KR20230140131A - Local path planning method based on bezier curve using spiral optimization and golden section search - Google Patents

Abstract

The present invention relates to a local route planning method based on a Bezier curve using a spiral optimization technique and a golden section search technique. The optimized third-order Bezier curve can be used to create a route that enables satisfactory autonomous driving even in a complex environment. It's about technology.

Description

Local path planning method based on bezier curve using spiral optimization and golden section search}

The present invention relates to a local route planning method based on a Bézier curve using a spiral optimization technique and a golden section search technique. More specifically, a method of planning a local route based on a Bézier curve using a spiral optimization technique and a golden section search technique is used in combination with the spiral optimization technique and the golden section search technique based on the results of regional route planning. It is about technology that can optimize cubic Bezier curves.

This study is about a local route planning method based on Bezier curves using spiral optimization and golden section search techniques that can generate routes that enable satisfactory autonomous driving even in complex environments through these optimized cubic Bezier curves.

Unmanned mobility systems such as mobile robots, drones, and unmanned cars are continuously evolving. Due to this continuous development, unmanned vehicles are providing services such as transportation and guidance in the service field. Additionally, in the industrial field, it is used to replace tasks that are dangerous for humans to perform directly, such as monitoring and surveying a wide area or inspecting hazardous facilities.

Autonomous technologies are largely environmental recognition technology that recognizes environmental conditions such as the location of the moving object and surrounding obstacles, path planning technology that creates a path to the destination based on the recognized location and obstacle information, and generated path (speed, posture) It is divided into control technologies to follow.

Among these, path planning technology considers various variables depending on the object and environment to be controlled and creates the optimal path under given conditions. Depending on the stage, it is divided into global path planning (GPP) and local path planning (LPP). Local Path Planning).

Wide-area route planning is a technology that creates a relatively long distance route in the form of a simple route, and creates a route to the final destination where the unmanned vehicle ultimately needs to travel based on map information obtained in advance.

Local route planning is a technology that generates a local route by avoiding static/dynamic obstacles that cannot be considered in wide-area route planning and considering the dynamics/kinematic constraints of the moving object. At this time, recognition of obstacles located around the moving object is required, so a map is created based on the installed sensor, and a path is created considering the generated map.

Generally, wide-area route planning for unmanned vehicles is performed based on graphs or grid maps. The algorithm for finding the shortest distance based on a graph is based on the Dijkstra algorithm and the A* algorithm, and neighboring nodes are included in the tree in order of the closest path calculated to date. If the final goal point is included in the tree, the final path is created by going backwards up the tree. In addition, route planning based on a grid map is limited to 8 directions (up, down, left, right and diagonal) based on the central node, and depending on the size of the grid map, it may be difficult to create an efficient route because it includes a large number of unnecessary nodes. . To solve this problem, algorithms that combine LOS (Line of Sight) with path planning through Bresenham's line algorithm are being proposed.

Recently, a route planning technique using Bezier curves has been proposed. Bezier curves are used in many path planning techniques because the curve equation is derived in the form of a polynomial from a number of control points in two dimensions, and in the case of Bezier curves of degree 3 or higher, the curvature is also derived in the form of a continuous polynomial.

However, most path planning techniques using conventional Bézier curves only consider curvature conditions when generating Bézier curves, and the location of the middle control point of the Bézier curve is fixed because it is derived from the angle between wide path points. A Bezier curve with the specified angle value is created. Accordingly, the shape of the curve is fixed, and in some environments, there is a problem in that it is not possible to create a path that takes obstacles into account.

Domestic Public Patent No. 10-2020-0037738 (publication date 2020.04.09.)

The present invention was developed to solve the problems of the prior art as described above. In the case of a path planning technique using a conventional Bezier curve, an appropriate path is achieved in a complex obstacle environment due to control point angle restrictions in generating the Bezier curve. In order to solve the impossibility of generating It provides a Bezier curve-based regional route planning method using spiral optimization techniques and golden section search techniques that can generate drivable routes.

