CN112033401A - Intelligent tunneling robot positioning and orienting method based on strapdown inertial navigation and oil cylinder - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及煤矿开采技术领域,具体涉及一种基于捷联惯导和油缸的智能掘进机器人定位定向方法。The invention relates to the technical field of coal mining, in particular to a method for positioning and orienting an intelligent excavation robot based on strapdown inertial navigation and an oil cylinder.
背景技术Background technique
煤炭作为我国能源重要的组成部分,在未来相当长的一段时间内仍将保持其主体地位。随着科技创新能力的不断提升,煤矿开采智能化水平大大提高,开采效率和安全性得到了保障。在目前煤矿开采过程中,掘进机的精确定位定向是综掘工作面智能化重要的研究方向。现阶段掘进机的掘进方向大多利用激光进行引导,该方法无法对掘进机的姿态信息进行测量,这就导致不能为掘进机掘进方向的自动纠偏提供姿态信息,在煤矿朝着智能化发展的过程中,该方法已经不能适应现在的需求。As an important part of my country's energy, coal will maintain its dominant position for a long time to come. With the continuous improvement of scientific and technological innovation capabilities, the intelligent level of coal mining has been greatly improved, and the mining efficiency and safety have been guaranteed. In the current coal mining process, the precise positioning and orientation of the roadheader is an important research direction for the intelligentization of the fully mechanized face. At this stage, the driving direction of the roadheader is mostly guided by lasers. This method cannot measure the attitude information of the roadheader, which leads to the inability to provide attitude information for the automatic correction of the roadheader's driving direction. In the process of coal mines developing towards intelligence , this method can no longer meet the current needs.
由于井下环境过于复杂,一些地面上可以使用的位姿测量方法并不适用于井下,而惯导凭借着不依赖外部信息,可全天候工作于地面、地下和空中各种环境的特点,使得其成为煤矿井下设备定位、定向的首选方式。然而纯惯导测量系统会随着时间的增加,其测量误差也会越来越大。Due to the complexity of the underground environment, some pose measurement methods that can be used on the ground are not suitable for the underground. However, inertial navigation can work in various environments on the ground, underground and in the air around the clock without relying on external information. The first choice for positioning and orientation of equipment in coal mines. However, the measurement error of pure inertial navigation measurement system will increase with time.
发明内容SUMMARY OF THE INVENTION
针对上述问题,本发明专利提供了一种基于捷联惯导和油缸的智能掘进机器人定位定向方法,利用油缸数据对捷联惯带数据进行校准,实现智能掘进机器人精准定位定向。In view of the above problems, the patent of the present invention provides a method for positioning and orienting an intelligent excavation robot based on strapdown inertial navigation and an oil cylinder.
为实现上述目的,本发明采取的技术方案为:To achieve the above object, the technical scheme adopted in the present invention is:
一种基于捷联惯导和油缸的智能掘进机器人定位定向方法,基于油缸推移智能掘进机器人前进的位移数据实现捷联惯导解算出的智能掘进机器人的位姿数据的校正,从而实现智能掘进机器人高精度的定位定向,其中,智能掘进机器人由机器人I和机器人II组成,机器人I和机器人II之间通过油缸进行连接,智能掘进机器人前进时,首先通过油缸将机器人I推送的预定位置,然后在通过油缸将机器人II拉到预定位置,具体的,包括以下步骤:A method of positioning and orienting an intelligent excavation robot based on strapdown inertial navigation and an oil cylinder. Based on the displacement data of the intelligent excavation robot moving forward by the oil cylinder, it realizes the correction of the pose data of the intelligent excavation robot calculated by the strapdown inertial navigation, so as to