# A Large-Scale Multibody Manipulator Soft Sensor Model and Experiment Validation

Authors: Wu Ren; Yunxin Wu; Zhaowei Zhang; Fan Hu
Journal: Journal of Robotics
 (2014)

---

## Abstract

Stress signal is difficult to obtain in the health monitoring of multibody manipulator. In order to solve this problem, a soft sensor method is presented. In the method, stress signal is considered as dominant variable and angle signal is regarded as auxiliary variable. By establishing the mathematical relationship between them, a soft sensor model is proposed. In the model, the stress information can be deduced by angle information which can be easily measured for such structures by experiments. Finally, test of ground and wall working conditions is done on a multibody manipulator test rig. The results show that the stress calculated by the proposed method is closed to the test one. Thus, the stress signal is easier to get than the traditional method. All of these prove that the model is correct and the method is feasible.


---

## Body

## 1. Introduction

Large-scale multibody manipulators often work in harsh conditions. Due to the frequently posture change, they are susceptible subject to vibration and shock. The structure stress increased during the working process. Thus, obtaining the structure stress information is significant in health monitoring of these machineries. The existing structure stress signal is obtained by pasting strain sensors onto the structures. However, the strain sensors are easily damaged and usually have short lifespan. The operators need to frequently repaste them during working process. Therefore, the cost increases largely and it is not suitable for long-term health monitoring.In the recent researches, Cazzulani et al. proposed a health monitoring algorithm for concrete displacing booms. The method is based on geometrical and dynamic knowledge by estimating the boom failure through a self-learning program. And the stress signals are got by pasting sensors onto the structure [1, 2]. Cazzulani et al. selected a 4-section boom mobile concrete pump truck and analyzed the load characteristics of them. Then, the boom damage was calculated by stress signal [3]. Sun et al. used a closed-loop detection and open-loop control strategy on the vibration suppression of a truck-mounted concrete displacing boom using angle signals [4]. Liu et al. calculated a truck mounted concrete boom dynamics characteristic using Lagrange principle and did the experiment on a commercial one which proved that the simulation model was correct [5]. Soft sensor method is also used in other fields. Facco et al. provided quality estimation by multivariate statistical soft sensor and got accurate measured results by it [6]. McElroy et al. provided a discrete element method (DEM) model of a rotating drum and used soft sensor method to detect the flow regime of it [7]. Deng et al. used soft sensors technology to build a data-driven model and provided online continuous prediction of specific variables [8]. Wang et al. proposed a soft sensor modeling algorithm with partial least squares. The approach is used in stationary and nonstationary behaviors monitoring of a blast furnace hearth wall and has good results [9].Soft sensor technology is used to obtain variable information which is difficult to be directly measured through parameters which are easy to obtain [10, 11]. This paper is organized as follow: Section 2 presents the boom structure of the test rig. Section 3 establishes the mathematical relationship between the booms and hydraulic cylinders. In Section 4, the soft sensor model of the boom test rig has been built. In the model, main variable is stress signal and auxiliary variable is angle signal. Section 5 gives the simulation and test results of the test points’ stress which proofs that the proposed model is correct. The stress information of two typical working conditions is calculated from angle signals then. Finally, conclusion is presented in Section 6. All of these provide real-time health monitoring for such mechanisms.


## 2. Multibody Manipulator Model and Parameters

The structure model is shown in Figure1. In the model, the multibody manipulator consists of 4 booms, several links, 4 hydraulic cylinders, and standoffs. The postures transformation is achieved by luffing mechanisms which are driven by corresponding hydraulic cylinders. The joints distance is expressed as a
i
j
(
i
=
0,1
,
2,3
,
4
;
j
=
1,2
,
3,4). The physical parameters of the structure are shown in Table 1.Table 1
Multibody manipulator parameters.
Boom
Length (m)
Angle (°)
Boom weight (N)
Boom bending angle (°)
Distance between joints (m)
Hydraulic cylinders weight (N)
1
L
1
θ
1
G
1
γ
12
a
11
,
a
12
,
a
13
G
g
1
2
L
2
θ
2
G
2
γ
21
,
γ
22
a
21
,
a
22
,
a
23
G
g
2
3
L
3
θ
3
G
3
γ
31
,
γ
32
a
31
,
a
32
,
a
33
G
g
3
4
L
4
θ
4
G
4
γ
41
a
41
G
g
4Figure 1
Multibody manipulator structure model and joint distance.