A local route planning method based on a Bezier curve using a spiral optimization technique and a golden section search technique in which each step is performed by an arithmetic processing means including a computer according to an embodiment of the present invention, which is an existing wide-area route planning technique. A global path point application step (S100) in which at least two global path points generated by (GPP, Global Path Planning) are input and some of the initial control points of the cubic Bezier curve are set (S100), spiral optimization Using the technique, the remaining initial control points are set with the condition that the corresponding Bezier curve continues through the initial control point set in the wide area path point application step (S100), and the corresponding control points for each Bezier curve are set. SPO particle creation step (S200) for generating a number of particles containing parameters, cost calculation step (S300) for calculating the cost for each particle through a pre-stored cost function, and calculation results by the cost calculation step (S300). Using the center particle setting step (S400), which sets the particle with the lowest cost as the center particle, the particles are rotated around the set center particle and all remaining particles are rotated based on a preset equation. Calculate the particle rotation step (S500) of performing the update and the distance between the particles rotated by the particle rotation step (S500) and the center particles, and if it is less than a preset value, determine it as an end condition for local path planning. , It is desirable to include an optimization parameter derivation step (S600) that sets the corresponding center particle as the parameter of the optimized Bezier curve and applies it to the local path planning (LPP) technique.

Furthermore, the cubic Bezier curve is a curve composed of a plurality of Bezier curves, and each Bezier curve is defined by the coordinates of four control points. In the global path point application step (S100), the starting point of each Bezier curve is It is desirable to set control point No. 1 and control point No. 4, which is the end point, and set control point No. 2 and control point No. 3, considering control point No. 1 and control point No. 4 for each Bezier curve in the SPO particle creation step (S200). do.

Furthermore, the SPO particle creation step (S200) uses the position coordinates of the four control points set for each Bezier curve to specify the positional relationship between the four control points and the positional relationship between the obstacle and the four control points. It is desirable to create parameters.

Furthermore, the Bezier curve-based local path planning method using the spiral optimization technique and the golden section search technique, after performing the SPO particle creation step (S200), uses the golden section search technique to It is desirable to further include a GSS optimization step (S210) in which optimization is performed on one parameter selected from among a plurality of parameters included in particles generated for each curve.

Furthermore, the particle rotation step (S500) preferably performs particle update through rotation of all remaining particles around the set center particle, so that the position coordinates of control points of all remaining particles are moved.

Furthermore, the optimization parameter derivation step (S600) calculates the distance between the center particle and the particle whose position coordinates are moved by being rotated by the particle rotation step (S500) to determine the end condition of the local path plan. If one distance value exceeds a preset predetermined value, it is preferable to repeat the cost calculation step (S300) using the center particle and the particle whose position coordinates have been moved.

The Bezier curve-based local path planning method using the spiral optimization technique and the golden section search technique of the present invention according to the above configuration takes into account not only the curvature but also the distance to obstacles in order to plan a route passing through a narrow passage. By adding optimization to the function, it is possible to create an efficient local route plan.

In addition, by adding the angles formed by the control points as optimization parameters and performing optimization, it is possible to create better local route plans under various environmental conditions.

Figure 1 is a sequence diagram showing a Bezier curve-based local path planning method using a spiral optimization technique and a golden section search technique according to an embodiment of the present invention.
Figures 2 and 3 show a local route planning method based on a Bezier curve using a spiral optimization technique and a golden section search technique according to an embodiment of the present invention, which is set by the global route point application step and the SPO particle creation step. This is an example diagram showing the control points of a Bezier curve.
Figure 4 is an example diagram showing particle parameter optimization set by the GSS optimization step in the Bezier curve-based local path planning method using the spiral optimization technique and the golden section search technique according to an embodiment of the present invention.
Figure 5 shows a Bezier curve in the process of calculating the cost for each particle by the cost calculation step in the Bezier curve-based local path planning method using the spiral optimization technique and the golden section search technique according to an embodiment of the present invention. This is an example diagram showing how to check the distance to an obstacle.

