# Pushing Pose Sensing of Underground Mobile Supporting Robot

Authors: Nan Wang; Hao Liu; Xiaobiao Li; Meizi Tian; Lin Zhang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The pushing pose of underground mobile supporting robot (MSR), i.e., hydraulic support, is a key factor to measure the straightness of the working face. Therefore, in order to independently complete the pushing process and ensure the straightness requirements of the pushing pose, by considering the pushing displacement of MSR and the pose of the middle groove of the scraper conveyor, this study proposes a fusion evaluation model combined with the least square straightness based on the pushing displacement and the straightness based on the pose of the middle groove. The pose sensing approach is established by estimating the pose of the middle groove and the displacement of MSR, analyzing, and extracting the data characteristics of acceleration signal; the OVR (one-versus-rest) method is used to realize the displacement state pattern recognition of hydraulic support based on SVM (support vector machine). The effectiveness of this approach is verified by building an experimental platform.


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## Body

## 1. Introduction

As an important intelligent equipment for fully mechanized mining, mobile supporting robot (MSR, also known as hydraulic support) uses high-pressure emulsion to realize the cyclic actions and provides support and protection for the fully mechanized mining face [1]. The pushing pose of MSR refers to the pose state formed by the middle groove of the scraper conveyor when MSR pushes forward with the working face, pushed and moved periodically [2]. In the process of coal mining, MSR, scraper conveyor, and coal wall need to maintain a certain straightness to ensure the smooth operation of coal mining equipment [3–6]. However, the pushing pose of MSR is the essential factor for the straightness of the working face. Therefore, in order to ensure the good straightness of the working face, it is necessary to study the sensing approach of the pushing pose of MSR and realize the straightness evaluation of the pose of MSR.At present, the pose sensing approach of MSR mainly depends on the displacement sensor installed in MSR pushing jack. However, approach has large systematic error. At the same time, it is complicated to replace the damaged sensors because of the poor working conditions and heavy equipment. Thus, it is very necessary to study a new approach to sense MSR pose. Based on the sensing of MSR pose and considering the influencing factors of the change of the middle groove pose, this study established the pushing pose straightness evaluation model based on the pushing displacement and the middle groove pose of the scraper conveyor, which provided the model basis and constraint target for the independent pushing of MSR.


## 2. Related Work

At present, the sensing approach for pose and straightness of hydraulic support mainly focus on simple on-site pull wire and infrared beam measurement. With the deep integration of intelligent detection technology into coal mine production, the inertial navigation technology [6, 7], Unity3D technology [8–11], and visual technology [12, 13] have been used gradually. Zhang et al. and Chen et al. [3, 14] proposed a pose monitoring method of hydraulic support based on multisensor fusion technology. Yang et al. [15] and Liang et al. [16] used the lidar and inclination sensors to measure the pose of hydraulic support, respectively. Wang et al. [17] proposed a method for measuring the height and straightness of the hydraulic support group based on point cloud; analyzing the geometric posture of single hydraulic support point cloud, the feature points are selected on each hydraulic support to solve the straightness, which effectively reduce the matching error. Wang et al. [18] realized the continuously adjusted for alignment without the interrupt of longwall face based on the reference target line with absolute direction. In addition, multisoftware cosimulation [19], information fusion [20, 21], and algorithm fusion [22, 23] are used in straightness detection of hydraulic support.Although the above approaches have been verified by theory and experiment, the environment in the coal mine has lots of dust and the oil circuit on the hydraulic support is complex, resulting in the obstruction of sight and the limited use of indirect measurement technology. Meanwhile, the existing position sensor is installed inside the hydraulic jack with high error. In order to solve these problems, in this study, the IMU (inertial measurement unit) installed on the middle groove of scraper conveyor is used to directly measure the displacement acceleration, and the MS-KF (multisegmental Kalman filter) approach is used to eliminate the accumulation error. By considering the sensing of the hydraulic support pose and the change of middle groove pose, established the pushing pose straightness evaluation model combined the pushing displacement and the middle groove pose, which provided the model basis and constraint target for the independent pushing of the hydraulic support.


## 3. Pose Sensing Based on Pushing State Recognition

At present, the sensors used by the electrohydraulic control system of MSR in collecting the displacement information are built in the push jack, but this method has sensing error and unfavorable for the installation and maintenance of the sensor. In order to solve these problems, IMU installed on the middle groove of the scraper conveyor is used to directly measure the displacement. However, there is a large time accumulation error in the method of using IMU to collect the acceleration in the process of moving and calculating the pushing displacement through integral processing. Therefore, it is necessary to study more effective error elimination methods to realize the accurate measurement of pushing pose based on IMU.In the pushing process of MSR, the jack will quickly enter the uniform motion state from the static state, which is called the instantaneous acceleration state. After a period of time, it will quickly enter the static state from the uniform state, which is called the instantaneous deceleration state. The instantaneous acceleration and instantaneous deceleration state are called variable velocity state (VVS). Uniform motion state is called constant velocity state (CVS). Other stages remain at static state which is called zero velocity state (ZVS).According to the above prior knowledge, the acceleration data in different states are processed in sections: the Kalman filtering method of the variable acceleration model be used in VVS, the Kalman filtering method of the zero acceleration model be used in CVS, and ZVS provides the reference point of zero velocity update for the whole process of displacement estimation. Compared with the traditional method, it does not use all the data for Kalman filtering calculation, but only uses the data in VVS and CVS periods, so it can reduce the source of cumulative error. In addition, a priori knowledge about velocity and acceleration is added in VVS and CVS periods; the Kalman state space conversion model in the two periods is refined, finally reducing the measurement error.


### 3.1. Methods

This method recognizes the pushing state with the acceleration signal collected; different Kalman filter state space conversion models are applied in different states; meanwhile, the reference point of ZUPT is provided in the ZVS period, which will reduce the measurement error. In essence, the method is called the multiphased Kalman filter (MS-KF) because of subsection handling a group of acceleration time series with the Kalman filter. The method architecture is shown in Figure1, and the key technical process is as follows.Figure 1
Pushing displacement sensing architecture.


