阅读说明：本技术 适用于无人机的无碰撞路径规划方法、系统及介质 (Collision-free path planning method, system and medium suitable for unmanned aerial vehicle ) 是由 丁烨 陈永学 董伟 于 2020-11-27 设计创作，主要内容包括：本发明提供了一种无人机无碰撞路径规划方法,通过对输入路径点使用B样条曲线进行插值得到初步飞行路径；使用球体和平面得到无人机和障碍物近似模型,在路径曲线离散点位检测碰撞情况,并获取碰撞区域的曲线参数区间；根据参数区间建立新的路径点,重新进行B样条曲线插值并重新进行碰撞检测,反复迭代直到得到最终的无人机无碰撞路径。本发明可解决给定任务空间飞行路径点时,连续的无碰撞路径规划问题,并具有极高的计算效率,具有重要的理论和现实意义,适用于无人机在复杂环境中执行任务时进行无碰撞的路径规划,提高安全性和飞行效率。(The invention provides a collision-free path planning method for an unmanned aerial vehicle, which is characterized in that a preliminary flight path is obtained by interpolating input path points by using a B spline curve; obtaining an unmanned aerial vehicle and obstacle approximate model by using the sphere and the plane, detecting a collision condition at discrete point positions of a path curve, and obtaining a curve parameter interval of a collision area; and establishing new path points according to the parameter interval, performing B spline curve interpolation again, performing collision detection again, and repeating iteration until a final collision-free path of the unmanned aerial vehicle is obtained. The method can solve the problem of continuous non-collision path planning when a task space flight path point is given, has extremely high calculation efficiency, has important theoretical and practical significance, is suitable for non-collision path planning when the unmanned aerial vehicle executes a task in a complex environment, and improves the safety and the flight efficiency.)

1. A collision-free path planning method suitable for an unmanned aerial vehicle is characterized by comprising the following steps:

step 1: b spline curve interpolation is carried out on the given path point to obtain a path curve;

step 2: carrying out unmanned aerial vehicle collision detection according to the acquired path curve;

and step 3: constructing a new path point for the path curve with collision in the collision detection result, and directly outputting a collision-free path for the path curve without collision in the collision detection result;

and 4, step 4: and (5) carrying out B-spline curve interpolation again on the new path point and returning to the step 2.

2. The method of claim 1, wherein the B-spline interpolation calculates the parameter values for a given path point using the following formula:

wherein p is_iI ∈ {0,1,2,3, …, N } represents a given i +1 th waypoint coordinate;

to correspond to p_iB spline curve parameter values of the points;

the node vector of the 5 th order B-spline curve is calculated using the following formula:

and solving the following linear equation set to obtain the control points of the B spline curve:

wherein N is_i,5(u), i ═ 0, 1.., N is the basis function of the 5 th-order B spline curve.

3. The collision-free path planning method for drones according to claim 1, characterized in that step 2 comprises replacing the three-dimensional model of drones by using sphere approximation and replacing the model of environmental obstacles by using sphere and directional plane approximation.

4. The method according to claim 1, wherein the path curve is discretized when performing the collision detection of the unmanned aerial vehicle in step 2, the collision detection is performed at discrete path points by calculating the distance between the sphere and the directed plane or between the sphere and the directed plane, and the curve parameter interval [ u ] of the path segment where the collision exists is output_s,i,u_e,i]I ∈ {1,2,3, …, M }, where u_s,iIs the first parameter value u of the i-th collision zone_e,iIs the last parameter value of the ith collision interval.

5. The method for collision-free path planning suitable for unmanned aerial vehicles according to claim 1, wherein step 3 performs classification processing according to the collision situation obtained in step 2.

6. The collision-free path planning method for unmanned aerial vehicles according to claim 5,

step 3.1: if no collision interval exists, outputting a collision-free path curve;

step 3.2: if there is a curve parameter interval where M sections of collision occur, according to each section of parameter interval [ u ]_s,i,u_e,i]I e {1,2,3, …, M }, generating a new path curve interpolation point p_m,iAnd according to the parameter valueAnd the path interpolation point obtained in step 1 or step 4Parameter valueThe magnitude relationship between p and p_m,iAnd adding the path interpolation point into a proper position of the path interpolation point list.