## 3. Boom Hydraulic Cylinder Model

### 3.1. The First Boom Cylinder Model

The first boom and standoffs are shown in Figure2. The angle between the cylinder and boom is β
1 and the cylinder length is l
1. They can be solved by
(1)
∠
O
A
B
=
arctan
⁡
(
a
02
a
01
)
,
l
1
=
(
a
01
2
+
a
02
2
+
a
11
2
-
2
·
a
01
2
+
a
02
2
h
h
·
a
11
·
cos
⁡
(
∠
O
A
B
+
θ
1
)
a
01
2
+
a
02
2
)
1
/
2
,
β
1
=
arcsin
⁡
(
a
01
2
+
a
02
2
·
sin
⁡
(
∠
O
A
B
+
θ
1
)
l
1
)
.Figure 2
Connection relationship between the first boom and the hydraulic cylinder.


### 3.2. The Other Three Boom Cylinder Models

The other three boom cylinder connection is shown in Figure3. The luffing mechanism parameters are in Table 2.Table 2
Multibody manipulator luffing mechanism parameters.
Boom
Length of links (m)
Length of cylinders (m)
Angles between cylinders and booms (°)
Angles between booms and links (m)
Angles between links (°)
1
b
11
,
b
12
l
2
β
2
α
12
,
α
21
ϕ
1
2
b
21
,
b
22
l
3
β
3
α
22
,
α
31
ϕ
2
3
b
31
,
b
32
l
4
β
4
α
32
,
α
41
ϕ
3Figure 3
Connection relationship of the other three booms, links, and hydraulic cylinders.


## 3.1. The First Boom Cylinder Model

The first boom and standoffs are shown in Figure2. The angle between the cylinder and boom is β
1 and the cylinder length is l
1. They can be solved by
(1)
∠
O
A
B
=
arctan
⁡
(
a
02
a
01
)
,
l
1
=
(
a
01
2
+
a
02
2
+
a
11
2
-
2
·
a
01
2
+
a
02
2
h
h
·
a
11
·
cos
⁡
(
∠
O
A
B
+
θ
1
)
a
01
2
+
a
02
2
)
1
/
2
,
β
1
=
arcsin
⁡
(
a
01
2
+
a
02
2
·
sin
⁡
(
∠
O
A
B
+
θ
1
)
l
1
)
.Figure 2
Connection relationship between the first boom and the hydraulic cylinder.


## 3.2. The Other Three Boom Cylinder Models

The other three boom cylinder connection is shown in Figure3. The luffing mechanism parameters are in Table 2.Table 2
Multibody manipulator luffing mechanism parameters.
Boom
Length of links (m)
Length of cylinders (m)
Angles between cylinders and booms (°)
Angles between booms and links (m)
Angles between links (°)
1
b
11
,
b
12
l
2
β
2
α
12
,
α
21
ϕ
1
2
b
21
,
b
22
l
3
β
3
α
22
,
α
31
ϕ
2
3
b
31
,
b
32
l
4
β
4
α
32
,
α
41
ϕ
3Figure 3
Connection relationship of the other three booms, links, and hydraulic cylinders.


