CN114200931A - Mobile robot path smoothing method based on B-spline curve optimization - Google Patents
Mobile robot path smoothing method based on B-spline curve optimization Download PDFInfo
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Abstract
The invention discloses a mobile robot path smoothing method based on B-spline curve optimization. The method comprises the following steps: acquiring a path output by a path planning method, taking one path point in the path as a path point to be processed, and setting a control point sequence on the current path point to be processed; setting a node vector so as to generate a B spline curve of the current path point to be processed; respectively carrying out line segment collision detection and curve collision detection on the B spline of the current path point to be processed, and adjusting a control point sequence until the path smoothing of the current path point to be processed is completed; and traversing the residual path points, and smoothing the path line segments of the residual path points to finally realize the smooth optimization of the current path. The invention improves the efficiency of the smoothing process and the performance index of the smoothed path in a B spline curve optimization mode, and realizes the excellent property of the smoothed path in the global range by a method of reserving the original path.
Description
Technical Field
The invention relates to a mobile robot path smoothing method in the field of mobile robots, in particular to a mobile robot path smoothing method based on B-spline curve optimization.
Background
It is important to provide a smooth and safe moving path for a mobile robot. The path designed by the current path planning method is often a discontinuous path formed by broken line segments, and when the robot runs along the path, the robot has to stop moving at a corner to turn, so that the moving time is increased. And there is a sudden change in curvature at these turns, which discontinuity also leads to instability of the control system and robot wear. There are currently some path smoothing methods that eliminate such path discontinuities as described above. However, these methods are often only directed at local environments or cannot ensure the safety of the smoothed path, and cannot provide a suitable path meeting the requirements of safety and continuity in the global scope for the robot.
Disclosure of Invention
The invention provides a mobile robot path smoothing method based on B-spline curve optimization to solve the technical problems. The method comprises the steps of inserting a limited number of B-spline curve control points near discontinuous path points in an original path, smoothing the original path, reserving the original path to the maximum extent so as to keep the excellent performance of the path in a global range, optimizing the path by using the properties of the B-spline curve, quickly and effectively completing the adjustment work of the original path, eliminating the discontinuity phenomenon in the path and ensuring the safety of the smoothed path.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the invention comprises the following steps:
s1: acquiring a path output by a path planning method, wherein the path comprises a starting point, a target point and each path point between the starting point and the target point;
s2: selecting a path point as a path point to be processed, setting 9 control points on two path line segments of the current path point to be processed and the current path point to be processed, wherein the 9 control points are symmetrically arranged about an angular bisector formed by the two path line segments;
s3: setting node vectors, and generating a B spline curve of the current path point to be processed by the 9 control points and the node vectors;
s4: performing line segment collision detection on the B spline curve of the current path point to be processed, if the line segment collision detection fails, moving a fourth control point and a sixth control point to a fifth control point along the corresponding path line segment, and repeating the line segment collision detection until the line segment collision detection is passed and the fourth control point and the sixth control point are fixed;
s5: moving the fifth control point to a midpoint between the fourth control point and the sixth control point along an angle bisection line formed by two path line segments, continuously performing curve collision detection on the B-spline curve generated after the control point is moved until collision occurs or the fifth control point is overlapped with the midpoint between the fourth control point and the sixth control point, fixing the fifth control point, replacing the path line segment between the first control point and the ninth control point of the current path point to be processed in S2 with the finally generated B-spline curve, and finishing path smoothing of the current path point to be processed;
s6: and traversing the residual path points, repeating the steps of S2-S5 to carry out smoothing processing on the path line segments of the residual path points, and finally realizing the smooth optimization of the current path.
In S2, a fifth control point is set at the current path point to be processed, first to fourth control points are sequentially set on one path line segment, sixth to ninth control points are sequentially set on the other path line segment, the first to fourth control points and the sixth to ninth control points are respectively and sequentially symmetrically arranged about an angle bisector formed by the two path line segments, the first and ninth control points are respectively set at the midpoints of the two path line segments, the distance between the second control point and the first control point does not exceed 1/4 of the distance between the first control point and the fifth control point, the distance between the eighth control point and the ninth control point does not exceed 1/4 of the distance between the ninth control point and the fifth control point, and the distance between the fourth control point and the fifth control point does not exceed 1/2 of the distance between the second control point and the fifth control point, the distance between the sixth control point and the fifth control point is no more than 1/2 times the distance between the eighth control point and the fifth control point.
