CN114397642A - A 3D LiDAR and IMU External Parameters Calibration Method Based on Graph Optimization - Google Patents
A 3D LiDAR and IMU External Parameters Calibration Method Based on Graph Optimization Download PDFInfo
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Abstract
本发明提供一种基于图优化的三维激光雷达与IMU外参标定方法,涉及多传感器标定技术领域,包括:获取设备中激光雷达和IMU的测量数据;对IMU的测量数据进行预积分,计算IMU残差;将激光雷达的测量数据经IMU坐标系投影至世界坐标系,获得点云图,计算激光雷达点与点云图中对应特征线及特征面的距离残差;基于图模型、IMU残差、距离残差获取初始目标函数及初始优化增量方程;设定恒定帧滑动窗口,获取边缘化增量优化方程,计算边缘化残差项;基于图模型、IMU残差、距离残差、边缘化残差项获取目标函数,计算激光雷达与IMU的外参标定。本发明通过恒定帧滑动窗口实时获取传感器设备的最新状态,实现外参实时标定。
The invention provides a three-dimensional laser radar and IMU external parameter calibration method based on graph optimization, which relates to the technical field of multi-sensor calibration, and includes: acquiring the measurement data of the laser radar and the IMU in the device; Residual: Project the measurement data of the lidar to the world coordinate system through the IMU coordinate system, obtain a point cloud image, and calculate the distance residual between the lidar point and the corresponding feature line and feature surface in the point cloud image; based on the graphical model, IMU residual, The distance residual obtains the initial objective function and the initial optimization increment equation; sets a constant frame sliding window, obtains the marginalization incremental optimization equation, and calculates the marginalization residual term; based on the graph model, IMU residual, distance residual, marginalization The residual term obtains the objective function, and calculates the external parameter calibration of the lidar and IMU. The invention obtains the latest state of the sensor device in real time through a constant frame sliding window, and realizes the real-time calibration of external parameters.
Description
技术领域technical field
本发明涉及多传感器标定技术领域,尤其是涉及一种基于图优化的三维激光雷达与IMU外参标定方法。The invention relates to the technical field of multi-sensor calibration, in particular to a method for calibrating external parameters of three-dimensional laser radar and IMU based on graph optimization.
背景技术Background technique
多传感器融合是无人车、移动机器人以及测绘仪器用来精确环境感知的一项重要技术。由于目前对机器人的工作要求越来越高,仅使用单一的传感器无法准确的实现机器人的环境感知工作。因此,多传感器融合技术受到很多国内外研究学者的关注;不同传感器特点不同,例如,惯性测量单元(IMU)具有高更新率,但传感器数据存在噪音和漂移;而激光雷达(LIDAR)具有精确的深度感知能力,但在运动过程中容易出现运动失真的问题;因此,单一传感器自身缺陷使得使用单个传感器进行机器人定位结果不够精确。因此,通过数据融合,可以使多传感器间相互弥补缺点,使载体整体感知能力得到显著的提高。Multi-sensor fusion is an important technology for unmanned vehicles, mobile robots, and surveying and mapping instruments for accurate environmental perception. Due to the increasingly high requirements for the work of robots, only a single sensor cannot accurately realize the robot's environmental perception work. Therefore, multi-sensor fusion technology has attracted the attention of many domestic and foreign researchers; different sensors have different characteristics, for example, inertial measurement unit (IMU) has high update rate, but sensor data has noise and drift; while lidar (LIDAR) has accurate The ability of depth perception, but the problem of motion distortion is prone to occur during the movement; therefore, the defects of a single sensor make the robot positioning results using a single sensor inaccurate. Therefore, through data fusion, the shortcomings of multiple sensors can be compensated for each other, and the overall perception capability of the carrier can be significantly improved.
对于IMU和激光雷达的数据融合,需要先进行激光雷达和IMU的外参标定,即计算两传感器坐标系之间的坐标转换。如图2所示,在不进行传感器间的外部参数标定的条件下,当机器人在位置A时,由雷达观察到的点P由IMU输出将变为P1。机器人在位置B时,由雷达观察到的点P由IMU输出将变为P2。由于坐标系的不一致性,点P产生两个点P1和P2。因此,只有得到两个传感器间精确的坐标变换关系(即计算各传感器坐标系之间的转换),通过数据融合,机器人才能在未知环境中,对环境的精准检测,完成自身的定位及并同时构建周围地图的过程。因此,传感器标定是一个十分具有应用前景的技术,具有很强的研究价值,对激光雷达与IMU传感器的外参标定的研究也非常必要。For the data fusion of the IMU and the lidar, the external parameter calibration of the lidar and the IMU needs to be performed first, that is, the coordinate transformation between the coordinate systems of the two sensors is calculated. As shown in Figure 2, without the external parameter calibration between sensors, when the robot is at position A, the point P observed by the radar will be output by the IMU to P1. When the robot is at position B, the point P observed by the radar will be changed to P2 by the IMU output. Due to the inconsistency of the coordinate system, point P produces two points P1 and P2. Therefore, only by obtaining the precise coordinate transformation relationship between the two sensors (that is, calculating the transformation between the coordinate systems of each sensor), through data fusion, the robot can accurately detect the environment in an unknown environment, complete its own positioning and at the same time. The process of building a surrounding map. Therefore, sensor calibration is a very promising technology with strong research value. It is also necessary to study the external parameter calibration of lidar and IMU sensors.
