CN110609556A - A collaborative control method for multiple unmanned boats based on LOS navigation method - Google Patents
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Abstract
一种基于LOS导航法的多无人艇协同控制方法,包括步骤:根据多无人艇的控制任务需要以及控制过程的信息传递过程,建立多无人艇闭环控制的基本框架;将无人艇的期望目标或者期望航线转化为期望航速ud和期望艏向角ψd;通过设计扰动观测器和滑模控制算法,将控制指令转化为实际的控制输入量,使无人艇保持期望的航向;选择其中一艘无人艇作为路径跟踪参考艇对其进行航线路径规划,其他无人艇保持与路径跟踪参考艇一致的航行路径;实时检测各无人艇的位置、艏向角、艇体速度,与期望航速ud和期望艏向ψd比较,从而调整当前的航行速度和航行艏向,形成一个完整的闭环控制。本发明能够让无人艇按照期望航线行驶,并且保持多无人艇的协同一致,具有安全、稳定、可靠的优点。
A method for collaborative control of multiple unmanned boats based on the LOS navigation method, comprising the steps of: establishing a basic framework for closed-loop control of multiple unmanned boats according to the control task requirements of the multi-unmanned boats and the information transfer process of the control process; The desired goal or desired route is transformed into the desired speed u d and desired heading angle ψ d ; by designing the disturbance observer and sliding mode control algorithm, the control command is converted into the actual control input, so that the unmanned vehicle maintains the desired heading ;Select one of the unmanned boats as the path tracking reference boat to plan its route path, and the other unmanned boats maintain the same navigation path as the path tracking reference boat; real-time detection of the position, heading angle, hull The speed is compared with the expected speed u d and the expected heading ψ d , so as to adjust the current sailing speed and sailing heading, forming a complete closed-loop control. The invention can make the unmanned boat travel according to the expected route, and maintain the coordination and consistency of multiple unmanned boats, and has the advantages of safety, stability and reliability.
Description
技术领域technical field
本发明属于无人艇控制技术领域,具体地说是一种基于LOS导航法的多无人艇协同控制方法。The invention belongs to the technical field of unmanned boat control, in particular to a multi-unmanned boat cooperative control method based on the LOS navigation method.
背景技术Background technique
对于一个完整的无人艇系统而言,所需的内核主要包括:雷达、无线通讯、光学感知模块、运动控制系统、以及动力执行机构等独立单元。目前无人艇的发展具有两个趋势,第一个趋势是从人工遥控驾驶过渡到无人自主驾驶,另一个趋势是从单艘无人艇的控制扩展到无人艇编队的控制。在自动驾驶逐渐取代人工遥控驾驶的大趋势下,运动控制在其中作为很重要的一个环节,主要包含以下六个研究方向:For a complete UAV system, the core required mainly includes independent units such as radar, wireless communication, optical perception module, motion control system, and power actuator. At present, there are two trends in the development of unmanned boats. The first trend is the transition from manual remote control to unmanned autonomous driving, and the other trend is to expand from the control of a single unmanned boat to the control of an unmanned boat formation. Under the general trend of automatic driving gradually replacing manual remote control driving, motion control is an important part of it, mainly including the following six research directions:
1)航速与航向控制;2)动力定位控制;3)路径跟踪;4)轨迹跟踪;5)智能规划、避障与导航;6)多智能体协作编队控制等。1) Speed and heading control; 2) Dynamic positioning control; 3) Path tracking; 4) Trajectory tracking; 5) Intelligent planning, obstacle avoidance and navigation; 6) Multi-agent cooperative formation control, etc.
在无人艇的航速与航向控制方面,国内外已经有了大量的研究和文献成果,其中主要的研究方法包括PID控制法、反步法、滑模控制理论、模糊控制法和自适应控制法等。在未来战争中仅靠单艘无人艇自主作战难以适应复杂的战场环境,而具备有效协同策略的无人艇集群编队能更好的完成任务。因为多船协作形成的船舶编队在海事搜救、海洋资源探测和环境监测、舰队协同作战等方面具有容错性强、适应性好及执行效率高等多重优点。因此,通过对船舶编队的控制方法开展必要研究,完成对多船编队的有效控制,在军事国防、生产运输等领域具有宽广的应用范畴与广阔的发展前景。In terms of speed and course control of unmanned boats, there have been a lot of research and literature results at home and abroad, and the main research methods include PID control method, backstepping method, sliding mode control theory, fuzzy control method and adaptive control method. Wait. In future wars, it is difficult to adapt to the complex battlefield environment only by relying on a single unmanned boat to operate autonomously, but a group formation of unmanned boats with effective coordination strategies can better complete the task. Because the ship formation formed by multi-ship cooperation has multiple advantages such as strong fault tolerance, good adaptability and high execution efficiency in maritime search and rescue, marine resource detection and environmental monitoring, and fleet coordinated operations. Therefore, through the necessary research on the control methods of ship formations, the effective control of multi-ship formations has a broad application scope and broad development prospects in the fields of military defense, production and transportation.