## 4. Soft Sensor Numerical Model

### 4.1. Test Points Tension and Bending Moments

Based on the multibody luffing mechanism connected relationship, the test points’ stress soft sensor model of the structure has been built according to Figure4. In order to calculate the realistic working conditions, the luffing mechanism joint friction is taken into account as well. And the friction type is Coulomb friction. The tension of the test points is calculated in the appendix ((A.1)–(A.6)). On the other hand, the bending moments are derived from (2) to (4).Figure 4
Boom tension calculation considering joints Coulomb friction.As shown in Figure4, the boom test points’ stress can be expressed as in (5).Here, in Figure4, F
i (i
=
1
,
2
,
3
,
4) is the joints’ tension on the boom. θ
i  (
i
=
1
,
2
,
3
,
4
) is the horizontal angle of boom i. The friction circle (dashed circle in Figure 4) radius of boom i is ρ. f is the friction coefficient, and r is the joint radius. φ
i is the front joint force horizontal angle of boom i. η
i
1 and η
i
2 are angles between joints and links. F
j
1
x and F
j
2
y are the joint forces between boom 1 and the standoffs. F
i
g are the cylinder forces of boom i  (
i
=
1
,
2
,
3
,
4
). F
(
i
-
1
)
1
l and F
(
i
-
1
)
2
l are joint forces between boom i and the links (
i
=
1
,
2
,
3
,
4
). G
i, G
g
i, and G
i
fare the respectively equivalent weight of boom i  (
i
=
1
,
2
,
3
,
4
), cylinder i  (
i
=
1
,
2
,
3
,
4
), and boom tip. The tension and bending moment parameters of the multibody boom structure are shown in Table 3.Table 3
Boom variables of the stress calculation.
Boom
Tension (N)
Bending moments (N·m)
Cross section dimension (m)
H
h
B
b
1
F
N
1
M
1
H
1
h
1
B
1
b
1
2
F
N
2
M
2
H
2
h
2
B
2
b
2
3
F
N
3
M
3
H
3
h
3
B
3
b
3
4
F
N
4
M
4
H
4
h
4
B
4
b
4As in Figure5, the boom cross section moment inertia of the x-axis can be written as
(2)
I
x
=
∫
A
y
2
d
A
=
2
∫
h
/
2
H
/
2
b
y
2
d
y
+
2
∫
-
H
/
2
H
/
2
(
B
-
b
2
)
y
2
d
y
=
1
12
(
B
H
3
-
b
h
3
)
.
The bending modulus is expressed as
(3)
W
=
I
x
y
max
⁡
=
(
1
/
12
)
(
B
H
3
-
b
h
3
)
H
/
2
=
B
H
3
-
b
h
3
6
H
.
And the test points’ cross section area is
(4)
A
=
b
(
H
-
h
)
+
(
B
-
b
)
H
.
Here, h and b are the boom cross section internal width and height. Meanwhile, H and B are the boom external cross section width and height.Figure 5
Boom cross section parameters.


### 4.2. Test Points’ Stress

Finally, the stress of the test points can be calculated based on the above tension and bending moments by(5)
σ
=
F
N
A
+
M
W
.The manipulator test rig parameters values are shown in Table4.Table 4
Boom test rig parameters value.
Parameters
Value
Boom weight
886.3 N, 371.42 N, 313.6 N, 179.34 N
Boom length
3.76 m, 2.83 m, 2.88 m, 3.21 m
Joint distance between booms
a
01
,
a
02: 0.13 m, 0.24 m
a
11
,
a
12
,
a
13: 0.65 m, 1.09 m, 0.24 m
a
21
,
a
22
,
a
23: 0.25 m, 0.67 m, 0.126 m
a
31
,
a
32
,
a
33: 0.135 m, 0.7 m, 0.12 m
a
41: 0.14 m
Boom bending angles
γ
12: 0.36π; γ
21
,
γ
22: 0.278π, 0.278π
γ
31
,
γ
32: 0.294π, 0.294π; γ
41: 0.3π
Links length
b
11
,
b
12: 0.4 m, 0.39 m
b
21
,
b
22: 0.18 m, 0.15 m
b
31
,
b
32: 0.24 m, 0.23 m
Cylinders weight
144 N, 180 N, 74.5 N, 24.5 N
Links weight
38 N, 4.8 N, 7.4 NThe simulation of the ground and wall conditions is done in Matlab software then. The posture angles of the booms are in Table5. Figure 6 is the ground and wall working condition postures in the simulation process.Table 5
The boom angles of the two working conditions (°).
Working condition
Boom 1
Boom 2
Boom 3
Boom 4
Ground
73
18
−27
−67
Wall
58
45
−2
−70Manipulator postures of ground condition (a) and wall condition (b).
(a)
(b)