目前,一些研究人员对LIDAR-IMU外参标定的研究取得了一定成效,现有的方法一种是借助于额外传感器或者人工设置特定目标来实现,费时费力;另一种是无目标的外参标定方法,其存在对实验环境平面特征要求较高和目标函数优化过程中计算强度较大的问题。同时,LIDAR-IMU外参一般为离线标定,需要专业人员将载体移动到固定校准环境中,当载体设备的传感器的机械配置稍有变化,就需要重复该标定工作,既复杂又费力。At present, some researchers have achieved certain results in the research on LIDAR-IMU external parameter calibration. One of the existing methods is to use additional sensors or manually set specific targets to achieve, which is time-consuming and labor-intensive; the other is targetless external parameters. The calibration method has the problems of high requirements on the plane characteristics of the experimental environment and high computational intensity in the optimization process of the objective function. At the same time, the external parameters of LIDAR-IMU are generally calibrated offline, which requires professionals to move the carrier to a fixed calibration environment. When the mechanical configuration of the sensor of the carrier device changes slightly, the calibration work needs to be repeated, which is complicated and laborious.
发明内容SUMMARY OF THE INVENTION
针对上述问题,本发明提供了一种基于图优化的三维激光雷达与IMU外参标定方法,实现快速实时的三维激光雷达与IMU外参标定。In view of the above problems, the present invention provides a method for calibrating external parameters of three-dimensional laser radar and IMU based on graph optimization, so as to realize fast and real-time external parameter calibration of three-dimensional laser radar and IMU.
为实现上述目的,本发明提供了一种基于图优化的三维激光雷达与IMU外参标定方法,包括:In order to achieve the above purpose, the present invention provides a method for calibrating external parameters of three-dimensional laser radar and IMU based on graph optimization, including:
分别获取传感器设备中激光雷达和IMU的测量数据;Obtain the measurement data of the lidar and IMU in the sensor device respectively;
对所述IMU的测量数据进行IMU预积分,根据所述IMU预积分获取IMU下一时刻的位姿变换估算值,计算IMU残差;Perform IMU pre-integration on the measurement data of the IMU, obtain the estimated value of the pose transformation of the IMU at the next moment according to the IMU pre-integration, and calculate the IMU residual error;
将所述激光雷达的测量数据投影至IMU坐标系,再投影至世界坐标系,获得点云图,获取激光雷达点与点云图中对应的特征线及特征面的距离残差;Projecting the measurement data of the laser radar to the IMU coordinate system, and then projecting it to the world coordinate system, obtaining a point cloud image, and obtaining the distance residuals between the laser radar points and the characteristic lines and characteristic surfaces corresponding to the point cloud image;
基于图模型,通过所述IMU残差、距离残差获取初始目标函数及初始优化增量方程;Based on the graphical model, the initial objective function and the initial optimization incremental equation are obtained through the IMU residual and the distance residual;
设定恒定帧滑动窗口,根据初始优化增量方程获取边缘化增量优化方程,并计算边缘化残差项;Set a constant frame sliding window, obtain the marginalization incremental optimization equation according to the initial optimization incremental equation, and calculate the marginalization residual term;
基于图模型,通过所述IMU残差、距离残差、边缘化残差项获取目标函数;Based on the graph model, the objective function is obtained through the IMU residuals, distance residuals, and marginalized residuals;
最小化所述目标函数,获得激光雷达与IMU的外参标定。Minimize the objective function to obtain the external parameter calibration of lidar and IMU.
作为本发明的进一步改进,根据所述IMU预积分获取IMU下一时刻的位姿变换估算值,包括:As a further improvement of the present invention, the estimated value of the pose transformation of the IMU at the next moment is obtained according to the IMU pre-integration, including:
构建IMU运动模型;Build an IMU motion model;
基于所述IMU运动模型,采用四元数的方式获取激光雷达点在相邻两帧之间的IMU位姿状态变换方程;Based on the IMU motion model, a quaternion method is used to obtain the IMU pose and state transformation equation of the lidar point between two adjacent frames;
根据所述IMU位姿状态变换方程计算IMU下一时刻的位姿变换估算值。Calculate the estimated value of the pose transformation of the IMU at the next moment according to the IMU pose state transformation equation.
作为本发明的进一步改进,根据所述IMU下一时刻的位姿变换估算值和所述IMU下一时刻的实际测量值,计算IMU残差。As a further improvement of the present invention, the IMU residual is calculated according to the estimated value of the pose transformation of the IMU at the next moment and the actual measurement value of the IMU at the next moment.