Fahimi将领航者-跟随者编队方法与滑模控制理论相结合,提出了l_ψ和l_l两种滑模控制律,用于完成对编队内各船相对位置的控制。在其控制律设计过程中,考虑到了运动模型参数变化和外界环境干扰等不利影响,但其控制器只能保证在光滑曲线下的运动稳定性,跟随船在拐点处容易发生航向振荡的问题,降低了该控制器在实际应用中的可靠性。Combining the leader-follower formation method with the sliding mode control theory, Fahimi proposed two sliding mode control laws, l_ψ and l_l, to control the relative positions of the ships in the formation. In the design process of its control law, the adverse effects such as changes in motion model parameters and external environmental disturbances have been considered, but its controller can only guarantee the stability of motion under smooth curves, and the following ship is prone to course oscillation at the inflection point. This reduces the reliability of the controller in practical applications.
发明内容Contents of the invention
为了解决上述的技术问题,本发明提供了一种基于LOS导航法的多无人艇协同控制方法。In order to solve the above technical problems, the present invention provides a cooperative control method for multiple unmanned boats based on the LOS navigation method.
为了解决上述技术问题,本发明采取以下技术方案:In order to solve the above technical problems, the present invention takes the following technical solutions:
一种基于LOS导航法的多无人艇协同控制方法,包括以下步骤:A method for cooperative control of multiple unmanned boats based on the LOS navigation method, comprising the following steps:
S1,根据无人艇的控制任务需要以及控制过程的信息传递过程,建立无人艇闭环控制的基本框架;S1, according to the control task requirements of the unmanned vessel and the information transmission process of the control process, establish the basic framework of the closed-loop control of the unmanned vessel;
S2,将无人艇的期望目标或者期望航线转化为期望航速ud和期望艏向角ψd;S2, converting the expected target or expected route of the UAV into expected speed u d and expected heading angle ψ d ;
S3,通过设计扰动观测器和滑模控制算法,将控制指令转化为实际的控制输入量,即分别对喷水推力T以及喷口角δ大小进行设计,使无人艇保持期望的航向;S3, by designing the disturbance observer and the sliding mode control algorithm, the control instruction is converted into the actual control input, that is, the thrust T of the water jet and the size of the nozzle angle δ are designed respectively, so that the unmanned vehicle maintains the desired course;
S4,采用协同控制方式,选择其中一艘无人艇作为路径跟踪参考艇对其进行航线路径规划,其他无人艇保持与路径跟踪参考艇一致的航行路径;S4, using the collaborative control method, select one of the unmanned boats as the path tracking reference boat to plan its route path, and the other unmanned boats maintain the same navigation path as the path tracking reference boat;
S5,实时检测各无人艇的位置、艏向角、艇体速度,反馈至步骤S2,与期望航速ud和期望艏向ψd比较,从而调整当前的航行速度和航行艏向,形成一个完整的闭环控制。S5, detect the position, heading angle, and hull speed of each unmanned boat in real time, feed back to step S2, compare with the expected speed u d and the expected heading ψ d , thereby adjusting the current sailing speed and sailing heading, forming a Complete closed loop control.