#### 3.1.1. Estimation of Middle Groove Pose

The acceleration signal collected by IMU is affected by gravity. In order to remove the influence caused by gravity, we need to obtain the direction of gravity component through pose estimation with the help of gyroscope information output by IMU and then remove the acceleration component caused by gravity. The pose of the middle groove can be estimated by the following formula:(1)qw,tGL=12qt−1GL⊗ωtL,qw,tGL=qw,t−1GL+qw,tGLΔt,where ωtL is the angular rate relative to the sensing coordinate system at time t, qt−1GL is the rotation quaternion of the world coordinate system relative to the sensing coordinate system at time t − 1, and qw,tGL is the rotation quaternion of the world coordinate system relative to the sensing coordinate system at t-time.Through the following formula, the acceleration signal in the sensing coordinate system can be converted into the acceleration signal in the world coordinate system.(2)g′G=Rqw,tGLαtL.Among them,R⋅ converts the pose represented by quaternion into matrix form, and the conversion formula is(3)Rq=q02+q12−q22−q322q1q2−q0q32q1q3+q0q22q1q2+q0q3q02−q12+q22−q322q2q3−q0q12q1q3−q0q22q3q2+q0q1q02−q12−q22+q32.Theoretically, the acceleration signal caused by gravity meets the following equation after conversion:(4)RΔqaccgrG=g′G,where grG is the true gravity vector, the theoretical value is grG=0,0,gT. In practice, deviation Δq^acc may exist. The final pose can be obtained by quaternion interpolation through SLERP and other methods:(5)qtGL=qwGL⊗Δq^acc.Through the above steps, it not only can calculate the pose of the middle groove but also can pretreat the acceleration signal, removing the component generated by gravity in the acceleration signal.


#### 3.1.2. Displacement Estimation Based on MS-KF

After the pose estimation of the middle groove, the collected acceleration signals are transformed into the acceleration time series without the influence of gravity, the data characteristics of the acceleration signals are analyzed and extracted, and the SVM is used for training. Finally, the displacement state of the acceleration time series can be recognized by using the trained SVM model.For acceleration time series under different transition states, MS-KF will use different state space models to estimate the transition displacement. Delimiting the displacement and velocity variablesxt and vt , respectively, the state space model of VVS section is(6)xe,tve,tae,tL=IΔtIIΔt2/20IRqtGLΔt00Ixe,t−1ve,t−1ae,t−1L+0−gΔt0+υt.Among them,υt refers to the processing noise. For the acceleration in the CVS period, theoretically, the acceleration should be 0, so the state space model adopted by CVS is(7)xi,t+1vi,t+1ai,t+1L=IΔtI1/2IΔt20IRqtGLΔt000xi,tvi,tai,tL+0−gΔt0+υt.Second, different initial state values need to be set for acceleration time series in different phases when Kalman filtering estimation is carried out. The initial value setting is shown in the following formula:(8)Xt=Xe,t|Xe,0=0,P0=0,meanxi>0,xi∈VVS,Xi,t,yi∈CVS,Xe,t|Xe,0=Xi,t,P0=0,meanxi<0,xi∈VVS.Among them,Xt is the state variable, Xt=xi,t,vi,t,ai,tLT, and Xe,0 and P0 are the initial values of state variables and estimation errors in Kalman filter estimation, respectively. MS-KF can be realized with the above steps.


### 3.2. Feature Extraction and Selection

Before realizing MS-KF, it is necessary to subsection the process of acceleration time series. In order to study the data characteristics of acceleration time series in the process of MSR pushing, the pushing displacement signal and acceleration signal collected in the laboratory environment are collected, as shown in Figures2(a) and 2(b), respectively, finally getting the schematic diagram of their characteristics with denoising and normalizing the signal, as shown in Figure 2(c). At the beginning of sliding, the positive component of acceleration is large and reaches the average speed of moving jack in a very short time. At the end of sliding, there is a small acceleration change. After the above actions, a sliding process is completed. It is the opposite when moving the support; first, at the beginning of support-moving, the negative component of acceleration is large and then moving at a uniform speed after reaching the average speed of support-moving. At the end of the support-moving, there is a small change, and then, it enters the static state.Figure 2
Feature samples of acceleration and displacement.
(a)(b)(c)MS-KF analysis is based on recognizing the acceleration in VVS, ZVS, and CVS periods. However, when jack is working in the VVS area, the time of accelerating and decelerating is very short, the feature discrimination corresponding to each state is low, and the final recognition effect will be affected. Therefore, it cannot improve the recognition rate through recognizing the state of acceleration signal directly. According to the above analysis of the pushing process, MSR corresponds to the four states of sliding start (S1), pushing end (S2), support-moving start (S3), and support-moving end (S4) in a pushing cycle. VVS corresponds to the area that state transition from one to another. CVS corresponds to the area not only between S1 and S2 but also between S3 and S4. ZVS corresponds to other areas. This method uses the prior knowledge of the transition system in state pattern recognition, which is more efficient and reliable, and the accuracy of final recognition will be improved.Extracting and selecting effective data features is the premise of pushing state pattern recognition. For the acceleration signal, the features that can be extracted are as follows:(1)
Average power: describing the vibration intensity of the signal,xn is the collected acceleration time series, where n is the length of the time series, n=1,2,3...N. The characteristic value can be calculated according to the following formula:(9)f1=∑n=1Nxn2.(2)
Sample entropy: measuring the complexity of time series, the specific definition and calculation formula can be carried out according to the method proposed by Richman et al. [24].(3)
Spectral entropy: quantitative processing the smoothness of spectrum, which is positive correlation with feature show, if the relative power spectrum probability ofxn is Pk, the spectral entropy can be calculated as follows:(10)f3=−∑K=0N/2−1PklnPk.(4)
Mean value: describing the average value of amplitude change of acceleration signal in each area, which can be calculated according to the following formula:(11)f4=1N∑n=1Nxn.(5)
Median frequency: a measure used to describe the frequency change. First, calculating the power spectrum corresponding to the acceleration signal and then dividing the power spectrum probability into two parts with equal energy, the detail calculation process as references [25].(6)
Standard deviation: describing the variation amplitude of acceleration signal, solving according to the following formula:(12)f6=1N−1∑n=1Nxn−x¯2.(7)
Skewness: a asymmetry measure of the vertical distribution near the mean, which is used to describe the asymmetry of acceleration signal when it changes and judge its change direction; the calculation is as follows:(13)f7=NN−1N−21/N∑n=1Nxn−x¯31/N∑n=1Nxn−x¯23.(8)
Kurtosis: reflecting the kurtosis of the square distribution, which is used to describe the amplitude of acceleration signal change, the calculation is as follows:(14)f8=N−1N−2N−3N+11/N∑n=1Nxn−x¯41/N∑n=1Nxn−x¯22−3N−1+3.(9)
Lempel-Ziv: a complex quantification method, reflecting the rate at which new patterns emerge in the time series and the detail calculation process as references [16].(10)
Crest factor: describing the peak sharpness of the signal, the calculation is as follows:(15)f10=maxxn1/N∑n=1Nxn2.Acceleration signals in 102 pushing periods are collected in the laboratory environment; each period corresponds to the acceleration time seriesxin of 4 pushing states, i = 1, 2, 3, …, 408; the length of each time series is 2000, and finally, the eigenvalues corresponding to each acceleration time series are shown as f1–f10 in Figure 3. It can be seen from the figure that all the eigenvalues have a good recognition for the pushing states 1 and 2, but f4 is an exception. Between the pushing states 1 and 4, f4 nearly unchanged, and the boundaries are extremely blurred. Compared with f4, f9 has a good recognition for pushing state 4. When the features f1, f2, f3, and f10 are recognized in the pushing states 2–4, the recognition is low.Figure 3
Features of samples.The other four eigenvalues, namely, f5–f8, have obvious boundaries for the four pushing states, especially f7 and f8. The consistency of all sample eigenvalues in the same state is very high, but the boundary of sample eigenvalues between different states is very obvious. Therefore, f5–f8 is the best choice among the above features used for pattern recognition of the pushing state. In order to verify the above assumption, first calculating the eigenvalues of all sample data and then arranging and combining all the eigenvalues, the total number of combinations is∑i=110c10i.Then, training each combination with SVM, calculating the k-fold cross-validation, and searching the optimal combination of each eigenvalue through the accuracy of the final 10-fold cross-validation, the final calculation results are obtained, as given in Table 1.Table 1
Combination result of the sample features.
f1f2f3f4f5f6f7f8f9f10CV√√√√0.998√√√√√√√0.998√√√√√√√√0.998√√√√√0.998√√√√√√0.998√√√√√√0.998√√√√0.997√√√√√0.997√√√√√√√√√√0.995√√√√√√0.995√√√√√√√0.995√√√√√0.995√√√0.995√√√√√√√√0.993……………………………The values in bold means the best combination considering the cross validation results and the less features used in the algorithm.It can be seen from the results that the inspection accuracy of six combinations reached 99.8%, meanwhile f5–f8 exist in the six eigenvalue combinations. Considering the complexity of calculation and inspection accuracy, the eigenvalues f5–f8 are selected as the optimal combination, which verify the judgment results of the above eigenvalue selection.


