CN114137991B - Robot continuous path optimization method based on second-order Bezier curve - Google Patents
Robot continuous path optimization method based on second-order Bezier curve Download PDFInfo
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Abstract
The method comprises the steps of firstly training a BP neural network by using a first control vector obtained by a second-order Bezier curve control point to obtain a prediction model, then comprehensively considering factors of path feasibility, safety and operating efficiency on the basis of the prediction model, constructing an evaluation function, converting a path planning problem into an optimization solving problem, carrying out iterative solution on an actual path to obtain a set consisting of the optimal path second-order Bezier curve control points meeting a termination condition, inputting a second-order Bezier curve function to solve a second-order Bezier curve corresponding to each turning point, and obtaining an optimized path. The method and the device can perform post-optimization processing on the traditional path planning algorithm of the image search type and the random sampling type, better meet the requirement of continuous advancing of the robot, prolong the service life of the motor, improve the efficiency of path optimization processing, and have the advantages of high solving speed, high safety and good smoothness.
Description
Technical Field
The application belongs to the technical field of path planning of mobile robots, and particularly relates to a robot continuous path optimization method based on a second-order Bezier curve.
Background
The path planning algorithm of the mobile robot comprises a graph search class, a random sampling class, a potential field class and a target optimization class, wherein the graph search class and the random sampling class path planning algorithm have the advantages of high operation efficiency, short solved path length and the like and are generally applied, but the problems of multiple path turning points, poor safety and smoothness and the like exist, for example, as shown in fig. 3, the path planning algorithm is a path schematic diagram obtained by adopting the traditional path planning algorithm of the graph search class or the random sampling class, a robot capable of turning in place must be selected, and the robot must stop walking and turn in place to walk along a path of the next stage each time the robot walks to the path turning point, the frequent starting of the motor aggravates the loss of the motor and reduces the service life of the motor. Due to the fact that the Bezier curve has good performance in smooth transition of the path, the Bezier curve is mostly adopted to carry out post-processing optimization on the walking path of the mobile robot at present, but in the prior art, more Bezier curves with more than three orders are used, control points of the Bezier curve are determined in a manual selection mode, and the defects that the solving speed is low and the subjectivity of an optimization processing result is high exist.
Disclosure of Invention
In view of the defects or shortcomings, the application aims to provide a method for optimizing a continuous path of a robot based on a second-order Bezier curve, a maximum offset prediction model of a second-order Bezier curve path control point is constructed through a BP neural network, subjectivity influence factors of manual selection of the path control point are eliminated, an evaluation function is constructed on the basis of the maximum offset prediction model, a path planning problem is converted into an optimized solving problem, then the optimized second-order Bezier curve control point obtained through solving is used for solving a second-order Bezier curve corresponding to each turning point in an actual path, an optimized path is obtained, the requirement of continuous traveling of the robot is met, the service life of a motor is prolonged, and the optimization processing efficiency is improved.
The application provides a robot continuous path optimization method based on a second-order Bezier curve, which comprises the following steps:
s1: constructing a first control vector, wherein the first control vector comprises a first interval, a second interval and a first included angle which are obtained by calculating 3 sequentially adjacent second-order Bezier curve control points, and the control point positioned in the middle of the 3 sequentially adjacent second-order Bezier curve control points is a turning point;
s2: training a prediction model, wherein the input of the prediction model is the first control vector; the output of the prediction model is the maximum offset corresponding to a transition point in a second-order Bezier curve control point of the first control vector;
s3: constructing an evaluation function by using the prediction model;
s4: loading an environment map to obtain a first path;
s5: extracting all control points in the first path to obtain a third set, wherein the third set comprises a starting point, an end point and all other turning points;
s6: identifying all turning points in the third set;
s7: selecting turning points in the third set one by one, and randomly acquiring control points on two sides sequentially adjacent to the turning points to form a fourth set;
s8: calculating first control vectors corresponding to all turning points in the fourth set to obtain a fifth set;
s9: inputting the fifth set into an evaluation function to obtain a first evaluation value;
s10: repeatedly executing S7-S9 to obtain a second evaluation value;
s11: comparing the first evaluation value with the second evaluation value, and keeping the smaller value of the first evaluation value and the second evaluation value and a corresponding fourth set, wherein the smaller value is used as the first evaluation value to continuously participate in the next comparison;
s12: repeatedly executing S10-S11 until a termination condition is reached to obtain a minimum evaluation value;
s13: acquiring a fourth set corresponding to the minimum evaluation value;
s14: selecting turning points in the fourth set corresponding to the minimum evaluation value and two side control points sequentially adjacent to the turning points one by one, and inputting a second-order Bezier curve function to obtain second-order Bezier curves corresponding to all the turning points;
s15: and sequentially connecting the second-order Bezier curves and the end points corresponding to all turning points from the initial point to obtain the optimized path.
