植保无人机作业效果评价方法Plant protection drone operation effect evaluation method
技术领域Technical field
本发明属于植保无人机技术领域,具体涉及一种植保无人机作业效果评价方法。The invention belongs to the technical field of plant protection drones, and particularly relates to an evaluation method for the operation effect of a planting maintenance drone.
背景技术Background technique
近年来,随着农业无人机(unmanned aerial vehicle,UAV)的出现,航空植保领域的研究与应用越来越广泛。当前,植保无人飞机发展迅速,尤其是在中国、日本、韩国等东亚地区。无人飞机在植保作业时,机具的作业效果和效率关系到生产成本和农田增收,直接影响农民使用无人机的积极性。In recent years, with the emergence of unmanned aerial vehicles (UAVs), research and application in the field of aviation plant protection has become more widespread. At present, plant protection unmanned aircraft is developing rapidly, especially in East Asia such as China, Japan and South Korea. When the unmanned aircraft is in plant protection operation, the operation effect and efficiency of the machine are related to the production cost and the increase of farmland, which directly affects the enthusiasm of farmers to use the drone.
因此急需发明一种植保无人机作业效果评价方法来计算有效喷洒率、漏喷率、重喷率、班次时间小时生产率等喷洒效果参数从而来评价植保无人机的作业效率和效果,从而为植保无人机的后续改进工作的开展奠定基础。Therefore, it is urgent to invent a planting protection drone operation evaluation method to calculate the effective spraying rate, leakage rate, re-spray rate, shift time hourly productivity and other spray effect parameters to evaluate the efficiency and effect of plant protection drones. The foundation for the follow-up improvement work of the plant protection drone.
发明内容Summary of the invention
本发明所要解决的技术问题是针对上述现有技术的不足提供一种植保无人机作业效果评价方法,本植保无人机作业效果评价方法能准确计算出植保无人机的有效喷洒率、漏喷率、重喷率、班次时间小时生产率、纯喷药时间小时生产率、时间利用率、使用可靠性系数和劳动生产率等喷洒效果参数,从而评价植保无人机的作业效率和效果。The technical problem to be solved by the present invention is to provide an evaluation method for the operation effect of the planting protection drone for the above-mentioned deficiencies of the prior art, and the method for evaluating the operation effect of the plant protection drone can accurately calculate the effective spraying rate and leakage of the plant protection drone. The spraying efficiency parameters of the plant protection drone are evaluated by the spraying effect parameters such as the spray rate, the re-spray rate, the hourly productivity of the shift, the hourly productivity of the pure spray, the time utilization rate, the use reliability coefficient, and the labor productivity.
为实现上述技术目的,本发明采取的技术方案为:To achieve the above technical purpose, the technical solution adopted by the present invention is:
一种植保无人机作业效果评价方法,包括作业效果评价系统,所述作业效果评价系统包括机载作业信息采集装置、云服务器和智能终端;所述机载作业信息采集装置安装在植保无人机上并用于测量植保无人机的飞行状态信息并将飞行状态信息通过4G无线网络发送到云服务器,云服务器用于根据飞行状态信息计算喷洒效果参数,智能终端用于登录云服务器从而查看喷洒效果参数;所述飞行状态信息包括植保无人机的飞行轨迹点的坐标信息,所述喷洒效果参数包括有效喷洒率、漏喷率、重喷率、班次时间小时生产率、纯喷药时间小时生产率、时间利用率、使用可靠性系数和劳动生产率;A planting protection drone operation effect evaluation method, comprising an operation effect evaluation system, the work effect evaluation system includes an onboard operation information collection device, a cloud server, and an intelligent terminal; and the onboard operation information collection device is installed in the plant protection On-board and used to measure the flight status information of the plant protection drone and send the flight status information to the cloud server through the 4G wireless network. The cloud server is used to calculate the spray effect parameter according to the flight state information, and the smart terminal is used to log in to the cloud server to view the spray effect. The flight status information includes coordinate information of a flight path point of the plant protection drone, and the spray effect parameter includes an effective spray rate, a leak rate, a re-spray rate, a shift time hourly productivity, a pure spray time hourly productivity, Time utilization, use reliability factor and labor productivity;