## 4.1. Test Points Tension and Bending Moments

Based on the multibody luffing mechanism connected relationship, the test points’ stress soft sensor model of the structure has been built according to Figure4. In order to calculate the realistic working conditions, the luffing mechanism joint friction is taken into account as well. And the friction type is Coulomb friction. The tension of the test points is calculated in the appendix ((A.1)–(A.6)). On the other hand, the bending moments are derived from (2) to (4).Figure 4
Boom tension calculation considering joints Coulomb friction.As shown in Figure4, the boom test points’ stress can be expressed as in (5).Here, in Figure4, F
i (i
=
1
,
2
,
3
,
4) is the joints’ tension on the boom. θ
i  (
i
=
1
,
2
,
3
,
4
) is the horizontal angle of boom i. The friction circle (dashed circle in Figure 4) radius of boom i is ρ. f is the friction coefficient, and r is the joint radius. φ
i is the front joint force horizontal angle of boom i. η
i
1 and η
i
2 are angles between joints and links. F
j
1
x and F
j
2
y are the joint forces between boom 1 and the standoffs. F
i
g are the cylinder forces of boom i  (
i
=
1
,
2
,
3
,
4
). F
(
i
-
1
)
1
l and F
(
i
-
1
)
2
l are joint forces between boom i and the links (
i
=
1
,
2
,
3
,
4
). G
i, G
g
i, and G
i
fare the respectively equivalent weight of boom i  (
i
=
1
,
2
,
3
,
4
), cylinder i  (
i
=
1
,
2
,
3
,
4
), and boom tip. The tension and bending moment parameters of the multibody boom structure are shown in Table 3.Table 3
Boom variables of the stress calculation.
Boom
Tension (N)
Bending moments (N·m)
Cross section dimension (m)
H
h
B
b
1
F
N
1
M
1
H
1
h
1
B
1
b
1
2
F
N
2
M
2
H
2
h
2
B
2
b
2
3
F
N
3
M
3
H
3
h
3
B
3
b
3
4
F
N
4
M
4
H
4
h
4
B
4
b
4As in Figure5, the boom cross section moment inertia of the x-axis can be written as
(2)
I
x
=
∫
A
y
2
d
A
=
2
∫
h
/
2
H
/
2
b
y
2
d
y
+
2
∫
-
H
/
2
H
/
2
(
B
-
b
2
)
y
2
d
y
=
1
12
(
B
H
3
-
b
h
3
)
.
The bending modulus is expressed as
(3)
W
=
I
x
y
max
⁡
=
(
1
/
12
)
(
B
H
3
-
b
h
3
)
H
/
2
=
B
H
3
-
b
h
3
6
H
.
And the test points’ cross section area is
(4)
A
=
b
(
H
-
h
)
+
(
B
-
b
)
H
.
Here, h and b are the boom cross section internal width and height. Meanwhile, H and B are the boom external cross section width and height.Figure 5
Boom cross section parameters.