作为本发明的进一步改进,所述获取激光雷达点与点云图中对应的特征线及特征面的距离残差,包括:As a further improvement of the present invention, the acquisition of the distance residuals of the characteristic lines and characteristic surfaces corresponding to the lidar point and the point cloud image includes:
对所述点云图进行特征提取,获得线特征点和面特征点;Perform feature extraction on the point cloud image to obtain line feature points and surface feature points;
分别构建所述激光雷达点到所述点云图中线特征点拟合的线以及到所述点云图中面特征点拟合的面的距离方程;respectively constructing the line fitting from the lidar point to the line feature point in the point cloud image and the distance equation to the surface fitting the surface feature point in the point cloud image;
最小化两所述距离方程,分别获得点到线的距离残差和点到面的距离残差。Minimize the two distance equations to obtain the point-to-line distance residual and the point-to-surface distance residual, respectively.
作为本发明的进一步改进,对所述点云图进行特征提取,获得线特征点和面特征点;包括:As a further improvement of the present invention, feature extraction is performed on the point cloud image to obtain line feature points and surface feature points; including:
将激光雷达坐标系下第k线激光雷达点i的空间坐标记为以i为中心附近邻点的集合记为S,则曲率c的公式为:Mark the spatial coordinates of the k-th line lidar point i in the lidar coordinate system as The set of adjacent points near the center of i is denoted as S, and the formula of the curvature c is:
根据曲率公式计算每个激光雷达点的曲率,将曲率大于0.1点的记作线特征点,曲率小于0.1的点记作面特征点。The curvature of each lidar point is calculated according to the curvature formula, and points with a curvature greater than 0.1 are recorded as line feature points, and points with a curvature less than 0.1 are recorded as surface feature points.
作为本发明的进一步改进,所述基于图模型,通过所述IMU残差、距离残差获取初始目标函数,包括:As a further improvement of the present invention, based on the graph model, the initial objective function is obtained through the IMU residual and distance residual, including:
基于图模型,所述激光雷达与IMU外参可以表示为最大似然估计:Based on the graphical model, the lidar and IMU extrinsic parameters can be expressed as maximum likelihood estimation:
其中,in,
Z表示测量值;Z represents the measured value;
F表示初始化目标函数;F represents the initialization objective function;
根据所述IMU残差、距离残差,初始化目标函数表示为:According to the IMU residual and distance residual, the initialization objective function is expressed as:
其中,in,
de、dp分别表示激光雷达点与点云图中对应的特征线及特征面的距离残差;de and dp represent the distance residuals between the lidar point and the corresponding feature line and feature surface in the point cloud image, respectively;
表示IMU残差。 represents the IMU residual.
作为本发明的进一步改进,所述获取初始优化增量方程包括:As a further improvement of the present invention, the obtaining the initial optimization incremental equation includes:
通过对多数目标函数进行非线性优化,得到增量优化方程:By nonlinear optimization of most objective functions, the incremental optimization equation is obtained:
HδX=bHδX=b
其中:in:
H=ΣJTC-1JH=ΣJ T C -1 J
b=ΣJTC-1rb=Σ J TC -1 r
J表示残差状态量的雅可比方程;J represents the Jacobian equation of the residual state quantity;
C表示状态的协方差矩阵;C represents the covariance matrix of the state;
r表示代价方程的残差;r represents the residual of the cost equation;
δX表示待估计的误差状态;δX represents the error state to be estimated;
通过求解得到的待估计的误差状态δX,更新需要优化的变量Xr,则:By solving the obtained error state δX to be estimated, and updating the variable X r to be optimized, then:
其中,in,
○表示四元数的小角度更新。○ indicates a small angle update of the quaternion.
作为本发明的进一步改进,所述设定恒定帧滑动窗口,根据初始优化增量方程获取边缘化增量优化方程,并计算边缘化残差项;包括:As a further improvement of the present invention, the constant frame sliding window is set, the marginalization incremental optimization equation is obtained according to the initial optimization incremental equation, and the marginalization residual term is calculated; including:
采用边缘化方法,当所述滑动窗口中进入一个关键帧时,同时保留对应要丢弃的关键帧的约束条件,则边缘化增量优化方程表示为:Using the marginalization method, when a key frame is entered in the sliding window, while retaining the constraints corresponding to the key frame to be discarded, the marginalization incremental optimization equation is expressed as:
采用消元法得到边缘化优化方程:The marginalization optimization equation is obtained by the elimination method:
其中,in,
Xm表示需要边缘化的优化量;X m represents the amount of optimization that needs to be marginalized;
Xr表示需要保留优化的变量;X r represents the variable that needs to be preserved for optimization;
根据初始化优化方程和边缘化优化方程,计算边缘化前后需要优化的变量Xr的估计值,获取边缘化误差项。According to the initialization optimization equation and the marginalization optimization equation, the estimated value of the variable X r to be optimized before and after marginalization is calculated, and the marginalization error term is obtained.