Hereinafter, the Bezier curve-based regional path planning method using the spiral optimization technique and the golden section search technique of the present invention will be described in detail with reference to the attached drawings. The drawings introduced below are provided as examples so that the idea of the present invention can be sufficiently conveyed to those skilled in the art. Accordingly, the present invention is not limited to the drawings presented below and may be embodied in other forms. Additionally, like reference numerals refer to like elements throughout the specification.

At this time, if there is no other definition in the technical and scientific terms used, they have the meaning commonly understood by those skilled in the art to which this invention pertains, and the gist of the present invention is summarized in the following description and attached drawings. Descriptions of known functions and configurations that may be unnecessarily obscure are omitted.

In addition, a system refers to a set of components including devices, mechanisms, and means that are organized and interact regularly to perform necessary functions.

As described above, path planning technology considers various variables depending on the object and environment to be controlled and creates an optimal path under given conditions. Depending on the stage, it is divided into global path planning (GPP) and regional path planning (GPP). It is divided into LPP (Local Path Planning).

The optimization-based route planning method, which is one of the local route planning techniques, represents the route creation method with a number of optimization parameters, and is performed by deriving the parameter that minimizes the cost function defined through an optimization algorithm. To achieve this, an optimization algorithm and a method for generating a path using relatively few parameters are required.

Spiral Optimization (SPO) is one of the meta-heuristic optimization techniques. It is an algorithm that does not use the differential value of the optimization target and can be generally optimized regardless of the optimization target.

This spiral optimization technique scatters random optimization parameters in the form of particles, and optimization proceeds by rotating around the particle with the lowest cost function.

A Bezier curve is a curve defined through a polynomial derived from a number of n control points. In the case of a Bezier curve of degree 2 or higher, the calculation of curvature is also derived by a polynomial, and is continuous and relatively easy to obtain. There is an advantage.

Even when creating a piecewise Bezier curve connecting multiple Bezier curves, there is an advantage in maintaining continuity if only simple conditions are met.

However, as described above, when using this for actual route planning, it is not easy to position each control point to generate a curve that takes into account wind conditions, obstacle avoidance, etc. In particular, it is not easy to ensure that the generated curve does not collide with obstacles. It is difficult to guarantee that

Accordingly, in the case of most Bézier curve-based path planning techniques, rather than using optimization techniques, optimization-based path planning is performed considering only some constraints such as curvature conditions under the condition of maintaining a sufficient safety distance, or determinism is performed within the safety distance. It is used in a limited way, such as performing path planning by defining rules for creating control points.

Considering this, the Bezier curve-based local path planning method using the spiral optimization technique and the golden section search technique according to an embodiment of the present invention is a Bezier curve optimized using the spiral optimization technique and the golden section search technique. It is about a curve-based regional route planning technique.

At this time, the spiral optimization technique has the advantage of being simple compared to other meta-heuristic techniques, making it easy to manage the code, and having performance similar to other algorithms. In addition, since all particles are moved based on the center particle, which is the particle with the lowest cost function, at each step using the convergence rate r value, there is an advantage in ensuring convergence at all times.

In summary, the Bezier curve-based regional path planning method using the spiral optimization technique and the golden section search technique according to an embodiment of the present invention consists of piecewise Bezier curve generation and GSS and SPO algorithms, and the cost under given conditions is The technical purpose is to create a curve that minimizes the function.

Here, the piecewise Bezier curve is a curve composed of multiple Bezier curves, and in the present invention, a cubic curve is used as each Bezier curve. In order to obtain an optimized Bezier curve, you must also specify which variables should be adjusted. A cubic Bezier curve is created from four control points, and the optimization parameters that can create four control points are defined as three variables, Φ, d _p , and d _o , and the optimization algorithm is Φ, d _p that minimizes the cost function. and d _o are found.