## 4.2. Test Points’ Stress

Finally, the stress of the test points can be calculated based on the above tension and bending moments by(5)
σ
=
F
N
A
+
M
W
.The manipulator test rig parameters values are shown in Table4.Table 4
Boom test rig parameters value.
Parameters
Value
Boom weight
886.3 N, 371.42 N, 313.6 N, 179.34 N
Boom length
3.76 m, 2.83 m, 2.88 m, 3.21 m
Joint distance between booms
a
01
,
a
02: 0.13 m, 0.24 m
a
11
,
a
12
,
a
13: 0.65 m, 1.09 m, 0.24 m
a
21
,
a
22
,
a
23: 0.25 m, 0.67 m, 0.126 m
a
31
,
a
32
,
a
33: 0.135 m, 0.7 m, 0.12 m
a
41: 0.14 m
Boom bending angles
γ
12: 0.36π; γ
21
,
γ
22: 0.278π, 0.278π
γ
31
,
γ
32: 0.294π, 0.294π; γ
41: 0.3π
Links length
b
11
,
b
12: 0.4 m, 0.39 m
b
21
,
b
22: 0.18 m, 0.15 m
b
31
,
b
32: 0.24 m, 0.23 m
Cylinders weight
144 N, 180 N, 74.5 N, 24.5 N
Links weight
38 N, 4.8 N, 7.4 NThe simulation of the ground and wall conditions is done in Matlab software then. The posture angles of the booms are in Table5. Figure 6 is the ground and wall working condition postures in the simulation process.Table 5
The boom angles of the two working conditions (°).
Working condition
Boom 1
Boom 2
Boom 3
Boom 4
Ground
73
18
−27
−67
Wall
58
45
−2
−70Manipulator postures of ground condition (a) and wall condition (b).
(a)
(b)


## 5. Experiment and Simulation Analysis

### 5.1. Experiment

In order to verify that the proposed method is reasonable and that the established soft sensor model is correct, an experiment has been done on a test rig. The main instruments are as follows.(a)
Dynamic data acquisition instrument: the Dewesoft data acquisition is adopted as in Figure7. It has 16 input and output channels, 6 acceleration channels, and 2 CAN modules. The collected pressure, displacement, strain, and data can be got and postprocessed in it.
(b)
Angle sensor: the SANG5000 angle sensors (see Figure8) are used too. Each angle sensor is pasted onto one boom so the angle signals can be got then.
(c)
Strain sensor: strain sensors are used to test the selected points’ stress. The strain sensors pasted on the four booms are as in Figure9. And Figure 10 is the strain sensor pasted onto the supports.
(d)
Truck mounted concrete pump boom test rig: the 13 m truck mounted concrete pump boom test rig (see Figure11) is used either. Each boom is separately driven by a hydraulic actuator.Figure 7
Dewesoft data acquisition process instrument.Figure 8
Angle sensor pasted on boom 1 during the experiment.Strain sensors of the test points pasted on boom 1 (a), boom 2 (b), boom 3 (c), and boom 4 (d) during the experiment.
(a)
(b)
(c)
(d)Figure 10
Strain sensor pasted on the supports during the experiment.Figure 11
The multibody boom test rig.


### 5.2. Experiment and Simulation Comparison

The test points’ stress simulation and experiment results of the ground and wall conditions are shown in Figure12.Stress comparison between test and numerical results of the boom.
(a)
Ground condition
(b)
Wall conditionAs can be seen in Figure12, the test points’ stress results of the two conditions agree well between experiment and numerical model. The maximum stress test value of the ground condition in Figure 12(a) is 100 Mpa on test point 1. Compared with the simulated value 95 Mpa of test point 1, the error between them is about 5 Mpa. And the largest error in this condition between them is about 10 Mpa on test point 7. The other points’ results are both in good agreement.The maximum test value of the wall condition in Figure12(b) is 84 Mpa of test point 1. Compared with the simulated values 82 Mpa, the error between them is 2 Mpa. And the largest error in this condition is about 10 Mpa on test points 6 and 7. The other points are both with good agreement in this working condition too.The maximum stress of both the two conditions is smaller than the allowable stress 230 Mpa of the boom structure. In the simulation process, the booms uniform mass is considered as concentrated mass; besides, the cross section area is regarded as uniform beam instead of nonuniform beam and the booms’ center of gravity moves backward in the numerical model. Therefore, the errors are inevitably. So, the soft sensor model established is correct and rational. Meanwhile, it is feasible and convenient to use angle signal to obtain stress of different postures.