### 3.3. SVM-Based Pushing State Recognition

Through the extraction and selection of the above feature values, finally, all the time series are converted into the training set (f5, f6, f7, f8) and the corresponding target state set (S1, S2, S3, S4) of pushing state pattern recognition; it can be trained and predicated according to the training set and the target state set.SVM is a machine learning method based on statistical theory proposed in the 1990s, which has a good application effect on pattern recognition problems with small samples and high dimensions. It can effectively avoid overfitting and has excellent nonlinear processing ability. By converting it into a convex quadratic programming problem, it can achieve the global optimum. If the given training samples are (x1, y1), (x2, y2), …, (xn, yn), in order to transform the input vector from a low-dimensional space x to a high-dimensional space z, first nonlinearly transform the input vector z = H(x), solving weight vector w and offset B, and satisfy the following equation:(16)yiwT⋅zi+b≥1i=1,2,…,l.The unit vector of the weight vector is the normal direction of the interface. Therefore, the distance between the points close to the interface of the two categories is(17)dw,b=minx|y=1zT⋅ww−maxx|y=−1zT⋅ww.When the optimal boundary is reached, it should have metwoT⋅z+bo=0, and the value of w0 meets the requirements of the following formula:(18)dwo,bo=2wo−2woT⋅wo¯.So far, the problem of solving the optimal interface is transformed into the following optimization problem:(19)minHw=12wT⋅w+V⋅∑i=1lai,s.tyiwT⋅zi+B≥1.Converting the objective function with the Lagrange multiplier algorithm,(20)Lw,b,λ=12wT⋅w+V⋅∑i=1lal−∑i=1lλiyiwTzi+b−1,fz=sgnwT⋅z+b=sgn∑i=1lλi⋅yi⋅zTzi=sgn∑SupportVectorλi⋅yi⋅zTzi+b.In essence, SVM transforms samples into high-dimensional linear separable space through nonlinear transformation functionH and constructs hyperplane to classify and recognize them. This nonlinear transformation function is also called kernel function, which satisfies the Mercer condition, K(xi, yi) = H (xi) H(xj). Different kernel functions have different effects on SVM performance. The selection of kernel functions includes the selection of type and parameters. The commonly used kernel functions are given in Table 2.Table 2
Commonly used kernel functions.
NameExpressionParametersLinear kernelKxi,xj=xiTxjNonePolynomial kernelKxi,xj=xiTxjdd≥1, polynomial degreeGaussian kernelKxi,xj=exp−xi−xj2/2σ2σ>0, bandwidthLaplace kernelKxi,xj=exp−xi−xj/σσ>0Sigmoid kernelKxi,xj=tanhβxiTxj+θβ>0 and θ<0In addition to the above common kernel functions, we can also customize the kernel functions. IfK1x,x′ and K2x,x′ are both kernel functions, we can customize the kernel functions through the following methods:(21)Kx,x′=c⋅K1x,x′Kx,x′=fx⋅K1x,x′⋅fx′Kx,x′=expK1x,x′Kx,x′=K1x,x′+K2x,x′Kx,x′=K1x,x′⋅K2x,x′Kx,x′=K1φx,φx′Kx,x′=xT⋅A⋅x′.In this section, the median frequency f5, standard deviation f6, skewness f7, and kurtosis f8 of the acceleration signal are used as the input vectors of SVM, and the OVR method is used to realize the pushing state pattern recognition of MSR based on SVM. After the normalized processing of the acceleration signal collected on-site, the training sample set data obtained are given in Table3.Table 3
Data samples after normalization.
f5f6f7f8Statef5f6f7f8State0.0250.3210.648−0.214S10.3020.5630.339−0.480S10.2930.4170.121−0.579S10.4990.6940.302−0.511S1−0.969−0.9110.197−1.000S10.1480.4470.422−0.570S10.2480.4980.428−0.626S10.5830.7510.341−0.566S10.3080.5380.358−0.601S10.4110.6630.447−0.348S1…………………………−0.996−0.9920.142−0.885S2−0.944−0.8340.202−0.963S2−0.980−0.9370.175−0.945S2−0.997−0.9920.249−0.815S2−0.953−0.8640.246−0.828S2−0.987−0.9550.095−0.823S2−0.987−0.9600.176−0.928S2−0.937−0.8150.231−0.943S2−0.990−0.9700.335−0.739S2−0.948−0.8400.158−0.924S2…………………………−0.591−0.270−0.4890.446S3−0.627−0.294−0.6870.175S3−0.625−0.301−0.7020.039S3−0.719−0.415−0.5920.163S3−0.475−0.127−0.6090.154S3−0.715−0.409−0.045−0.537S3−0.656−0.347−0.8750.770S3−0.675−0.354−0.272−0.371S3−0.637−0.322−0.7990.763S3−0.765−0.486−0.4590.070S3…………………………−0.469−0.1090.400−0.708S4−0.436−0.0670.178−0.938S4−0.525−0.1730.250−0.867S4−0.519−0.1580.228−0.924S4−0.2050.1550.264−0.804S4−0.464−0.0980.270−0.838S4−0.1240.2360.046−0.841S4−0.1470.2040.386−0.796S4−0.440−0.0690.144−0.809S4−0.0740.2870.092−0.846S4…………………………Taking 60% of the sample data as the training set and the remaining 40% as the test set, the LibSVM library is used to realize the pushing state pattern recognition program in the MATLAB environment and calculating the k-fold cross test accuracy (k = 10) of the training set and the SVM classification results of the test set with different kernel functions. The results are given in Table 4.Table 4
SVM detection result using different kernel functions.
Kernel functionk-foldTest accuracyLinear kernel0.99380.9919Polynomial kernel0.98751.0000RBF kernel0.99391.0000Sigmoid kernel0.22500.2279It can be seen that RBF kernel function has better recognition accuracy when recognizing the pushing state in SVM, and the average recognition accuracy can reach 99.39%. Therefore, using RBF kernel function can achieve a better SVM classification effect and then realize the pushing state pattern recognition with high accuracy.