realize the intelligent excavation robot. High-precision positioning and orientation, among which, the intelligent excavation robot is composed of robot I and robot II. The connection between robot I and robot II is through the oil cylinder. When the intelligent excavation robot moves forward, it first pushes robot I to the predetermined position through the oil cylinder, and then in Pull the robot II to the predetermined position through the oil cylinder. Specifically, it includes the following steps:
S1、将捷联惯导安装在机器人I上,并建立载体坐标系和导航坐标系;S1, install the strapdown inertial navigation on the robot I, and establish the carrier coordinate system and the navigation coordinate system;
S101、将捷联惯导安装在机器人I上,以智能掘进机器人的重心作为坐标原点,智能掘进机器人前进方向为Y轴正方向,智能掘进机器人右侧垂直于Y轴方向为X轴正方向,垂直智能掘进机器人向上方向作为Z轴正方向,建立载体坐标系OXYZ;S101, install the strapdown inertial navigation on the robot I, take the center of gravity of the intelligent excavation robot as the coordinate origin, the forward direction of the intelligent excavation robot is the positive direction of the Y axis, and the right side of the intelligent excavation robot perpendicular to the Y axis is the positive direction of the X axis, The upward direction of the vertical intelligent excavation robot is used as the positive direction of the Z axis, and the carrier coordinate system OXYZ is established;
S102、以捷联惯导安装所在位置的“东-北-天”坐标系作为导航坐标系O1X1Y1Z1;S102, using the "east-north-sky" coordinate system at the location where the strapdown inertial navigation is installed as the navigation coordinate system O 1 X 1 Y 1 Z 1 ;
S103、智能掘进机器人在载体坐标系下,绕Z轴旋转的角度称为航向角,记为绕X轴旋转的角度称为俯仰角,记为θ,绕Y轴旋转的角度称为横滚角,记为γ,则智能掘进机器人从导航坐标系到载体坐标系的姿态矩阵如下: S103. In the carrier coordinate system, the rotation angle of the intelligent excavation robot around the Z axis is called the heading angle, and is recorded as The angle rotated around the X axis is called the pitch angle, denoted as θ, and the angle rotated around the Y axis is called the roll angle, denoted as γ, then the attitude matrix of the intelligent excavation robot from the navigation coordinate system to the carrier coordinate system is as follows:
S2、将捷联惯导和油缸构成航位推算系统,并对其中包含的误差进行分析;S2. Form a dead reckoning system with strapdown inertial navigation and oil cylinder, and analyze the errors contained in it;
S201、构建捷联惯导误差模型:S201. Build a strapdown inertial navigation error model:
式中,φE、φN、φU分别为计算导航坐标系与理想导航坐标系之间的失准角误差,ωE、ωN、ωU分别为陀螺仪的测量值,vE、vN、vU分别为智能掘进机器人在导航坐标系中的速度,分别为智能掘进机器人在导航坐标系中的速度误差,RNh、RMh分别为子午圈半径和卯酉圈半径,fE、fN、fU分别为加速度计测量值,L为当地的纬度.δL、δλ、δh分别为纬度、经度和高度误差,εE、εN、εU分别为陀螺仪零偏误差,分别为加速度计零偏误差,ge为赤道重力,β、β1、β2分别为0.005302、3.08×10-6、8.08×10-9;In the formula, φ E , φ N , and φ U are the misalignment angle errors between the calculated navigation coordinate system and the ideal navigation coordinate system, respectively, ω E , ω N , and ω U are the measured values of the gyroscope, respectively, v E , v N and v U are the speeds of the intelligent excavation robot in the navigation coordinate system, respectively, are the speed errors of the intelligent excavation robot in the navigation coordinate system, respectively, R Nh and R Mh are the radius of the meridian circle and the radius of the unitary circle, respectively, f E , f N , and f U are the measured values of the accelerometer, and L is the local latitude .δL, δλ, δh are the latitude, longitude and altitude errors, respectively, ε E , ε N , ε U are the gyroscope bias errors, respectively, are the zero bias error of the accelerometer, g e is the equatorial gravity, and β, β 1 , and β 2 are 0.005302, 3.08×10 -6 , and 8.08×10 -9 respectively;
