping torque. With the same
attitude parameters good tracking performance. In
order to compare the performance of different
control methods, the control convergence is taken as
the test index, and the contrast results are obtained,
as shown in Figure 3, the analysis shows that this
method has better convergence, higher stability and
better performance improvement in gait tracking
control of machine legs.
0 10 20 30 40 50 60 70 80 90 100
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
本文方法
传统方法
Fig. 3 Control convergence comparison of different
methods
5 CONCLUSION
In this paper, the robust control of gait of the legs is
studied to improve the robustness of the bionic gait
control and the stability of walking. A gait tracking
control method based on damping torque feedback is
proposed in this paper. The adaptive optimization of
the step sensing information of the robot leg with the
parameters of the gait motion and the damping
torque as the constraint index. An inverse
stabilization control method is introduced to modify
the error feedback of the gait tracking parameter of
the machine leg. The feedback adjustment of
damping torque is realized by combining the
nonlinear adaptive inversion integral method, and
the gait stability tracking control of the machine leg
is realized. The simulation results show that the
control performance is good.
ACKNOWLEDGEMENTS
This project is supported by and 2017
Undergraduate Scientific and Technological
Innovation Project Fund of Guangdong Province
(pdjh2017a0938).
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