Figure 1 is a sequence diagram showing a Bezier curve-based local path planning method using a spiral optimization technique and a golden section search technique according to an embodiment of the present invention. With reference to Figure 1, a Bezier curve-based local path planning method using a spiral optimization technique and a golden section search technique according to an embodiment of the present invention will be described in detail.

The Bezier curve-based local path planning method using the spiral optimization technique and the golden section search technique according to an embodiment of the present invention is a technology in which each step is performed by an arithmetic processing means including a computer, and is shown in FIG. 1 As described above, the wide-area path point application step (S100), the SPO particle creation step (S200), the cost calculation step (S300), the center particle setting step (S400), the particle rotation step (S500), and the optimization parameter derivation step (S600). It is desirable to be configured to include.

To briefly summarize the Bezier curve-based local path planning method using the spiral optimization technique and the golden section search technique according to an embodiment of the present invention, the optimized SPO particle is a multidimensional vector consisting of Φ, d _p , and d _o . Therefore, a large number of particles are required for SPO optimization. Multiple particles are randomly generated from initial values.

After particle creation, GSS inside SPO performs optimization for d _p , and SPO performs optimization for Φ and d _p .

That is, Φ, d _p are first generated through SPO, and then d _p is optimized through GSS. After calculating the entire cost function, the center particle that generates the smallest cost function is selected, and all particles rotate around the center particle, resulting in one cycle of the overall SPO.

To learn more about each step,

In the global path point application step (S100), the calculation processing means receives at least two global path points generated by a global path planning technique (GPP, Global Path Planning) in advance, and generates a cubic Bezier curve (piecewise). This sets some of the initial control points of the Bezier curve.

At this time, as an example of at least two wide-area route points by a wide-area route generated by a wide-area route planning technique inputted in the wide-area route point authorization step (S100), the RPF-based wide-area route planning algorithm A wide area route is possible.

In detail, the RPF-based wide-area route planning algorithm is a technique that generates a route using the edges of obstacles as feature points. It repeatedly performs the process of searching the edge of obstacles in the map, creating nodes, and confirming LOS (Line Of Sight) with nodes. I do it. This RPF algorithm assumes that the direction change point for creating the shortest distance on a 2D map is always located at the edge of the obstacle. The main concept of the RPF algorithm is to detect the edge of the obstacle from the grid map and connect the detected node and the existing It can be summarized as creating a path by checking the LOS between trees.

The SPO particle creation step (S200) uses a spiral optimization technique (SPO, Spiral Optimization) in the calculation processing means to create a corresponding Bezier curve through the initial control point set in the wide-area path point application step (S100). The remaining initial control points with consecutive conditions are set, and a number of paricles containing the parameters of the corresponding control points for each Bezier curve are created.

That is, as described above, a cubic Bézier curve is a curve composed of multiple Bézier curves, and each Bézier curve is defined by four control point coordinates.

In the global path point application step (S100), control point No. 1, which is the starting point of each Bezier curve, and control point No. 4, which is the end point (destination), are set, and in the SPO particle creation step (S200), control point No. 1 is set for each Bezier curve. Taking control points 2 and 4 into consideration, control points 2 and 3 are set.

First, the cubic Bezier curve is defined using the coordinates of four control points and the parameter t, which is expressed in Equation 1 below.

)(

)

t is defined as a real number in the range of 0 to 1, and returns the coordinates on the Bezier curve through P(t). Therefore, the Bezier curve-based local path planning method using the spiral optimization technique and the golden section search technique according to an embodiment of the present invention ultimately finds the optimal P1, P2, P3, and P4 that minimize the cost function. . Once we find the optimal P1, P2, P3, and P4, we can use a random t to generate all path points in the range.

