CN113031592A - Robot path smoothing method and system based on fifth-order Bezier curve - Google Patents
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Abstract
The invention discloses a robot path smoothing method and system based on a fifth-order Bezier curve. A robot path smoothing method based on a fifth-order Bezier curve comprises the following steps: acquiring raster map information and a broken line path connecting a starting point and a target point; setting multiple sections of fifth-order Bezier curves according to the broken line path, wherein each section of fifth-order Bezier curve is a fifth-order polynomial, six control points of each section of fifth-order Bezier curve are used as optimization variables, the smoothness of each section of fifth-order Bezier curve is used as an optimization target, and linear equality constraint conditions and linear inequality constraint conditions are established; and solving by adopting a quadratic programming algorithm to obtain an optimal smooth path connecting the starting point and the target point. According to the invention, on the basis of a broken line path, a convex optimization model based on a fifth-order Bezier curve is established, a quadratic programming algorithm is designed to carry out fast optimization to obtain a smooth path, the calculation amount in the whole process is small, the accuracy is high, and the stability of the robot motion is ensured.
Description
Technical Field
The invention relates to the technical field of mobile robots, in particular to a robot path smoothing method and system based on a fifth-order Bezier curve.
Background
The mobile robot technology is a key technology and an important driving force in the national industrialization and informatization process, and is widely applied to the fields of agricultural production, ocean development, social services, entertainment, transportation, medical rehabilitation, aerospace, national defense, universe exploration and the like. Therefore, various technologies related to mobile robots have attracted intensive research by researchers in various countries. The mobile robot has the ability of sensing environmental information and self state to complete complex tasks in the environment with static and dynamic obstacles. In the navigation process, the mobile robot accurately models the surrounding environment, realizes self positioning, plans a global path from a starting point to a target point and dynamically responds to a local track of environmental change in real time. Among these studies, mobile robot navigation technology is one of the most interesting issues. The mobile robot moves from a starting point to a target point without leaving global path planning, wherein the global path planning refers to finding an optimal or near optimal path from the starting point to the target point and avoiding obstacles according to certain performance indexes, such as minimum working cost, shortest walking route, shortest walking time and the like. The smooth path planning of the mobile robot means that a smooth path which is connected with a starting point and a target point and avoids obstacles is planned on the basis of the global broken line path according to the smoothness index. In recent years, many scholars have studied the path planning problem of mobile robots, and classical path planning methods include graph search-based and sampling-based planning algorithms, which are currently widely adopted. However, the problem of low efficiency in a complex and large environment generally exists, and the obtained path is generally a broken line path and the tangent direction is discontinuous. The broken line path can obtain a smooth path through curve interpolation. Curve interpolation is defined as the process of constructing and inserting a new set of waypoints from a known set of reference waypoints, i.e., generating a smoother path. Different curve interpolation algorithms adopt different path smoothing and curve generation technologies, and common methods include line segments, arcs, clothoids, polynomial curves, Bezier curves, spline curves and the like.
Some researchers apply intelligent bionic algorithms such as a genetic algorithm, an ant colony algorithm, a particle swarm algorithm, a simulated annealing algorithm and the like to the global path planning research of the mobile robot, and a great deal of results are obtained. While the feasibility of these intelligent algorithms has been proven, they are generally only effective in solving certain types of problems, they focus more on the optimality of the solution and ignore the efficiency of the algorithm.
Disclosure of Invention
In order to solve the technical problems, the invention provides a robot path smoothing method and system based on a fifth-order Bezier curve, and the technical scheme of the invention is as follows:
a robot path smoothing method based on a fifth-order Bezier curve comprises the following steps:
s1 obtaining raster map information and a broken line path connecting the starting point and the target point;
s2, setting multiple sections of fifth-order Bezier curves according to the broken line path, wherein each section of fifth-order Bezier curve is a fifth-order polynomial, six control points of each section of fifth-order Bezier curve are used as optimization variables, the smoothness of each section of fifth-order Bezier curve is used as an optimization target, and linear equality constraint conditions and linear inequality constraint conditions are established;
s3, solving by adopting a quadratic programming algorithm to obtain an optimal smooth path connecting the starting point and the target point.
