技术领域technical field
本申请属于无人机智能控制领域，具体涉及基于A*/minimum_snap算法的无人机轨迹控制系统和方法。The present application belongs to the field of UAV intelligent control, and specifically relates to a UAV trajectory control system and method based on the A*/minimum_snap algorithm.
背景技术Background technique
随着自动化控制、计算机信息、网络通信技术发展，无人机轨迹规划技术由最初的人工轨迹规划逐渐转变为自主轨迹规划。无人机自主轨迹规划以飞行路线最短、飞行时间最短为准则，探寻障碍环境中初始点至终点的最优轨迹。因此需要应用智能算法，实现无人机在障碍环境中的自主轨迹规划。With the development of automatic control, computer information, and network communication technology, the UAV trajectory planning technology has gradually changed from the initial manual trajectory planning to the autonomous trajectory planning. The autonomous trajectory planning of UAV is based on the shortest flight route and shortest flight time, and explores the optimal trajectory from the initial point to the end point in the obstacle environment. Therefore, it is necessary to apply intelligent algorithms to realize autonomous trajectory planning of UAVs in obstacle environments.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于提供一种基于A*/minimum_snap算法的无人机轨迹控制系统和方法，在仓库管理无人机的应用背景下，实现无人机在障碍环境中自主轨迹规划。The purpose of the present invention is to provide a UAV trajectory control system and method based on the A*/minimum_snap algorithm, which realizes the autonomous trajectory planning of the UAV in the obstacle environment under the application background of the warehouse management UAV.
为实现上述目的，本发明提供如下技术方案：To achieve the above object, the present invention provides the following technical solutions:
本申请实施例公开了一种基于A*/minimum_snap算法的无人机轨迹控制方法，包括：The embodiment of the present application discloses a UAV trajectory control method based on the A*/minimum_snap algorithm, including:
采用A*算法获得无人机运动轨迹的离散坐标点；Using A* algorithm to obtain discrete coordinate points of UAV trajectory;
利用minimum_snap算法对轨迹的离散坐标点进行拟合，获得规划的运动轨迹。Use the minimum_snap algorithm to fit the discrete coordinate points of the trajectory to obtain the planned motion trajectory.
优选的，在上述的基于A*/minimum_snap算法的无人机轨迹控制方法中，还包括：Preferably, in the above-mentioned UAV trajectory control method based on the A*/minimum_snap algorithm, it also includes:
以无人机的姿态误差作为输入，采用模糊PID方法控制无人机飞行。Taking the attitude error of the UAV as the input, the fuzzy PID method is used to control the UAV flight.
优选的，在上述的基于A*/minimum_snap算法的无人机轨迹控制方法中，规划的运动轨迹的各点位置的约束条件至少包括最大加速度和最大角速度。Preferably, in the above-mentioned UAV trajectory control method based on the A*/minimum_snap algorithm, the constraints on the position of each point of the planned motion trajectory include at least the maximum acceleration and the maximum angular velocity.
优选的，在上述的基于A*/minimum_snap算法的无人机轨迹控制方法中，所述无人机包括控制装置，控制装置导入含有障碍物信息的环境数字地图， A*算法对环境数字地图进行路径规划并获得轨迹的离散坐标点。Preferably, in the above-mentioned UAV trajectory control method based on the A*/minimum_snap algorithm, the UAV includes a control device, the control device imports an environmental digital map containing obstacle information, and the A* algorithm performs Path planning and obtain the discrete coordinate points of the trajectory.
优选的，在上述的基于A*/minimum_snap算法的无人机轨迹控制方法中，控制装置采用Stm32F1芯片。Preferably, in the above-mentioned UAV trajectory control method based on the A*/minimum_snap algorithm, the control device adopts a Stm32F1 chip.
