Applied Mechanics and Materials
ISSN: 1662-7482, Vols. 204-208, pp 4845-4850
doi:10.4028/www.scientific.net/AMM.204-208.4845
© 2012 Trans Tech Publications, Switzerland
Online: 2012-10-26
Structure Optimal Design for Portable Exoskeleton Using Improved
Particle Swarm Optimization
Fang Liu1, a, Wenming Cheng 2,b and Yi Zhou3,c
1
School of Mechanical Engineering of South-west Jiaotong University, Chengdu, Sichuan Province,
Mainland China, Zip Code: 610031
2
School of Mechanical Engineering of South-west Jiaotong University, Chengdu, Sichuan Province,
Mainland China, Zip Code: 610031
3
School of Mechanical Engineering of South-west Jiaotong University, Chengdu, Sichuan Province,
Mainland China, Zip Code: 610031
a
[email protected], [email protected], [email protected]
Keywords: Portable Exoskeleton; Three-hinge Mechanism; Particle Swarm Optimization; Structure
Optimal Design; Finite Element Calculation
Abstract. Portable exoskeleton is directed at providing necessary support and help for loaded legged
locomotion. The kernel of whole mechanical construction of the exoskeleton is lower extremities.
The lower extremities consist of exoskeleton thigh, exoskeleton shank, hydraulic cylinder and
corresponding joints. In order to find the optimal combination of design parameters of lower
extremities, an improved particle swarm optimization algorithm based on simulated annealing is
proposed. To improve global and local search ability of the proposed approach, the inertia weight is
varied over time, and jumping probability of simulated annealing is adopted in updating the position
vector of particles. Experimental results show that the improved algorithm can obtain the optimal
design solutions stably and effectively with less iteration compared to the standard particle swarm
optimization and simulated annealing; using ANSYS software build finite element model with the
optimization result, then analyzes the strength of the model, these stress results verify the of accuracy
of the improved particle swarm optimization.
Introduction
Portable exoskeleton is a new type of wearable mechanical devices involving mechanical, bionic,
sensing, controlling, information processing technologies and many other technologies, which
making human body have the strength, speed and endurance of a machine[1-5].
Lower limb bearing subsystem is the core part of the whole mechanical structure of portable
exoskeleton. It is composed of bionic thigh, calf, actuating cylinder and corresponding joints, which
match the human skeleton. The burden carried by human body is transferred via the carrying system
to the power-assisted lower extremity subsystem and the sensing boots. The vertical burden is mainly
carried by the actuating cylinder, and the system can adjust the support force according to different
body postures and motions. Therefore, the proper selection of structure parameters for lower
Extremity power subsystem directly determines the overall system performance and is of great
practical significance to optimum analysis.
Particle Swarm Optimization (PSO) is a bionic intelligent optimization algorithm simulating
foraging behavior of bird groups established by Kennedy, a psychologist, and Eberhart, an electrical
engineer, in 1995 [6]. It can avoid the shortcoming of traditional optimization algorithm that is
dependent on characteristic of a problem, thus is more suitable for structure optimization design of
complicated multivariable nonlinear objective functions [7-9]. In this thesis the author will simplify the
structure of thigh, calf and actuating cylinder to established a stress model according to stress of
bionic thigh, calf and actuating cylinder, put forwarded an improved PSO algorithm based on the
standard PSO algorithm, and illustrate the feasibility and effectiveness of the improved PSO
algorithm in solving such kind of nonlinear Constrained Optimization Problems.
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Progress in Industrial and Civil Engineering
Lower Extremity Stress Model
Ideally, when a person stands uprights stably, the thigh structure will pass the vertical force through
the calf to the ground, without actuating cylinder subjected to forces in the vertical direction. This
thesis takes this ideal state as a basis for the research to analyze the stress on three-hinge system
composed of thigh, calf and hydraulic cylinder. The three-hinge model was shown in Fig. 1.
F
1
21
L1
G自
1
S
F缸
S
22
¦ 2Â
¦ 3Â
¦ È
S2
l自
¦ 1Â
23
3
2
Figure 1 Force Model of Simplified Three-hinge Mechanism
Among them, point O21 is the hinge point for hydraulic cylinder and thigh, point O22 is the hinge
point for thigh and calf, point O23 is the hinge point for hydraulic cylinder and calf, point O1 is the
load point, point O2 is the hinge point for calf and ankle. The length of rod O21O22 is S1, the length of
rod O21O23 (the hydraulic cylinder) is S2, the length of rod O22O23 is S3, the angle between hydraulic
cylinder and thigh is β1, the angle between hydraulic cylinder and calf is β2, the angle between calf
and level direction is θ, the length of rod O1O22 is L1, the force on rod O21O23 (the hydraulic cylinder)
is Fcylinder.
When human body is in the stable standing state, the whole tree-hinge mechanism is a balanced
system with resultant force of 0, which simplifies the stress on the upper fulcrum of hydraulic
cylinder to a force F in the vertical direction. The following relation is the result of stress analysis of
the whole mechanism:
F × L1 × cos( β 2 − θ ) + Gz × Lz × cos( β 2 − θ )
(1)
Fcylinder＝
S1 × cos β1
According to analysis of operating principle, the optical design parameter of the stress on hydraulic
cylinder should be 0, therefore the objective function of parameter optimization for the portable
powered exoskeletons lower Extremity system is formula (1).
Based on stress analysis of Fig. 1, under the cosine theorem, the relations between each variable of
the objective functions and the rod length S1, S2 and S3 are as follows:

S12 + S22 − S32
β
=
arccos
 1
2S1S2

(2)

2
2
2
S
+
S
−
S
 β = arccos 1
3
2
 2
2S1S3
This thesis will optimize S1, S2, S3 and θ.
As the portable exoskeleton system functions as an assistant device for human body
weight-bearing exercises, human factors must be taken into account in designing of the mechanism,
which are design constraints brought about by the upper limit of human body weight-bearing capacity
and human body size. A normal adult maximum load is generally 60kg, combined with self weight of
20kg of portable exoskeleton, the maximum bearable stress F can be 800N (this thesis takes 800N).
Due to individual differences, a universal standard must be set to make the product designed
applicable generally. In this thesis, based on the national standard of structure size for Chinese adults
GB/T 10000-1988, the human body standard of No. 95 percentile of Chinese southerners [10] is
adopted to establish constraint ranges of design variables as follows:
Applied Mechanics and Materials Vols. 204-208
 F = 800N, L1 = 462m
 l = 230mm, G = 13.3Nm
 自
自

<
S
<
< S2 < 430
335
345
,
420
1

 80 < S3 < 90 , 72° < θ < 80°

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(3)
Algorithm Design
Through the above modeling process, the optimization design of actuating cylinder three-hinge
luffing mechanism parameters can be regarded as a general nonlinear constraint optimization
problem:
min f (x)


s.t. gi (x) ≤ 0, i =1,2,...,n
 h(x )=0, j =1,2,...,m

(4)
Formulas above contain both inequality and equality constraint. To solve such problems with
optimization algorithm, it is necessary to convert constrained optimization into unconstrained
optimization with penalty functions. Presently there are plenty of penalty function processing
methods, such as external point method, interior point method, multiplier method, exact penalty
function method and so on. This thesis adopts non-differentiable penalty function method, of which
the specific conversion formula is shown as follow:
m
 n