作为本发明的进一步改进,所述基于图模型,通过所述IMU残差、距离残差、边缘化残差项获取目标函数;包括:As a further improvement of the present invention, based on the graph model, the objective function is obtained through the IMU residuals, distance residuals, and marginalization residuals; including:
基于图模型,所述激光雷达与IMU外参可以表示为最大似然估计:Based on the graphical model, the lidar and IMU extrinsic parameters can be expressed as maximum likelihood estimation:
其中,in,
Z表示测量值;Z represents the measured value;
F(X)表示目标函数;F(X) represents the objective function;
根据所述IMU残差、距离残差和边缘化残差项,所述目标函数表示为:According to the IMU residual, distance residual and marginalization residual terms, the objective function is expressed as:
其中,in,
de、dp分别表示激光雷达点与点云图中对应的特征线及特征面的距离残差;de and dp represent the distance residuals between the lidar point and the corresponding feature line and feature surface in the point cloud image, respectively;
表示IMU残差; Represents the IMU residual;
rp表示边缘化残差项。r p represents the marginalized residual term.
作为本发明的进一步改进,采用高斯牛顿法最小化所述目标函数中的IMU残差、距离残差和边缘化残差项,得到激光雷达与IMU外参标定。As a further improvement of the present invention, the Gauss-Newton method is used to minimize the IMU residuals, distance residuals and marginalized residuals in the objective function to obtain the external parameter calibration of lidar and IMU.
与现有技术相比,本发明的有益效果为:Compared with the prior art, the beneficial effects of the present invention are:
本发明相较于现有技术通过设置滑动窗口实时获取传感器设备的最新状态实现激光雷达与IMU的外参实时标定,简便快捷;同时,本发明在标定计算中,利用激光雷达坐标系和IMU坐标系之间的关系生成点云图,并对应点云图中的特征线和特正面分别获取激光雷达点对面和激光雷达点对线的距离残差,将距离残差作为外参标定的约束条件,提高了外参标定的精准度。Compared with the prior art, the present invention realizes the real-time calibration of the external parameters of the laser radar and the IMU by setting a sliding window to obtain the latest state of the sensor device in real time, which is simple and fast; at the same time, the present invention uses the laser radar coordinate system and the IMU coordinate in the calibration calculation. The relationship between the systems is used to generate a point cloud map, and the distance residuals of the LiDAR point-to-surface and LiDAR point-to-line are respectively obtained corresponding to the feature lines and special faces in the point cloud map, and the distance residuals are used as constraints for external parameter calibration. The accuracy of external parameter calibration.
本发明为保证优化过程的计算复杂度,设定滑动窗口为固定帧,实现计算效率和精确性的平衡的同时,满足实时标定的要求。In order to ensure the computational complexity of the optimization process, the invention sets the sliding window as a fixed frame, realizes the balance of computational efficiency and accuracy, and meets the requirements of real-time calibration.
本发明采用固定帧滑动窗口时,为避免丢弃状态数据的影响,采用边缘化方法获取边缘化残差项,进而将边缘化残差项作为目标函数的构成项,进一步提高激光雷达与IMU外参优化的精确度。When the invention adopts a fixed frame sliding window, in order to avoid the influence of discarding state data, the marginalization method is used to obtain the marginalized residual item, and then the marginalized residual item is used as the constituent item of the objective function, so as to further improve the external parameters of lidar and IMU. Optimized accuracy.
附图说明Description of drawings
图1为本发明一种实施例公开的基于图优化的三维激光雷达与IMU外参标定方法流程图;FIG. 1 is a flowchart of a method for calibrating external parameters of 3D lidar and IMU based on graph optimization disclosed by an embodiment of the present invention;
图2为本发明背景技术公开的多传感器设备中各传感器坐标系差别展示图;FIG. 2 is a diagram showing the difference between the coordinate systems of each sensor in the multi-sensor device disclosed in the background of the present invention;
图3为本发明一种实施例公开的基于图优化的三维激光雷达与IMU外参标定方法简要示意图;FIG. 3 is a schematic diagram of a method for calibrating external parameters of 3D lidar and IMU based on graph optimization disclosed by an embodiment of the present invention;
图4为本发明一种实施例公开的图模型中激光雷达因子和IMU因子关系示意图;4 is a schematic diagram of the relationship between a lidar factor and an IMU factor in a graph model disclosed by an embodiment of the present invention;
图5为本发明一种实施例公开的点云图展示图;FIG. 5 is a display diagram of a point cloud image disclosed by an embodiment of the present invention;
图6为本发明一种实施例公开的线特征点示意图;6 is a schematic diagram of a line feature point disclosed in an embodiment of the present invention;
图7为本发明一种实施例公开的面特征点示意图;7 is a schematic diagram of a surface feature point disclosed by an embodiment of the present invention;
图8为本发明一种实施例公开的点到线和点到面的几何约束示意图。FIG. 8 is a schematic diagram of geometric constraints of point-to-line and point-to-surface disclosed in an embodiment of the present invention.
具体实施方式Detailed ways
为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明的一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动的前提下所获得的所有其他实施例,都属于本发明保护的范围。In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present invention.