In detail, for path planning through optimization techniques, the control points of the Bezier curve must be divided into several optimization parameters. At this time, the position of the control point of the Bezier curve can be indicated through the condition that the cubic Bezier curve is continuous.

Figure 2 shows the conditions under which the front and back curves in this third-order Bezier curve will continue to each other. Figure 2a) represents one Bezier curve, and Figure 2b) is two curves connected.

는 상기 광역 경로점 인가 단계(S100)에 의해 입력받은 광역 경로 계획의 한 점 위에 생성되며

는 상기 SPO 파티클 생성 단계(S200)에 의해

로부터 일정거리 만큼 떨어진 위치에 생성된다. 이때, 도 2의 b)와 같이 인접한 두 곡선이 서로 연속적이기 위해서는 k번째 곡선의

제어점과 k+1번째 곡선의

제어점은 같은 위치에 존재하여야 하며,

는 같은 직선상에 위치하여야 한다.In detail, in a) of Figure 2

is created on a point of the wide-area route plan input by the wide-area route point authorization step (S100),

By the SPO particle creation step (S200)

It is created at a certain distance away from . At this time, in order for two adjacent curves to be continuous, as shown in b) of Figure 2, the kth curve

Control point and k+1th curve

Control points must exist at the same location,

must be located on the same straight line.

제어점인 시작점과 도착점이 광역 경로점 위에 생성되므로

제어점의 위치를 알 수 있으며,

제어점의 경우, 3차 베지어 곡선(piecewise bezier curve)이 연속하게 이어질 조건에 따라서

를 지나는 직선 상에 높이게 되므로

의 위치를

를 중심으로 하는 극 좌표계를 통해 나타낼 수 있다.

Since the starting point and destination point, which are control points, are created on the wide route point,

You can know the location of the control point,

In the case of control points, according to the condition that the cubic Bezier curve (piecewise Bezier curve) continues continuously,

Because it is raised on a straight line passing through

location of

It can be expressed through a polar coordinate system centered on .

Through this, as shown in FIG. 3, a control point position expression can be displayed.

에서 각도

,

점으로부터 떨어진 거리

를 통해 나타낼 수 있다. In detail,

angle from

,

distance from point

It can be expressed through .

이 장애물로부터 떨어진 거리를 나타낼 필요가 있다.Additionally, in the present invention, the curve considers the distance away from the obstacle, so the control point

We need to indicate the distance away from this obstacle.

라 할 때, 하나의 베지어 곡선 생성을 위한 파라미터는

의 3가지 파라미터가 되며, 다수의 곡선을 연결할 때는 3n개의 파라미터가 생성되게 된다.This

In this case, the parameters for creating one Bezier curve are

There are three parameters, and when connecting multiple curves, 3n parameters are created.

는 각각

제어점과 직선이 이루는 각도,

제어점이 장애물로부터 떨어진 거리,

제어점이

제어점으로부터 떨어진 거리를 나타내며, 광역 경로점을

라 할 때,

는 하기의 수학식 2와 같이 정의된다. That is, as shown in Figure 3,

are respectively

The angle between the control point and the straight line,

The distance the control point is from the obstacle,

control point

Indicates the distance from the control point and represents the wide route point.

When you say,

is defined as Equation 2 below.

(Here, the rotation matrix Is lim.)

Accordingly, the variable that generates the Bezier curve is It is defined as , and when creating a path by connecting j arbitrary Bezier curves, a total of 3j variables are required.

Meanwhile, for optimization It is necessary to set the initial value of . The initial value of is set as half the angle formed by the kth global path point and the k+1th global path point, The initial value of is initialized to 0. The two values are the distance to the obstacle and Since it indicates the location of the control point, it is initialized to 0 to be the same as the global route point, and increases as optimization progresses.

The SPO particle creation step (S200) uses the positional coordinates of the four control points set for each Bezier curve through the above-described process to specify the positional relationship between the four control points and the positional relationship between the obstacle and the four control points. Multiple parameters are created.