The S4 specifically includes:
taking a line segment formed by connecting a fourth control point and a sixth control point of a current path point to be processed as a line segment collision detection area, judging whether an obstacle area exists on the line segment collision detection area, and if so, not detecting the line segment collision; and simultaneously moving the fourth control point and the sixth control point to the fifth control point along the corresponding path line segments, wherein the fourth control point and the sixth control point are symmetrically arranged around an angular bisector formed by the two path line segments all the time, repeatedly detecting a line segment collision detection area formed between the fourth control point and the sixth control point until no obstacle area exists on the line segment collision detection area, and then detecting and fixing the fourth control point and the sixth control point through line segment collision.
In S5, if an obstacle area exists on the B-spline curve generated after the control point is moved, a collision occurs, otherwise, no collision occurs.
In S5, the distance that the fifth control point moves to the midpoint between the fourth control point and the sixth control point is calculated by bisection.
And setting the repetition degrees of the first node and the last node of the node vector in the S3 as p +1, wherein p is the order of the B spline curve.
Compared with other existing path smoothing technologies, the method has the beneficial effects that:
1) as a general path processing method, the invention can adjust the path obtained by any path planning algorithm to meet the moving requirement of the robot, and in addition, the invention adopts the method of adjusting only aiming at discontinuous parts in the path, thereby retaining the characteristics of the original path to the maximum extent and maintaining the initial design targets of the original path, such as optimal energy, optimal length and the like.
2) The invention reserves the maximum length of the original path in the adjusting process so as to ensure the excellent performance of the path under the global environment, and in addition, a larger turning radius is adopted as much as possible in the adjusting process so as to reduce the curvature of the path, thereby shortening the path length and facilitating the turning of the robot.
3) The invention ensures the continuity of C1 and C2 orders at any position in the path, thereby ensuring the smoothness of the path, ensuring the continuous and smooth transition of the speed and the acceleration of the robot in the running process, improving the safety and the stability of the motion of the robot, and reducing the mechanical abrasion and the energy loss caused by the sudden change of the speed.
4) The method effectively utilizes the characteristic that the original path does not collide with the barrier, reduces collision detection and barrier avoidance work in the smoothing process, and improves the calculation speed. In addition, the strong convex hull of the B-spline curve is utilized, the control points are used for replacing the B-spline curve to carry out obstacle avoidance detection, and a large amount of calculation amount caused by carrying out obstacle avoidance detection on the B-spline curve is reduced. The robot moving path can be adjusted in time, and the requirement of the robot moving on the real-time performance of the path obtaining process is met.
Drawings
FIG. 1 is a general flow diagram of the process;
fig. 2 is a robot mobile simulation map constructed by the operation of the method, wherein the map (a) is an indoor environment simulation map with a size of 50 × 50 pixels, the map (b) is an indoor complex environment simulation map with a size of 150 × 150 pixels, and the map (c) is an outdoor random environment simulation map with a size of 50 × 50 pixels;
FIG. 3 is a schematic diagram of the positions of the control points at the beginning of the B-spline curve in the method.
Detailed Description
Aiming at the problem of path smoothness, the method can adjust the path obtained by any path planning method, so that the method meets the requirements of robot movement on path safety and smoothness. Here, taking the paths obtained by the a and RRT path planning algorithm as an example, the specific embodiment of the present invention will be described with reference to the drawings.