Specifically, the first path is an actual path obtained by using a conventional path planning algorithm of a graph search type or a random sampling type.
The evaluation function is
In the formula (I), the compound is shown in the specification,K i indicating an evaluation value.
The second order Bezier curve function is
B i = (1-t i )2P i-1 + 2t i (1-t i )P i + t i 2P i+1 （7）
In the formula, B i Indicating a first path turning point P i A corresponding second order bezier curve; p i-1And P i+1Indicating a point of inflection P with respect to a first path i Two-order Bezier curve control points on two sides which are adjacent in sequence; t is t i Denotes a scale factor and t i ∈[0,1]。
According to the embodiment of the application, the prediction model is
S i = f (d i 1, d i 2,β i ) （1）
In the formula (I), the compound is shown in the specification,S i the maximum offset corresponding to the turning point of the second-order bezier curve,iis more than or equal to 1 and is a natural number;d i1representing a first pitch;d i2representing a second pitch;β i indicating a first angle.
In particular, the method comprises the following steps of,d i1、d i2、β i corresponding to 3 input layers in the prediction model,S i corresponding to an output layer in the predictive model.
According to the embodiment of the application, the prediction model is constructed by adopting a BP neural network and comprises an input layer, an output layer and a hidden layer, wherein the hidden layer comprises 60 neurons.
Specifically, the BP neural network is a three-layer neural network topology structure, and includes 3 input layers, 1 output layer and 1 hidden layer, and it can be known from the universal approximation theory that the three-layer neural network topology structure can implement nonlinear mapping from an input vector to a target output vector with any precision, and the more the number of neurons in the hidden layer is, the higher the fitting precision is, but the slower the model solving speed is, so the solving precision and the calculating speed are considered comprehensively, and the number of neurons in the hidden layer is selected to be 60.
According to the embodiment of the present application, after step S7, the method further includes the following steps:
s71: taking the control points P which are adjacent in sequence in the fourth set i 、P i+1、P i+2And P i+3；
Wherein the control point is P i And P i+3The control point P is two adjacent turning points in the first path i+1、P i+2To be located at P i And P i+3Two second order bezier curve control points on the path between;
s72: comparison
And
，
if it is not
＜
Then, thenp i =0, which indicates that the acquired fourth set is valid, and the next step is continued;
if it is not
≥
Then, thenp i =1, the acquired fourth set is invalid, and the process returns to step S7;
wherein, the
Is a turning point P i And P i+3The spacing therebetween; the above-mentioned
Is a control point P i And P i+1The spacing therebetween; the above-mentioned
Is a control point P i+2And P i+3A distance therebetween, saidp i Is a distance penalty factor.
Specifically, in the process of path optimization, if two adjacent second-order bezier curves are intersected, the robot cannot smoothly enter the next path arc curve after leaving the current path arc curve, and the phenomenon that the robot deviates from the planned path inevitably occurs, so that whether the two adjacent second-order bezier curves in the robot walking path are intersected or not must be comprehensively considered. Therefore, a distance penalty factor is introduced into the evaluation functionp i Setting upIn a certain line P of the first path i →P i+3In the process, after optimization solution, two second-order Bezier curve control points P are obtained i+1、P i+2If, if
＜
Then, thenp i =0, otherwisep i When the control point P of the second-order Bezier curve needs to be obtained again at the moment 1 i+1、P i+2And (6) continuing to optimize and solve.
Introducing a distance penalty factor on the basis of the evaluation function (2)p i Then, the specific formula of the evaluation function is as follows,
in the formula (I), the compound is shown in the specification,p i a distance penalty factor is represented.
According to the embodiment of the present application, after step S72, the method further includes the following steps:
s73: selecting turning points P in the fourth set one by one i And two side control points P sequentially adjacent thereto i-1And P i+1Inputting a second-order Bezier curve function to obtain second-order Bezier curves corresponding to all turning points;
s74: respectively acquiring coordinates of all points on a second-order Bezier curve corresponding to all turning points to form a first coordinate set;
s75: respectively acquiring coordinates of all points on the edge of each obstacle in the environment map to form a second coordinate set;
s76: acquiring a distance between any point in the first coordinate set and any point in the second coordinate set to obtain a third distance set;
s77: acquiring a minimum distance in the third distance set;
s78: comparing the minimum distance with a minimum safe distance for the robot to travel,
if the minimum distance is larger than or equal to the minimum safety distance, thenc i =0, which indicates that the fourth set is valid, the next step is continued;
if the minimum spacing is less than the minimum safety spacingc i =1, the fourth set is invalid, and the process returns to step S7;
wherein, thec i Is a collision penalty factor.