## 3.1. Methods

This method recognizes the pushing state with the acceleration signal collected; different Kalman filter state space conversion models are applied in different states; meanwhile, the reference point of ZUPT is provided in the ZVS period, which will reduce the measurement error. In essence, the method is called the multiphased Kalman filter (MS-KF) because of subsection handling a group of acceleration time series with the Kalman filter. The method architecture is shown in Figure1, and the key technical process is as follows.Figure 1
Pushing displacement sensing architecture.


### 3.1.1. Estimation of Middle Groove Pose

The acceleration signal collected by IMU is affected by gravity. In order to remove the influence caused by gravity, we need to obtain the direction of gravity component through pose estimation with the help of gyroscope information output by IMU and then remove the acceleration component caused by gravity. The pose of the middle groove can be estimated by the following formula:(1)qw,tGL=12qt−1GL⊗ωtL,qw,tGL=qw,t−1GL+qw,tGLΔt,where ωtL is the angular rate relative to the sensing coordinate system at time t, qt−1GL is the rotation quaternion of the world coordinate system relative to the sensing coordinate system at time t − 1, and qw,tGL is the rotation quaternion of the world coordinate system relative to the sensing coordinate system at t-time.Through the following formula, the acceleration signal in the sensing coordinate system can be converted into the acceleration signal in the world coordinate system.(2)g′G=Rqw,tGLαtL.Among them,R⋅ converts the pose represented by quaternion into matrix form, and the conversion formula is(3)Rq=q02+q12−q22−q322q1q2−q0q32q1q3+q0q22q1q2+q0q3q02−q12+q22−q322q2q3−q0q12q1q3−q0q22q3q2+q0q1q02−q12−q22+q32.Theoretically, the acceleration signal caused by gravity meets the following equation after conversion:(4)RΔqaccgrG=g′G,where grG is the true gravity vector, the theoretical value is grG=0,0,gT. In practice, deviation Δq^acc may exist. The final pose can be obtained by quaternion interpolation through SLERP and other methods:(5)qtGL=qwGL⊗Δq^acc.Through the above steps, it not only can calculate the pose of the middle groove but also can pretreat the acceleration signal, removing the component generated by gravity in the acceleration signal.


### 3.1.2. Displacement Estimation Based on MS-KF

After the pose estimation of the middle groove, the collected acceleration signals are transformed into the acceleration time series without the influence of gravity, the data characteristics of the acceleration signals are analyzed and extracted, and the SVM is used for training. Finally, the displacement state of the acceleration time series can be recognized by using the trained SVM model.For acceleration time series under different transition states, MS-KF will use different state space models to estimate the transition displacement. Delimiting the displacement and velocity variablesxt and vt , respectively, the state space model of VVS section is(6)xe,tve,tae,tL=IΔtIIΔt2/20IRqtGLΔt00Ixe,t−1ve,t−1ae,t−1L+0−gΔt0+υt.Among them,υt refers to the processing noise. For the acceleration in the CVS period, theoretically, the acceleration should be 0, so the state space model adopted by CVS is(7)xi,t+1vi,t+1ai,t+1L=IΔtI1/2IΔt20IRqtGLΔt000xi,tvi,tai,tL+0−gΔt0+υt.Second, different initial state values need to be set for acceleration time series in different phases when Kalman filtering estimation is carried out. The initial value setting is shown in the following formula:(8)Xt=Xe,t|Xe,0=0,P0=0,meanxi>0,xi∈VVS,Xi,t,yi∈CVS,Xe,t|Xe,0=Xi,t,P0=0,meanxi<0,xi∈VVS.Among them,Xt is the state variable, Xt=xi,t,vi,t,ai,tLT, and Xe,0 and P0 are the initial values of state variables and estimation errors in Kalman filter estimation, respectively. MS-KF can be realized with the above steps.


## 3.1.1. Estimation of Middle Groove Pose

The acceleration signal collected by IMU is affected by gravity. In order to remove the influence caused by gravity, we need to obtain the direction of gravity component through pose estimation with the help of gyroscope information output by IMU and then remove the acceleration component caused by gravity. The pose of the middle groove can be estimated by the following formula:(1)qw,tGL=12qt−1GL⊗ωtL,qw,tGL=qw,t−1GL+qw,tGLΔt,where ωtL is the angular rate relative to the sensing coordinate system at time t, qt−1GL is the rotation quaternion of the world coordinate system relative to the sensing coordinate system at time t − 1, and qw,tGL is the rotation quaternion of the world coordinate system relative to the sensing coordinate system at t-time.Through the following formula, the acceleration signal in the sensing coordinate system can be converted into the acceleration signal in the world coordinate system.(2)g′G=Rqw,tGLαtL.Among them,R⋅ converts the pose represented by quaternion into matrix form, and the conversion formula is(3)Rq=q02+q12−q22−q322q1q2−q0q32q1q3+q0q22q1q2+q0q3q02−q12+q22−q322q2q3−q0q12q1q3−q0q22q3q2+q0q1q02−q12−q22+q32.Theoretically, the acceleration signal caused by gravity meets the following equation after conversion:(4)RΔqaccgrG=g′G,where grG is the true gravity vector, the theoretical value is grG=0,0,gT. In practice, deviation Δq^acc may exist. The final pose can be obtained by quaternion interpolation through SLERP and other methods:(5)qtGL=qwGL⊗Δq^acc.Through the above steps, it not only can calculate the pose of the middle groove but also can pretreat the acceleration signal, removing the component generated by gravity in the acceleration signal.