In order to design the moving route of the robot, a map of the environment where the robot is located is set as a grid map composed of square cells, and each square cell has two states of 0 and 1 to indicate whether the robot is allowed to pass or not. (the squares in the figure, which are shown as different colours in black and white, where black represents that the barrier is not allowed to pass and white represents that it is allowed to pass). To illustrate the generality of the method, as shown in fig. 2, three different maps are provided to simulate the movement of the robot in different environments, where fig. 2 (a) is an indoor environment, fig. 2 (b) is a complex large-scale indoor environment, and fig. 2 (c) is a random obstacle environment. Wherein the indoor environment simulation map and the outdoor random environment simulation map are designated as 50 × 50 pixel size, and the indoor complex environment simulation map is designated as 150 × 150 pixel size.And the initial point and the target point of the 50 by 50 pixel size map are designated (46, 4), (9, 47), respectively, and the initial point and the target point of the 150 by 150 pixel size map are designated (8, 7), (132, 135), respectively. Respectively processing different maps by an A-star and RRT path planning algorithm to obtain paths { S, T from a starting point to an end point0,T1,T2,...Tn,G}。
The method ensures the smoothness of the trimmed path represented by the B-spline curve by utilizing the continuity property of the B-spline curve. Specifically, the B-spline curve continuity property means that the B-spline curve is C at a node with a repetition degree of kp-kContinuous (where p refers to the order of the B-spline curve and k refers to the degree of repetition of any node on the B-spline curve). Thus selecting order p>k + 2B-spline curve can make B-spline curve have C2The continuous characteristic ensures the continuous and smooth transition of the speed and the acceleration in the running process of the robot, improves the safety and the stability of the motion of the robot, and reduces the mechanical abrasion and the energy loss caused by the sudden change of the speed.
The method reasonably selects the position of the control point and the node sequence, so that the generated B spline curve can be smoothly connected to the original path. For the B-spline curve, the curve does not pass through the starting and ending control points, and in order to enable the calculated B-spline curve to be smoothly connected into the original path, the repetition degree of the first node and the last node in the node sequence of the B-spline curve is defined as p +1, and a clamped-B-spline curve is formed and made to pass through the positions of the starting and ending control points. And four collinear control points P0, P1, P2, P4, P5, P6, P7 and P8 are respectively arranged at two sides of a turning point position (namely the current point H position) in the path, and the beginning and the end of a convex hull guarantee curve of a B spline are taken as straight ends, so that the C2 is kept continuous with an original path formed by straight segments. And moreover, the slopes of the P0, the P1, the P7 and the P8 are consistent with the slope of the straight line in the original path, so that the beginning and end straight line ends of the B spline curve keep C1 continuity with the original path, and the smoothed path is smoothly inserted into the original path.
In order to improve the property of the smoothed path, the method adjusts the control points of the B-spline curve, and reduces the included angle between line segments formed by connecting the control points so as to increase the curvature in the path and reduce the length of the path.
In order to improve the rapidity of calculation while ensuring the safety of the path, the method utilizes the strong convex hull property of the B spline curve in the collision detection process. Specifically, the strong convex hull property of the B spline curve refers to the condition that if a node u of the B spline curve is in a node interval [ u ]i,ui+1) Then by point c (u) in the curve corresponding to node u, at a sequence of control points { P }i-p,Pi-p+1,...,PiThe control points contained in the Chinese character are connected in sequence to form a convex hull. Thus, in the adjusting process of step S4, it is ensured that the appropriate control point sequence does not collide with the obstacle, i.e. it is ensured that the B-spline surrounded by the control point sequence also does not collide with the obstacle to a great extent, and at the same time, it is avoided that the B-spline is used for obstacle avoidance detection, so that the control point adjusting process is well balanced in terms of timeliness and safety, and a timely and safe path is provided for the robot to move.
As shown in the attached figure 1, the general implementation flow of the method is as follows:
s1: acquiring a path output by a path planning method, wherein the path comprises a starting point, a target point and each path point between the starting point and the target point; the path is recorded as a sequence of path points S, T0,T1,T2,...TnG, wherein S and G are respectively a starting point and a target point of a movement task, T0,T1,T2,...TnAll the paths are path points, and the path is formed by connecting a starting point, each path point and a target point by a path line segment in sequence.
S2: selecting a path point as a path point to be processed, and setting 9 control points, namely P0, P1, P8 and 9 control points, on two path line segments of the current path point to be processed and the current path point to be processed, wherein the 9 control points are symmetrically arranged about an angle bisector formed by the two path line segments;
as shown in fig. 3, in S2, the fifth control point is set at the current path point to be processed, the first to fourth control points are sequentially set on one path segment, the sixth to ninth control points are sequentially set on another path segment, and the sixth to ninth control points are sequentially set on the other path segmentThe first control point, the fourth control point and the sixth control point, the sixth control point and the ninth control point are respectively and sequentially arranged symmetrically about an angular bisector formed by two path line segments, the first control point and the ninth control point are respectively arranged at the middle points of the two path line segments, the distance between the second control point and the first control point is not more than 1/4 of the distance between the first control point and the fifth control point, the distance between the eighth control point and the ninth control point is not more than 1/4 of the distance between the ninth control point and the fifth control point, the distance between the fourth control point and the fifth control point is not more than 1/2 of the distance between the second control point and the fifth control point, the distance between the sixth control point and the fifth control point is not more than 1/2 of the distance between the eighth control point and the fifth control point, the third control point is arranged on the path line segment between the second control point and the fourth control point, the seventh control point is disposed on the path segment between the sixth control point and the eighth control point. In the present invention, the first and second control points P0、P1And the eighth and ninth control points P7、P8The slope between the two lines is set to be consistent with the slope of the line segment of the original path, so that the final B-spline curve is ensured to be inserted into the position C in the line segment of the original path1、C2Continuity.