Specifically, in the path optimization process, the operation safety condition of the robot needs to be considered, that is, whether the distance between the optimized path and the obstacle in the environment map meets the minimum safety distance for the operation of the robot, and if the distance does not meet the minimum safety distance for the operation of the robot, the robot inevitably collides with the obstacle when operating along the optimized path, so that a safety accident occurs. Therefore, a collision penalty factor is introduced into the evaluation function to reflect the operation safety of the mobile robot, namely when the distance between the optimized path and the barrier is more than or equal to the minimum safety distance,c i =0, otherwisec i And =1, the position of the control point of the second-order bezier curve does not meet the path optimization requirement at the moment, and the calculation needs to be returned and solved again.
Introducing a collision penalty factor on the basis of the evaluation function (3)c i Then, the specific formula of the evaluation function is as follows,
in the formula (I), the compound is shown in the specification,c i representing a collision penalty factor.
According to the embodiment of the present application, after step S78, the method further includes the following steps:
s79: respectively acquiring maximum curvatures on second-order Bezier curves corresponding to all turning points to form a first curvature set;
s710: obtaining a maximum curvature of the first curvature set;
s711: comparing the maximum curvature with a maximum curvature of the robot turn,
if the maximum curvature is less than or equal to the maximum curvature of the turning of the robot, thenr i =0, which indicates that the fourth set is valid, the next step is continued;
if the maximum curvature > maximum curvature of the robot turn, thenr i =1, the fourth set is invalid, and the process returns to step S7;
wherein, ther i A penalty factor for path feasibility.
Specifically, in the path optimization process, whether the curvature of the second-order bezier curve in the optimized path can meet the turning requirement of the robot needs to be considered, and if the curvature of the second-order bezier curve cannot meet the turning requirement of the robot, the robot inevitably deviates from the planned path. Therefore, a path feasibility penalty factor is introduced into the evaluation functionr i Namely, if the maximum curvature of each section of the second-order Bezier curve obtained after optimization is less than or equal to the maximum curvature of the turning of the robot, thenr i =0, otherwiser i And =1, the second-order bezier curve control point does not meet the path optimization requirement at this time, and the calculation needs to be solved again.
Introducing a path feasibility penalty factor on the basis of the evaluation function (4)r i Then, the specific formula of the evaluation function is as follows,
in the formula (I), the compound is shown in the specification,r i a path feasibility penalty factor is represented.
According to the embodiment of the present application, after step S711, the following steps are further included:
s712: respectively acquiring the minimum critical speed on each second-order Bezier curve corresponding to all turning points to form a first speed set;
s713: acquiring a minimum speed in the first speed set;
s714: comparing the minimum speed with the robot running speed,
if the minimum speed is larger than or equal to the running speed of the robot, the robot runs at the maximum speedu i =0, which indicates that the fourth set is valid, the next step is continued;
if the minimum speed < the running speed of the robot, thenu i =1, the fourth set is invalid, and the process returns to step S7;
wherein, theu i A penalty factor for the speed of movement.
Specifically, in the path optimization process, it is also required to consider whether the running speed of the robot is less than the minimum critical speed of the second-order bezier curve corresponding to each turning point, and if the running speed of the robot is greater than the minimum critical speed of the second-order bezier curve corresponding to the turning point, the robot will inevitably deviate from the planned path, so a motion speed penalty factor is introduced into the evaluation functionu i That is, if the running speed of the robot is less than or equal to the minimum critical speed of the second-order Bezier curve corresponding to each turning point, thenu i =0, otherwise, thenu i And =1, the position of the control point of the second-order bezier curve does not meet the path optimization requirement at the moment, and the calculation needs to be returned and solved again.
Introducing a motion speed penalty factor on the basis of the evaluation function (5)u i Then, the specific formula of the evaluation function is as follows,
in the formula (I), the compound is shown in the specification,u i representing a motion velocity penalty factor.
According to the embodiment of the application, a preset number of first control vectors are obtained by using a Latin hypercube sampling method.
Specifically, the turning point is P i Control point P i-1And P i+1Representing and said turning point P i Two-side second-order Bezier curve control points which are adjacent in sequence, wherein the first distance is the turning point P i And a control point P i-1At a distance ofd i1(ii) a The second distance is the turning point P i And a control point P i+1At a distance ofd i2(ii) a A first included angle is formed between the first distance and the second distanceβ i (ii) a The above-mentionedd i1And saidd i2The value range of (1) is 0-50; the above-mentionedβ iThe value range of the maximum offset prediction model is 0-180 degrees, and in order to ensure the accuracy of the maximum offset prediction model, 1000 groups of data are taken to form a first set by adopting a Latin hypercube sampling method in each value range for training the prediction model.