7. The method of claim 5, wherein step 3.2 generates the interpolation point p based on B-spline interpolation iteration number, one of which_m,i，

Step 3.2.1, if the iteration number of the B spline interpolation is less than or equal to a certain set threshold value, the order is givenWherein du is a parameter step length taken when discretizing the curve;

order toWherein, s (u) represents the coordinate of the B-spline curve when the parameter is u, and k is set to 1 as an initial proportion;

to at p_m,iCollision detection is carried out on the unmanned aerial vehicle model, and if collision occurs, the command is sent

Meanwhile, the ratio k is appropriately increased: k is k + dk, wherein dk > 0 is a preset ratio updating step length;

recalculating p_m,iAnd iterating until at p_m,iUntil the unmanned aerial vehicle model and the environment do not collide.

8. The method of claim 5, wherein step 3.2 generates the interpolation point p according to B-spline interpolation iteration number and the other case_m,i，

Step 3.2.2: if the B spline interpolation iteration number is larger than a set threshold value, the following steps are carried out:

order toWherein p is_randFor randomly generated unit vectors, k_rIs a scale factor, is initially set to k_r2r, wherein r is the radius of a sphere simulating the unmanned aerial vehicle;

to at p_m,iThe unmanned aerial vehicle model carries out collision detection, and if the collision happens, p is regenerated_m,iAnd increase k appropriately_rIterating until p is reached_m,iUntil the unmanned aerial vehicle model and the environment do not collide.

9. A collision-free path planning system suitable for unmanned aerial vehicles, comprising:

module M1: b spline curve interpolation is carried out on the given path point to obtain a path curve;

module M2: carrying out unmanned aerial vehicle collision detection according to the acquired path curve;

module M3: constructing a new path point for the path curve with collision in the collision detection result, and directly outputting a collision-free path for the path curve without collision in the collision detection result;

module M4: and inputting the new path point into the module M2 after B spline curve interpolation is carried out again.

10. A computer-readable medium, characterized in that it stores a computer program executable by a collision-free path planning apparatus adapted for a drone, which, when run on the collision-free path planning apparatus adapted for a drone, causes the collision-free path planning apparatus adapted for a drone to perform the steps of the collision-free path planning method adapted for a drone of any one of claims 1-8.

Technical Field

The invention relates to the technical field of unmanned aerial vehicle obstacle avoidance, in particular to a collision-free path planning method and system suitable for an unmanned aerial vehicle and a computer readable medium.

Background

Trajectory planning is one of the most important tasks in autonomous cruising of unmanned aerial vehicles, and the problem is generally solved through two steps of path generation and speed planning. In order to meet the task requirements, path generation needs to obtain a geometric curve passing through a given path point, and meanwhile, the unmanned aerial vehicle is required not to collide with obstacles in the environment on the curve. To constrain the jerk of the unmanned aerial vehicle when being favorable to speed planning, path curves are generally required to be continuous. Common path generation algorithms include an artificial potential field method, a heuristic search method, a geometric method and the like.

The heuristic search method represented by the A-algorithm has long calculation time and low efficiency; the calculated amount of the artificial potential field method is relatively small, but the artificial potential field method is easy to fall into local optimum; the geometric method greatly shortens the generation time of the collision path by geometrically modeling the environment.

In the existing geometric methods, some methods are complex in model construction, and have adverse effects on planning efficiency, and meanwhile, many methods cannot ensure the smoothness of a curve under the condition of passing through a given path point.

Through retrieval, patent document CN111580563A discloses an unmanned aerial vehicle autonomous obstacle avoidance flight method based on seed search, which is directed at complex and changeable urban building environments, in the prior art, firstly, uniformly spreading a plurality of seeds in a task space, then setting the flight direction of the unmanned aerial vehicle by taking a terminal point as a target, and starting the unmanned aerial vehicle to fly; unmanned aerial vehicle is at the flight in-process, whether there is the barrier in real time detection the place ahead, if detect the place ahead and have the barrier, then search for near the seed of unmanned aerial vehicle according to certain rule, then use this seed to reset unmanned aerial vehicle flight direction as the target, when treating that unmanned aerial vehicle flies to this seed position, again with terminal point position target setting flight direction, continue flight detection, so relapse, be less than the threshold value that sets up until the position of unmanned aerial vehicle distance terminal point to accomplish the flight task. However, the prior art has the defects that the model construction is still complex and the planning efficiency is not high.