具体包括以下步骤:Specifically, the following steps are included:
(1)机载作业信息采集装置记录植保无人机的作业幅宽、采集植保无人机的飞行轨迹点的坐标以及统计植保无人机的作业班次时间,并将植保无人机的作业幅宽、飞行轨迹点的坐标和作业班次时间发送到云服务器;(1) The on-board operation information collection device records the operation width of the plant protection drone, the coordinates of the flight path point of the plant protection drone, and the working shift time of the plant protection drone, and the operation width of the plant protection drone The width, the coordinates of the flight path point, and the job shift time are sent to the cloud server;
(2)云服务器根据植保无人机的作业幅宽、飞行轨迹点的坐标和作业班次时间计算作业班次时间内相邻作业时刻对应的两个轨迹点之间的喷洒面积;(2) The cloud server calculates the spray area between the two track points corresponding to the adjacent work time in the work shift time according to the operation width of the plant protection drone, the coordinates of the flight track point, and the work shift time;
(3)云服务器根据步骤(2)计算的结果统计作业班次时间内的总喷洒面积,并根据植保无人机的总喷洒面积计算植保无人机的有效喷洒率、漏喷率、重喷率、班次时间小时生产率、纯喷药时间小时生产率、时间利用率、使用可靠性系数和劳动生产率。(3) The cloud server counts the total spray area during the shift time according to the result calculated in step (2), and calculates the effective spray rate, leak rate and re-spray rate of the plant protection drone according to the total spray area of the plant protection drone. , shift time hourly productivity, pure spray time hourly productivity, time utilization, use reliability factor and labor productivity.
作为本发明进一步改进的技术方案,所述步骤(3)包括:As a further improved technical solution of the present invention, the step (3) includes:
(a)作业班次时间内相邻作业时刻对应的两个轨迹点之间的喷洒面积依次为S
1,S
2,…,S
N,通过布尔运算,得到喷洒作业班次时间内的总喷洒面积S
A:
(a) The spraying area between the two track points corresponding to the adjacent working time in the working shift time is S 1 , S 2 ,..., S N , and the total spraying area S in the spraying operation time is obtained by Boolean operation. A :
S
A=S
1∪S
2∪S
3∪…∪S
N,
S A =S 1 ∪S 2 ∪S 3 ∪...∪S N ,
(b)顺序连接植保无人机需要喷洒的作业面的每个顶点从而得到需要喷洒的作业面的几何面积S
F,则喷洒作业的有效面积为:
(b) sequentially connecting each vertex of the working surface of the plant protection drone that needs to be sprayed to obtain the geometrical area S F of the working surface to be sprayed, and the effective area of the spraying operation is:
S
v=S
F∩S
A,
S v =S F ∩S A ,
则漏喷面积S
m和重喷面积S
o分别为:
Then, the leakage spray area S m and the heavy spray area S o are respectively:
S
m=S
F-S
V,S
o=(S
1∩S
A)∪(S
2∩S
A)∪…∪(S
N∩S
A),
S m =S F -S V , S o =(S 1 ∩S A )∪(S 2 ∩S A )∪...∪(S N ∩S A ),
则有效喷洒率η
v、漏喷率η
m和重喷率η
o分别为:
The effective spraying rate η v , the leakage rate η m and the re-injection rate η o are respectively:
则班次时间小时生产率为:Then the hourly productivity of the shift is:
其中W
b为班次时间小时生产率,T
b为作业班次时间;
Where W b is the hourly productivity of the shift, and T b is the shift time of the shift;
则纯喷药时间小时生产率为:The pure spray time hourly productivity is:
其中W
s为纯喷药小时生产率,T
s为纯喷药时间;
Where W s is the pure spray hourly productivity and T s is the pure spray time;
则时间利用率为:Then the time utilization is:
其中η
T为时间利用率;
Where η T is time utilization;
则使用可靠性系数为:Then use the reliability factor:
其中τ
k为使用可靠性系数;T
g为故障时间;
Where τ k is the reliability factor used; T g is the fault time;
则劳动生产率为:The labor productivity is:
其中G
j为劳动生产率,A
j为机组作业人数。
Where G j is labor productivity and A j is the number of crew operations.