According to the embodiment of the application, the algorithm for solving the optimized path comprises a genetic algorithm, a simulated annealing algorithm and a particle swarm algorithm.
Specifically, a genetic algorithm, a simulated annealing algorithm or a particle swarm algorithm can be selected to perform iterative computation by taking an evaluation function as a target function, and finally, each turning point P in the first path is solved under the condition that a preset termination condition is met i Corresponding maximum offsetS i The arrangement of the control points of the second order Bezier curve when the sum is maximum, the target value at that timeK i And minimum.
In summary, the present application provides a second-order bezier curve-based robot continuous path optimization method, which includes sequentially selecting three second-order bezier curve control points (where a control point located in the middle is a turning point), calculating a first distance, a second distance, and a first included angle corresponding to the three control points, and constructing a first control vector according to the first distance, the second distance, and the first included angle; the method also calculates the maximum offset corresponding to the turning point, namely: the turning points in the second-order Bezier curve correspond to a first control vector and a maximum offset. After a sufficient amount of samples are obtained, the first control vector is used as input, the maximum offset is used as output, the neural network is trained to obtain a prediction model, and when a group of first control vectors are input into the prediction model, the maximum offset can be output by the prediction model, namely, the step establishes the prediction relation between the first control vectors and the maximum offset.
In the process of actually planning a path, a first path displayed on an environment map can be obtained through calculation by loading the environment map, a plurality of control points exist on the first path, when the robot travels to the first path, the robot capable of steering in place must be selected, and when the robot travels to a turning point, the robot must be stopped and the direction must be adjusted to travel along the path of the next stage, which can cause the robot to be incapable of continuously traveling, low efficiency, and frequent starting and stopping of a motor, aggravate loss and reduce service life. The method constructs a third set by all control points on the first path, namely: the third set comprises coordinates of all control points distributed along the first path, and the other control points are turning points except the two control points of the starting point and the ending point.
Extracting coordinates of all turning points in the third set, selecting the turning points one by one, and then randomly obtaining second-order Bezier curve control points which are positioned on the first path and are adjacent to each other in sequence at two sides of the turning points to obtain a fourth set, namely: the fourth set includes: each turning point and control points at both sides of each turning point. And calculating a first control vector corresponding to each turning point in the fourth set, and inputting an evaluation function constructed by a prediction model to obtain a first evaluation value.
And then randomly obtaining second-order Bezier curve control points which are positioned on the first path and are adjacent to each other in sequence at two sides of each turning point to obtain a fourth set, namely: the fourth set includes: each turning point and control points at both sides of each turning point. And calculating a first control vector corresponding to each turning point in the fourth set, and inputting an evaluation function constructed by a prediction model to obtain a second evaluation value.
Comparing the first evaluation value with the second evaluation value, and keeping the smaller value of the first evaluation value and the second evaluation value and a corresponding fourth set, wherein the smaller value is used as the first evaluation value to continuously participate in the next comparison; repeating: and then randomly obtaining second-order Bezier curve control points which are positioned on the first path and are adjacent to each other in sequence at two sides of each turning point to obtain a fourth set, namely: the fourth set includes: each turning point and control points at both sides of each turning point. And calculating a first control vector corresponding to each turning point of the fourth set, and inputting an evaluation function constructed by a prediction model to obtain a second evaluation value. Comparing the first evaluation value with the second evaluation value, and keeping the smaller value of the first evaluation value and the second evaluation value and a corresponding fourth set, wherein the smaller value is used as the first evaluation value to continuously participate in the next comparison; and repeating the steps until the termination condition is reached to obtain the minimum evaluation value and the corresponding fourth set.
And acquiring a fourth set corresponding to the minimum evaluation value, namely each turning point corresponding to the minimum evaluation value and control points on two sides of each turning point.
In the fourth set, turning points and two side control points sequentially adjacent to the turning points are selected one by one, a second-order Bezier curve function is respectively input, a second-order Bezier curve corresponding to all the turning points is obtained through solving, and finally the second-order Bezier curves corresponding to all the turning points and the end points are sequentially connected from the starting point, so that an optimized path which meets the continuous traveling of the robot is obtained.
The method includes the steps of performing key optimization planning on turning points on a first path, firstly extracting the turning points on the first path, randomly selecting points on two sides of the turning points on the first path as second-order Bezier curve control points on two sides of the turning points according to all the turning points, obtaining final second-order Bezier curve control points on two sides, corresponding to the turning points and enabling an evaluation function output value to be minimum, through iterative calculation, forming a fourth set by the turning points and the final second-order Bezier curve control points on the two sides of the turning points, planning a Bezier curve according to the fourth set to enable the robot to smoothly transition at the turning points, and then sequentially connecting all the curves from a starting point to a stopping point to obtain an optimized path. Compared with the prior art, the method can fully optimize and plan the path at the turning point on the first path, effectively solves the problems of narrow selection range of the robot types and low service life of frequent starting and stopping of the motor in the prior art, improves the optimization processing speed, and eliminates the defect of strong subjectivity of the optimization result.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings.