Preferably, the grid map information includes a distance map and a map origin coordinate.
Preferably, the distance map contains distance information of each grid from the obstacle.
Preferably, after receiving the polyline path connecting the starting point and the target point, the method further includes the following steps: judging whether the broken line path is newly generated, if so, preprocessing the path point, and entering the step S2; otherwise, the method continues to wait for receiving the broken line path.
Preferably, the step S2 specifically includes the following steps:
and setting a multi-section fifth-order Bezier curve according to the broken line path, wherein the ith section fifth-order Bezier curve equation is expressed as:
wherein the parameter ui∈[0，1]The six control points include a path start point p0End point p5And four intermediate control points p arranged between the starting point and the end point in sequence from the starting point to the end point1、p2、p3And p4(ii) a Two endpoints S of the Bezier curvei(0)、Si(1) The position, the first derivative, the second derivative and the control point of (1) satisfy the following relations:
Si(0)＝P0 Si(1)＝P5
S′i(0)＝5(P1-P0) S′i(1)＝5(P5-P4)
S″i(0)＝20(P0-2P1+P2) S″i(1)＝20(P3-2P4+P5)
the optimization variables for designing the fifth-order Bezier curve are as follows:
wherein, the total number of variables is 12 xM, wherein M is the number of curve segments, and the state is composed of 6 control points:
the i-th bezier curve can be rewritten as: si(ui)＝QT(ui)XiWherein, in the step (A),
the smoothness of the fifth order bezier curve is designed as an optimization target:
wherein k is1And k2Are the weighting coefficients of the second and third derivatives respectively,
establishing a linear equation constraint condition:
Si(1)＝Si+1(0)
S′i(1)＝S′i+1(0)
S″i(1)＝S″i+1(0)
establishing a linear inequality constraint condition:
wherein j is 0, 1, 5, Ri0，Ri1，Ri2，Ri3The four endpoints of the rectangular bounding box.
Preferably, the rectangular bounding box is generated by expanding straight line segments in the polygonal line path until the straight line segments intersect with an obstacle.
A five-order bezier curve based smooth path planning system for a robot path, the system comprising:
the information acquisition module is used for acquiring raster map information and a broken line path connecting a starting point and a target point, and generating an initial distance map according to the raster map information;
the global broken line path preprocessing module is used for carrying out data processing on the broken line path and extracting information required by the path smoothing algorithm module;
and the smooth path planning module is used for establishing a convex optimization mathematical model for path smoothing and generating an optimal smooth path by using a quadratic planning solver.
Preferably, the system further comprises:
the image updating module is used for acquiring laser data and updating the initial distance map according to the laser data to obtain a real-time updated distance map;
and the broken line path updating module is used for updating the broken line path according to the real-time updated distance map and sending the updated broken line path to the global broken line path preprocessing module.
Based on the technical scheme, the invention has the beneficial effects that: according to the invention, on the basis of a broken line path, a convex optimization model based on a fifth-order Bezier curve is established, and a quadratic programming algorithm is designed to carry out rapid optimization to obtain a smooth path. The smooth path is represented by a segmented fifth-order Bezier curve, and the method has the following advantages: 1. the property of each section of curve is determined by six control points, so that the path planning problem can be converted into a parameter optimization problem, and the calculation amount is small; 2. the tangent direction and the curvature at the joint of the two curves are continuous, so that the stability of the robot motion is ensured.