优选的，在上述的基于A*/minimum_snap算法的无人机轨迹控制方法中，minimum_snap算法包括：Preferably, in the above-mentioned UAV trajectory control method based on the A*/minimum_snap algorithm, the minimum_snap algorithm includes:
通过轨迹的离散坐标点，构建无人机运动轨迹点函数：Through the discrete coordinate points of the trajectory, the UAV motion trajectory point function is constructed:
其中，p0,p1,…,pn为轨迹参数，令p＝[p0,p1,…,pn]T，得：Among them, p0 , p1 ,...,pn are trajectory parameters, let p=[p0 ,p1 ,...,pn ]T , we get:
p(t)＝[1，t，t2，…tn]p (3)p(t)=[1, t, t2 ,...tn ]p (3)
则在t0时刻相应的约束函数表示为：Then the corresponding constraint function at time t0 is expressed as:
位置约束location constraints
速度约束speed constraint
加速度约束acceleration constraint
minimum_snap轨迹为最小加加加速度轨迹，jerk为加加速度，表示所受力的变化率；snap为加加加速度，表示所受力的变化率的变化，The minimum_snap trajectory is the minimum jerk trajectory, jerk is the jerk, indicating the rate of change of the force; snap is the jerk, indicating the change in the rate of change of the force,
构建优化函数：Build the optimization function:
添加t时刻无人机的速度、加速度、加加速度、加加加速度约束：Add the speed, acceleration, jerk, and jerk constraints of the drone at time t:
速度：v(t)＝p'(t)＝[0,1,2t,3t2,4t3,...,ntn-1]·p (8)Speed: v(t)=p'(t)=[0, 1, 2t, 3t2 , 4t3 ,...,ntn-1 ]·p (8)
加速度：a(t)＝p”(t)＝[0,0,2,6t,12t2,...,n(n-1)tn-2]·p (9)Acceleration: a(t)=p"(t)=[0,0,2,6t,12t2 ,...,n(n-1)tn-2 ]·p (9)
加加速度：Jerk:
加加加速度：Jerk:
利用t时刻无人机的速度、加速度、加加速度、加加加速度约束，求解构建的优化函数，获得各轨迹离散坐标点的姿态信息。Using the constraints of the speed, acceleration, jerk, and jerk of the UAV at time t, the constructed optimization function is solved to obtain the attitude information of the discrete coordinate points of each trajectory.
本申请实施例还公开了一种基于A*/minimum_snap算法的无人机轨迹控制系统，包括：The embodiment of the present application also discloses a UAV trajectory control system based on the A*/minimum_snap algorithm, including:
执行机构；executive body;
控制装置，采用A*算法获得无人机运动轨迹的离散坐标点；并利用 minimum_snap算法对轨迹的离散坐标点进行拟合，获得规划的运动轨迹。The control device adopts the A* algorithm to obtain the discrete coordinate points of the UAV motion trajectory; and uses the minimum_snap algorithm to fit the discrete coordinate points of the trajectory to obtain the planned motion trajectory.
优选的，在上述的基于A*/minimum_snap算法的无人机轨迹控制系统中，控制装置以无人机的姿态误差作为输入，采用模糊PID方法控制执行机构。Preferably, in the above-mentioned UAV trajectory control system based on the A*/minimum_snap algorithm, the control device uses the attitude error of the UAV as an input, and uses the fuzzy PID method to control the actuator.
优选的，在上述的基于A*/minimum_snap算法的无人机轨迹控制系统中，规划的运动轨迹的各点位置的约束条件至少包括最大加速度和最大角速度。Preferably, in the above-mentioned UAV trajectory control system based on the A*/minimum_snap algorithm, the constraints on the position of each point of the planned motion trajectory include at least the maximum acceleration and the maximum angular velocity.
优选的，在上述的基于A*/minimum_snap算法的无人机轨迹控制系统中，控制装置导入含有障碍物信息的环境数字地图，A*算法对环境数字地图进行路径规划并获得轨迹的离散坐标点。Preferably, in the above-mentioned UAV trajectory control system based on the A*/minimum_snap algorithm, the control device imports an environmental digital map containing obstacle information, and the A* algorithm performs path planning on the environmental digital map and obtains discrete coordinate points of the trajectory .