S3: selecting the order of B spline curve as 3 times, setting node vector comprising 9 control points and node vector { u }0,u1,...,umGenerating a B spline curve of the current path point to be processed, wherein the node vector (u)0,u1,...,umThe value is {0,0,0,0,1/6,2/6,3/6,4/6,5/6,1,1,1,1}, and the node vector repetition degree refers to the repetition degree of the node values, such as: u. of0-u3The values are all 0, and the repetition degree is 4, u4Value 1/6, degree of repetition 1;
s4: performing line segment collision detection on the B spline curve of the current path point to be processed, if the line segment collision detection fails, moving a fourth control point and a sixth control point to a fifth control point along the corresponding path line segment, and repeating the line segment collision detection until the line segment collision detection is passed and the fourth control point and the sixth control point are fixed;
s4 specifically includes:
taking a line segment formed by connecting a fourth control point and a sixth control point of a current path point to be processed as a line segment collision detection area, judging whether an obstacle area exists on the line segment collision detection area, and if so, not detecting the line segment collision; specifically, a plurality of collision detection points are uniformly selected in a line segment collision detection area, and if one collision detection point exists as an obstacle area, line segment collision detection is not passed. And simultaneously moving the fourth control point and the sixth control point to the fifth control point along the corresponding path line segments, wherein the fourth control point and the sixth control point are symmetrically arranged around an angular bisector formed by the two path line segments all the time, repeatedly detecting a line segment collision detection area formed between the fourth control point and the sixth control point until no obstacle area exists on the line segment collision detection area, and then detecting and fixing the fourth control point and the sixth control point through line segment collision.
S5: moving the fifth control point to a midpoint between the fourth control point and the sixth control point along an angle bisection line formed by two path line segments, continuously performing curve collision detection on the B-spline curve generated after the control point is moved until collision occurs or the fifth control point is overlapped with the midpoint between the fourth control point and the sixth control point, fixing the fifth control point, replacing the path line segment between the first control point and the ninth control point of the current path point to be processed in S2 with the finally generated B-spline curve, and finishing path smoothing of the current path point to be processed;
in S5, if an obstacle region exists on the B-spline curve generated after the control point is moved, a collision occurs, otherwise, no collision occurs. Specifically, a plurality of collision detection points are uniformly selected on a B-spline generated after moving the control point, and if there is one collision detection point as an obstacle region, a collision occurs. And selecting collision detection points in the control point sequence of the B-spline curve, connecting the collision detection points to form a line segment for collision detection, and evaluating the safety of the B-spline curve representative path.
In S5, the distance that the fifth control point moves to the midpoint between the fourth control point and the sixth control point is calculated by bisection. And taking the distance between the middle point between the fourth control point and the sixth control point and the fifth control point as the initial distance, wherein the distance of the first movement is half of the initial distance, and then the distance of each movement is half of the last movement.
S6: and traversing the residual path points, repeating the steps of S2-S5 to carry out smoothing processing on the path line segments of the residual path points, and finally realizing the smooth optimization of the current path.
The results of experiments performed on the method by combining two different path planning algorithm paths on three different maps are shown in table 1. It can be seen that the method can be combined with A-or rrt algorithm to obtain a path with shorter length and the maximum curvature meeting the motion requirement of the robot on the basis of the original segmented linear path in the environment with different scenes and different map sizes, and the time consumed by the smoothing method is much shorter than that consumed by the path planning process, so that the real-time requirement of the motion of the robot is met.