所述步骤S1具体包括:The step S1 specifically includes:
建立无向图(vp,εp),无向图(vp,εp)来表示无人艇之间的通信网络,其中vp={1,…,p}为有限非空节点集,表示边集,节点i对应无人艇i,节点j对应无人艇j,边(i,j)∈εp表示无人艇i和无人艇j可以互相得到对方的消息,节点的数量等于无人艇的数量,确定其中一个节点为路径跟踪参考节点,其他节点分别与路径跟踪参考节点连通,路径跟踪参考节点对应路径跟踪参考艇,其他节点对应其他无人艇,从而使得其他无人艇均能够与路径跟踪参考艇进行信息连通。Establish an undirected graph (v p ,ε p ), an undirected graph (v p ,ε p ) to represent the communication network between UAVs, where v p ={1,…,p} is a finite non-empty node set , Represents the edge set, node i corresponds to unmanned boat i, node j corresponds to unmanned boat j, edge (i,j)∈ε p means that unmanned boat i and unmanned boat j can get each other’s messages, and the number of nodes is equal to The number of unmanned boats, determine one of the nodes as the path-tracking reference node, and the other nodes are respectively connected with the path-tracking reference node, the path-tracking reference node corresponds to the path-tracking reference boat, and the other nodes correspond to other unmanned boats, so that other unmanned boats Both can communicate with the path tracking reference ship.
所述步骤S2具体包括:Described step S2 specifically comprises:
S201,确定无人艇的航行路径即期望航线,并在二维平面进行标记;S201, determine the navigation path of the unmanned boat, that is, the desired route, and mark it on the two-dimensional plane;
S202,给定期望航速,采用LOS导航法计算当前位置下无人艇的期望艏向角ψd,采用如下函数计算得到:S202, given the expected speed, using the LOS navigation method to calculate the expected heading angle ψ d of the unmanned boat at the current position, using the following function to calculate:
从航行路径中取出两个相邻的路径点,分别为Pk(xk,yk)和Pk+1(xk+1,yk+1),无人艇所在位置的坐标为(x,y),其中ψr为当前航向与期望航向间的相对夹角,e为横向跟踪误差,αk为航行路径方向角,误差e以无人艇在期望路径右侧为正,无人艇在左侧则为负。Take out two adjacent waypoints from the navigation path, which are P k (x k ,y k ) and P k+1 (x k+1 ,y k+1 ), and the coordinates of the unmanned boat are ( x, y), where ψ r is the relative angle between the current heading and the expected heading, e is the lateral tracking error, α k is the direction angle of the navigation path, and the error e is positive when the unmanned boat is on the right side of the expected path. The boat is negative on the left side.
所述步骤S3具体包括:Described step S3 specifically comprises:
S301,选取三自由度无人艇运动模型,各自由度上的扰动函数用w1、w2和w3表示;S301, select a three-degree-of-freedom unmanned vehicle motion model, and the disturbance functions on each degree of freedom are represented by w 1 , w 2 and w 3 ;
S302,设定无人艇的航行速度为恒定速度,相应的对喷水推力T以及喷口角δ大小保持相对恒定;S302, set the sailing speed of the unmanned boat to be a constant speed, and keep relatively constant the corresponding water jet thrust T and nozzle angle δ;
S303,采用滑模控制算法使无人艇的当前艏向角与期望艏向角相同或者误差在设定范围内。S303, using a sliding mode control algorithm to make the current heading angle of the unmanned boat the same as the expected heading angle or the error is within a set range.
所述步骤S303具体为:The step S303 is specifically:
定义无人艇的真实艏向为ψ,期望艏向为ψd,则相应的期望艏向误差为设计如下关于艏向误差的一阶滑模面S1,其中滑模变量用λ示,转艏的角速度用r表示,无人艇的横向航速和纵向航速分别用u、v表示:Define the true heading of the unmanned boat as ψ and the expected heading as ψ d , then the corresponding expected heading error is Design the following first-order sliding mode surface S 1 about the heading error, where the sliding mode variable is denoted by λ, the angular velocity of turning the bow is denoted by r, and the lateral speed and longitudinal speed of the UV are denoted by u and v respectively:
定义Lyapunov函数:Define the Lyapunov function:
对等式两边分别求导:Differentiate both sides of the equation:
其中使用到的质量系数m,阻尼系数d均为已知量,k1为扰动增益。The mass coefficient m and damping coefficient d used in it are all known quantities, and k 1 is the disturbance gain.
定义期望喷口角为δd,且满足如下条件:Define the desired nozzle angle as δ d , and satisfy the following conditions:
δd=δ1+δ2 δ d = δ 1 + δ 2
式中δ1表示期望艏向角下的喷口角,δ2表示经过控制调整的喷口角。In the formula, δ 1 represents the nozzle angle at the desired heading angle, and δ 2 represents the nozzle angle adjusted by control.