作为本发明进一步改进的技术方案,所述的步骤(1)包括:As a further improvement of the technical solution of the present invention, the step (1) includes:
(a)所述机载作业信息采集装置包括定位天线、定位模块和主控单元;所述定位模块通过两个定位天线分别采集植保无人机的喷杆的两端的坐标并发送到主控模块,主控单元根据植保无人机的喷杆的两端的坐标计算植保无人机的飞行轨迹点的坐标,所述飞行轨迹点的坐标为两个定位天线检测的两个坐标点连线的中点坐标;(a) The on-board operation information collecting device comprises a positioning antenna, a positioning module and a main control unit; the positioning module separately collects coordinates of two ends of the spray bar of the plant protection drone through two positioning antennas and sends the coordinates to the main control module The main control unit calculates the coordinates of the flight path point of the plant protection drone according to the coordinates of the two ends of the spray bar of the plant protection drone, and the coordinates of the flight path point are the two coordinate points detected by the two positioning antennas. Point coordinates
(b)所述机载作业信息采集装置的主控单元采集植保无人机内部液泵的工作状态从而统计植保无人机的作业班次时间;(b) The main control unit of the onboard operation information collecting device collects the working state of the internal liquid pump of the plant protection drone to calculate the working shift time of the plant protection drone;
(c)所述机载作业信息采集装置记录植保无人机的作业幅宽并将植保无人机的作业幅宽、飞行轨迹点的坐标和作业班次时间发送到云服务器。(c) The onboard operation information collecting device records the working width of the plant protection drone and transmits the working width of the plant protection drone, the coordinates of the flight path point, and the work shift time to the cloud server.
作为本发明进一步改进的技术方案,所述的步骤(2)包括:As a further improvement of the technical solution of the present invention, the step (2) includes:
(a)根据作业班次时间内每一个作业时刻植保无人机的喷杆的延伸方向与飞行轨迹线的夹角、作业幅宽和飞行轨迹点的坐标计算作业班次时间内每一个作业时刻的轨迹点对应的两个喷洒端点的坐标;(a) Calculate the trajectory of each working time in the working shift time according to the angle between the extending direction of the spray bar of the plant protection drone and the flight trajectory, the working width and the coordinates of the flight path at each working time. The coordinates of the two spray endpoints corresponding to the points;
(b)连接作业班次时间内相邻作业时刻对应的两个轨迹点的喷洒端点,得到四边形的喷洒形状,计算四边形的喷洒形状的面积从而得到班次作业时间内相邻作业时刻对应的两个轨迹点之间的喷洒面积。(b) Connect the spray end points of the two track points corresponding to the adjacent work time in the work shift time to obtain the spray shape of the quadrilateral, calculate the area of the spray shape of the quadrilateral to obtain the two tracks corresponding to the adjacent work time in the shift operation time. The area of the spray between the points.
本发明的有益效果为:本发明通过植保无人机作业效果评价方法能有效并准确的计算出植保无人机的有效喷洒率、漏喷率、重喷率、班次时间小时生产率、纯喷药时间小时生产率、时间利用率、使用可靠性系数和劳动生产率等喷洒效果参数,从而实现对植保无人机的作业效率和效果的评价,为植保无人机的后续改进工作的开展奠定基础。The invention has the beneficial effects that the invention can effectively and accurately calculate the effective spraying rate, the leakage rate, the re-spray rate, the shift time, the hourly productivity, and the pure spraying of the plant protection drone by the planting protection drone operation effect evaluation method. Time-hour productivity, time utilization, reliability factor and labor productivity are used to evaluate the efficiency and effectiveness of plant protection drones, laying the foundation for the subsequent improvement of plant protection drones.
附图说明DRAWINGS
图1为本发明的结构示意图。Figure 1 is a schematic view of the structure of the present invention.
图2为本发明的工作流程图。Figure 2 is a flow chart of the operation of the present invention.
具体实施方式Detailed ways
下面根据图1和图2对本发明的具体实施方式作出进一步说明:The specific embodiments of the present invention are further described below with reference to FIGS. 1 and 2.
本实施例提供的一种植保无人机作业效果评价方法,包括作业效果评价系统,参见图1,所述作业效果评价系统包括机载作业信息采集装置、云服务器和智能终端;所述机载作业信息采集装置安装在植保无人机上并用于测量植保无人机的飞行状态信息并将飞行状态信息通过4G无线网络发送到云服务器,云服务器根据飞行状态信息计算喷洒效果参数,智能终端用于登录云服务器从而查看喷洒效果参数;所述飞行状态信息包括植保无人机的飞行轨迹点,所述喷洒效果参数包括有效喷洒率、漏喷率、重喷率、班次时间小时生产率、纯喷药时间小时生产率、时间利用率、使用可靠性系数和劳动生产率。The method for evaluating the operation effect of the planting maintenance drone provided by the embodiment includes the operation effect evaluation system. Referring to FIG. 1, the operation effect evaluation system includes an onboard operation information collection device, a cloud server, and an intelligent terminal; The operation information collecting device is installed on the plant protection drone and is used for measuring the flight state information of the plant protection drone and transmitting the flight state information to the cloud server through the 4G wireless network, and the cloud server calculates the spraying effect parameter according to the flight state information, and the smart terminal is used for Logging in to the cloud server to view the spray effect parameter; the flight state information includes a flight path point of the plant protection drone, and the spray effect parameters include an effective spray rate, a leak rate, a re-spray rate, a shift time hourly productivity, and a pure spray Time-hour productivity, time utilization, use reliability factor, and labor productivity.