与现有技术相比，本发明的优点在于：Compared with the prior art, the advantages of the present invention are:
1.本发明将数字地图导入无人机控制装置后，控制装置采用A*算法避开障碍物，并快速、准确地获得无人机最优轨迹的离散轨迹点；1. After the digital map is imported into the UAV control device in the present invention, the control device adopts the A* algorithm to avoid obstacles, and obtains the discrete trajectory points of the UAV optimal trajectory quickly and accurately;
2.本发明利用minimum_snap算法对由A*算法处理获得的离散轨迹点进行拟合，得到各个轨迹点上的加速度、速度以及位置的设置值。将无人机的目标姿态与其当前姿态进行对比，获得姿态误差。在此基础上，添加无人机各方向的最大加速度、最大角速度作为约束，获得更准确的无人机的轨迹控制信号；2. The present invention uses the minimum_snap algorithm to fit the discrete trajectory points obtained by processing the A* algorithm, and obtains the set values of acceleration, velocity and position on each trajectory point. Compare the target attitude of the UAV with its current attitude to obtain the attitude error. On this basis, the maximum acceleration and maximum angular velocity of the UAV in all directions are added as constraints to obtain a more accurate trajectory control signal of the UAV;
3.本发明将无人机姿态误差输入模糊PID控制器进行控制，实现无人机达到目标位置的控制。3. In the present invention, the attitude error of the drone is input into the fuzzy PID controller for control, so as to realize the control of the drone reaching the target position.
附图说明Description of drawings
为了更清楚地说明本申请实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本申请中记载的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only These are some embodiments described in this application. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without any creative effort.
图1所示为本发明具体实施例中无人机运动装置整体结构示意图；1 is a schematic diagram of the overall structure of the UAV motion device in a specific embodiment of the present invention;
图2所示为本发明具体实施例中控制装置的控制原理方框图；FIG. 2 is a block diagram showing the control principle of the control device in the specific embodiment of the present invention;
图3所示为本发明具体实施例中无人机轨迹流程控制示意图；FIG. 3 is a schematic diagram of a UAV trajectory process control diagram in a specific embodiment of the present invention;
图4所示为本发明具体实施例中minimum_snap算法流程图；Fig. 4 shows the minimum_snap algorithm flow chart in the specific embodiment of the present invention;
图5所示为本发明具体实施例中模糊PID控制流程图。FIG. 5 shows a flowchart of fuzzy PID control in a specific embodiment of the present invention.
具体实施方式Detailed ways
通过应连同所附图式一起阅读的以下具体实施方式将更完整地理解本发明。本文中揭示本发明的详细实施例；然而，应理解，所揭示的实施例仅具本发明的示范性，本发明可以各种形式来体现。因此，本文中所揭示的特定功能细节不应解释为具有限制性，而是仅解释为权利要求书的基础且解释为用于教示所属领域的技术人员在事实上任何适当详细实施例中以不同方式采用本发明的代表性基础。The present invention will be more fully understood from the following detailed description, which should be read in conjunction with the accompanying drawings. Detailed embodiments of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments are merely exemplary of the invention, which may be embodied in various forms. Therefore, specific functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and for teaching one skilled in the art to vary in virtually any suitable detailed embodiment. The manner adopts the representative basis of the present invention.
图1是本发明实施例中无人机运动装置整体结构图，包括控制装置1和执行机构2。FIG. 1 is an overall structural diagram of an unmanned aerial vehicle motion device in an embodiment of the present invention, including a control device 1 and an actuator 2 .
控制装置1包括Stm32F1芯片、姿态检测传感器等。The control device 1 includes a Stm32F1 chip, an attitude detection sensor, and the like.
执行机构2包括：旋翼、无刷电机、电调等。The actuator 2 includes a rotor, a brushless motor, an ESC, and the like.
控制装置1与上位机之间可以实现通信，上位机可以为手持终端，比如遥控器、手机等，也可以为计算机。Communication between the control device 1 and the upper computer can be realized, and the upper computer can be a handheld terminal, such as a remote control, a mobile phone, etc., or a computer.
在一实施例中，上位机将处理过障碍物的环境数字地图发送到无人机的控制装置。当需要修改或更新无人机的控制程序时，可以通过控制装置的下载接口进行程序修改或更新。In one embodiment, the upper computer sends the digital map of the environment that has processed obstacles to the control device of the drone. When the control program of the drone needs to be modified or updated, the program modification or update can be performed through the download interface of the control device.
上位机可以实现运动可视化，包括：将姿态传感器测量获得的无人机姿态数据在上位机端进行可视化显示。The host computer can realize motion visualization, including: visual display of the UAV attitude data obtained by the attitude sensor measurement on the host computer side.