Fig. 1 is a diagram illustrating the maximum offset of the turning point of the second-order bezier curve.
Fig. 2 is a schematic diagram of a path optimization process.
Fig. 3 is a schematic diagram of an actual path obtained by using a conventional path planning algorithm.
Fig. 4 is a schematic diagram of a first path obtained by using a conventional path planning algorithm in the embodiment of the present application.
Fig. 5 is a schematic diagram of an optimized path obtained by optimizing the first path shown in fig. 4 by using the optimization method of the present application.
Fig. 6 is a flowchart of a continuous path optimization method according to the present application.
Detailed Description
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the present invention are shown in the drawings.
The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
The diagram of the maximum offset of the turning point of the second order bezier curve shown in fig. 1 includes three sequentially adjacent control points P of the second order bezier curve0、P1、P2In which P is1Is the turning point.
Control point P0And P1Is a first pitch, i.e.
Die length ofd 11(ii) a Control point P1And P2Is a second pitch, i.e.
Die length ofd 21First pitch of
And a second pitch
Form a first included angleβ 1Is less than P0P1P2. The turning point P can be obtained by geometric calculation by using the first distance, the second distance and the first included angle1Maximum offset ofS 1。
Constructing a first control vector by using the first distance, the second distance and the first included angle (
、
、∠P0P1P2) Setting the value ranges of the first interval and the second interval to be 0-50, and setting the value range of the first included angle to be 0-180 degrees. In the value range, 1000 groups of first control vectors are obtained by adopting a Latin hypercube sampling method to form a first set, namely (A)
、∠P i-1P i P i+1) As shown in table 1.
Calculating all turning points P in the first set i Corresponding maximum offsetS i And a second set is formed as shown in table 1.
TABLE 1
Creating a second-order Bezier curve turning point P by using BP neural network i Correspond toMaximum offset ofS i The predictive model of (1). The BP neural network is a three-layer neural network topological structure and comprises 3 input layers, 1 output layer and 1 hidden layer, and the universal approximation theory shows that the three-layer neural network topological structure can realize nonlinear mapping from input vectors to target output vectors with any precision, the more the number of neurons of the hidden layer is, the higher the fitting precision is, the slower the model solving speed is, so that the solving precision and the calculating speed are comprehensively considered, and the number of neurons of the hidden layer is selected to be 60.
Training the BP neural network by using the training samples shown in the table 1 by using the first set as input and the second set as output to obtain the turning point P capable of accurately predicting the second-order Bezier curve i Corresponding maximum offsetS i And the predictive model is expressed by the following formula,
S i = f (d i 1, d i 2,β i ) （1）
in the formula (I), the compound is shown in the specification,S i the maximum offset corresponding to the turning point of the second-order bezier curve,iis more than or equal to 1 and is a natural number;d i1representing a first pitch;d i2representing a second pitch;β i indicating a first angle.
The analysis shows that the turning point P of the second-order Bezier curve i Corresponding maximum offsetS i The larger the curve, the shorter and smoother the second-order Bezier curve, so that when each turning point P in the first path is i Corresponding maximum offsetS i When the sum is maximum, the shortest and the smoothest optimized path are obtained, in order to convert the path planning problem into an optimized solving problem, an evaluation function for evaluating the optimization degree of the path is constructed by adopting the reciprocal of a prediction model, the specific formula is as follows,
in the formula (I), the compound is shown in the specification,K i indicating an evaluation value.