In other words, the SPO technique in the SPO particle generation step (S200) is an algorithm that performs optimization based on particles, and generates a number of particles at the start of the optimization process. The particles are It consists of as many as the number of Bezier curves. exists, and is defined as Equation 3 below.

M particles as in Equation 3 above are generated, and SPO generates particles based on randomness. This is because the center particle is selected and updated based on the difference in the initial value of the particle, and optimization is carried out. Therefore, each particle contains a certain level of random value from the initial value.

As shown in Figure 1, the Bezier curve-based local path planning method using the spiral optimization technique and the golden section search technique according to an embodiment of the present invention is performed after performing the SPO particle creation step (S200). , the GSS optimization step (S210) is further performed.

The GSS optimization step (S210) uses the Golden Section Search (GSS) technique to optimize one parameter selected among a number of parameters included in the particles generated for each Bezier curve. do.

First, let's look at the golden section search technique. It is an optimization algorithm that mainly optimizes one-dimensional parameters, This is an algorithm that finds the minimum value of the unimodal function.

GSS finds the extreme values of an object in a similar way to the bipartite search method, but unlike the bipartite search that divides the region based on the median value of the object, GSS divides both regions according to the golden ratio and is defined as Equation 4 below. .

here is the value for dividing x ₁ and x ₄ into the golden ratio. When the function for which the minimum value is to be sought is f(x), the golden section search calculates Equation 5 below to update the ranges x ₁ and x ₄ for the next step.

In this way, GSS repeats recursively for new areas x ₁ and x ₄ , and this is repeated until the termination condition is satisfied. Finally, the intersection value of areas x ₁ and x ₄ is returned as the optimized value.

Considering this, the GSS optimization step (S210) is used to optimize d _p . in other words Among the three parameters, only d _p is optimized using GSS, and the remaining parameters are optimized through SPO.

GSS is an optimization algorithm that runs between the intervals x ₁ and x _4. It creates two points x ₂ and x ₃ that divide x ₁ and x ₄ into the golden ratio, and is done as follows.

Figure 4a) indicates the first iteration of the GSS algorithm, and Figure 4b) indicates the second iteration.

Referring to FIG. 4, the process of performing the GSS optimization step (S210) is summarized as the following seven steps.

1. Create x ₂ , x ₃ by dividing the interval x ₁ , x ₄ by the golden ratio

2. Find the point that lowers the cost function among the two points x ₂ and x ₃ .

3. If x ₃ is lower than x ₂ , x ₂ is designated as the section x ₁ of the next iteration.

4. Conversely, if x ₂ is lower, designate x ₃ as the section x ₄ of the next iteration.

_5. Create new x ₁ and x ₄ by dividing them by _the golden ratio

6. Check termination conditions, if not met, repeat from 2

7. When the termination condition is satisfied, the midpoint of the interval x ₁ and x ₄ is output as an optimized variable.

In the cost calculation step (S300), the cost for each particle is calculated using a pre-stored cost function.

That is, the cost function for optimizing parameters consists of a total of three terms, and is shown in Equation 6 below.

Here, cost _map is the cost representing the distance to the obstacle, cost _distance is the cost due to the length of the wide path and Bezier curve, and cost _curvature is the cost due to curvature.

The cost _map is calculated by measuring the distance to surrounding obstacles from a curve generated from given parameters. As shown in Figure 5, when the point on the Bezier curve generated from the parameter t is C, the distance from C to the nearest obstacle is measured. At this time, when measuring the distance from point C to all obstacles on the map, the calculation takes a very long time, so only the distance to the obstacles within it is calculated by cutting a certain distance from point C.

Figure 5 shows a method of cutting a certain area from point C. The above calculation is performed at all C points generated by the parameter t on the Bézier curve. Therefore, point C cannot be increased indefinitely and varies depending on the design.