## 3.1.2. Displacement Estimation Based on MS-KF

After the pose estimation of the middle groove, the collected acceleration signals are transformed into the acceleration time series without the influence of gravity, the data characteristics of the acceleration signals are analyzed and extracted, and the SVM is used for training. Finally, the displacement state of the acceleration time series can be recognized by using the trained SVM model.For acceleration time series under different transition states, MS-KF will use different state space models to estimate the transition displacement. Delimiting the displacement and velocity variablesxt and vt , respectively, the state space model of VVS section is(6)xe,tve,tae,tL=IΔtIIΔt2/20IRqtGLΔt00Ixe,t−1ve,t−1ae,t−1L+0−gΔt0+υt.Among them,υt refers to the processing noise. For the acceleration in the CVS period, theoretically, the acceleration should be 0, so the state space model adopted by CVS is(7)xi,t+1vi,t+1ai,t+1L=IΔtI1/2IΔt20IRqtGLΔt000xi,tvi,tai,tL+0−gΔt0+υt.Second, different initial state values need to be set for acceleration time series in different phases when Kalman filtering estimation is carried out. The initial value setting is shown in the following formula:(8)Xt=Xe,t|Xe,0=0,P0=0,meanxi>0,xi∈VVS,Xi,t,yi∈CVS,Xe,t|Xe,0=Xi,t,P0=0,meanxi<0,xi∈VVS.Among them,Xt is the state variable, Xt=xi,t,vi,t,ai,tLT, and Xe,0 and P0 are the initial values of state variables and estimation errors in Kalman filter estimation, respectively. MS-KF can be realized with the above steps.


## 3.2. Feature Extraction and Selection

Before realizing MS-KF, it is necessary to subsection the process of acceleration time series. In order to study the data characteristics of acceleration time series in the process of MSR pushing, the pushing displacement signal and acceleration signal collected in the laboratory environment are collected, as shown in Figures2(a) and 2(b), respectively, finally getting the schematic diagram of their characteristics with denoising and normalizing the signal, as shown in Figure 2(c). At the beginning of sliding, the positive component of acceleration is large and reaches the average speed of moving jack in a very short time. At the end of sliding, there is a small acceleration change. After the above actions, a sliding process is completed. It is the opposite when moving the support; first, at the beginning of support-moving, the negative component of acceleration is large and then moving at a uniform speed after reaching the average speed of support-moving. At the end of the support-moving, there is a small change, and then, it enters the static state.Figure 2
Feature samples of acceleration and displacement.
(a)(b)(c)MS-KF analysis is based on recognizing the acceleration in VVS, ZVS, and CVS periods. However, when jack is working in the VVS area, the time of accelerating and decelerating is very short, the feature discrimination corresponding to each state is low, and the final recognition effect will be affected. Therefore, it cannot improve the recognition rate through recognizing the state of acceleration signal directly. According to the above analysis of the pushing process, MSR corresponds to the four states of sliding start (S1), pushing end (S2), support-moving start (S3), and support-moving end (S4) in a pushing cycle. VVS corresponds to the area that state transition from one to another. CVS corresponds to the area not only between S1 and S2 but also between S3 and S4. ZVS corresponds to other areas. This method uses the prior knowledge of the transition system in state pattern recognition, which is more efficient and reliable, and the accuracy of final recognition will be improved.Extracting and selecting effective data features is the premise of pushing state pattern recognition. For the acceleration signal, the features that can be extracted are as follows:(1)
Average power: describing the vibration intensity of the signal,xn is the collected acceleration time series, where n is the length of the time series, n=1,2,3...N. The characteristic value can be calculated according to the following formula:(9)f1=∑n=1Nxn2.(2)
Sample entropy: measuring the complexity of time series, the specific definition and calculation formula can be carried out according to the method proposed by Richman et al. [24].(3)
Spectral entropy: quantitative processing the smoothness of spectrum, which is positive correlation with feature show, if the relative power spectrum probability ofxn is Pk, the spectral entropy can be calculated as follows:(10)f3=−∑K=0N/2−1PklnPk.(4)
Mean value: describing the average value of amplitude change of acceleration signal in each area, which can be calculated according to the following formula:(11)f4=1N∑n=1Nxn.(5)
Median frequency: a measure used to describe the frequency change. First, calculating the power spectrum corresponding to the acceleration signal and then dividing the power spectrum probability into two parts with equal energy, the detail calculation process as references [25].(6)
Standard deviation: describing the variation amplitude of acceleration signal, solving according to the following formula:(12)f6=1N−1∑n=1Nxn−x¯2.(7)
Skewness: a asymmetry measure of the vertical distribution near the mean, which is used to describe the asymmetry of acceleration signal when it changes and judge its change direction; the calculation is as follows:(13)f7=NN−1N−21/N∑n=1Nxn−x¯31/N∑n=1Nxn−x¯23.(8)
Kurtosis: reflecting the kurtosis of the square distribution, which is used to describe the amplitude of acceleration signal change, the calculation is as follows:(14)f8=N−1N−2N−3N+11/N∑n=1Nxn−x¯41/N∑n=1Nxn−x¯22−3N−1+3.(9)
Lempel-Ziv: a complex quantification method, reflecting the rate at which new patterns emerge in the time series and the detail calculation process as references [16].(10)
Crest factor: describing the peak sharpness of the signal, the calculation is as follows:(15)f10=maxxn1/N∑n=1Nxn2.Acceleration signals in 102 pushing periods are collected in the laboratory environment; each period corresponds to the acceleration time seriesxin of 4 pushing states, i = 1, 2, 3, …, 408; the length of each time series is 2000, and finally, the eigenvalues corresponding to each acceleration time series are shown as f1–f10 in Figure 3. It can be seen from the figure that all the eigenvalues have a good recognition for the pushing states 1 and 2, but f4 is an exception. Between the pushing states 1 and 4, f4 nearly unchanged, and the boundaries are extremely blurred. Compared with f4, f9 has a good recognition for pushing state 4. When the features f1, f2, f3, and f10 are recognized in the pushing states 2–4, the recognition is low.Figure 3
Features of samples.The other four eigenvalues, namely, f5–f8, have obvious boundaries for the four pushing states, especially f7 and f8. The consistency of all sample eigenvalues in the same state is very high, but the boundary of sample eigenvalues between different states is very obvious. Therefore, f5–f8 is the best choice among the above features used for pattern recognition of the pushing state. In order to verify the above assumption, first calculating the eigenvalues of all sample data and then arranging and combining all the eigenvalues, the total number of combinations is∑i=110c10i.Then, training each combination with SVM, calculating the k-fold cross-validation, and searching the optimal combination of each eigenvalue through the accuracy of the final 10-fold cross-validation, the final calculation results are obtained, as given in Table 1.Table 1
Combination result of the sample features.
f1f2f3f4f5f6f7f8f9f10CV√√√√0.998√√√√√√√0.998√√√√√√√√0.998√√√√√0.998√√√√√√0.998√√√√√√0.998√√√√0.997√√√√√0.997√√√√√√√√√√0.995√√√√√√0.995√√√√√√√0.995√√√√√0.995√√√0.995√√√√√√√√0.993……………………………The values in bold means the best combination considering the cross validation results and the less features used in the algorithm.It can be seen from the results that the inspection accuracy of six combinations reached 99.8%, meanwhile f5–f8 exist in the six eigenvalue combinations. Considering the complexity of calculation and inspection accuracy, the eigenvalues f5–f8 are selected as the optimal combination, which verify the judgment results of the above eigenvalue selection.