S202、构建航位推算的位置误差模型:S202. Build a position error model for dead reckoning:
式中,LD、λD、hD分别为航位推算时智能掘进机器人所在位置的纬度、经度和高度,VDE、VDN、VDU分别为航位推算时智能掘进机器人的东向速度、北向速度和天向速度,αθ为捷联惯导和智能掘进机器人之间的安装偏差角,δKD为油缸推移系数误差;In the formula, L D , λ D , and h D are the latitude, longitude and altitude of the location of the intelligent excavation robot during dead reckoning, respectively, and V DE , V DN , and V DU are the eastward speed of the intelligent excavation robot in dead reckoning, respectively. , the north speed and the sky speed, α θ is the installation deviation angle between the strapdown inertial navigation and the intelligent excavation robot, and δK D is the cylinder displacement coefficient error;
S203、构建杆臂误差模型:S203. Build a lever arm error model:
式中,δl为油缸相对于捷联惯导的位置矢量;In the formula, δl is the position vector of the cylinder relative to the strapdown inertial navigation;
S3、通过标准卡尔曼滤波算法,实现捷联惯导和油缸的数据的融合;S3. Through the standard Kalman filtering algorithm, the data fusion of the strapdown inertial navigation and the oil cylinder is realized;
S301、综合考虑捷联惯导误差、航位推算误差和杆臂误差,建立捷联惯导和油缸的系统状态方程;S301, comprehensively consider the strapdown inertial navigation error, dead reckoning error and lever arm error, and establish the system state equation of the strapdown inertial navigation and oil cylinder;
其中,系统的状态变量为:Among them, the state variables of the system are:
式中,φT为计算导航坐标系与理想导航坐标系之间的失准角误差,(δv)T为智能掘进机器人的速度误差,(δp)T为智能掘进机器人的位置误差,(δpD)T为航位推算时的位置误差,(δpGL)T为杆臂误差,(εb)T为陀螺仪零偏误差,为加速度计零偏误差,l为捷联惯导和油缸的位置矢量;In the formula, φ T is the misalignment angle error between the calculated navigation coordinate system and the ideal navigation coordinate system, (δv) T is the speed error of the intelligent excavation robot, (δp) T is the position error of the intelligent excavation robot, (δp D )T is the position error during dead reckoning, (δp GL ) T is the lever arm error, (ε b ) T is the gyroscope bias error, is the zero bias error of the accelerometer, l is the position vector of strapdown inertial navigation and oil cylinder;
组合测量系统的状态方程为:The state equation of the combined measurement system is:
其中,in,
和分别为陀螺角速度测量白噪声和加速度计比力测量白噪声; and are the white noise of gyro angular velocity measurement and the white noise of accelerometer specific force measurement;
根据S201,S202,S203中的误差模型,状态转移矩阵F中的参数如下所示:According to the error model in S201, S202, S203, the parameters in the state transition matrix F are as follows:
S302、建立捷联惯导和油缸的系统量测方程S302. Establish the system measurement equation of strapdown inertial navigation and oil cylinder
以捷联惯导解算的位置与航位推算的位置之差来构建观测向量,即The observation vector is constructed by the difference between the position calculated by the strapdown inertial navigation and the position calculated by the dead reckoning, namely
Z=δp-δpD Z=δp-δp D
则系统的量测方程为Then the measurement equation of the system is