As can be seen, the evaluation valueK i The smaller the path is, the shorter and the more gentle the path is after optimization, and finally an evaluation value is obtained through optimal solutionK i Minimum corresponding second order Bezier curve control point P0、P1、P2And obtaining a second-order Bezier curve by solving and calculating a second-order Bezier curve function
The specific formula of the second-order Bezier curve function is as follows,
B i = (1-t i )2P i-1 + 2t i (1-t i )P i + t i 2P i+1 （7）
in the formula, B i Indicating a turning control point P i A corresponding second order bezier curve; p i-1And P i+1Indicates the turning point P i Two second-order Bezier curve control points which are adjacent in the front-back sequence; t is t i Denotes a scale factor and t i ∈[0,1]。
Example 1
According to the flowchart shown in fig. 6, the optimization method of the present application is used to optimize the first path shown in fig. 4, where the horizontal axis is an x coordinate, the vertical axis is a y coordinate, a white area in the diagram represents an obstacle-free area, and other color areas are obstacle areas, and the method includes the following steps:
s1: constructing the first control vector;
s2: training a prediction model;
s3: constructing an evaluation function (2) by the prediction model;
s4: loading the environment map shown in fig. 4, and obtaining a first path a-B-C-D-E shown in fig. 4, namely a conventional path, by using a conventional path planning algorithm of a graph search class or a random sampling class;
s5: extracting all control points in the first path to obtain a third set, where the third set includes all control points of the first path, and coordinates of each control point from a starting point a to an end point E are, in order, a (0.5 ), B (0.5, 6.5), C (2.5, 8.5), D (8.5 ), and E (9.5 ) as shown in fig. 4;
s6: identifying all turning points B, C, D in the third set;
s7: selecting the turning point B, C, D in the third set one by one and a randomly obtained second-order Bezier curve control point P0、P1、P2、P3、P4、P5Forming a fourth set;
wherein the control point P0On path A-B, control point P1、P2On path B-C, control point P3、P4On path C-D, control point P5Located on path D-E, and 0 <
＜
，0＜
，
；
S8: calculating the first control vectors of the maximum offset corresponding to all turning points B, C, D in the fourth set to obtain a fifth set, wherein the fifth set comprises (A)
，∠P0BP1）、 
；
S9: selection genetic algorithmSetting a termination condition, and taking the fifth set as an input evaluation function (2) to obtain a first evaluation valueK 1；
Wherein the termination condition comprises that the maximum iteration number is 100, the population size is 50, the crossing rate is 0.6, and the variation rate is 0.05;
s10: repeatedly executing S7-S9 to obtain a second evaluation valueK 2；
S11: comparing the first evaluation valueK 1And the second evaluation valueK 2Such asK 1＜K 2Then remainK 1AndK 1a corresponding fourth set, the first evaluation valueK 1Continuing to participate in the next comparison;
s12: repeatedly executing S10-S11 until the termination condition is reached to obtain the minimum evaluation valueK min；
S13: obtaining a minimum evaluation valueK minA corresponding fourth set comprising second order Bezier curve control points P0、B、P1、P2、C、P3、P4、D、P5；
S14: selecting the turning point B in the fourth set corresponding to the minimum evaluation value and two-side second-order Bezier curve control points P sequentially adjacent to the turning point B0、P1Inputting a second-order Bezier curve function (7) to obtain a second-order Bezier curve corresponding to the turning point B, and so on to obtain second-order Bezier curves corresponding to other turning points C, D;
s15: and sequentially connecting the second-order bezier curve corresponding to the turning point B, C, D and the end point E from the starting point a to obtain the optimized path shown in fig. 5.
Further, the schematic diagram of the path optimization process shown in fig. 2 is black as an obstacle, A, P1、P4B is a first path A-P1-P4Control point of B, where P1、P4Is a turning point, and is also a second order Bezier curve maximum offset control point, and A-P0-
-P2-P3-
-P5B is the simulated optimization path, where P0、P2、P3、P5For the second order bezier curve control points,
is a turning point P1The corresponding second-order bezier curve is shown,
is a turning point P4Corresponding second order bezier curves.
In the process of path optimization, if two adjacent second-order Bezier curves
And
if the intersection exists, the robot leaves the arc curve of the current path
Then can not smoothly enter the arc curve of the next path
The phenomenon that the robot deviates from the planned path inevitably occurs, so whether the two adjacent second-order bezier curves in the walking path of the robot intersect or not must be comprehensively considered. P in the first path1→P4Two Bezier curve control points P are included in the stroke2、P3If, if
Then, thenp i =0, otherwisep i When the value is 1, the control needs to be reselectedSystem point P0、P2、P3、P5And (6) continuing to optimize and solve.
Introducing a distance penalty factor on the basis of the evaluation function (2)p i The specific formula of the post-evaluation function is as follows,
in the formula (I), the compound is shown in the specification,p i a distance penalty factor is represented.
Example 2
The optimization method as described in embodiment 1 is used to optimize the first path as shown in fig. 4, except that:
s3: constructing an evaluation function (3) by the prediction model;
the method also comprises the following steps after the step S7:
s71: take the control point B, P in the fourth set1、P2、C、P3、P4、D；
S72: comparison
And
、
and
，
if it is not
＜
And is
＜
Then, thenp i =0, indicating that the fourth set is valid, the next step is continued,
if it is not
≥
Or
≥
Then, thenp i =1, it is described that the fourth set is invalid, and the process returns to step S7.
Wherein, the
Is the distance between the turning points B, C
The spacing between inflection points C, D; the above-mentioned
Are control points B and P1The spacing therebetween; the above-mentioned
Is a control point P2And C; the above-mentioned
Are control points C and P3The spacing therebetween; the above-mentioned
Is a control point P4And D, and D.