下面结合附图对本发明做进一步的详细描述:Below in conjunction with accompanying drawing, the present invention is described in further detail:
如图1、3所示,本发明提供的一种基于图优化的三维激光雷达与IMU外参标定方法,包括:As shown in Figures 1 and 3, the present invention provides a method for calibrating external parameters of 3D lidar and IMU based on graph optimization, including:
S1、分别获取传感器设备中激光雷达和IMU的测量数据;S1. Obtain the measurement data of the lidar and the IMU in the sensor device respectively;
S2、对IMU的测量数据进行IMU预积分,根据IMU预积分获取IMU下一时刻的位姿变换估算值,计算IMU残差;S2. Perform IMU pre-integration on the measurement data of the IMU, obtain the estimated value of the pose transformation of the IMU at the next moment according to the IMU pre-integration, and calculate the IMU residual error;
其中,包括:Among them, including:
构建IMU运动模型;Build an IMU motion model;
基于IMU运动模型,采用四元数的方式获取激光雷达点在相邻两帧之间的IMU位姿状态变换方程;Based on the IMU motion model, the quaternion method is used to obtain the IMU pose state transformation equation of the lidar point between two adjacent frames;
根据IMU位姿状态变换方程计算IMU下一时刻的位姿变换估算值;Calculate the estimated value of the pose transformation of the IMU at the next moment according to the IMU pose state transformation equation;
根据IMU下一时刻的位姿变换估算值和IMU下一时刻的实际测量值,计算IMU残差。The IMU residual is calculated according to the estimated value of the pose transformation of the IMU at the next moment and the actual measurement value of the IMU at the next moment.
具体的:specific:
由IMU测量的角速度和线速度,构建IMU运动模型;设定字母b表示IMU载体坐标系,字母W表示世界坐标系,用表示世界坐标系到IMU坐标系的旋转变换矩阵,可以得到:The angular velocity and linear velocity measured by the IMU build the IMU motion model; set the letter b to represent the IMU carrier coordinate system, the letter W to represent the world coordinate system, and use Representing the rotation transformation matrix from the world coordinate system to the IMU coordinate system, we can get:
其中,in,
wg表示的是世界坐标系下的重力向量。wg represents the gravity vector in the world coordinate system.
分别表示IMU坐标系下测量的某一时刻的加速度和某一时刻的角速度;ab(t),wb(t)分别表示IMU坐标系下加速度和角速度的真实值,其中含有自身偏差和随机噪声的干扰。respectively represent the acceleration at a certain moment and the angular velocity at a certain moment measured in the IMU coordinate system; a b (t), w b (t) respectively represent the true values of the acceleration and angular velocity in the IMU coordinate system, including their own deviation and random noise interference.
ba(t),bg(t)分别表示加速度计偏差和加速度计的随机噪声;b a (t), b g (t) represent the accelerometer bias and the random noise of the accelerometer, respectively;
na(t),ng(t)分别表示陀螺仪偏差和陀螺仪的随机噪声。n a (t), n g (t) represent the gyro bias and gyro random noise, respectively.
进而得到IMU运动方程:And then get the IMU motion equation:
其中,pW,vW,aW分别代表世界坐标系下的位置,速度以及加速度;Among them, p W , v W , a W represent the position, velocity and acceleration in the world coordinate system respectively;
使用四元数的方式将两个激光雷达关键帧之间的IMU位姿状态表示为:The IMU pose state between two lidar keyframes is expressed as:
其中:in:
IMU预积分可以避免重复积分问题,IMU预积分时需要将参考系从世界坐标系转换为IMU坐标系,即将上式两边同时乘以得到bk+1时刻在IMU坐标系下的IMU位姿状态:IMU pre-integration can avoid the problem of repeated integration. During IMU pre-integration, it is necessary to convert the reference system from the world coordinate system to the IMU coordinate system, that is, multiply both sides of the above equation by Get the IMU pose state in the IMU coordinate system at the time of bk+1:
其中,α,β和γ即为IMU预积分的结果:Among them, α, β and γ are the results of IMU pre-integration:
利用中值法将IMU预积分的结果离散化得到:Using the median method to discretize the result of IMU pre-integration, we get:
其中:in:
根据计算获得的IMU位姿变换估算值以及下一时刻的实际IMU测量值(如:将m+1帧激光雷达数据到来时IMU的位姿数据与m帧激光雷达时IMU的位姿信息预测得到的m+1帧IMU位姿信息相减,得到IMU在m帧激光雷达数据时刻的位姿残差),对两时刻之间的状态进行约束,求得IMU残差:According to the estimated value of IMU pose transformation obtained by calculation and the actual IMU measurement value at the next moment (for example: the pose data of the IMU when m+1 frames of lidar data arrives and the pose information of the IMU when m frames of lidar data are predicted to get The m+1 frames of IMU pose information are subtracted to obtain the pose residual of the IMU at the time of m frames of lidar data), and the state between the two moments is constrained to obtain the IMU residual:
S3、将激光雷达的测量数据投影至IMU坐标系,再投影至世界坐标系,获得点云图(如图5所示),获取激光雷达点与点云图中对应的特征线及特征面的距离残差;S3. Project the measurement data of the lidar to the IMU coordinate system, and then project it to the world coordinate system to obtain a point cloud image (as shown in Figure 5), and obtain the distance residual between the lidar point and the characteristic line and characteristic surface corresponding to the point cloud image. Difference;
其中,包括:Among them, including:
对点云图进行特征提取,获得线特征点和面特征点(如图6、7所示);Perform feature extraction on the point cloud image to obtain line feature points and surface feature points (as shown in Figures 6 and 7);
分别构建激光雷达点到点云图中线特征点拟合的线以及到点云图中面特征点拟合的面的距离方程;Construct the line fitted from the lidar point to the line feature point in the point cloud image and the distance equation to the surface fitted by the feature point in the point cloud image;
最小化两距离方程,分别获得点到线的距离残差和点到面的距离残差。Minimize the two distance equations to obtain the point-to-line distance residual and the point-to-surface distance residual, respectively.