机载作业信息采集装置精确记录植保无人机的飞机状态数据,将实时采集到的飞机状态数据,通过4G无线网络发送给云服务器。当一个飞行架次结束后,云服务器将数据汇总,并计算出喷洒效果参数,包括喷洒覆盖率、重喷漏喷率、无人机工作效率、使用可靠性等指标。用户可以通过智能终端,例如电脑或手机来直接查看喷洒情况。The onboard operation information collection device accurately records the aircraft state data of the plant protection drone, and transmits the aircraft state data collected in real time to the cloud server through the 4G wireless network. When a flight is over, the cloud server aggregates the data and calculates the spray effect parameters, including spray coverage, re-spray leakage rate, drone efficiency, and reliability. Users can view the spray directly through a smart terminal such as a computer or mobile phone.
参见图2,植保无人机作业效果评价方法具体包括以下步骤:Referring to FIG. 2, the method for evaluating the effect of the plant protection drone includes the following steps:
(1)注册机载作业信息采集装置,将SIM卡插入机载作业信息采集装置机盖内,机载作业信息采集装置内部设有4G通信模块和4G天线,通过4G通信模块、4G天线和SIM卡与云服务器通信连接;所述机载作业信息采集装置内部还包括两个GPS定位天线、定位模块和主控单元;(1) Registering the on-board operation information collection device, inserting the SIM card into the cover of the on-board operation information collection device, and the on-board operation information collection device is internally provided with a 4G communication module and a 4G antenna, through the 4G communication module, the 4G antenna and the SIM The card is connected to the cloud server; the onboard operation information collection device further includes two GPS positioning antennas, a positioning module and a main control unit;
(2)将机载作业信息采集装置安装在植保无人机上,安装步骤如下:(2) Install the onboard operation information collection device on the plant protection drone. The installation steps are as follows:
a、将两个GPS定位天线固定到植保无人机上,即喷杆的两端且卫星信号不受遮挡的合适位置;a. Fix two GPS positioning antennas to the plant protection drone, that is, the two ends of the boom and the satellite signal is not blocked at a suitable position;
b、将机载作业信息采集装置的壳体固定到植保无人机上。b. Fix the housing of the onboard operation information collection device to the plant protection drone.
c、确保4G天线已旋好连接到机载作业信息采集装置上。c. Ensure that the 4G antenna is screwed up to the onboard operation information collection device.
(3)在机载作业信息采集装置上记录植保无人机的作业幅宽,植保无人机的作业幅宽可以根据植保无人机的使用说明书得到,是已知值,机载作业信息采集装置通过定位天线采集植保无人机的飞行轨迹点的坐标以及通过主控单元统计植保无人机的作业班次 时间,并将植保无人机的作业幅宽、飞行轨迹点的坐标和作业班次时间发送到云服务器;(3) Record the working width of the plant protection drone on the airborne operation information collecting device, and the working width of the plant protection drone can be obtained according to the instruction manual of the plant protection drone, which is a known value, and the onboard operation information is collected. The device collects the coordinates of the flight path point of the plant protection drone through the positioning antenna and counts the operation shift time of the plant protection drone through the main control unit, and the operation width of the plant protection drone, the coordinates of the flight track point and the work shift time. Send to the cloud server;
(4)云服务器根据植保无人机的作业幅宽、飞行轨迹点的坐标和作业班次时间计算作业班次时间内相邻作业时刻对应的两个轨迹点之间的喷洒面积;(4) The cloud server calculates the spray area between the two track points corresponding to the adjacent work time in the work shift time according to the operation width of the plant protection drone, the coordinates of the flight track point and the work shift time;
(5)云服务器根据步骤(4)计算的结果统计作业班次时间内的总喷洒面积,并根据植保无人机的总喷洒面积计算植保无人机的有效喷洒率、漏喷率、重喷率、班次时间小时生产率、纯喷药时间小时生产率、时间利用率、使用可靠性系数和劳动生产率;(5) The cloud server counts the total spray area during the shift time according to the result calculated in step (4), and calculates the effective spray rate, leak rate and re-spray rate of the plant protection drone according to the total spray area of the plant protection drone. Time, hourly productivity, pure spray time, hourly productivity, time utilization, use reliability factor, and labor productivity;