Z=HX+VZ=HX+V
其中,H=[03×6 I3×3 -I3×3 03×15],V为测量噪声;Wherein, H=[0 3×6 I 3×3 -I 3×3 0 3×15 ], V is the measurement noise;
S303、建立捷联惯导和油缸标准卡尔曼滤波方程,得到系统状态的最优估计值,其迭代过程可分为以下5步S303, establish the strapdown inertial navigation and oil cylinder standard Kalman filter equation to obtain the optimal estimated value of the system state, and the iterative process can be divided into the following five steps
1)通过状态方程和系统上一时刻的状态对当前时刻状态进行一步预测1) One-step prediction of the state at the current moment through the state equation and the state of the system at the previous moment
X(k/k-1)=F·X(k-1)X(k/k-1)=F·X(k-1)
其中X(k-1)为k-1时刻系统的状态量;where X(k-1) is the state quantity of the system at time k-1;
2)对当前时刻预测状态的误差的均方差阵进行求解2) Solve the mean square error matrix of the error of the predicted state at the current moment
P(k/k-1)=FP(k-1)FT+QP(k/k-1)=FP(k-1)F T +Q
P(k-1)为k-1时刻系统状态误差的均方差矩阵,Q为系统噪声矩阵;P(k-1) is the mean square error matrix of the system state error at time k-1, and Q is the system noise matrix;
3)求解卡尔曼增益K3) Solve the Kalman gain K
Kk=P(k/k-1)HT(HP(k/k-1)HT+R)-1 K k =P(k/k-1)H T (HP(k/k-1)H T +R) -1
R为量测噪声矩阵R is the measurement noise matrix
4)结合卡尔曼增益K,对当前时刻状态的最优估计值进行更新4) Combine the Kalman gain K to update the optimal estimated value of the state at the current moment
X(k)=X(k/k-1)+Kk(Zk-HX(k/k-1))X(k)=X(k/k-1)+ Kk ( Zk -HX(k/k-1))
5)对当前时刻状态的最优估计值误差的均方差矩阵进行更新5) Update the mean square error matrix of the optimal estimated value error of the state at the current moment
P(k)=(I-KkH)P(k/k-1)P(k)=(IK k H)P(k/k-1)
S4、根据油缸推移智能掘进机器人前进的位移数据和捷联惯导数据的融合结果得出智能掘进机器人的位姿曲线,实现掘进工作面精准定位定向。S4. According to the fusion result of the forward displacement data of the cylinder-moving intelligent excavation robot and the strapdown inertial navigation data, the pose curve of the intelligent excavation robot is obtained, so as to realize the precise positioning and orientation of the excavation face.
进一步地,智能掘进机器人直线前进时,智能掘进机器人左右两侧油缸推移量相等,此时智能掘进机器人位移量与油缸推移量相等;当智能掘进机器人纠偏时,左右两侧油缸推移量不等,由于捷联惯导与机器人I固连,所以机器人I的位移与捷联惯导的位移等效,而捷联惯导的位移可以用其在机器人I盾体后面的投影位移近似等效,此时智能掘进机器人位移的位移数据如下:Further, when the intelligent excavation robot moves straight forward, the displacement of the oil cylinders on the left and right sides of the intelligent excavation robot is equal, and at this time, the displacement of the intelligent excavation robot is equal to the displacement of the oil cylinder; Since the SINS is fixedly connected to the robot I, the displacement of the robot I is equivalent to the displacement of the SINS, and the displacement of the SINS can be approximately equivalent to the projected displacement behind the shield of the robot I. This The displacement data of the intelligent excavation robot displacement is as follows:
式中,a为捷联惯导投影与机器人I盾体左表面的距离,b为捷联惯导投影与机器人I盾体右表面的距离,Ll为智能掘进机器人左侧油缸的推移量,Lr为智能掘进机器人右侧油缸的推移量。In the formula, a is the distance between the SINS projection and the left surface of the robot I shield, b is the distance between the SINS projection and the right surface of the robot I shield, L l is the displacement of the left oil cylinder of the intelligent excavation robot, L r is the displacement of the right oil cylinder of the intelligent excavation robot.