结合图2所示，控制装置对轨迹规划数据进行处理，获得各轨迹点的加速度、角速度信息。通过导航解算，获得无人机的目标姿态，与其当前姿态进行对比，得到姿态误差，在此基础上，添加无人机各方向的最大加速度、最大角速度作为约束。并将姿态误差发送至控制装置系统中的模糊PID控制器，控制器将控制信号发送给执行机构，实现无人机高精度的轨迹控制。With reference to Fig. 2, the control device processes the trajectory planning data to obtain the acceleration and angular velocity information of each trajectory point. Through the navigation solution, the target attitude of the UAV is obtained, and the attitude error is obtained by comparing with its current attitude. On this basis, the maximum acceleration and maximum angular velocity of the UAV in all directions are added as constraints. The attitude error is sent to the fuzzy PID controller in the control device system, and the controller sends the control signal to the actuator to realize the high-precision trajectory control of the UAV.
结合图3所示，无人机轨迹流程控制包括：Combined with Figure 3, the UAV trajectory process control includes:
S101：开始；S101: start;
S102：参数初始化；S102: parameter initialization;
S103：导入数字地图；S103: import digital map;
S104：A*算法全局规划；S104: A* algorithm global planning;
S105：minimum_snap算法轨迹拟合；S105: minimum_snap algorithm trajectory fitting;
S106：信息处理后生成控制信号；S106: Generate a control signal after information processing;
S107：判断是否到达目标点；S107: determine whether the target point is reached;
S108：结束。S108: End.
具体地，控制装置系统接收开始指令，首先进行参数初始化，之后将处理过障碍物的环境数字地图发送到控制装置，采用A*算法对处理过障碍物的环境数字地图进行全局规划，minimum_snap算法对轨迹的离散坐标点进行拟合，在此基础上，添加无人机各方向的最大加速度、最大角速度作为约束，获得各轨迹离散坐标点的姿态信息，将其发送到模糊PID控制器获得控制信号，实现无人机轨迹的精确控制。Specifically, the control device system receives the start instruction, first initializes parameters, and then sends the digital map of the environment that has processed obstacles to the control device, and uses the A* algorithm to perform global planning on the digital map of the environment that has processed obstacles. The discrete coordinate points of the trajectory are fitted. On this basis, the maximum acceleration and maximum angular velocity of the UAV in each direction are added as constraints, and the attitude information of the discrete coordinate points of each trajectory is obtained, which is sent to the fuzzy PID controller to obtain the control signal. , to achieve precise control of the UAV trajectory.
在一实施例中，A*算法(A-star算法)包括：In one embodiment, the A* algorithm (A-star algorithm) includes:
A*算法的核心是：The core of the A* algorithm is:
F＝G+H (1)F=G+H (1)
其中，G为从初始点到途径点的移动耗费；H为从途径点到目标点的预耗费。当H＝0时，A*即为Dijkstra算法，常用的H主要有曼哈顿、对角线、欧几里得距离。A*主要步骤如下：Among them, G is the moving cost from the initial point to the way point; H is the pre-cost from the way point to the target point. When H=0, A* is the Dijkstra algorithm, and the commonly used H mainly include Manhattan, diagonal, and Euclidean distance. The main steps of A* are as follows:
1.计算当前单元的所有相邻单元的成本；1. Calculate the cost of all adjacent cells of the current cell;
2.将它们添加到有效列表中；2. Add them to the valid list;
3.从有效列表中找到总成本最小的单元格，使其成为下一个迭代的父单元格，并使其不可用于下一个总成本最小的单元格比较；3. Find the cell with the smallest total cost from the valid list, make it the parent cell of the next iteration, and make it unavailable for the next cell comparison with the smallest total cost;
4.把当前总成本最小的单元格放到无效列表中，使其在下一步不被访问；4. Put the cell with the smallest current total cost into the invalid list so that it will not be accessed in the next step;
5.循环运行，直到成本最小的单元格是目标单元，结束。5. Run the loop until the cell with the smallest cost is the target cell, end.
在一实施例中，结合图4所示，minimum_snap算法流程框图，包括：In one embodiment, with reference to FIG. 4 , the minimum_snap algorithm flowchart includes:
S201：开始；S201: start;
S202：初始轨迹分段与时间分配；S202: initial trajectory segmentation and time allocation;
S203：构建等式约束方程；S203: Construct an equality constraint equation;
S204：构建优化函数；S204: Build an optimization function;
S205：构建不等式约束。S205: Constructing inequality constraints.