## 3.3. SVM-Based Pushing State Recognition

Through the extraction and selection of the above feature values, finally, all the time series are converted into the training set (f5, f6, f7, f8) and the corresponding target state set (S1, S2, S3, S4) of pushing state pattern recognition; it can be trained and predicated according to the training set and the target state set.SVM is a machine learning method based on statistical theory proposed in the 1990s, which has a good application effect on pattern recognition problems with small samples and high dimensions. It can effectively avoid overfitting and has excellent nonlinear processing ability. By converting it into a convex quadratic programming problem, it can achieve the global optimum. If the given training samples are (x1, y1), (x2, y2), …, (xn, yn), in order to transform the input vector from a low-dimensional space x to a high-dimensional space z, first nonlinearly transform the input vector z = H(x), solving weight vector w and offset B, and satisfy the following equation:(16)yiwT⋅zi+b≥1i=1,2,…,l.The unit vector of the weight vector is the normal direction of the interface. Therefore, the distance between the points close to the interface of the two categories is(17)dw,b=minx|y=1zT⋅ww−maxx|y=−1zT⋅ww.When the optimal boundary is reached, it should have metwoT⋅z+bo=0, and the value of w0 meets the requirements of the following formula:(18)dwo,bo=2wo−2woT⋅wo¯.So far, the problem of solving the optimal interface is transformed into the following optimization problem:(19)minHw=12wT⋅w+V⋅∑i=1lai,s.tyiwT⋅zi+B≥1.Converting the objective function with the Lagrange multiplier algorithm,(20)Lw,b,λ=12wT⋅w+V⋅∑i=1lal−∑i=1lλiyiwTzi+b−1,fz=sgnwT⋅z+b=sgn∑i=1lλi⋅yi⋅zTzi=sgn∑SupportVectorλi⋅yi⋅zTzi+b.In essence, SVM transforms samples into high-dimensional linear separable space through nonlinear transformation functionH and constructs hyperplane to classify and recognize them. This nonlinear transformation function is also called kernel function, which satisfies the Mercer condition, K(xi, yi) = H (xi) H(xj). Different kernel functions have different effects on SVM performance. The selection of kernel functions includes the selection of type and parameters. The commonly used kernel functions are given in Table 2.Table 2
Commonly used kernel functions.
NameExpressionParametersLinear kernelKxi,xj=xiTxjNonePolynomial kernelKxi,xj=xiTxjdd≥1, polynomial degreeGaussian kernelKxi,xj=exp−xi−xj2/2σ2σ>0, bandwidthLaplace kernelKxi,xj=exp−xi−xj/σσ>0Sigmoid kernelKxi,xj=tanhβxiTxj+θβ>0 and θ<0In addition to the above common kernel functions, we can also customize the kernel functions. IfK1x,x′ and K2x,x′ are both kernel functions, we can customize the kernel functions through the following methods:(21)Kx,x′=c⋅K1x,x′Kx,x′=fx⋅K1x,x′⋅fx′Kx,x′=expK1x,x′Kx,x′=K1x,x′+K2x,x′Kx,x′=K1x,x′⋅K2x,x′Kx,x′=K1φx,φx′Kx,x′=xT⋅A⋅x′.In this section, the median frequency f5, standard deviation f6, skewness f7, and kurtosis f8 of the acceleration signal are used as the input vectors of SVM, and the OVR method is used to realize the pushing state pattern recognition of MSR based on SVM. After the normalized processing of the acceleration signal collected on-site, the training sample set data obtained are given in Table3.Table 3
Data samples after normalization.
f5f6f7f8Statef5f6f7f8State0.0250.3210.648−0.214S10.3020.5630.339−0.480S10.2930.4170.121−0.579S10.4990.6940.302−0.511S1−0.969−0.9110.197−1.000S10.1480.4470.422−0.570S10.2480.4980.428−0.626S10.5830.7510.341−0.566S10.3080.5380.358−0.601S10.4110.6630.447−0.348S1…………………………−0.996−0.9920.142−0.885S2−0.944−0.8340.202−0.963S2−0.980−0.9370.175−0.945S2−0.997−0.9920.249−0.815S2−0.953−0.8640.246−0.828S2−0.987−0.9550.095−0.823S2−0.987−0.9600.176−0.928S2−0.937−0.8150.231−0.943S2−0.990−0.9700.335−0.739S2−0.948−0.8400.158−0.924S2…………………………−0.591−0.270−0.4890.446S3−0.627−0.294−0.6870.175S3−0.625−0.301−0.7020.039S3−0.719−0.415−0.5920.163S3−0.475−0.127−0.6090.154S3−0.715−0.409−0.045−0.537S3−0.656−0.347−0.8750.770S3−0.675−0.354−0.272−0.371S3−0.637−0.322−0.7990.763S3−0.765−0.486−0.4590.070S3…………………………−0.469−0.1090.400−0.708S4−0.436−0.0670.178−0.938S4−0.525−0.1730.250−0.867S4−0.519−0.1580.228−0.924S4−0.2050.1550.264−0.804S4−0.464−0.0980.270−0.838S4−0.1240.2360.046−0.841S4−0.1470.2040.386−0.796S4−0.440−0.0690.144−0.809S4−0.0740.2870.092−0.846S4…………………………Taking 60% of the sample data as the training set and the remaining 40% as the test set, the LibSVM library is used to realize the pushing state pattern recognition program in the MATLAB environment and calculating the k-fold cross test accuracy (k = 10) of the training set and the SVM classification results of the test set with different kernel functions. The results are given in Table 4.Table 4
SVM detection result using different kernel functions.
Kernel functionk-foldTest accuracyLinear kernel0.99380.9919Polynomial kernel0.98751.0000RBF kernel0.99391.0000Sigmoid kernel0.22500.2279It can be seen that RBF kernel function has better recognition accuracy when recognizing the pushing state in SVM, and the average recognition accuracy can reach 99.39%. Therefore, using RBF kernel function can achieve a better SVM classification effect and then realize the pushing state pattern recognition with high accuracy.