进一步地,将捷联惯导解算得到的智能掘进机器人姿态数据和油缸推移智能掘进机器人前进的位移数据结合,构成航位推算系统,并构建航位推算系统的误差模型。Further, the attitude data of the intelligent excavation robot obtained by the strapdown inertial navigation solution and the forward displacement data of the cylinder-moving intelligent excavation robot are combined to form a dead reckoning system, and an error model of the dead reckoning system is constructed.
进一步地,考虑油缸位置与捷联惯导安装位置不同而产生的杆臂误差,并构建杆臂误差模型。Further, the lever-arm error caused by the difference between the position of the oil cylinder and the installation position of the strapdown inertial navigation system is considered, and the lever-arm error model is constructed.
进一步地,综合考虑捷联惯导系统的误差、航位推算系统的误差和杆臂误差,利用标准卡尔曼滤波实现捷联惯导数据和油缸数据的融合,得到智能掘进机器人高精度的定位定向数据。Further, considering the error of the strapdown inertial navigation system, the error of the dead reckoning system and the lever arm error, the standard Kalman filter is used to realize the fusion of the strapdown inertial navigation data and the oil cylinder data, and the high-precision positioning and orientation of the intelligent roadheading robot is obtained. data.
本发明具有以下有益效果:The present invention has the following beneficial effects:
(1)利用油缸推移智能掘进机器人前进的位移数据来补偿捷联惯导的累计误差,克服了纯惯导解算会导致智能掘进机器人定位定向误差随时间发散的缺点;(1) Compensate the accumulated error of the strapdown inertial navigation by using the displacement data of the intelligent excavation robot moving forward by the cylinder, and overcome the disadvantage that the positioning and orientation error of the intelligent excavation robot will diverge with time due to the pure inertial navigation solution;
(2)能够适应煤矿井下复杂的坏境,实现智能掘进机器人位姿数据的自主测量。(2) It can adapt to the complex underground environment of coal mines and realize the autonomous measurement of the pose data of the intelligent excavation robot.
附图说明Description of drawings
图1是本发明的原理图。FIG. 1 is a schematic diagram of the present invention.
图2是本发明的安装示意图;Fig. 2 is the installation schematic diagram of the present invention;
图中:1-油缸;2-油缸底座;3-捷联惯导;4-机器人I;5-机器人II;6-惯导投影位置。In the figure: 1- oil cylinder; 2- oil cylinder base; 3- strapdown inertial navigation; 4- robot I; 5- robot II; 6- inertial navigation projection position.
图3是本发明的纠偏示意图。FIG. 3 is a schematic diagram of deviation correction of the present invention.
图4是本发明的坐标系图。FIG. 4 is a coordinate system diagram of the present invention.
图5是本发明的流程图。Figure 5 is a flow chart of the present invention.
具体实施方式Detailed ways
下面结合具体实施例对本发明进行详细说明。以下实施例将有助于本领域的技术人员进一步理解本发明,但不以任何形式限制本发明。应当指出的是,对本领域的普通技术人员来说,在不脱离本发明构思的前提下,还可以做出若干变形和改进。这些都属于本发明的保护范围。The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.