具体的:specific:
S3.1对激光雷达点云进行特征提取,提取特征的具体过程包括如下子步骤:S3.1 extracts features from the lidar point cloud. The specific process of extracting features includes the following sub-steps:
(1)处理激光雷达点云畸变问题。假设机器人等载体在工作过程中做的是匀速运动,即在激光雷达一次扫描过程中激光雷达的线速度和角速度保持恒定不变。假设为激光雷达开始扫描的起始时刻,为激光雷达完成一次扫描的结束时刻,激光雷达在时刻相对于时刻的相对位姿变换记作,然后可以根据下面公式对激光雷达点云i进行补偿:(1) Deal with the point cloud distortion problem of lidar. It is assumed that the carrier such as the robot moves at a uniform speed during the working process, that is, the linear velocity and angular velocity of the lidar remain constant during one scan of the lidar. Assuming that it is the starting moment when the lidar starts scanning, and the end moment when the lidar completes a scan, the relative pose transformation of the lidar relative to the moment is recorded as, and then the lidar point cloud i can be compensated according to the following formula:
(2)将经过激光雷达点云畸变处理后的点云记为T,点云T中的某一点记为i,以i为中心附近邻点的集合记为S,每个点的曲率记为c,将激光雷达坐标系下第k线激光雷达点i的空间坐标记为则曲率的公式为:(2) Denote the point cloud after lidar point cloud distortion processing as T, a certain point in the point cloud T as i, the set of adjacent points around i as the center as S, and the curvature of each point as c, mark the spatial coordinates of the k-th line lidar point i in the lidar coordinate system as Then the formula for curvature is:
(3)将每一帧的激光雷达点云等分为六份,对每份区域中的点进行曲率计算,计算出每个点的曲率后按照曲率的大小依次排序,将曲率大于0.1的记作线特征点,将曲率小于0.1记作面特征点。(3) Divide the lidar point cloud of each frame into six equal parts, and calculate the curvature of the points in each area. After calculating the curvature of each point, sort them according to the size of the curvature. As line feature points, the curvature less than 0.1 is recorded as surface feature points.
S3.2将激光雷达点利用坐标变换投影到IMU,利用IMU预积分投影到世界坐标系下将当前雷达的特征点云与生成的点云图中对应的特征面和特征线进行基于点对面和点对线的雷达特征匹配;利用最近邻查找算法(KDTree搜索方法)找到点i在局部点云图中最近的一点j,并在j周围找到次近点l,于是将(j,l)称为点i在点云拼接成的图中的边对应;关联平面特征方法:同理,先找到i在点云拼接成的图中最近的一点j,在j周围找次近点l和m,将(j,l,m)称为点i为点云图中的面对应。S3.2 Project the lidar point to the IMU using coordinate transformation, and use the IMU pre-integration to project it to the world coordinate system. The feature point cloud of the current radar and the feature surface and feature line corresponding to the generated point cloud image are processed based on point-to-point and point-to-point Match the radar feature of the line; use the nearest neighbor search algorithm (KDTree search method) to find the closest point j of point i in the local point cloud image, and find the next closest point l around j, so (j, l) is called a point i corresponds to the edge in the graph spliced into the point cloud; the associated plane feature method: in the same way, first find the closest point j in the graph spliced by i in the point cloud, find the next closest points l and m around j, and set ( j,l,m) is called point i as the surface corresponding to the point cloud image.
如图8所示,根据点到线和点到面的几何约束图可以构建得到点到线以及点到面的距离方程,将其作为IMU测量数据和激光雷达的测量数据的关联参数。则激光雷达点到线以及点到面的距离残差表示为:As shown in Figure 8, the point-to-line and point-to-surface distance equations can be constructed according to the point-to-line and point-to-surface geometric constraint graphs, which are used as the associated parameters of the IMU measurement data and the lidar measurement data. Then the LiDAR point-to-line and point-to-surface distance residuals are expressed as:
其中,i,j,v,w为对应的特征关联点,为第k+1帧点云的线特征点的坐标,为第k+1帧点云的面特征点的坐标。Among them, i, j, v, w are the corresponding feature association points, is the coordinate of the line feature point of the point cloud of the k+1th frame, is the coordinate of the surface feature point of the point cloud of the k+1th frame.