## 4. Experimental Research

### 4.1. Experimental Platform

Build the pose sensing experimental system of MSR through adding an IMU sensor to the original MSR sensing system. For the higher acquisition frequency and detection accuracy, the ADIS16448 IMU sensor is used for pushing pose sensing, as shown in Figure4(a). In order to realize the pushing pose sensing, the whole experimental platform includes 4 MSRs, 1 shearer, 1 scraper conveyor, and other equipment. The experimental site is shown in Figure 4(b).Figure 4
IMU sensor installation position and experimental site. (a) IMU sensor installation position. (b) Experimental platform site.
(a)(b)The MSR controller designed in this study is shown in Figure5. The upper computer is installed with the monitoring software based on openPOWERLINK, which is an open-source industrial ethernet stack implementing the POWERLINK protocol for managing node and controlled node, designed to realize the remote operation of the controller, and the following action of MSR is controlled through POWERLINK. At the same time, the virtual monitoring system of MSR based on Unity3D is designed in C#.NET platform, which reproduces the pose of the real MSR in real time through the action of the virtual model of MSR with the pose data uploaded by Ethernet; the user interface is shown in Figure 5.Figure 5
Experimental platform for the AFM control system. (a) Autonomous follow-up controller. (b) Virtual monitoring system.
(a)(b)


### 4.2. Experiment and Analysis

The pushing pose of MSR includes the attitude angle and displacement of the middle groove. The attitude angle of the middle groove can be calculated directly according to IMU, but the displacement needs more in-depth research. In order to verify the effectiveness of the pushing sensing method based on pushing state pattern recognition proposed in this study, the IMU sensor is installed on the middle groove of the scraper conveyor to obtain the inertia information in the moving process.The denoising data samples of acceleration and angular velocity are shown in Figure6. It can be seen from the figure that four state changes will occur in a cycle. When the state changes, the acceleration and angular velocity will change. According to the change characteristics of acceleration data, the pattern recognition of pushing state can be realized, and then, the acceleration data are processed in phases. Through the structural parameters of MSR, the theoretical sliding and support-moving speeds can be calculated. While, according to the measured displacement, the sliding and support-moving speeds can be calculated as 14.53 mm/s and 35.19 mm/s, respectively. Due to the influence of the current experimental environment and sensor noise, there is a certain error between the measured value and the theoretical value, and the error is given in Table 5.Figure 6
Data samples for pushing pose sensing.Table 5
Pushing velocities.
ActionGround truth (mm/s)Measurement (mm/s)Error (%)Sliding15.0014.530.13Support-moving35.0035.190.54Conduct the denoised IMU data with time interception, calculate the eigenvalues f5, f6, f7, and f8 corresponding to the IMU data in each time window, and identify the state in the current time window with the trained SVM model. Each state mode identified in a time window is shown in Figure7 There is high accuracy in identifying the SVM state with eigenvalues f5, f6, f7, and f8, but there are also abnormalities in the case of large vibration. In Figure 7, the recognition rates of the three states of sliding start, support-moving start, and support-moving end are accurate and the corresponding times are (12.53, 13.08), (66.41, 67.24), and (80.27, 81.46), respectively. However, there is a large vibration before the end of sliding, so the recognition rate in this area is low. In order to eliminate the influence of vibration on the pattern recognition of pushing state, it is clustered into the nearest state pattern in the time domain, and the vibration area in the figure is determined as the end of sliding.Figure 7
Recognition result of the pushing state.According to the pattern recognition results of the pushing state, different IMU data phases are obtained, as shown in Figure7; phase (1) is the sliding start phase, the sliding speed increases from 0 to the theoretical speed, corresponding to the first VVS phase (VVS1); phase (3) is the sliding end phase, which is the deceleration phase, corresponding to the second VVS phase (VVS2). Between VVS1 and VVS2 is the uniform speed phase, which is the first CVS phase (CVS). For VVS and CVS phase, Kalman filter estimation is performed according to their corresponding state space models, and the results are shown in Figures 8(a)–8(c).Figure 8
Segmental sensing result. (a) VVS1 segment. (b) CVS1 segment. (c) CVS2 segment.
(a)(b)(c)In the VVS1 phase, if the integral method is directly adopted, a large cumulative error will occur in the acceleration phase of pushing jack. As shown in Figure8(a), the final speed obtained by the integral method is more than 30 mm/s, while the theoretical value is only 15 mm/s. The value estimated by IFOA-KF is more accurate, and the final speed is maintained near the theoretical value. Similarly, for the estimation of displacement, the final result of IFOA-KF is closer to the theoretical value, and its mean square error MSE is 1.4615.In the CVS1 phase, the initial displacement and velocity are determined by VVS1, and its initial condition isy0,v0,a0T=5.69,15.02,0T. Due to the longtime of this period, the possibility of time cumulative error is greater. As shown in Figure 8(b), theoretically, this phase should move at a uniform speed, and the speed should be maintained at about 15 mm/s; however, the direct integration method produces a large error, resulting in a large displacement error in the final integration. In the VVS2 phase, the initial condition is the end condition of the CVS phase, that is, y0,v0,a0T=397.80,18.01,0T. The results of integration and estimation are shown in Figure 8(c). The error of velocity and displacement estimated by IFOA-KF is much smaller than that obtained by the direct integration method, and the error analysis results are given in Table 6.Table 6
Error analysis result.
PhaseMSEIFOA-KF methodIntegration methodVVS10.3490.581CVS5.83012.442VVS228.21831.472