具体地，控制装置接收A*算法产生的轨迹的离散坐标点，构建无人机运动轨迹点函数：Specifically, the control device receives the discrete coordinate points of the trajectory generated by the A* algorithm, and constructs the UAV motion trajectory point function:
其中，p0,p1,…,pn为轨迹参数，令p＝[p0,p1,…,pn]T，得：Among them, p0 , p1 ,...,pn are trajectory parameters, let p=[p0 ,p1 ,...,pn ]T , we get:
p(t)＝[1,t,t2,…tn]p (3)p(t)=[1,t,t2 ,...tn ]p (3)
时间分配：假设每段轨迹点之间速度满足匀速或梯形速度变化，根据每段的距离对总时间t进行分配。Time allocation: Assuming that the speed between each track point satisfies a uniform or trapezoidal speed change, the total time t is allocated according to the distance of each segment.
则在t0时刻相应的约束函数表示为：Then the corresponding constraint function at time t0 is expressed as:
位置约束location constraints
速度约束speed constraint
加速度约束acceleration constraint
minimum_snap轨迹为最小加加加速度轨迹，jerk为加加速度，表示所受力的变化率；snap为加加加速度，表示所受力的变化率的变化，The minimum_snap trajectory is the minimum jerk trajectory, jerk is the jerk, indicating the rate of change of the force; snap is the jerk, indicating the change in the rate of change of the force,
根据minimum_snap轨迹规划算法，最小化目标函数为:According to the minimum_snap trajectory planning algorithm, the minimized objective function is:
min f(p)＝min(p(4)(t))2min f(p)=min(p(4) (t))2
从最小化目标函数中构建优化函数：Build the optimization function from the minimized objective function:
其中，in,
添加t时刻无人机的速度、加速度、加加速度、加加加速度约束：Add the speed, acceleration, jerk, and jerk constraints of the drone at time t:
速度：v(t)＝p'(t)＝[0,1,2t,3t2,4t3,...,ntn-1]·p (8)Speed: v(t)=p'(t)=[0, 1, 2t, 3t2 , 4t3 ,...,ntn-1 ]·p (8)
加速度：a(t)＝p”(t)＝[0,0,2,6t,12t2,...,n(n-1)tn-2]·p (9)Acceleration: a(t)=p"(t)=[0,0,2,6t,12t2 ,...,n(n-1)tn-2 ]·p (9)
加加速度：Jerk:
加加加速度：Jerk:
添加相邻轨迹段之间的位置、速度、加速度连续等式约束：Add position, velocity, acceleration continuity equation constraints between adjacent trajectory segments:
利用t时刻无人机的速度、加速度、加加速度、加加加速度和相邻轨迹段之间的位置、速度、加速度连续的约束，求解构建的优化函数，获得各轨迹离散坐标点的姿态信息。Using the velocity, acceleration, jerk, jerk of the UAV at time t and the continuous constraints of position, velocity and acceleration between adjacent trajectory segments, the constructed optimization function is solved to obtain the attitude information of discrete coordinate points of each trajectory.
在一实施例中，结合图5所示，模糊PID控制流程框图，包括：In one embodiment, with reference to Fig. 5, the fuzzy PID control flow diagram includes:
S301：输入；S301: input;
S302；模糊控制器；S302; fuzzy controller;
S303：PID控制器；S303: PID controller;
S304：控制对象。S304: Controlling the object.
本申请基于A*/minimum_snap算法，在避开障碍物的基础上，快速、准确地获得规划轨迹的离散坐标点，结合无人机的最大加速度、最大角速度的运动约束，对轨迹的离散坐标点进行拟合，得到规划的运动轨迹。在规划的运动轨迹基础上，采用模糊PID控制实现无人机运动轨迹的控制。This application is based on the A*/minimum_snap algorithm. On the basis of avoiding obstacles, the discrete coordinate points of the planned trajectory can be quickly and accurately obtained. Combined with the motion constraints of the maximum acceleration and maximum angular velocity of the UAV, the discrete coordinate points of the trajectory are determined. Fitting is performed to obtain the planned motion trajectory. On the basis of the planned motion trajectory, fuzzy PID control is used to realize the control of the UAV motion trajectory.