Further, as shown in the schematic diagram of the path optimization process shown in fig. 2, in the path optimization process, it is also required to consider whether the distance between the robot operation path and each obstacle in the environment map satisfies the minimum safe distance for the robot operation, and if the distance does not satisfy the minimum safe distance for the robot operation, the robot will inevitably collide with the obstacle when operating along the optimized path, and a safety accident occurs, so a collision penalty factor is introduced into the evaluation functionc i And reflecting the operation safety of the mobile robot. The optimized path A-P is defined when the robot runs along the optimized path and does not send collision with the obstacle0-
-P2-P3-
-P5When the distances between each point on-B and the barrier are all larger than or equal to the minimum safety distance,c i =0, otherwisec i =1, indicating the path control point P at this time0、P2、P3、P5The position does not meet the path optimization requirement and needs to reselect the control point P0、P2、P3、P5And (6) optimizing and solving. Introducing a collision penalty factor on the basis of the evaluation function (3)c i The specific formula of the post-evaluation function is as follows,
in the formula (I), the compound is shown in the specification,c i representing a collision penalty factor.
Example 3
The optimization method as described in embodiment 2 is used to optimize the first path as shown in fig. 4, except that:
s3: constructing an evaluation function (4) by the prediction model;
the method also comprises the following steps after the step S72:
s73: selecting the turning point B in the fourth set and two-side second-order Bezier curve control points P sequentially adjacent to the turning point B0、P1Inputting a second-order Bezier curve function (7) to obtain a second-order Bezier curve corresponding to the turning point B, and so on to obtain second-order Bezier curves corresponding to other turning points C, D;
s74: respectively acquiring coordinates of all points on a second-order Bezier curve corresponding to the turning point B, C, D to obtain a first coordinate set;
s75: respectively acquiring coordinates of all points on the edge of the obstacle in the black area in the environment map to obtain a second coordinate set;
s76: acquiring a distance between any point in the first coordinate set and any point in the second coordinate set to obtain a third distance set;
s77: obtaining the minimum distance d in the third distance setmin；
S78: comparing the minimum distances dminMinimum safe distance D from robot operationmin，
If the minimum spacing dminNot less than minimum safety distance DminThen, thenc i =0, which indicates that the fourth set is valid, the next step is continued;
if the minimum spacing dmin< minimum safety distance DminThen, thenc i =1, it is described that the fourth set is invalid, and the process returns to step S7.
Further, as shown in the schematic diagram of the path optimization process shown in fig. 2, in the path optimization process, it is also necessary to consider whether the curvature of the second-order bezier curve in the optimized path can satisfy the turning requirement of the robot, and if the curvature of the second-order bezier curve in the optimized path cannot satisfy the turning requirement of the robot, a phenomenon that the robot deviates from the planned path will inevitably occur, that is, if the second-order bezier curve obtained after the optimization is obtained
And is
The maximum curvature is less than or equal to the maximum curvature of the turning of the robot, thenr i =0, otherwiser i =1, representing the curve control point P at this time0、P2、P3、P5Not meeting the path optimization requirement and needing to reselect the control point P0、P2、P3、P5And (6) optimizing and solving. Introducing a path feasibility penalty factor on the basis of the evaluation function (4)r i The specific formula of the post-evaluation function is as follows,
in the formula (I), the compound is shown in the specification,r i a path feasibility penalty factor is represented.
Example 4
The optimization method as described in embodiment 3 is used to optimize the first path as shown in fig. 4, except that:
s3: constructing an evaluation function (5) by the prediction model;
the method also comprises the following steps after the step S78:
s79: respectively acquiring the maximum curvature R on each second-order Bezier curve corresponding to the turning point B, C, DB max、RC max、RD maxForming a first curvature set;
s710: obtaining a maximum curvature R in the first curvature setD max；
S711: comparing the maximum curvature RD maxMaximum curvature R of turning with robotmax，
If the maximum curvature R isD maxMaximum curvature R of turning of robot is less than or equal tomaxThen, thenr i =0, which indicates that the fourth set is valid, the next step is continued;
if the maximum curvature R isD maxRobot maximum curvature of turn RmaxThen, thenr i =1, it is described that the fourth set is invalid, and the process returns to step S7.