式中k2表示控制参数;f(S1)表示控制算法的趋近律函数,本发明中为饱和函数sat(S1),饱和函数的数学格式为:In the formula, k 2 represents the control parameter; f(S 1 ) represents the reaching law function of the control algorithm, which is the saturation function sat(S 1 ) in the present invention, and the mathematical format of the saturation function is:
当S1>κ或S1<-κ时:When S 1 >κ or S 1 <-κ:
令δ=δd,且k2>|S1|/(4k1),则:Let δ=δ d , and k 2 >|S 1 |/(4k 1 ), then:
因此|S1|数值将逐渐收敛小于κ。Therefore the value of |S 1 | will gradually converge to be smaller than κ.
当-κ≤S1≤κ时:When -κ≤S 1 ≤κ:
当艏向角误差收敛于零时,完成对期望航向的控制。When heading angle error When it converges to zero, the control of the desired heading is completed.
所述步骤S4具体包括:Described step S4 specifically comprises:
各艘无人艇之间建立连通拓扑结构,各个无人艇均可以和路径跟踪参考艇进行信息连通,令无人艇之间实时交换目标点的参数xi,根据邻居的目标点的值调整自己的值,给出一致性算法:A connection topology structure is established between each unmanned boat, and each unmanned boat can communicate with the path tracking reference boat, so that the parameter x i of the target point can be exchanged between the unmanned boats in real time, and adjusted according to the value of the neighbor's target point own value, given the consensus algorithm:
其中,aij为无向图的邻接矩阵。Among them, a ij is the adjacency matrix of the undirected graph.
附图说明Description of drawings
附图1为本发明流程示意图;Accompanying drawing 1 is the schematic flow chart of the present invention;
附图2为无人艇行驶路径示意图;Accompanying drawing 2 is a schematic diagram of the driving path of the unmanned boat;
附图3为多无人艇无向图。Accompanying drawing 3 is an undirected graph of many unmanned boats.
具体实施方式Detailed ways
为能进一步了解本发明的特征、技术手段以及所达到的具体目的、功能,下面结合附图与具体实施方式对本发明作进一步详细描述。In order to further understand the features, technical means, and specific objectives and functions achieved by the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.
如附图1-3所示,本发明揭示了一种基于LOS导航法的多无人艇协同控制方法,包括以下步骤:As shown in accompanying drawings 1-3, the present invention discloses a method for cooperative control of multiple unmanned boats based on the LOS navigation method, comprising the following steps:
S1,根据无人艇的控制任务需要以及控制过程的信息传递过程,建立无人艇闭环控制的基本框架;S1, according to the control task requirements of the unmanned vessel and the information transmission process of the control process, establish the basic framework of the closed-loop control of the unmanned vessel;
S2,将无人艇的期望目标或者期望航线转化为期望航速ud和期望艏向角ψd;S2, converting the expected target or expected route of the UAV into expected speed u d and expected heading angle ψ d ;
S3,通过设计扰动观测器和滑模控制算法,将控制指令转化为实际的控制输入量,即分别对喷水推力T以及喷口角δ大小进行设计,使无人艇保持期望的航向;S3, by designing the disturbance observer and the sliding mode control algorithm, the control instruction is converted into the actual control input, that is, the thrust T of the water jet and the size of the nozzle angle δ are designed respectively, so that the unmanned vehicle maintains the desired course;
S4,采用协同控制方式,选择其中一艘无人艇作为路径跟踪参考艇对其进行航线路径规划,其他无人艇保持与路径跟踪参考艇一致的航行路径;S4, using the collaborative control method, select one of the unmanned boats as the path tracking reference boat to plan its route path, and the other unmanned boats maintain the same navigation path as the path tracking reference boat;
S5,实时检测各无人艇的位置、艏向角、艇体速度,反馈至步骤S2,与期望航速ud和期望艏向ψd比较,从而调整当前的航行速度和航行艏向,形成一个完整的闭环控制。S5, detect the position, heading angle, and hull speed of each unmanned boat in real time, feed back to step S2, compare with the expected speed u d and the expected heading ψ d , thereby adjusting the current sailing speed and sailing heading, forming a Complete closed loop control.