F ( x) = f ( x) + M  ∑ max(0, gi ( x )) 2 + ∑ h 2j ( x ) 
j =1
 i =1

0.5
(5)
In the formula above, M is the penalty factor. Normally, the bigger the M value is the better the
result will be. But in practical application, it is necessary to conduct certain numerical experiment to
select an appropriate. F(x) is the target function of algorithm optimization after conversion.
Improved Particle Swarm Optimization Based on Simulated Annealing (IPSO)
As for particle swarm optimization (PSO), how to balance the global search and local improvement
capability is of extreme importance for enhancemance of algorithm efficiency. In order to enforce the
optimizing ability of PSO, this thesis tries to improve the standard PSO from the prospective of
inertial weight renewal and particle location renewal. As the most important parameter that affecting
the particle speed renewal, the inertial weight ω directly performs control over speed and direction.
Larger ω is helpful for enhancing global optimizing capability of the algorithm, while smaller ω will
increase the convergence rate. This thesis adopts the method of dynamically reducing the inertial
weight to allow it renew with the iteration change:
(6)
ω=ωmax-t×(ωmax-ωmin)/tmax
In this expression, ωmax and ωmin are the maximum and minimum values of inertial weight; t is the
iteration; tmax is the maximum iteration. When a new solution is worked out, it will be compared to the
adaptive value corresponding to the last solution. If the variation ∆E≤0, the new value will be
accepted, otherwise the new value will be accepted according to criteria exp(-∆E/T)>rand(0,1).
Calculation Results and Analysis
In order to test the validity of the algorithm put forward in this thesis, experimental analysis is
conducted with combination of the mathematical model established. In the experimental process, the
parameters are set as: T0=1000; α=0.9; b=0.22, the inner loop times are 300. The parameters of PSO
and IPSO are set as: number of particle N=50; ωmax=0.8; ωmin=0.2; T0=1000; α=0.9; iteration times
are both 300. The experiment has operated the two algorithms 10 times separately, and made
statistical analysis then. Table 1 shows the statistic result of the 10 times of the two algorithms. Table
1 shows that IPSO has found the optimum solution in all the 10 times of algorithms. In this case PSO
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Progress in Industrial and Civil Engineering
is relatively poorer, having only found out the approximate solutions. Therefore, IPSO has very stable
capability for solving nonlinear constrained optimization problems such as structure parameter
optimization of portable powered exoskeleton lower Extremity, and can converge to the global
optimum solution of the problem at a faster speed.
Algorithms
PSO
IPSO
Target
Values
Fcylinder
best
worse
best
worse
Table 1 Algorithms Analysis
Function
Variable Values
1.23e-11
2.59e-4
0
0
S1
424.44
429.09
426.66
426.66
S2
337.92
344.11
342.45
342.45
S3
89.21
86.83
86.94
86.94
θ
74.13
76.82
73.91
73.91
Establishment and Calculation of Finite Element Model
In the finite element calculation, the backrest system has a little effect on the stress distribution
between hip bearing system and power-assisted lower extremity subsystem. And the model is
relatively complex, in order to save the calculation time, increase calculation efficiency and they are
deleted, then according to the calculation results of IPSO, Solidworks software is used to establish the
three-dimensional entity model of the exoskeletons system with the vertical stand state
accompanying type, and the model is translated into X_T format, besides Parasolid is used as the
standard format for data transfer between Solidworks and ANSYS software.
This modeling use m System of Units, and All mechanical components of the portable exoskeleton
use aluminum alloy as the material, which elastic modulus is 7.2 × 1010Pa, Poisson’s ratio is 0.33 and
density is 2700kg/m3. The material of hydraulic cylinder is steel 45, which elastic modulus is
2.1×1011Pa, Poisson’s ratio is 0.27 and density is 7890kg/m3. To set the appropriate material
properties in ANSYS, select the SOLID92 units, and assign the corresponding element attributes for
each component in the mechanical structure of portable exoskeleton, the finite element model can be
obtained, as shown in Fig. 2.
Figure 2 Finite Element Model of Portable Exoskeleton
At the hip bearing system surface, four nodes are selected to put down vertical force 200 N, and
sensing boots surface all are under constraint, considering influence of weight and finite element is
calculated to get the overall stresses of portable exoskeleton (Fig. 3) and hydraulic cylinder on lower
limbs bearing system (Fig. 4).
Figure 3 Stress Contour of the Overall Model
Applied Mechanics and Materials Vols. 204-208
4849
Figure 4 Stress Contour of Hydraulic Cylinder on Lower Limbs Bearing System
Names
Stress values
Location of
maximum stress
Table 2 Stress calculation results
Maximum stress of hydraulic Maximum stress of
cylinder
overall model
5.76 Mpa
128 Mpa
the joint between hydraulic
the joint between
cylinder and calf
thigh and calf
Allowable stress
values
140/264.9 Mpa
—
According to the calculation results of the table 2, the maximum stress is at the joint between thigh
and calf, which stress value is 128 Mpa smaller than the allowable stress value [σ1] =140MPa; the
maximum stress of power-assisted lower extremity subsystem is 5.76 Mpa, far less than the allowable
stress value [σ2] =264.9MPa, and the force on hydraulic cylinder is minimum, which are accord with
the optimization goal of objective function, and prove that the optimization results with improved
particle swarm optimization based on simulated annealing have a high accuracy and meet the
optimization requirements.
Conclusions
1) This thesis has put forward the algorithm IPSO based on simulated annealing for the structure
parameter optimization design of portable powered exoskeleton lower Extremity. The local and
global search capabilities are enhanced by dynamically renewing the inertial weight and renewing
particle position vector of the new iteration, and the constraint conditions are dealt with the
non-differentiable penalty function method. Through comparing the results of the example
calculations, the thesis has drawn the conclusion that compared to SA and PSO, IPSO has advantages
of being able to work out the optimum solution with fewer iterations and having high reliability and
stability.
2) Using ANSYS software to establish a three-dimensional model based on the optimization results,
and the strength values are calculated, the resulting stress calculation results show that the IPSO
optimization results have high accuracy and meet project technical requirements.
Acknowledgements: This research was supported by the National Natural Science Foundation of
China (No.51175442), Supported by the Fundamental Research Funds the Central Universities
(No.SWJTU12CX040) and the Fundamental Research Funds for the Central Universities
(No.2010ZT03).
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Progress in Industrial and Civil Engineering
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Progress in Industrial and Civil Engineering
10.4028/www.scientific.net/AMM.204-208
Structure Optimal Design for Portable Exoskeleton Using Improved Particle Swarm Optimization
10.4028/www.scientific.net/AMM.204-208.4845
DOI References
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(BLEEX). IEEE/ASME Transactions on Mechatronics. 2006, 11(2): 128-38.
10.1109/TMECH.2006.871087