本发明实施例提供了一种基于捷联惯导和油缸的智能掘进机器人定位定向方法,所述智能掘进机器人由机器人I和机器人II组成,机器人I和机器人II之间通过油缸进行连接,智能掘进机器人前进时,首先通过油缸将机器人I推送的预定位置,然后在通过油缸将机器人II拉到预定位置,所述定位定向方法包括如下步骤:An embodiment of the present invention provides a method for positioning and orienting an intelligent excavation robot based on strapdown inertial navigation and an oil cylinder. The intelligent excavation robot is composed of a robot I and a robot II. When the robot moves forward, firstly, the robot I is pushed to the predetermined position by the oil cylinder, and then the robot II is pulled to the predetermined position by the oil cylinder. The positioning and orientation method includes the following steps:
S1、将捷联惯导安装在机器人I上,并建立载体坐标系和导航坐标系;S1, install the strapdown inertial navigation on the robot I, and establish the carrier coordinate system and the navigation coordinate system;
S101、以智能掘进机器人的重心作为坐标原点,智能掘进机器人前进方向为Y轴正方向,智能掘进机器人右侧垂直于Y轴方向为X轴正方向,垂直智能掘进机器人向上方向作为Z轴正方向,建立载体坐标系OXYZ;S101. Take the center of gravity of the intelligent excavation robot as the coordinate origin, the forward direction of the intelligent excavation robot is the positive direction of the Y axis, the right side of the intelligent excavation robot perpendicular to the Y axis is the positive direction of the X axis, and the upward direction of the vertical intelligent excavation robot is the positive direction of the Z axis , establish the carrier coordinate system OXYZ;
S102、以捷联惯导安装所在位置的“东-北-天”坐标系作为导航坐标系O1X1Y1Z1;S102, using the "east-north-sky" coordinate system at the location where the strapdown inertial navigation is installed as the navigation coordinate system O 1 X 1 Y 1 Z 1 ;
S103、智能掘进机器人在载体坐标系下,绕Z轴旋转的角度称为航向角,记为绕X轴旋转的角度称为俯仰角,记为θ,绕Y轴旋转的角度称为横滚角,记为γ,则智能掘进机器人从导航坐标系到载体坐标系的姿态矩阵如下: S103. In the carrier coordinate system, the rotation angle of the intelligent excavation robot around the Z axis is called the heading angle, and is recorded as The angle rotated around the X axis is called the pitch angle, denoted as θ, and the angle rotated around the Y axis is called the roll angle, denoted as γ, then the attitude matrix of the intelligent excavation robot from the navigation coordinate system to the carrier coordinate system is as follows:
S2、智能掘进机器人直线前进时,智能掘进机器人左右两侧油缸推移量相等,此时智能掘进机器人位移量与油缸推移量相等;当智能掘进机器人纠偏时,左右两侧油缸推移量不等,由于捷联惯导与机器人I固连,所以机器人I的位移与捷联惯导的位移等效,而捷联惯导的位移可以用其在机器人I盾体后面的投影位移近似等效(见图3),此时智能掘进机器人位移的数学模型如下S2. When the intelligent excavation robot moves in a straight line, the displacement of the left and right cylinders of the intelligent excavation robot is equal. At this time, the displacement of the intelligent excavation robot is equal to the displacement of the oil cylinder; when the intelligent excavation robot corrects the deviation, the displacement of the left and right oil cylinders is not equal. The SINS is fixedly connected to the robot I, so the displacement of the robot I is equivalent to the displacement of the SINS, and the displacement of the SINS can be approximately equivalent to the projected displacement behind the shield of the robot I (see Fig. 3), the mathematical model of the displacement of the intelligent excavation robot is as follows
式中,a为捷联惯导投影与机器人I盾体左表面的距离,b为捷联惯导投影与机器人I盾体右表面的距离,Ll为智能掘进机器人左侧油缸的推移量,Lr为智能掘进机器人右侧油缸的推移量;In the formula, a is the distance between the SINS projection and the left surface of the robot I shield, b is the distance between the SINS projection and the right surface of the robot I shield, L l is the displacement of the left oil cylinder of the intelligent excavation robot, L r is the displacement of the right oil cylinder of the intelligent excavation robot;