所述步骤S1具体包括:The step S1 specifically includes:
建立无向图(vp,εp),无向图(vp,εp)来表示无人艇之间的通信网络,其中vp={1,…,p}为有限非空节点集,表示边集,节点i对应无人艇i,节点j对应无人艇j,边(i,j)∈εp表示无人艇i和无人艇j可以互相得到对方的消息,节点的数量等于无人艇的数量,确定其中一个节点为路径跟踪参考节点,其他节点分别与路径跟踪参考节点连通,路径跟踪参考节点对应路径跟踪参考艇,其他节点对应其他无人艇,从而使得其他无人艇均能够与路径跟踪参考艇进行信息连通。Establish an undirected graph (v p ,ε p ), an undirected graph (v p ,ε p ) to represent the communication network between UAVs, where v p ={1,…,p} is a finite non-empty node set , Represents the edge set, node i corresponds to unmanned boat i, node j corresponds to unmanned boat j, edge (i,j)∈ε p means that unmanned boat i and unmanned boat j can get each other’s messages, and the number of nodes is equal to The number of unmanned boats, determine one of the nodes as the path-tracking reference node, and the other nodes are respectively connected with the path-tracking reference node, the path-tracking reference node corresponds to the path-tracking reference boat, and the other nodes correspond to other unmanned boats, so that other unmanned boats Both can communicate with the path tracking reference ship.
所述步骤S2具体包括:Described step S2 specifically comprises:
S201,确定无人艇的航行路径即期望航线,并在二维平面进行标记;S201, determine the navigation path of the unmanned boat, that is, the desired route, and mark it on the two-dimensional plane;
S202,给定期望航速,采用LOS导航法计算当前位置下无人艇的期望艏向角ψd,采用如下函数计算得到:S202, given the expected speed, using the LOS navigation method to calculate the expected heading angle ψ d of the unmanned boat at the current position, using the following function to calculate:
从航行路径中取出两个相邻的路径点,分别为Pk(xk,yk)和Pk+1(xk+1,yk+1),无人艇所在位置的坐标为(x,y),其中ψr为当前航向与期望航向间的相对夹角,e为横向跟踪误差,αk为航行路径方向角,误差e以无人艇在期望路径右侧为正,无人艇在左侧则为负。Take out two adjacent waypoints from the sailing path, which are P k (x k ,y k ) and P k+1 (x k+1 ,y k+1 ), and the coordinates of the position of the unmanned boat are ( x, y), where ψ r is the relative angle between the current heading and the expected heading, e is the lateral tracking error, α k is the direction angle of the navigation path, and the error e is positive when the unmanned boat is on the right side of the expected path, and the unmanned The boat is negative on the left side.
所述步骤S3具体包括:Described step S3 specifically comprises:
S301,选取三自由度无人艇运动模型,各自由度上的扰动函数用w1、w2和w3表示;S301, select a three-degree-of-freedom unmanned vehicle motion model, and the disturbance functions on each degree of freedom are represented by w 1 , w 2 and w 3 ;
S302,设定无人艇的航行速度为恒定速度,相应的对喷水推力T以及喷口角δ大小保持相对恒定;S302, set the sailing speed of the unmanned boat to be a constant speed, and keep relatively constant the corresponding water jet thrust T and nozzle angle δ;
S303,采用滑模控制算法使无人艇的当前艏向角与期望艏向角相同或者误差在设定范围内。S303, using a sliding mode control algorithm to make the current heading angle of the unmanned boat the same as the expected heading angle or the error is within a set range.
5、根据权利要求4所述的基于LOS导航法的多无人艇协同控制方法,其特征在于,所述步骤S303具体为:5. The multi-unmanned boat cooperative control method based on the LOS navigation method according to claim 4, wherein the step S303 is specifically:
定义无人艇的真实艏向为ψ,期望艏向为ψd,则相应的期望艏向误差为设计如下关于艏向误差的一阶滑模面S1,其中滑模变量用λ示,转艏的角速度用r表示,无人艇的横向航速和纵向航速分别用u、v表示:Define the true heading of the unmanned boat as ψ and the expected heading as ψ d , then the corresponding expected heading error is Design the following first-order sliding mode surface S 1 about the heading error, where the sliding mode variable is denoted by λ, the angular velocity of turning the bow is denoted by r, and the lateral speed and longitudinal speed of the UV are denoted by u and v respectively:
定义Lyapunov函数:Define the Lyapunov function:
对等式两边分别求导:Differentiate both sides of the equation:
其中使用到的质量系数m,阻尼系数d均为已知量,k1为扰动增益。The mass coefficient m and damping coefficient d used in it are all known quantities, and k 1 is the disturbance gain.