From one point C, the distance z to the nearest obstacle is generated. When the reciprocal of z is called x _c and the set of x _c is called X, the cost _map is obtained as shown in Equation 7 below.

Here, c represents the index value of x _c , the reciprocal of the distance to the obstacle, and it is assumed that the set X is sorted in descending order. In other words, the cost _map is calculated using the average of the largest 30% of the values of x _c stored in the set

This calculation method was established as follows because, in the case of a general average, the distance z to the nearest obstacle can be ignored, and conversely, if the minimum distance is used, the overall curve and the distance to the obstacle can be ignored.

Distance cost is cost _distance . The cost _distance is a cost that indicates how long the Bezier curve has become compared to the straight line distance of the wide-area route points. It is a term that prevents the curve from moving too far away from the existing route points, and is the distance between the wide-area route points. , the length of the bezier curve is When , it is expressed as Equation 8 below.

Next is the curvature cost am. is obtained from the curvature calculation formula of the Bezier curve and is expressed as Equation 9 below.

The coefficient of the term is as shown in Equation 10 below.

curvature is calculated using Equation 11 below.

is the curvature, as shown in Equation 12 below: It is defined as the maximum value of .

The center particle setting step (S400) uses the calculation result from the cost calculation step (S300) to set the particle with the lowest cost as the center particle.

That is, in the center particle setting step (S400), optimization of SPO begins with selecting the particle with the smallest cost function among the plurality of generated particles. In other words, the cost function is calculated for m particle parameters, and the particle that generates the smallest cost is designated as the center particle.

The particle rotation step (S500) performs particle update through rotation of all remaining particles based on a preset mathematical equation centered on the center particle set by the center particle setting step (S400).

The particle rotation step (S500) performs particle update through rotation of all remaining particles around the center particle set in the center particle setting step (S400), so that the position coordinates of the control points of all remaining particles are will be moved.

In detail, particle rotation is a process of updating the remaining particles around the center particle, and SPO updates the particles of the next iteration through rotation around the center particle. The particle rotation equation is as shown in Equation 13 below.

here, is the particle of the next iteration. silver center particle, is the particle of the current iteration.

In other words, all particles are rotated around the center particle and the convergence rate R value is multiplied so that all particles move slightly to the center particle. Represents a particle in a rotated position. indicates the position of the particle before rotation. Each particle is expressed as a two-dimensional vector. is the rotation angle.

Equation 13 above is the rotation angle This represents the rotation of a two-dimensional particle with a convergence rate during rotation. Multiply the values so that all particles move slightly towards the center particle.

If the dimension of the particle exceeds 2 dimensions, a rotation matrix such as Equation 14 below is used.

here, represents the identity matrix, and the dimension is specified as the dimension of the particle - 1 (i.e., the dimension of the rotation matrix is the same as the dimension of the particle).

SPO creates new particles through particle rotation, and selects the center particle among the new particles to continue rotation.

The optimization parameter derivation step (S600) calculates the distance between the particles rotated by the particle rotation step (S500) and the center particles, and if it is less than a preset value, determines it as an end condition for local path planning, By setting the center particle as the parameter of the optimized Bezier curve, the optimization parameters applied to the local path planning (LPP, Local Path Planning) technique are derived.

That is, the optimization parameter derivation step (S600) calculates the distance between the center particle and the particle whose position coordinates are moved by being rotated by the particle rotation step (S500) to determine the end condition of the local path plan. If the distance value exceeds a preset value, the cost calculation step (S300) is repeated using the center particle and a particle whose position coordinates have moved by rotating.

In detail, after rotating the particle, the cost function is calculated again and a new Select and the rotation is repeated. Ultimately, all particles a certain distance centered on Once they come together, optimization ends. Because Spiral Optimization uses a convergence rate R, it has the characteristic of always converging after a certain iteration.