综上所述：In summary:
(1)、本发明通过将A*算法和minimum_snap算法结合，通过添加无人机各方向的最大加速度、最大角速度作为约束，确保无人机飞行的可行性；(1), the present invention ensures the feasibility of UAV flight by combining the A* algorithm and the minimum_snap algorithm, and by adding the maximum acceleration and the maximum angular velocity of the UAV in all directions as constraints;
(2)、本发明通过将A*算法和minimum_snap算法结合，在A*算法获得轨迹的离散路径坐标点的基础上，根据轨迹点的数目对轨迹进行分段、时间分配、构建优化函数，通过解算优化函数，获得规划的运动轨迹，包括加速度、速度、位置参数。满足起点和终点的速度和加速度、轨迹连接处位置和速度连续的要求，同时解决A*算法规划的路径点比较稀疏、不平滑的问题；(2), the present invention combines the A* algorithm with the minimum_snap algorithm, and on the basis of the discrete path coordinate points of the trajectory obtained by the A* algorithm, the trajectory is segmented, time allocated, and an optimization function is constructed according to the number of trajectory points. Solve the optimization function to obtain the planned motion trajectory, including acceleration, velocity, and position parameters. It can meet the requirements of the speed and acceleration of the starting point and the end point, and the continuous position and speed of the trajectory connection, and solve the problem that the path points planned by the A* algorithm are relatively sparse and not smooth;
(3)、采用模糊PID控制，实现在线调整PID参数。模糊PID控制的滞后量和超调量均明显小于经典PID控制，具有更好的快速性、精确性、鲁棒性等特点。(3) Using fuzzy PID control to realize online adjustment of PID parameters. The lag and overshoot of fuzzy PID control are significantly smaller than those of classical PID control, and it has better rapidity, accuracy and robustness.
本发明的各方面、实施例、特征及实例应视为在所有方面为说明性的且不打算限制本发明，本发明的范围仅由权利要求书界定。在不背离所主张的本发明的精神及范围的情况下，所属领域的技术人员将明了其它实施例、修改及使用。The aspects, embodiments, features, and examples of the present invention are to be considered in all respects illustrative and not intended to limit the invention, the scope of which is defined only by the claims. Other embodiments, modifications, and uses will be apparent to those skilled in the art without departing from the spirit and scope of the claimed invention.
在本申请案中标题及章节的使用不意味着限制本发明；每一章节可应用于本发明的任何方面、实施例或特征。The use of headings and sections in this application is not meant to limit the invention; each section is applicable to any aspect, embodiment or feature of the invention.
在本申请案通篇中，在将组合物描述为具有、包含或包括特定组份之处或者在将过程描述为具有、包含或包括特定过程步骤之处，预期本发明教示的组合物也基本上由所叙述组份组成或由所叙述组份组成，且本发明教示的过程也基本上由所叙述过程步骤组成或由所叙述过程步骤组组成。Throughout this application, where a composition is described as having, comprising or including particular components, or where a process is described as having, comprising or including particular process steps, it is contemplated that the compositions of the present teachings will also be substantially The above consists of or consists of the recited components, and the processes taught herein also consist essentially of, or consist of, the recited process steps.
在本申请案中，在将元件或组件称为包含于及/或选自所叙述元件或组件列表之处，应理解，所述元件或组件可为所叙述元件或组件中的任一者且可选自由所叙述元件或组件中的两者或两者以上组成的群组。此外，应理解，在不背离本发明教示的精神及范围的情况下，本文中所描述的组合物、设备或方法的元件及/或特征可以各种方式组合而无论本文中是明确说明还是隐含说明。In this application, where an element or component is referred to as being included in and/or selected from a list of recited elements or components, it is to be understood that the element or component can be any of the recited elements or components and The group may be selected from two or more of the recited elements or components. Furthermore, it should be understood that the elements and/or features of the compositions, apparatuses or methods described herein may be combined in various ways, whether expressly or implicitly herein, without departing from the spirit and scope of the present teachings. Instructions included.
除非另外具体陈述，否则术语“包含(include、includes、including)”、“具有(have、has或having)”的使用通常应理解为开放式的且不具限制性。The use of the terms "include, includes, including," "have, has, or having" should generally be understood to be open-ended and not limiting unless specifically stated otherwise.