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The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
FIG. 1: the invention relates to a robot path smoothing method flow chart based on a fifth-order Bezier curve;
FIG. 2: the invention relates to a Bezier curve schematic diagram in a robot path smoothing method based on a fifth-order Bezier curve;
FIG. 3: the invention relates to a grid map in a robot path smoothing method based on a fifth-order Bezier curve;
FIG. 4: the invention relates to a robot path smoothing method based on a fifth-order Bezier curve, which is a global broken line path;
FIG. 5: the invention relates to a rectangular constraint frame in a robot path smoothing method based on a fifth-order Bezier curve;
FIG. 6: the invention relates to an optimal smooth path in a robot path smoothing method based on a fifth-order Bezier curve.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
Example one
As shown in fig. 1 to 6, the robot path smoothing method based on the fifth-order bezier curve of the present invention is further described by taking the global smooth path planning of the mobile robot in the company indoor environment as an example, and includes the following specific steps:
acquiring grid map information as shown in fig. 3, the black part indicates that the grid is occupied, there is an obstacle, the white part indicates that the grid is free, there is no obstacle, the resolution is 5cm, and the origin coordinates are [ -10.01, -12.31,0.0 ]. Then, a distance map can be obtained according to the map, namely the distance between each grid and the nearest obstacle is obtained;
receiving a broken line path connecting the starting point and the target point, judging whether the path is newly generated, if so, preprocessing the path point, then entering a path smoothing program, and if not, continuously waiting for receiving the broken line path. As shown in FIG. 4, a new polyline path is received.
Setting a multi-segment fifth-order Bezier curve according to the broken-line path, wherein the schematic diagram of the Bezier curve is shown in FIG. 2, and the control point on the plane comprises two coordinates of x and y, which are expressed as
The ith stage fifth order bezier curve equation is expressed as:
wherein the parameter ui∈[0，1]As shown in FIG. 2, the six control points include a path start point p0End point p5And four intermediate control points p arranged between the starting point and the end point in sequence from the starting point to the end point1、p2、p3And p4；
Two endpoints S of the Bezier curvei(0)、Si(1) The position, the first derivative, the second derivative and the control point of (1) satisfy the following relations:
Si(0)＝P0 Si(1)＝P5
S′i(0)＝5(P1-P0) S′i(1)＝5(P5-P4)
S″i(0)＝20(P0-2P1+P2)S″i(1)＝20(P3-2P4+P5)
the optimization variables for designing the fifth-order Bezier curve are as follows:
wherein, the total number of variables is 12 xM, wherein M is the number of curve segments, and the state is composed of 6 control points:
the i-th bezier curve can be rewritten as: si(ui)＝QT(ui)XiWherein, in the step (A),
the smoothness of the fifth order bezier curve is designed as an optimization target:
wherein k is1And k2Are the weighting coefficients of the second and third derivatives, respectively, from which S ″', can be deducedi(ui)、S″′i(ui)，
In order to meet the conditions of continuity and smoothness at the end points of two adjacent curves, a linear equation constraint condition is established:
Si(1)＝Si+1(0)
S′i(1)＝S′i+1(0)
S″i(1)＝S″i+1(0)
in order to avoid collision between the fifth-order Bezier curve and the obstacle, a linear inequality constraint condition is established according to an input distance graph rectangular constraint frame and a control point required to be in the rectangular constraint frame:
wherein j is 0, 1, 5, Ri0，Ri1，Ri2，Ri3The four endpoints of the rectangular bounding box are shown in fig. 5, and the rectangular bounding box is generated by continuously expanding straight line segments in the broken line path until the straight line segments intersect with the obstacle;
the quadratic programming algorithm is used for solving, and an optimal smooth path connecting the starting point and the target point is obtained, as shown in fig. 6.
Example two
A robot path smooth path planning system based on a fifth-order Bezier curve comprises:
the information acquisition module is used for acquiring raster map information and a broken line path connecting a starting point and a target point, and generating an initial distance map according to the raster map information;
the global broken line path preprocessing module is used for carrying out data processing on the broken line path and extracting information required by the path smoothing algorithm module;
and the smooth path planning module is used for establishing a convex optimization mathematical model for path smoothing and generating an optimal smooth path by using a quadratic planning solver.
In this embodiment, a robot path smooth path planning system based on a fifth-order bezier curve further includes:
the image updating module is used for acquiring laser data and updating the initial distance map according to the laser data to obtain a real-time updated distance map;
and the broken line path updating module is used for updating the broken line path according to the real-time updated distance map and sending the updated broken line path to the global broken line path preprocessing module.
The above description is only a preferred embodiment of the robot path smoothing method and system based on the fifth-order bezier curve disclosed in the present invention, and is not intended to limit the scope of the embodiments of the present disclosure. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the embodiments of the present disclosure should be included in the protection scope of the embodiments of the present disclosure.