S3、将捷联惯导和油缸构成航位推算系统,并对其中包含的误差进行分析,具体结果如下:S3. The dead reckoning system is formed by the strapdown inertial navigation and the oil cylinder, and the errors contained in it are analyzed. The specific results are as follows:
S301、捷联惯导误差模型:S301, strapdown inertial navigation error model:
式中,φE、φN、φU分别为计算导航坐标系与理想导航坐标系之间的失准角误差,ωE、ωN、ωU分别为陀螺仪的测量值,vE、vN、vU分别为智能掘进机器人在导航坐标系中的速度,分别为智能掘进机器人在导航坐标系中的速度误差,RNh、RMh分别为子午圈半径和卯酉圈半径,fE、fN、fU分别为加速度计测量值,L为当地的纬度,δL、δλ、δh分别为纬度、经度和高度误差,εE、εN、εU分别为陀螺仪零偏误差,分别为加速度计零偏误差,ge为赤道重力,β、β1、β2分别为0.005302、3.08×10-6、8.08×10-9;In the formula, φ E , φ N , and φ U are the misalignment angle errors between the calculated navigation coordinate system and the ideal navigation coordinate system, respectively, ω E , ω N , and ω U are the measured values of the gyroscope, respectively, v E , v N and v U are the speeds of the intelligent excavation robot in the navigation coordinate system, respectively, are the speed errors of the intelligent excavation robot in the navigation coordinate system, respectively, R Nh and R Mh are the radius of the meridian circle and the radius of the unitary circle, respectively, f E , f N , and f U are the measured values of the accelerometer, and L is the local latitude , δL, δλ, δh are the latitude, longitude and altitude errors, respectively, ε E , ε N , ε U are the gyroscope bias errors, respectively, are the zero bias error of the accelerometer, g e is the equatorial gravity, and β, β 1 , and β 2 are 0.005302, 3.08×10 -6 , and 8.08×10 -9 respectively;
S302、航位推算的位置误差模型如下:S302. The position error model of dead reckoning is as follows:
式中,LD、λD、hD分别为航位推算时智能掘进机器人所在位置的纬度、经度和高度,VDE、VDN、VDU分别为航位推算时智能掘进机器人的东向速度、北向速度和天向速度,αθ为捷联惯导和智能掘进机器人之间的安装偏差角,δKD为油缸推移系数误差;In the formula, L D , λ D , and h D are the latitude, longitude and altitude of the location of the intelligent excavation robot during dead reckoning, respectively, and V DE , V DN , and V DU are the eastward speed of the intelligent excavation robot in dead reckoning, respectively. , the north speed and the sky speed, α θ is the installation deviation angle between the strapdown inertial navigation and the intelligent excavation robot, and δK D is the cylinder displacement coefficient error;
S303、杆臂误差模型如下:S303, the lever arm error model is as follows:
式中,δl为油缸相对于捷联惯导的位置矢量。In the formula, δl is the position vector of the cylinder relative to the SINS.
S4、通过标准卡尔曼滤波算法,将捷联惯导和油缸的数据进行融合,具体如下:S4. Integrate the data of the strapdown inertial navigation and the oil cylinder through the standard Kalman filtering algorithm, as follows:
S401、综合考虑捷联惯导误差、航位推算误差和杆臂误差,建立捷联惯导和油缸的系统状态方程;S401, comprehensively consider the strapdown inertial navigation error, dead reckoning error and lever arm error, establish the system state equation of the strapdown inertial navigation and the oil cylinder;
其中,系统的状态变量为:Among them, the state variables of the system are:
式中,φT为计算导航坐标系与理想导航坐标系之间的失准角误差,(δv)T为智能掘进机器人的速度误差,(δp)T为智能掘进机器人的位置误差,(δpD)T为航位推算时的位置误差,(δpGL)T为杆臂误差,(εb)T为陀螺仪零偏误差,为加速度计零偏误差,l为捷联惯导和油缸的位置矢量。组合测量系统的状态方程为:In the formula, φ T is the misalignment angle error between the calculated navigation coordinate system and the ideal navigation coordinate system, (δv) T is the speed error of the intelligent excavation robot, (δp) T is the position error of the intelligent excavation robot, (δp D ) T is the position error during dead reckoning, (δp GL ) T is the lever arm error, (ε b ) T is the gyroscope bias error, is the zero bias error of the accelerometer, l is the position vector of strapdown inertial navigation and oil cylinder. The state equation of the combined measurement system is:
其中,in,
和分别为陀螺角速度测量白噪声和加速度计比力测量白噪声; and are the white noise of gyro angular velocity measurement and the white noise of accelerometer specific force measurement;
根据S201,S202,S203中的误差模型,状态转移矩阵F中的参数如下所示:According to the error model in S201, S202, S203, the parameters in the state transition matrix F are as follows:
S402、建立捷联惯导和油缸的系统量测方程S402. Establish the system measurement equation of strapdown inertial navigation and oil cylinder
以捷联惯导解算的位置与航位推算的位置之差来构建观测向量,即The observation vector is constructed by the difference between the position calculated by the strapdown inertial navigation and the position calculated by the dead reckoning, namely
Z=δp-δpD Z=δp-δp D
则系统的量测方程为Then the measurement equation of the system is
Z=HX+VZ=HX+V
其中,H=[O3×6 I3×3 -I3×3 O3×15],V为测量噪声;Wherein, H=[O 3×6 I 3×3 -I 3×3 O 3×15 ], V is the measurement noise;
S403、建立捷联惯导和油缸标准卡尔曼滤波方程,得到系统状态的最优估计值,其迭代过程可分为以下5步S403, establish the strapdown inertial navigation and the standard Kalman filter equation of the oil cylinder, and obtain the optimal estimated value of the system state, and the iterative process can be divided into the following 5 steps
1)通过状态方程和系统上一时刻的状态对当前时刻状态进行一步预测1) One-step prediction of the state at the current moment through the state equation and the state of the system at the previous moment
X(k/k-1)=F·X(k-1)X(k/k-1)=F·X(k-1)
其中X(k-1)为k-1时刻系统的状态量。where X(k-1) is the state quantity of the system at time k-1.
2)对当前时刻预测状态的误差的均方差阵进行求解2) Solve the mean square error matrix of the error of the predicted state at the current moment
P(k/k-1)=FP(k-1)FT+QP(k/k-1)=FP(k-1)F T +Q
P(k-1)为k-1时刻系统状态误差的均方差矩阵,Q为系统噪声矩阵。P(k-1) is the mean square error matrix of the system state error at time k-1, and Q is the system noise matrix.
3)求解卡尔曼增益K3) Solve the Kalman gain K
Kk=P(k/k-1)HT(HP(k/k-1)HT+R)-1 K k =P(k/k-1)H T (HP(k/k-1)H T +R) -1
其中,R为量测噪声矩阵where R is the measurement noise matrix
4)结合卡尔曼增益K,对当前时刻状态的最优估计值进行更新4) Combine the Kalman gain K to update the optimal estimated value of the state at the current moment
X(k)=X(k/k-1)+Kk(Zk-HX(k/k-1))X(k)=X(k/k-1)+ Kk ( Zk -HX(k/k-1))
5)对当前时刻状态的最优估计值误差的均方差矩阵进行更新5) Update the mean square error matrix of the optimal estimated value error of the state at the current moment
P(k)=(I-KkH)P(k/k-1)P(k)=(IK k H)P(k/k-1)
S6、根据油缸推移智能掘进机器人前进的位移数据和捷联惯导数据的融合结果得出智能掘进机器人的位姿曲线,实现掘进工作面精准定位定向。S6. According to the fusion result of the forward displacement data of the cylinder-moving intelligent excavation robot and the strapdown inertial navigation data, the pose curve of the intelligent excavation robot is obtained, so as to realize the precise positioning and orientation of the excavation face.
以上对本发明的具体实施例进行了描述。需要理解的是,本发明并不局限于上述特定实施方式,本领域技术人员可以在权利要求的范围内做出各种变化或修改,这并不影响本发明的实质内容。在不冲突的情况下,本申请的实施例和实施例中的特征可以任意相互组合。Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above-mentioned specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essential content of the present invention. The embodiments of the present application and features in the embodiments may be combined with each other arbitrarily, provided that there is no conflict.
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