Therefore, an unmanned aerial vehicle obstacle avoidance method which is clear in logic, simple in configuration and high in planning efficiency needs to be researched and developed urgently.

Disclosure of Invention

In view of the drawbacks of the prior art, it is an object of the present invention to provide a collision-free path planning method, system and computer readable medium suitable for unmanned aerial vehicles, which can generate a continuous collision-free path through a given path point. The method is suitable for collision-free path planning when the unmanned aerial vehicle executes tasks in a complex environment, and improves safety and flight efficiency.

The invention provides a collision-free path planning method suitable for an unmanned aerial vehicle, which is characterized by comprising the following steps of:

step 1: b spline curve interpolation is carried out on the given path point to obtain a path curve;

step 2: carrying out unmanned aerial vehicle collision detection according to the acquired path curve;

and step 3: constructing a new path point for the path curve with collision in the collision detection result, and directly outputting a collision-free path for the path curve without collision in the collision detection result;

and 4, step 4: and (5) carrying out B-spline curve interpolation again on the new path point and returning to the step 2.

Preferably, the B-spline interpolation in step 1 calculates the parameter value for a given path point using the following formula:

wherein p is_iI ∈ {0,1,2,3, …, N } represents a given i +1 th waypoint coordinate;

to correspond to p_iB-spline curve parameter values for the points.

The node vector of the 5 th order B-spline curve is calculated using the following formula:

and solving the following linear equation set to obtain the control points of the B spline curve:

wherein N is_i,5(u), i is 0,1, and N is a basis function of a 5-degree B-spline curve, thereby obtaining a 5-degree B-spline curve s (u) passing through the input path point, and u ∈ [0,1]]. Interpolating the B-spline by the number of iterations N_intIs set to 0.

Preferably, step 2 comprises:

according to the three-dimensional model of unmanned aerial vehicle, obtain the minimum radius spheroid that can wrap up this unmanned aerial vehicle completely, use this spheroid as the approximate replacement of unmanned aerial vehicle, hereinafter referred to as the unmanned aerial vehicle ball.

Obstacles in the task space are classified, obstacles such as wall surfaces, large cubes and the like are replaced by directed planes, hereinafter referred to as obstacle surfaces, and rotators, small cubes and some other irregular obstacles are approximately replaced by one or a series of spheres, hereinafter referred to as obstacle balls. The replacement process needs to ensure that the obstacle is completely positioned on one side of the obstacle surface or the obstacle ball completely covers the obstacle.

Discretizing the path curve S (u) by the parameter step length du to obtain a series of discrete path points S (u)_i). And calculating the distance between the unmanned plane ball and each obstacle surface and the obstacle ball at each discrete path point, and marking the discrete point if the unmanned plane ball collides with any obstacle surface or any obstacle ball.

Finally outputting a curve parameter interval [ u ] of the M section of the collision_s,i,u_e,i]I ∈ {1,2,3, …, M }, where u_s,iIs the first parameter value u of the i-th collision zone_e,iIs the last parameter value of the ith collision interval.

Preferably, step 3 performs a classification process according to the collision situation obtained in step 2.

Preferably, step 3 comprises the steps of:

step 3.1: if no collision interval exists, outputting a collision-free path curve;

step 3.2: if there is a curve parameter interval where M sections of collision occur, according to each section of parameter interval [ u ]_s,i,u_e,i]I e {1,2,3, …, M }, generating a new path curve interpolation point p_m,iAnd according to the parameter valueAnd the path interpolation point parameter value obtained in step 1 or step 4The magnitude relationship between p and p_m,iAnd adding the path interpolation point into a proper position of the path interpolation point list.