S4、基于图模型,通过IMU残差、距离残差获取初始目标函数及初始优化增量方程;S4. Based on the graphical model, the initial objective function and the initial optimization incremental equation are obtained through the IMU residual and the distance residual;
其中,in,
基于图模型,激光雷达与IMU外参可以表示为最大似然估计:Based on the graphical model, the external parameters of lidar and IMU can be expressed as maximum likelihood estimation:
其中,in,
Z表示测量值;Z represents the measured value;
F表示初始化目标函数;F represents the initialization objective function;
根据IMU残差、距离残差,初始化目标函数表示为:According to the IMU residual and distance residual, the initialization objective function is expressed as:
其中,in,
de、dp分别表示激光雷达点与点云图中对应的特征线及特征面的距离残差;de and dp represent the distance residuals between the lidar point and the corresponding feature line and feature surface in the point cloud image, respectively;
表示IMU残差; Represents the IMU residual;
然后,通过对多数目标函数进行非线性优化,得到增量优化方程:Then, the incremental optimization equation is obtained by nonlinear optimization of most objective functions:
HδX=bHδX=b
其中:in:
J表示残差状态量的雅可比方程;J represents the Jacobian equation of the residual state quantity;
C表示状态的协方差矩阵;C represents the covariance matrix of the state;
r表示代价方程的残差;r represents the residual of the cost equation;
δX表示待估计的误差状态;δX represents the error state to be estimated;
通过求解得到的待估计的误差状态δX,更新需要优化的变量Xr,则:By solving the obtained error state δX to be estimated, and updating the variable X r to be optimized, then:
其中,in,
○表示四元数的小角度更新。○ indicates a small angle update of the quaternion.
S5、设定恒定帧滑动窗口,根据初始优化增量方程获取边缘化增量优化方程,并计算边缘化残差项;S5. Set a constant frame sliding window, obtain the marginalization incremental optimization equation according to the initial optimization incremental equation, and calculate the marginalization residual term;
其中,包括:Among them, including:
现有技术中,目标函数的优化过程,计算量会随着关键帧数量,待优化状态量的规模增大而增大,为了保证优化过程中的计算复杂度,本申请目标函数的优化在一个滑动窗口中完成,滑动窗口中保持恒定的帧数,如:保持11帧的状态量,通过设定帧数可以实现计算效率和精确性的平衡;在新的关键帧到来后,需要从滑动窗口中移出一个旧的关键帧。而直接丢弃旧帧的状态量,会导致滑动窗口内其他帧与该帧之间的约束信息丢失。采用边缘化,可以保留对应丢弃状态量的约束信息,作为先验残差项(边缘化残差项)。In the prior art, in the optimization process of the objective function, the amount of calculation will increase with the number of key frames and the scale of the state to be optimized. It is completed in the sliding window, and a constant number of frames is maintained in the sliding window, for example, the state quantity of 11 frames is maintained, and the balance between calculation efficiency and accuracy can be achieved by setting the number of frames; Move out an old keyframe. Directly discarding the state quantity of the old frame will result in the loss of constraint information between other frames in the sliding window and this frame. By adopting marginalization, the constraint information corresponding to the discarded state quantity can be retained as a priori residual term (marginalized residual term).
采用边缘化方法,当滑动窗口中进入一个关键帧时,同时保留对应要丢弃的关键帧的约束条件,则边缘化增量优化方程表示为:Using the marginalization method, when a key frame is entered in the sliding window, while retaining the constraints corresponding to the key frame to be discarded, the marginalization incremental optimization equation is expressed as:
采用Schur进行消元:Elimination using Schur:
消元后得到边缘化优化方程:After elimination, the marginalization optimization equation is obtained:
其中,in,
Xm表示需要边缘化的优化量;X m represents the amount of optimization that needs to be marginalized;
Xr表示需要保留优化的变量;X r represents the variable that needs to be preserved for optimization;
由于边缘化优化方程是通过消元得到的,实际上方程中并未丢失任何约束信息,只不过是在保留的优化变量中增加了更多的约束而已,定义HP,bpo为:Since the marginalization optimization equation is obtained by elimination, in fact, no constraint information is lost in the equation, but more constraints are added to the reserved optimization variables. Define HP and b po as:
在边缘化进行时,将表示为后续状态。在下一个优化中,后续状态的新估计将采用的形式,它将返回新的为:During marginalization, the Represented as a follow-up state. In the next optimization, the new estimate of the subsequent state will take form, it will return the new for:
此外,当边缘化发生时,bpo是固定的,通过提供Hp和bp,根据初始化优化方程和边缘化优化方程,计算边缘化前后需要优化的变量Xr的估计值,获取边缘化误差项;边缘化误差项可以写成:In addition, when the marginalization occurs, b po is fixed, by providing H p and b p , according to the initialization optimization equation and the marginalization optimization equation, calculate the estimated value of the variable X r that needs to be optimized before and after marginalization, and obtain the marginalization error term; the marginalization error term can be written as:
S6、基于图模型,通过IMU残差、距离残差、边缘化残差项获取目标函数;S6. Based on the graph model, the objective function is obtained through IMU residual, distance residual, and marginalization residual;
其中,in,