所述步骤(5)包括:The step (5) includes:
(a)作业班次时间内相邻作业时刻对应的两个轨迹点之间的喷洒面积依次为S
1,S
2,…,S
N,通过布尔运算,得到喷洒作业班次时间内的总喷洒面积S
A:
(a) The spraying area between the two track points corresponding to the adjacent working time in the working shift time is S 1 , S 2 ,..., S N , and the total spraying area S in the spraying operation time is obtained by Boolean operation. A :
S
A=S
1∪S
2∪S
3∪…∪S
N,
S A =S 1 ∪S 2 ∪S 3 ∪...∪S N ,
(b)顺序连接植保无人机需要喷洒的作业面的每个顶点从而得到需要喷洒的作业面的几何面积S
F,则喷洒作业的有效面积为:
(b) sequentially connecting each vertex of the working surface of the plant protection drone that needs to be sprayed to obtain the geometrical area S F of the working surface to be sprayed, and the effective area of the spraying operation is:
S
v=S
F∩S
A,
S v =S F ∩S A ,
则漏喷面积S
m和重喷面积S
o分别为:
Then, the leakage spray area S m and the heavy spray area S o are respectively:
S
m=S
F-S
V,S
o=(S
1∩S
A)∪(S
2∩S
A)∪…∪(S
N∩S
A),
S m =S F -S V , S o =(S 1 ∩S A )∪(S 2 ∩S A )∪...∪(S N ∩S A ),
则有效喷洒率η
v、漏喷率η
m和重喷率η
o分别为:
The effective spraying rate η v , the leakage rate η m and the re-injection rate η o are respectively:
则班次时间小时生产率为:Then the hourly productivity of the shift is:
其中W
b为班次时间小时生产率,T
b为作业班次时间;
Where W b is the hourly productivity of the shift, and T b is the shift time of the shift;
则纯喷药时间小时生产率为:The pure spray time hourly productivity is:
其中W
s纯喷药小时生产率,T
s为纯喷药时间;
Where W s pure spray hourly productivity, T s is pure spray time;
则时间利用率为:Then the time utilization is:
其中η
T为时间利用率;
Where η T is time utilization;
则使用可靠性系数为:Then use the reliability factor:
其中τ
k为使用可靠性系数;T
g为故障时间;
Where τ k is the reliability factor used; T g is the fault time;
则劳动生产率为:The labor productivity is:
其中G
j为劳动生产率,A
j为机组作业人数。
Where G j is labor productivity and A j is the number of crew operations.
所述的步骤(3)包括:The step (3) described includes:
(a)所述定位模块通过两个定位天线分别采集作业班次时间内每一个作业时刻对应的植保无人机的喷杆的两端的坐标并发送到主控模块,主控单元根据植保无人机的喷杆的两端的坐标计算植保无人机的飞行轨迹点的坐标,所述飞行轨迹点的坐标为两个定位天线检测的两个坐标点连线的中点坐标;(a) The positioning module separately collects the coordinates of the two ends of the spray bar of the plant protection drone corresponding to each work time in the work shift time through two positioning antennas and sends the coordinates to the main control module according to the plant protection drone The coordinates of the two ends of the spray bar are used to calculate the coordinates of the flight path point of the plant protection drone, and the coordinates of the flight track point are the midpoint coordinates of the two coordinate points detected by the two positioning antennas;
(b)采用基于直流互感原理的非接触式测量方法,检测植保无人飞机内部液泵的当前工作状态。具体为:霍尔元件(磁芯线圈的非接触方法)实时检测液泵的工作电流从而检测液泵是否工作,霍尔元件将检测的信号发送到机载作业信息采集装置的主控单元内,进而实现主控单元对液泵工作状态的实时检测,统计植保无人机的作业班次时间;(b) Using the non-contact measurement method based on the DC mutual inductance principle to detect the current working state of the internal liquid pump of the plant protection unmanned aerial vehicle. Specifically, the Hall element (non-contact method of the magnetic core coil) detects the working current of the liquid pump in real time to detect whether the liquid pump operates, and the Hall element transmits the detected signal to the main control unit of the onboard operation information collecting device. Further realizing the real-time detection of the working state of the liquid pump by the main control unit, and counting the working shift time of the plant protection drone;
(c)所述机载作业信息采集装置记录植保无人机的作业幅宽并将植保无人机的作业幅宽、飞行轨迹点的坐标和作业班次时间发送到云服务器。(c) The onboard operation information collecting device records the working width of the plant protection drone and transmits the working width of the plant protection drone, the coordinates of the flight path point, and the work shift time to the cloud server.