Preferably, step 3.2 generates the interpolation point p according to the number of B-spline interpolation iterations, one of which_m,i，

Step 3.2.1, if B spline interpolation iteration number N_intIs less than or equal to a certain set threshold value, then orderWherein du is a parameter step length taken when discretizing the curve;

order toWherein, s (u) represents the coordinate of the B-spline curve when the parameter is u, and k is set to 1 as an initial proportion;

to at p_m,iCollision detection is carried out on the unmanned aerial vehicle model, and if collision occurs, the command is sent

Meanwhile, the ratio k is appropriately increased: k is k + dk, wherein dk > 0 is a preset ratio updating step length;

recalculating p_m,iAnd iterating until at p_m,iUntil the unmanned aerial vehicle model and the environment do not collide.

Preferably, step 3.2 generates the interpolation point p according to the number of B-spline interpolation iterations, the other case_m,i，

Step 3.2.2: if B spline interpolation iteration number N_intIf the threshold value is larger than a set threshold value:

order toWherein p is_randFor randomly generated unit vectors, k_rIs a scale factor, is initially set to k_r2r, wherein r is the radius of a sphere simulating the unmanned aerial vehicle;

to at p_m,iThe unmanned aerial vehicle model carries out collision detection, and if the collision happens, p is regenerated_m,iAnd increase k appropriately_rIterating until p is reached_m,iUntil the unmanned aerial vehicle model and the environment do not collide.

Preferably, step 4 comprises:

interpolating the path points in the interpolation point list obtained in the step 3 by using a B spline curve for 5 times by adopting the same interpolation method as the step 1 to obtain a new path curve S (u), wherein u belongs to [0,1]]Updating the iteration times of B spline interpolation: n is a radical of_int＝N_intAnd +1, returning to the step 2 to detect the collision of the unmanned aerial vehicle.

The invention provides a collision-free path planning system suitable for an unmanned aerial vehicle, which comprises:

module M1: b spline curve interpolation is carried out on the given path point to obtain a path curve;

module M2: carrying out unmanned aerial vehicle collision detection according to the acquired path curve;

module M3: constructing a new path point for the path curve with collision in the collision detection result, and directly outputting a collision-free path for the path curve without collision in the collision detection result;

module M4: and inputting the new path point into the module M2 after B spline curve interpolation is carried out again.

According to the present invention, there is provided a computer-readable medium storing a computer program executable by a collision-free path planning apparatus for a drone, the computer program causing the collision-free path planning apparatus for a drone to execute any one of the above-described collision-free path planning methods for a drone, when the computer program is run on the collision-free path planning apparatus for a drone.

Compared with the prior art, the invention has the following beneficial effects:

1. according to the method, the curve parameter interval of the collision area is obtained, the new path point is established according to the parameter interval, the B-spline curve interpolation is carried out again, the collision detection is carried out again, iteration is carried out repeatedly until the final collision-free path of the unmanned aerial vehicle is obtained, the problem of continuous collision-free path planning when the flight path point of the task space is given is solved, the calculation efficiency is high, and the method has important theoretical and practical significance.

2. The method is suitable for collision-free path planning when the unmanned aerial vehicle executes tasks in a complex environment, and improves safety and flight efficiency.

3. The method has the advantages of simple model construction, contribution to improving the planning efficiency, and capability of ensuring the smoothness of the curve while meeting the requirement of passing through the given path point.

Drawings

Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:

FIG. 1 is a schematic flow diagram of the present invention;

fig. 2 is a schematic diagram of a quad-rotor unmanned aerial vehicle and a corresponding minimum external sphere in the invention;

fig. 3 is a diagram of the mission space and the planned flight path in the present invention.

Detailed Description

The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.

As shown in fig. 1, the method for planning collision-free paths of unmanned aerial vehicles according to the present invention includes the following steps:

step 1: b spline curve interpolation is carried out on the given path point to obtain a preliminary path, and the B spline curve interpolation in the step 1 comprises the steps of reading input N +1 pathsUnmanned aerial vehicle waypoint p_i,i∈{0,1,2,3,…,N}；

The parameter values for a given waypoint are calculated using the following formula:

the node vector of the 5 th order B-spline curve is calculated using the following formula:

and solving the following linear equation set to obtain the control points of the B spline curve:

wherein N is_i,5(u), i is 0,1, and N is a basis function of a 5-degree B-spline curve, thereby obtaining a 5-degree B-spline curve s (u) passing through the input path point, and u ∈ [0,1]]. Interpolating the B-spline by the number of iterations N_intIs set to 0.