除非另外具体陈述，否则本文中单数的使用包含复数(且反之亦然)。此外，除非上下文另外清楚地规定，否则单数形式“一(a、an)”及“所述(the)”包含复数形式。另外，在术语“约”的使用在量值之前之处，除非另外具体陈述，否则本发明教示还包括特定量值本身。The use of the singular herein includes the plural (and vice versa) unless specifically stated otherwise. Also, the singular forms "a (a, an)" and "the (the)" include the plural forms unless the context clearly dictates otherwise. Additionally, where the use of the term "about" precedes a magnitude, the teachings of the present invention also include the particular magnitude itself, unless specifically stated otherwise.
应理解，各步骤的次序或执行特定动作的次序并非十分重要，只要本发明教示保持可操作即可。此外，可同时进行两个或两个以上步骤或动作。It should be understood that the order of the steps or the order in which the particular actions are performed is not critical so long as the present teachings remain operable. Furthermore, two or more steps or actions may be performed simultaneously.
应理解，本发明的各图及说明已经简化以说明与对本发明的清楚理解有关的元件，而出于清晰性目的消除其它元件。然而，所属领域的技术人员将认识到，这些及其它元件可为合意的。然而，由于此类元件为此项技术中众所周知的，且由于其不促进对本发明的更好理解，因此本文中不提供对此类元件的论述。应了解，各图是出于图解说明性目的而呈现且不作为构造图式。所省略细节及修改或替代实施例在所属领域的技术人员的范围内。It should be understood that the figures and descriptions of the present invention have been simplified to illustrate elements relevant to a clear understanding of the present invention, while other elements have been eliminated for clarity. However, one skilled in the art will recognize that these and other elements may be desirable. However, since such elements are well known in the art, and since they do not facilitate a better understanding of the present invention, no discussion of such elements is provided herein. It should be understood that the figures are presented for illustrative purposes and not as construction drawings. Omitted details and modifications or alternative embodiments are within the scope of those skilled in the art.
可了解，在本发明的特定方面中，可由多个组件替换单个组件且可由单个组件替换多个组件以提供一元件或结构或者执行一或若干给定功能。除了在此替代将不操作以实践本发明的特定实施例之处以外，将此替代视为在本发明的范围内。It will be appreciated that, in certain aspects of the invention, a single component may be replaced by a plurality of components and a plurality of components may be replaced by a single component to provide an element or structure or to perform a given function or functions. Except where such substitutions would not operate to practice specific embodiments of the invention, such substitutions are considered to be within the scope of the invention.
尽管已参考说明性实施例描述了本发明，但所属领域的技术人员将理解，在不背离本发明的精神及范围的情况下可做出各种其它改变、省略及/或添加且可用实质等效物替代所述实施例的元件。另外，可在不背离本发明的范围的情况下做出许多修改以使特定情形或材料适应本发明的教示。因此，本文并不打算将本发明限制于用于执行本发明的所揭示特定实施例，而是打算使本发明将包含归属于所附权利要求书的范围内的所有实施例。此外，除非具体陈述，否则术语第一、第二等的任何使用不表示任何次序或重要性，而是使用术语第一、第二等来区分一个元素与另一元素。Although the present invention has been described with reference to illustrative embodiments, those skilled in the art will understand that various other changes, omissions and/or additions and the like may be made without departing from the spirit and scope of the invention Effects replace elements of the described embodiments. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from its scope. Therefore, it is not intended herein to limit the invention to the particular embodiments disclosed for carrying out the invention, but it is intended that this invention include all embodiments falling within the scope of the appended claims. Furthermore, unless specifically stated, any use of the terms first, second, etc. does not denote any order or importance, but rather the terms first, second, etc. are used to distinguish one element from another.
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| CN201910236729.1ACN109857134A (en) | 2019-03-27 | 2019-03-27 | Unmanned plane tracking control system and method based on A*/minimum_snap algorithm |
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| CN201910236729.1ACN109857134A (en) | 2019-03-27 | 2019-03-27 | Unmanned plane tracking control system and method based on A*/minimum_snap algorithm |
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| CN201910236729.1APendingCN109857134A (en) | 2019-03-27 | 2019-03-27 | Unmanned plane tracking control system and method based on A*/minimum_snap algorithm |
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