The systems, devices, modules or units illustrated in the above embodiments may be implemented by a computer chip or an entity, or by a product with certain functions. One typical implementation device is a computer. In particular, the computer may be, for example, a personal computer, a laptop computer, a cellular telephone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.
Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The embodiments in the present specification are all described in a progressive manner, and the same and similar parts among the embodiments can be referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the system embodiment, since it is substantially similar to the method embodiment, the description is simple, and for the relevant points, reference may be made to the partial description of the method embodiment.
Claims (8)
1. A robot path smoothing method based on a fifth-order Bezier curve is characterized by comprising the following steps:
s1 obtaining raster map information and a broken line path connecting the starting point and the target point;
s2, setting multiple sections of fifth-order Bezier curves according to the broken line path, wherein each section of fifth-order Bezier curve is a fifth-order polynomial, six control points of each section of fifth-order Bezier curve are used as optimization variables, the smoothness of each section of fifth-order Bezier curve is used as an optimization target, and linear equality constraint conditions and linear inequality constraint conditions are established;
s3, solving by adopting a quadratic programming algorithm to obtain an optimal smooth path connecting the starting point and the target point.
2. The method of claim 1, wherein the grid map information comprises a distance map and map origin coordinates.
3. The method of claim 2, wherein the distance map comprises distance information of each grid from an obstacle.
4. The method of claim 1, wherein after receiving the polygonal line path connecting the start point and the target point, the method further comprises the following steps:
s12, judging whether the broken line path is newly generated, if yes, preprocessing the path point, and entering the step S2; otherwise, the method continues to wait for receiving the broken line path.
5. The robot path smoothing method based on fifth-order bezier curve according to claim 1, wherein the step S2 specifically includes the following steps:
and setting a multi-section fifth-order Bezier curve according to the broken line path, wherein the ith section fifth-order Bezier curve equation is expressed as:
wherein the parameter ui∈[0，1]The six control points include a path start point p0End point p5And four intermediate control points p arranged between the starting point and the end point in sequence from the starting point to the end point1、p2、p3And p4；
Two endpoints S of the Bezier curvei(0)、Si(1) The position, the first derivative, the second derivative and the control point of (1) satisfy the following relations:
Si(0)＝P0 Si(1)＝P5
S′i(0)＝5(P1-P0) S′i(1)＝5(P5-P4)
S″i(0)＝20(P0-2P1+P2) S″i(1)＝20(P3-2P4+P5)
the optimization variables for designing the fifth-order Bezier curve are as follows:
wherein, the total number of variables is 12 xM, wherein M is the number of curve segments, and the state is composed of 6 control points:
the i-th bezier curve can be rewritten as: si(ui)＝QT(ui)XiWherein, in the step (A),
the smoothness of the fifth order bezier curve is designed as an optimization target:
wherein k is1And k2Are the weighting coefficients of the second and third derivatives respectively,
establishing a linear equation constraint condition:
Si(1)＝Si+1(0)
S′i(1)＝S′i+1(0)
S″i(1)＝S″i+1(0)
establishing a linear inequality constraint condition:
wherein j is 0, 1, 5, Ri0，Ri1，Ri2，Ri3The four endpoints of the rectangular bounding box.
6. The method of claim 5, wherein the rectangular bounding box is generated by expanding straight line segments in the polygonal line path until the straight line segments intersect with an obstacle.
7. A robot path smooth path planning system based on a fifth-order Bezier curve is characterized by comprising:
the information acquisition module is used for acquiring raster map information and a broken line path connecting a starting point and a target point, and generating an initial distance map according to the raster map information;
the global broken line path preprocessing module is used for carrying out data processing on the broken line path and extracting information required by the path smoothing algorithm module;
and the smooth path planning module is used for establishing a convex optimization mathematical model for path smoothing and generating an optimal smooth path by using a quadratic planning solver.
8. The system for planning a smooth path of a robot path based on a fifth-order bezier curve according to claim 7, further comprising:
the image updating module is used for acquiring laser data and updating the initial distance map according to the laser data to obtain a real-time updated distance map;
and the broken line path updating module is used for updating the broken line path according to the real-time updated distance map and sending the updated broken line path to the global broken line path preprocessing module.
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