Step 2: carry out unmanned aerial vehicle collision detection, also be exactly according to unmanned aerial vehicle's three-dimensional model, obtain the minimum radius spheroid that can wrap up this unmanned aerial vehicle completely, use this spheroid as unmanned aerial vehicle's approximate replacement, following as unmanned aerial vehicle ball in the future.

Obstacles in the task space are classified, obstacles such as wall surfaces, large cubes and the like are replaced by directed planes, hereinafter referred to as obstacle surfaces, and rotators, small cubes and some other irregular obstacles are approximately replaced by one or a series of spheres, hereinafter referred to as obstacle balls. The replacement process needs to ensure that the obstacle is completely positioned on one side of the obstacle surface or the obstacle ball completely covers the obstacle.

Discretizing the path curve S (u) by the parameter step length du to obtain a series of discrete path points S (u)_i). Calculating the distance between the unmanned plane ball and each obstacle surface and obstacle ball at each discrete path point, if the unmanned plane ball is not in useWhen the plane ball collides with any barrier surface or barrier ball, the discrete point is marked.

Finally outputting a curve parameter interval [ u ] of the M section of the collision_s,i,u_e,i]I ∈ {1,2,3, …, M }, where u_s,iIs the first parameter value u of the i-th collision zone_e,iIs the last parameter value of the ith collision interval. .

And step 3: adding a new path point or outputting a collision-free path according to the collision condition, and processing the collision curve according to the collision curve parameter interval obtained in the step 2 in two conditions:

case 1: if there is no collision zone, i.e., M is 0, a collision-free path curve s (u) is output, and u belongs to [0,1 ].

Case 2: if the curve parameter interval with collision exists, namely M is more than 0, according to each section of parameter interval [ u_s,i,u_e,i]I e {1,2,3, …, M }, generating a new path curve interpolation point p_m,iAnd according to the parameter valueAnd the path interpolation point parameter value obtained in step 1 or step 4The magnitude relationship between p and p_m,iAnd adding the path interpolation point into a proper position of the path interpolation point list.

Number of iterations N according to B-spline interpolation in case 2_intGenerating interpolation points p in two cases_m,i：

Case 2.1: if B spline interpolation iteration number N_intIs less than or equal to a certain set threshold value, then order

Wherein du is the parameter step length taken when discretizing the curve in step 2.

Order to

Wherein S (u) represents the coordinates of the B-spline curve at parameter u,

set k to 1 as the initial ratio.

To at p_m,iCollision detection is carried out on the unmanned ball, and if collision occurs, updating is carried out

Meanwhile, the ratio k is appropriately increased:

k＝k+dk

and dk > 0 is a preset ratio updating step length.

Recalculating p_m,iAnd iterating until at p_m,iUntil the unmanned ball is not collided with the environment.

Case 2.2: if B spline interpolation iteration number N_intIf it is greater than a predetermined threshold value, then

Order to

Wherein p is_randFor randomly generated unit vectors, k_rIs a scale factor, is initially set to k_rR is the radius of the drone sphere 2 r.

To at p_m,iThe unmanned aerial vehicle model carries out collision detection, and if the collision happens, p is regenerated_m,iAnd increase k appropriately_rIterating until p is reached_m,iUntil the unmanned aerial vehicle model and the environment do not collide.

And 4, step 4: b spline curve interpolation is carried out again and the step 2 is returned, the path points in the interpolation point list obtained in the step 3 are interpolated by using the B spline curve for 5 times by adopting the same interpolation method as the step 1, and a new path curve is obtainedLine S (u), u ∈ [0,1]]Updating the iteration times of B spline interpolation: n is a radical of_int＝N_int+1。

Example (b):

as shown in fig. 1, the specific process of this embodiment includes: b spline curve interpolation is carried out on the given path point to obtain a path curve; carrying out unmanned aerial vehicle collision detection according to the acquired path curve; constructing a new path point for the path curve with collision in the collision detection result, and directly outputting a collision-free path for the path curve without collision in the collision detection result; and (5) carrying out B-spline curve interpolation again on the new path point and returning to the step 2.