所述的步骤(4)包括:The step (4) described includes:
(a)云服务器通过自适应高斯滤波算法对飞行轨迹点的坐标进行滤波;(a) The cloud server filters the coordinates of the flight path point by an adaptive Gaussian filtering algorithm;
t
i时刻对应的轨迹点P
i的坐标x,y滤波后的值为:
The coordinates x, y of the track point P i corresponding to the time t i are filtered:
其中x(t
i),y(t
i)分别为t
i时刻的轨迹点P
i滤波前的x,y坐标,i=0,1,2,…;σ为滤波核函数的宽带参数,根据采样频率确定;
Where x (t i), y ( t i) are x front track point in time t i P i of the filter, y coordinates, i = 0,1,2, ...; σ is the broadband filter kernel function parameters, in accordance with The sampling frequency is determined;
(b)根据每一个作业时刻植保无人机的喷杆的延伸方向与飞行轨迹线的夹角、作业幅宽和飞行轨迹点的坐标计算作业班次时间内每一个作业时刻的轨迹点对应的两个喷洒端点的坐标;(b) Calculate the two points corresponding to the trajectory points of each working time in the working shift time according to the angle between the extending direction of the spray bar of the plant protection drone and the flight trajectory, the working width and the coordinates of the flight path point. The coordinates of the spray endpoints;
定义轨迹点P
i对应的两个喷洒端点的坐标分别为
其中:
The coordinates of the two spray end points corresponding to the defined track point P i are respectively among them:
其中
w
i为植保无人机的作业幅宽,θ
i为t
i时刻喷杆的延伸方向与飞行轨迹线的夹角;飞行轨迹线为每一个轨迹点的连线;
among them w i is the working width of the plant protection drone, θ i is the angle between the extending direction of the spray bar and the flight trajectory at time t i ; the flight trajectory is the line connecting each track point;
(c)连接作业班次时间内相邻作业时刻对应的两个轨迹点P
i,P
i+1的喷洒端点,得到四边形的喷洒形状P
i1P
i2P
i+11P
i+12,计算四边形的喷洒形状的面积从而得到班次作业时间内相邻作业时刻对应的两个轨迹点之间的喷洒面积;其中
为轨迹点P
i的坐标滤波后的值,
为轨迹点P
i+1的坐标滤波后的值,
为轨迹点P
i对应的两个喷洒端点的坐标值,
为轨迹点P
i+1对应的两个喷洒端点的坐标值;轨迹点P
i+1对应的两个喷洒端点的坐标值可用步骤(b)的公式得到;
(c) connecting the spray end points of the two track points P i , P i+1 corresponding to the adjacent work time in the work shift time to obtain the quadrilateral spray shape P i1 P i2 P i+11 P i+12 , calculating the quadrilateral shape Spraying the area of the shape to obtain the spray area between the two track points corresponding to the adjacent work time during the shift operation time; The value filtered for the coordinates of the track point P i , The filtered value of the coordinates of the track point P i+1 , The coordinate values of the two spray end points corresponding to the track point P i , The coordinate values of the two spray end points corresponding to the track point P i+1 ; the coordinate values of the two spray end points corresponding to the track point P i+1 can be obtained by the formula of the step (b);
则相邻的两个轨迹点P
i,P
i+1的喷洒面积为:
The spray area of the adjacent two track points P i , P i+1 is:
本发明的保护范围包括但不限于以上实施方式,本发明的保护范围以权利要求书为准,任何对本技术做出的本领域的技术人员容易想到的替换、变形、改进均落入本发明 的保护范围。The scope of the present invention includes, but is not limited to, the above embodiments, and the scope of the present invention is defined by the claims, and any substitutions, modifications, and improvements which are obvious to those skilled in the art to which the present invention is made fall within the scope of the present invention. protected range.