## 5.1. Experiment

In order to verify that the proposed method is reasonable and that the established soft sensor model is correct, an experiment has been done on a test rig. The main instruments are as follows.(a)
Dynamic data acquisition instrument: the Dewesoft data acquisition is adopted as in Figure7. It has 16 input and output channels, 6 acceleration channels, and 2 CAN modules. The collected pressure, displacement, strain, and data can be got and postprocessed in it.
(b)
Angle sensor: the SANG5000 angle sensors (see Figure8) are used too. Each angle sensor is pasted onto one boom so the angle signals can be got then.
(c)
Strain sensor: strain sensors are used to test the selected points’ stress. The strain sensors pasted on the four booms are as in Figure9. And Figure 10 is the strain sensor pasted onto the supports.
(d)
Truck mounted concrete pump boom test rig: the 13 m truck mounted concrete pump boom test rig (see Figure11) is used either. Each boom is separately driven by a hydraulic actuator.Figure 7
Dewesoft data acquisition process instrument.Figure 8
Angle sensor pasted on boom 1 during the experiment.Strain sensors of the test points pasted on boom 1 (a), boom 2 (b), boom 3 (c), and boom 4 (d) during the experiment.
(a)
(b)
(c)
(d)Figure 10
Strain sensor pasted on the supports during the experiment.Figure 11
The multibody boom test rig.


## 5.2. Experiment and Simulation Comparison

The test points’ stress simulation and experiment results of the ground and wall conditions are shown in Figure12.Stress comparison between test and numerical results of the boom.
(a)
Ground condition
(b)
Wall conditionAs can be seen in Figure12, the test points’ stress results of the two conditions agree well between experiment and numerical model. The maximum stress test value of the ground condition in Figure 12(a) is 100 Mpa on test point 1. Compared with the simulated value 95 Mpa of test point 1, the error between them is about 5 Mpa. And the largest error in this condition between them is about 10 Mpa on test point 7. The other points’ results are both in good agreement.The maximum test value of the wall condition in Figure12(b) is 84 Mpa of test point 1. Compared with the simulated values 82 Mpa, the error between them is 2 Mpa. And the largest error in this condition is about 10 Mpa on test points 6 and 7. The other points are both with good agreement in this working condition too.The maximum stress of both the two conditions is smaller than the allowable stress 230 Mpa of the boom structure. In the simulation process, the booms uniform mass is considered as concentrated mass; besides, the cross section area is regarded as uniform beam instead of nonuniform beam and the booms’ center of gravity moves backward in the numerical model. Therefore, the errors are inevitably. So, the soft sensor model established is correct and rational. Meanwhile, it is feasible and convenient to use angle signal to obtain stress of different postures.


## 6. Conclusion

Large-scale multibody manipulator stress value is difficult to obtain during the long-time working process. But the boom angle information is easy to measure and the stability and lifespan of angle sensors are better than strain sensors. By analyzing the mathematical relationships between the angle and the strain information, a soft sensor model has been established. In the model, the joint Coulomb friction is considered too. Then, the stress value can be obtained conveniently by angle signals of the booms. The stress results calculated by the model agree well with the experimental ones of the ground and wall conditions. Thus, the long-time signal acquisition will be feasible and the working efficiency will be improved. Next, by comparing the experimental and numerical results, it is proved that the soft sensor model of the test rig is correct. This provides help for long-term health monitoring for such manipulators and greatly reduces cost.



---

*Source: 769783-2014-02-06.xml*