In the following embodiments, as shown in fig. 2-3, 8 small balls with the same size in fig. 3 are the unmanned balls at given 8 path points, two planes and three larger balls are the obstacle surface and the obstacle ball representing the obstacle, the solid line represents the path curve obtained by the first interpolation, and the dotted line represents the final collision-free flight path curve. Given the path points as shown by the 8 balls in FIG. 3, the coordinates are as follows:

x(m)	y(m)	z(m)
			0	0	0
1	3	15
			8	-9	18
10	21	5
			15	30	9
22	27	3
			25	20	21
30	14	12

the method provided by the invention is used for planning the collision-free path. The method comprises the following specific steps:

first, a preliminary path is obtained

Read 8 unmanned aerial vehicle waypoints of input

The parameter values at the 8 path points were calculated using the following formula:

to obtain

The node vector of the B-spline curve of 5 degrees is calculated by using the following formula:

and solving the following linear equation set to obtain the control points of the B spline curve:

wherein the content of the first and second substances,

N_i,5(u), i ═ 0, 1.., N is the basis function of the 5 th-order B spline curve.

Obtaining the coordinates of the control points:

this results in a 5-th-order B-spline curve S (u), u ∈ [0,1], as shown by the solid line in FIG. 3.

Setting B spline interpolation iteration number N_int＝0。

Second, collision detection

According to unmanned aerial vehicle's three-dimensional model, set up unmanned aerial vehicle ball and be four rotor unmanned aerial vehicle's minimum external ball, as 2 show, the radius is 1.

According to the task space obstacle, the obstacle surface is set to be two planes of-1 and 15, the coordinates of the sphere center of the obstacle sphere are set to be [10,10,3], [0,7,10], [1,6,12], and the radius is 5,2, 2. The obstacle surface and the obstacle ball are shown in fig. 3.

Discretizing the path curve S (u) by the parameter step size du being 0.01 to obtain a series of discrete path points S (u)_i). And calculating the distance between the unmanned plane ball and each obstacle surface and the obstacle ball at each discrete path point, and marking the discrete point if the unmanned plane ball collides with any obstacle surface or any obstacle ball.

And finally outputting 4 sections of curve parameter intervals with collision:

[0.01,0.05],[0.11,0.12],[0.39,0.45],[0.89,0.97]

third, generating new path interpolation points

Because the above detection has collision curve parameter interval, for each parameter interval [ u_s,i,u_e,i]I ∈ {1,2,3,4}, a new path curve interpolation point p needs to be generated_m,iAnd according to the parameter valueAnd the above-mentioned obtained path interpolation point parameter valueThe magnitude relationship between p and p_m,iAnd adding the path interpolation point into a proper position of the path interpolation point list.

Due to N_intWhen p is 0, p is generated as follows_m,i：

Take the first parameter interval [0.01,0.05] as an example, let

Setting k to 1 as initial proportion and making

To at p_m,1And (4) carrying out collision detection on the unmanned aerial vehicle ball, wherein the detection result is that no collision occurs. Due to the fact thatAt the position ofAndin between, so p_m,1Join into unmanned aerial vehicle path interpolation point p₀And p₁In the meantime.

And fourthly, interpolating the path points in the obtained new interpolation point list by using a B spline curve for 5 times by adopting the same interpolation method as the first step to obtain a new path curve S (u), wherein u belongs to [0,1 ]. Updating the iteration times of B spline interpolation:

N_int＝N_int+1＝1。

and returning to the second step to perform collision detection of the unmanned aerial vehicle.

Through multiple iterations, a collision-free path curve S (u) of the unmanned aerial vehicle is finally obtained, and u belongs to [0,1], as shown by a dotted line in FIG. 3.

The method can solve the problem of continuous non-collision path planning when a flight path point of a given task space is given, has extremely high calculation efficiency, and has important theoretical and practical significance.

Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, units provided by the present invention as pure computer readable program code, the system and its various devices, modules, units provided by the present invention can be fully implemented by logically programming method steps in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system and various devices, modules and units thereof provided by the invention can be regarded as a hardware component, and the devices, modules and units included in the system for realizing various functions can also be regarded as structures in the hardware component; means, modules, units for performing the various functions may also be regarded as structures within both software modules and hardware components for performing the method.

The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.