## 4.1. Experimental Platform

Build the pose sensing experimental system of MSR through adding an IMU sensor to the original MSR sensing system. For the higher acquisition frequency and detection accuracy, the ADIS16448 IMU sensor is used for pushing pose sensing, as shown in Figure4(a). In order to realize the pushing pose sensing, the whole experimental platform includes 4 MSRs, 1 shearer, 1 scraper conveyor, and other equipment. The experimental site is shown in Figure 4(b).Figure 4
IMU sensor installation position and experimental site. (a) IMU sensor installation position. (b) Experimental platform site.
(a)(b)The MSR controller designed in this study is shown in Figure5. The upper computer is installed with the monitoring software based on openPOWERLINK, which is an open-source industrial ethernet stack implementing the POWERLINK protocol for managing node and controlled node, designed to realize the remote operation of the controller, and the following action of MSR is controlled through POWERLINK. At the same time, the virtual monitoring system of MSR based on Unity3D is designed in C#.NET platform, which reproduces the pose of the real MSR in real time through the action of the virtual model of MSR with the pose data uploaded by Ethernet; the user interface is shown in Figure 5.Figure 5
Experimental platform for the AFM control system. (a) Autonomous follow-up controller. (b) Virtual monitoring system.
(a)(b)


## 4.2. Experiment and Analysis

The pushing pose of MSR includes the attitude angle and displacement of the middle groove. The attitude angle of the middle groove can be calculated directly according to IMU, but the displacement needs more in-depth research. In order to verify the effectiveness of the pushing sensing method based on pushing state pattern recognition proposed in this study, the IMU sensor is installed on the middle groove of the scraper conveyor to obtain the inertia information in the moving process.The denoising data samples of acceleration and angular velocity are shown in Figure6. It can be seen from the figure that four state changes will occur in a cycle. When the state changes, the acceleration and angular velocity will change. According to the change characteristics of acceleration data, the pattern recognition of pushing state can be realized, and then, the acceleration data are processed in phases. Through the structural parameters of MSR, the theoretical sliding and support-moving speeds can be calculated. While, according to the measured displacement, the sliding and support-moving speeds can be calculated as 14.53 mm/s and 35.19 mm/s, respectively. Due to the influence of the current experimental environment and sensor noise, there is a certain error between the measured value and the theoretical value, and the error is given in Table 5.Figure 6
Data samples for pushing pose sensing.Table 5
Pushing velocities.
ActionGround truth (mm/s)Measurement (mm/s)Error (%)Sliding15.0014.530.13Support-moving35.0035.190.54Conduct the denoised IMU data with time interception, calculate the eigenvalues f5, f6, f7, and f8 corresponding to the IMU data in each time window, and identify the state in the current time window with the trained SVM model. Each state mode identified in a time window is shown in Figure7 There is high accuracy in identifying the SVM state with eigenvalues f5, f6, f7, and f8, but there are also abnormalities in the case of large vibration. In Figure 7, the recognition rates of the three states of sliding start, support-moving start, and support-moving end are accurate and the corresponding times are (12.53, 13.08), (66.41, 67.24), and (80.27, 81.46), respectively. However, there is a large vibration before the end of sliding, so the recognition rate in this area is low. In order to eliminate the influence of vibration on the pattern recognition of pushing state, it is clustered into the nearest state pattern in the time domain, and the vibration area in the figure is determined as the end of sliding.Figure 7
Recognition result of the pushing state.According to the pattern recognition results of the pushing state, different IMU data phases are obtained, as shown in Figure7; phase (1) is the sliding start phase, the sliding speed increases from 0 to the theoretical speed, corresponding to the first VVS phase (VVS1); phase (3) is the sliding end phase, which is the deceleration phase, corresponding to the second VVS phase (VVS2). Between VVS1 and VVS2 is the uniform speed phase, which is the first CVS phase (CVS). For VVS and CVS phase, Kalman filter estimation is performed according to their corresponding state space models, and the results are shown in Figures 8(a)–8(c).Figure 8
Segmental sensing result. (a) VVS1 segment. (b) CVS1 segment. (c) CVS2 segment.
(a)(b)(c)In the VVS1 phase, if the integral method is directly adopted, a large cumulative error will occur in the acceleration phase of pushing jack. As shown in Figure8(a), the final speed obtained by the integral method is more than 30 mm/s, while the theoretical value is only 15 mm/s. The value estimated by IFOA-KF is more accurate, and the final speed is maintained near the theoretical value. Similarly, for the estimation of displacement, the final result of IFOA-KF is closer to the theoretical value, and its mean square error MSE is 1.4615.In the CVS1 phase, the initial displacement and velocity are determined by VVS1, and its initial condition isy0,v0,a0T=5.69,15.02,0T. Due to the longtime of this period, the possibility of time cumulative error is greater. As shown in Figure 8(b), theoretically, this phase should move at a uniform speed, and the speed should be maintained at about 15 mm/s; however, the direct integration method produces a large error, resulting in a large displacement error in the final integration. In the VVS2 phase, the initial condition is the end condition of the CVS phase, that is, y0,v0,a0T=397.80,18.01,0T. The results of integration and estimation are shown in Figure 8(c). The error of velocity and displacement estimated by IFOA-KF is much smaller than that obtained by the direct integration method, and the error analysis results are given in Table 6.Table 6
Error analysis result.
PhaseMSEIFOA-KF methodIntegration methodVVS10.3490.581CVS5.83012.442VVS228.21831.472


## 5. Conclusion

By analyzing the composition and characteristics of pushing pose of MSR and middle groove, a fusion evaluation model, which combines the pushing displacement-based least squares straightness and the pushing pose-based straightness of the middle groove, is established for realizing pushing pose alignment. To improve accuracy and reliability in the straightness evaluation process, a segmented sensing approach based on pushing state pattern recognition is proposed by selecting 4 difference features from typical IMU data features. The selected features are used for SVM training. The trained model can effectively recognize the pushing state pattern of MSR. To test and analyze the feasibility of proposed approach, a pose sensing experiment platform is built, and different motion stages of MSR are verified by experiments. Results show that estimation errors are significantly reduced compared with the traditional algorithm.



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*Source: 6978943-2022-06-08.xml*