如图4所示,激光雷达与IMU外参求解问题可以使用图模型来表示;图结构主要由两部分组成:节点和边。在图4中节点C表示要求解的激光雷达与IMU的外参,其中表示旋转,表示平移,黑色方块表示的是激光雷达因子,黑色圆圈表示的是IMU因子,节点In表示IMU在时间tn时的姿势和速度。上标n表示来自激光雷达的第n次扫描,下标W表示世界坐标系。该标定方法的目标主要是用来估计激光雷达与IMU的外参C以及每次激光雷达扫描的IMU方向R、位置P和速度V等信息。可以使用X表示主要估计的状态,即:As shown in Figure 4, the problem of solving the external parameters of lidar and IMU can be represented by a graph model; the graph structure mainly consists of two parts: nodes and edges. In Figure 4, node C represents the external parameters of the lidar and IMU to be solved, which represents rotation and translation, the black square represents the lidar factor, the black circle represents the IMU factor, and the node In represents the IMU at time tn. posture and speed. The superscript n denotes the nth scan from the lidar, and the subscript W denotes the world coordinate system. The goal of this calibration method is mainly to estimate the external parameters C of the lidar and the IMU, as well as the information such as the direction R, position P and velocity V of the IMU for each lidar scan. The state of the main estimate can be represented using X, namely:
激光雷达与IMU外参可以表示为最大似然估计,即:The external parameters of lidar and IMU can be expressed as maximum likelihood estimation, namely:
其中,in,
Z表示测量值;Z represents the measured value;
F(X)表示目标函数;F(X) represents the objective function;
本文提出的标定方法中加入了滑动窗口控制优化量的处理机制,会涉及到边缘化处理丢弃帧的先验残差问题,由此可以通过最小化激光雷达残差的点到面距离以及点到线的距离、IMU测量残差以及边缘化先验残差来解决该外参标定问题。即:根据IMU残差、距离残差和边缘化残差项求解外参,因此目标函数可以表示为:The calibration method proposed in this paper adds a sliding window to control the optimization amount, which will involve the problem of marginalizing the prior residual of discarded frames, so that the point-to-surface distance and the point-to-surface distance of the lidar residual can be minimized. The distance of the line, the residual of the IMU measurement, and the residual of the marginalized prior are used to solve the problem of external parameter calibration. That is: solve the external parameters according to the IMU residual, distance residual and marginalized residual terms, so the objective function can be expressed as:
其中,in,
de、dp分别表示激光雷达点与点云图中对应的特征线及特征面的距离残差;de and dp represent the distance residuals between the lidar point and the corresponding feature line and feature surface in the point cloud image, respectively;
表示IMU残差; Represents the IMU residual;
rp表示边缘化残差项。r p represents the marginalized residual term.
S7、最小化目标函数,获得激光雷达与IMU的外参标定。S7. Minimize the objective function to obtain the external parameter calibration of the lidar and IMU.
其中,in,
采用高斯牛顿法最小化目标函数中的IMU残差、距离残差和边缘化残差项,得到激光雷达与IMU外参标定。The Gauss-Newton method is used to minimize the IMU residuals, distance residuals and marginalized residuals in the objective function, and the external parameter calibration of lidar and IMU is obtained.
本发明的优点:Advantages of the present invention:
本发明相较于现有技术通过设置滑动窗口实时获取传感器设备的最新状态实现激光雷达与IMU的外参实时标定,简便快捷;同时,本发明在标定计算中,利用激光雷达坐标系和IMU坐标系之间的关系生成点云图,并对应点云图中的特征线和特正面分别获取激光雷达点对面和激光雷达点对线的距离残差,将距离残差作为外参标定的约束条件,提高了外参标定的精准度。Compared with the prior art, the present invention realizes the real-time calibration of the external parameters of the laser radar and the IMU by setting a sliding window to obtain the latest state of the sensor device in real time, which is simple and fast; at the same time, the present invention uses the laser radar coordinate system and the IMU coordinate in the calibration calculation. The relationship between the systems is used to generate a point cloud map, and the distance residuals of the LiDAR point-to-surface and LiDAR point-to-line are obtained corresponding to the feature lines and special faces in the point cloud map, and the distance residuals are used as constraints for external parameter calibration. The accuracy of external parameter calibration.
本发明为保证优化过程的计算复杂度,设定滑动窗口为固定帧,实现计算效率和精确性的平衡的同时,满足实时标定的要求。In order to ensure the computational complexity of the optimization process, the present invention sets the sliding window as a fixed frame, achieves a balance between computational efficiency and accuracy, and meets the requirements of real-time calibration.
本发明采用固定帧滑动窗口时,为避免丢弃状态数据的影响,采用边缘化方法获取边缘化残差项,进而将边缘化残差项作为目标函数的构成项,进一步提高激光雷达与IMU外参优化的精确度。When the invention adopts a fixed frame sliding window, in order to avoid the influence of discarding state data, the marginalization method is used to obtain the marginalized residual item, and then the marginalized residual item is used as the constituent item of the objective function, so as to further improve the external parameters of lidar and IMU. Optimized accuracy.
以上仅为本发明的优选实施例而已,并不用于限制本发明,对于本领域的技术人员来说,本发明可以有各种更改和变化。凡在本发明的精神和原则之内,所作的任何修改、等同替换、改进等,均应包含在本发明的保护范围之内。The above are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.
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