Table 1: performance results of the method in different maps
Claims (6)
1. A mobile robot path smoothing method based on B-spline curve optimization is characterized by comprising the following steps:
s1: acquiring a path output by a path planning method, wherein the path comprises a starting point, a target point and each path point between the starting point and the target point;
s2: selecting a path point as a path point to be processed, setting 9 control points on two path line segments of the current path point to be processed and the current path point to be processed, wherein the 9 control points are symmetrically arranged about an angular bisector formed by the two path line segments;
s3: setting node vectors, and generating a B spline curve of the current path point to be processed by the 9 control points and the node vectors;
s4: performing line segment collision detection on the B spline curve of the current path point to be processed, if the line segment collision detection fails, moving a fourth control point and a sixth control point to a fifth control point along the corresponding path line segment, and repeating the line segment collision detection until the line segment collision detection is passed and the fourth control point and the sixth control point are fixed;
s5: moving the fifth control point to a midpoint between the fourth control point and the sixth control point along an angle bisection line formed by two path line segments, continuously performing curve collision detection on the B-spline curve generated after the control point is moved until collision occurs or the fifth control point is overlapped with the midpoint between the fourth control point and the sixth control point, fixing the fifth control point, replacing the path line segment between the first control point and the ninth control point of the current path point to be processed in S2 with the finally generated B-spline curve, and finishing path smoothing of the current path point to be processed;
s6: and traversing the residual path points, repeating the steps of S2-S5 to carry out smoothing processing on the path line segments of the residual path points, and finally realizing the smooth optimization of the current path.
2. The B-spline curve optimization-based mobile robot path smoothing method of claim 1, wherein in S2, a fifth control point is set at the path point to be processed, first-fourth control points are set on one path segment in turn, sixth-ninth control points are set on the other path segment in turn, the first-fourth control points and the sixth-ninth control points are respectively symmetrically arranged about a bisector of an angle formed by the two path segments, the first and ninth control points are respectively set at midpoints of the two path segments, a distance between the second control point and the first control point does not exceed 1/4 of a distance between the first control point and the fifth control point, a distance between the eighth control point and the ninth control point does not exceed 1/4 of a distance between the ninth control point and the fifth control point, the distance between the fourth control point and the fifth control point is not more than 1/2 of the distance between the second control point and the fifth control point, and the distance between the sixth control point and the fifth control point is not more than 1/2 of the distance between the eighth control point and the fifth control point.
3. The method for smoothing the path of the mobile robot based on the B-spline curve optimization according to claim 1, wherein the S4 specifically comprises:
taking a line segment formed by connecting a fourth control point and a sixth control point of a current path point to be processed as a line segment collision detection area, judging whether an obstacle area exists on the line segment collision detection area, and if so, not detecting the line segment collision; and simultaneously moving the fourth control point and the sixth control point to the fifth control point along the corresponding path line segments, wherein the fourth control point and the sixth control point are symmetrically arranged around an angular bisector formed by the two path line segments all the time, repeatedly detecting a line segment collision detection area formed between the fourth control point and the sixth control point until no obstacle area exists on the line segment collision detection area, and then detecting and fixing the fourth control point and the sixth control point through line segment collision.
4. The mobile robot path smoothing method based on B-spline curve optimization of claim 1, wherein in S5, if there is an obstacle area on the B-spline curve generated after moving the control point, a collision occurs, otherwise, no collision occurs.
5. The method for smoothing the path of the mobile robot based on the B-spline curve optimization of claim 1, wherein in the step S5, the distance that the fifth control point moves to the midpoint between the fourth control point and the sixth control point is calculated by a bisection method.
6. The method for smoothing the path of the mobile robot based on the B-spline curve optimization of claim 1, wherein the repetition degrees of the first node and the last node of the node vector in S3 are both set to p +1, and p is the order of the B-spline curve.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114995391A (en) * | 2022-05-10 | 2022-09-02 | 安徽工程大学 | 4-order B spline curve path planning method for improving A-star algorithm |
| CN115357032A (en) * | 2022-10-20 | 2022-11-18 | 上海仙工智能科技有限公司 | NURBS-based mobile robot path generation method, system and storage medium |
| CN117313976A (en) * | 2023-11-24 | 2023-12-29 | 广州斯沃德科技有限公司 | Roadmap optimization method, roadmap optimization system, computer equipment and readable storage medium |
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