定义期望喷口角为δd,且满足如下条件:Define the desired nozzle angle as δ d , and satisfy the following conditions:
δd=δ1+δ2 δ d = δ 1 + δ 2
式中δ1表示期望艏向角下的喷口角,δ2表示经过控制调整的喷口角。In the formula, δ 1 represents the nozzle angle at the desired heading angle, and δ 2 represents the nozzle angle adjusted by control.
式中k2表示控制参数;f(S1)表示控制算法的趋近律函数,本发明中为饱和函数sat(S1),饱和函数的数学格式为:In the formula, k 2 represents the control parameter; f(S 1 ) represents the reaching law function of the control algorithm, which is the saturation function sat(S 1 ) in the present invention, and the mathematical format of the saturation function is:
当S1>κ或S1<-κ时:When S 1 >κ or S 1 <-κ:
令δ=δd,且k2>|S1|/(4k1),则:Let δ=δ d , and k 2 >|S 1 |/(4k 1 ), then:
因此|S1|数值将逐渐收敛小于κ。Therefore the value of |S 1 | will gradually converge to be smaller than κ.
当-κ≤S1≤κ时:When -κ≤S 1 ≤κ:
当艏向角误差收敛于零时,完成对期望航向的控制。When heading angle error When it converges to zero, the control of the desired heading is completed.
所述步骤S4具体包括:Described step S4 specifically comprises:
各艘无人艇之间建立连通拓扑结构,各个无人艇均可以和路径跟踪参考艇进行信息连通,令无人艇之间实时交换目标点的参数xi,根据邻居的目标点的值调整自己的值,给出一致性算法:A connection topology structure is established between each unmanned boat, and each unmanned boat can communicate with the path tracking reference boat, so that the parameter x i of the target point can be exchanged between the unmanned boats in real time, and adjusted according to the value of the neighbor's target point own value, given the consensus algorithm:
其中,aij为无向图的邻接矩阵。Among them, ai j is the adjacency matrix of the undirected graph.
通过船载附属设备如GPS、罗经、速度传感器等采集无人艇的位置、艏向角、艇体速度等信息,并将信息反馈的部分不再赘述。The position, heading angle, hull speed and other information of the unmanned boat are collected through ship-borne auxiliary equipment such as GPS, compass, speed sensor, etc., and the part of information feedback will not be repeated.
通过航行控制仿真,可以得出结论:本文发明的LOS引导算法对曲线路径跟踪具有良好的控制效果。需要重点说明的是,本发明的路径跟踪控制方法,无论是针对直线路径跟踪或者曲线路径跟踪,均是通过将航向引导律与航向控制分离,在两个独立计算单元的联合控制下,无人艇能够顺利完成路径跟踪的任务。该方法的优点在于:Through the navigation control simulation, it can be concluded that the LOS guidance algorithm invented in this paper has a good control effect on the curve path tracking. It should be emphasized that the path tracking control method of the present invention, whether it is for straight line path tracking or curved path tracking, separates the heading guidance law from the heading control, and under the joint control of two independent computing units, no one The boat can successfully complete the task of path tracking. The advantages of this method are:
1.通过对控制任务划分层次,使控制流程直观易理解,且两个控制单元的性能互不影响,在控制器调试时简单易实现;1. By dividing the control tasks into levels, the control process is intuitive and easy to understand, and the performance of the two control units does not affect each other, which is simple and easy to implement during controller debugging;
2.所设计的艏向引导律形式简单、计算量较小,便于转化应用于实船路径跟踪。2. The designed heading guidance law has a simple form and a small amount of calculation, which is easy to transform and apply to real ship path tracking.
需要说明的是,以上仅为本发明的优选实施例而已,并不用于限制本发明,尽管参照实施例对本发明进行了详细的说明,对于本领域的技术人员来说,其依然可以对前述实施例所记载的技术方案进行修改,或者对其中部分技术特征进行等同替换,但是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。It should be noted that the above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art can still implement the foregoing Modifications to the technical solutions described in the examples, or equivalent replacements for some of the technical features, but within the spirit and principles of the present invention, any modifications, equivalent replacements, improvements, etc., shall be included in the protection of the present invention. within range.
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