Based on this, the termination condition is checked after particle rotation. Checking the termination condition calculates how close all particles are to each other, and the value is a certain value. If it is smaller than , the optimization algorithm ends and returns the center particle as the optimized parameter. Afterwards, the returned value is used to create a Bezier curve and the route planning is completed.

As described above, the present invention has been described with reference to specific details such as specific components and drawings of limited embodiments, but this is only provided to facilitate a more general understanding of the present invention, and the present invention is not limited to the above-mentioned embodiment. No, those skilled in the art can make various modifications and variations from this description.

Accordingly, the spirit of the present invention should not be limited to the described embodiments, and all matters that are equivalent or equivalent to the claims of this patent as well as the claims described below shall fall within the scope of the spirit of the present invention. .

Claims (6)

A local path planning method based on a Bezier curve using a spiral optimization technique and a golden section search technique in which each step is performed by computational processing means including a computer,
A global path point authorization step that receives at least two global path points generated by an existing global path planning technique (GPP) and sets some of the initial control points of the third-order Bezier curve. (S100);
Using the spiral optimization technique, the remaining initial control points are set under the condition that the corresponding Bezier curve continues through the initial control point set in the wide area path point application step (S100), and the corresponding Bezier curve for each Bezier curve is set. SPO particle generation step (S200) of generating a plurality of particles including parameters of control points;
A cost calculation step (S300) of calculating the cost for each particle through a pre-stored cost function;
A center particle setting step (S400) of setting the particle with the lowest cost as a center particle using the calculation result of the cost calculation step (S300);
A particle rotation step (S500) of performing particle update through rotation of all remaining particles based on a preset mathematical equation, centering on the set center particle; and
Calculate the distance between the particles rotated by the particle rotation step (S500) and the center particles, and if it is less than a preset value, determine it as an end condition for local path planning, and apply the corresponding center particle to an optimized Bezier curve. An optimization parameter derivation step (S600) set as a parameter and applied to a local path planning (LPP) technique;
A Bezier curve-based local path planning method using a spiral optimization technique and a golden section search technique, including.
According to clause 1,
The cubic Bezier curve is a curve composed of multiple Bezier curves, and each Bezier curve is defined by the coordinates of four control points,
In the wide area route point authorization step (S100),
Set control point 1, which is the starting point of each Bezier curve, and control point 4, which is the ending point,
In the SPO particle creation step (S200),
A Bezier curve-based regional path planning method using spiral optimization and golden section search techniques to set control points 2 and 3 by considering control points 1 and 4 for each Bézier curve.
According to clause 2,
The SPO particle creation step (S200) is
Spiral optimization technique and golden section search that use the position coordinates of the four control points set for each Bezier curve to generate a number of parameters that specify the positional relationship between the four control points and the positional relationship between the obstacle and the four control points. Bezier curve-based regional route planning method using the technique.
According to clause 3,
The Bezier curve-based regional route planning method using the spiral optimization technique and the golden section search technique is
After performing the SPO particle creation step (S200),
A GSS optimization step (S210) of performing optimization on one parameter selected from among a plurality of parameters included in the particles generated for each Bezier curve using the golden section search technique;
A Bezier curve-based local path planning method using a spiral optimization technique and a golden section search technique, further comprising:
According to clause 1,
The particle rotation step (S500) is
Centering on the set center particle, particle update is performed through the rotation of all remaining particles, and the position coordinates of the control points of all remaining particles are moved, based on a Bezier curve using a spiral optimization technique and a golden section search technique. Local route planning method.
According to clause 5,
The optimization parameter derivation step (S600) is
Calculate the distance between the center particle and the particle whose position coordinates are moved by being rotated by the particle rotation step (S500) to determine the end condition of the local path plan,
If the calculated distance value exceeds a preset value, a spiral optimization technique and a golden section search technique are used to repeatedly perform the cost calculation step (S300) using the center particle and the particles whose position coordinates have moved. A local route planning method based on a Bezier curve.