Further, as shown in the schematic diagram of path optimization processing shown in fig. 2, in the path optimization process, it is also necessary to consider whether the operation speed of the robot is less than the minimum critical speed on the second-order bezier curve corresponding to each turning point, and if the operation speed of the robot is greater than the minimum critical speed on any second-order bezier curve, a phenomenon that the robot deviates from the planned path inevitably occurs, so a motion speed penalty factor is introduced into the evaluation functionu i 。
Setting the running speed of the robot to be less than or equal to the minimum critical speed of the second-order Bezier curve corresponding to any turning point, and thenu i =0, if the running speed of the robot is greater than the minimum critical speed of the second-order bezier curve corresponding to any turning point, thenu i =1, representing the second order bezier curve control point P at this time0、P2、P3、P5The position does not meet the path optimization requirement and needs to reselect the control point P0、P2、P3、P5And (6) optimizing and solving. Introducing a motion speed penalty factor on the basis of the evaluation function (5)u i The specific formula of the post-evaluation function is as follows,
in the formula (I), the compound is shown in the specification,u i representing a motion velocity penalty factor.
Example 5
The optimization method as described in embodiment 4 is used to optimize the first path as shown in fig. 4, except that:
s3: constructing an evaluation function (6) by the prediction model;
the following steps are also included after step S711:
s712: respectively acquiring the minimum critical point on each second-order Bezier curve corresponding to the turning point B, C, DVelocity VB min、VC min、VD minForming a first speed set;
s713: obtaining a minimum velocity V in the first velocity setC min；
S714: comparing said minimum speed VC minIn conjunction with the running speed V of the robot,
if said minimum speed V isC minNot less than the running speed V of the robotu i =0, which indicates that the fourth set is valid, the next step is continued;
if said minimum speed V isC min< running speed V of the robot, thenu i =1, it is described that the fourth set is invalid, and the process returns to step S7.
Example 6
The optimization method as described in embodiment 5 is used to optimize the first path as shown in fig. 4, except that:
s9: selecting a simulated annealing algorithm, setting a termination condition, and taking the fifth set as an input evaluation function (6) to obtain a first evaluation valueK 1；
The termination condition is that the maximum iteration number is 100, the disturbance number is 20, the initial temperature is 0.1 ℃, the proportion of each attenuation is 0.99, the number of the population is 10, the number of times of each disturbance is 5, and the probability of the disturbance is 0.5.
Example 7
The optimization method as described in embodiment 5 is used to optimize the first path as shown in fig. 4, except that:
s9: selecting a particle swarm algorithm, setting a termination condition, and taking the fifth set as an input evaluation function (6) to obtain a first evaluation valueK 1；
Wherein, the termination condition is that the maximum iteration number is 100 times, and the population number is 50.
By combining the technical scheme, the application discloses a robot continuous path optimization method based on a second-order Bezier curve, which comprises the steps of firstly adopting a Latin hypercube sampling method to obtain a first set and a second set for controlling the second-order Bezier curve, training a prediction model constructed by a BP neural network by using a training sample consisting of the first set and the second set to obtain a prediction model with high precision and good reliability, improving the accuracy of solving a control point of the second-order Bezier curve, eliminating subjective influence factors of manually selecting a path control point, then taking the prediction model as a basis, comprehensively considering path feasibility, safety and operation speed factors, constructing an evaluation function, converting a path planning problem into an optimized solving problem, and then using the evaluation function to iteratively solve a fourth set randomly obtained on the first path, the method comprises the steps of obtaining a fourth set consisting of optimal path second-order Bezier curve control points meeting various constraint conditions, then selecting each turning point and two control points sequentially adjacent to the turning point in front and back of the turning point one by one in the fourth set, inputting a second-order Bezier curve function to obtain a second-order Bezier curve corresponding to each turning point, and finally sequentially connecting the second-order Bezier curves and end points corresponding to all the turning points from a starting point to further obtain an optimized path, so that the post-optimization smooth processing of the moving path of the mobile robot is realized, the requirement of continuous moving of the mobile robot is well met, the selection range of robot types is widened, the service life of a robot motor is prolonged, the efficiency of the path optimization processing is also improved, and the method has the advantages of high solving speed, high safety and good smoothness.
The above description is only a preferred embodiment of the application and is illustrative of the principles of the technology employed. It will be appreciated by a person skilled in the art that the scope of the invention as referred to in the present application is not limited to the embodiments with a specific combination of the above-mentioned features, but also covers other embodiments with any combination of the above-mentioned features or their equivalents without departing from the inventive concept. For example, the above features may be replaced with (but not limited to) features having similar functions disclosed in the present application.
Claims (8)
1. A robot continuous path optimization method based on a second-order Bezier curve is characterized by comprising the following steps:
s1: constructing a first control vector, wherein the first control vector comprises a first interval, a second interval and a first included angle which are obtained by calculating 3 sequentially adjacent second-order Bezier curve control points, and the control point positioned in the middle of the 3 sequentially adjacent second-order Bezier curve control points is a turning point;
s2: training a prediction model, wherein the input of the prediction model is the first control vector; the output of the prediction model is the maximum offset corresponding to a transition point in a second-order Bezier curve control point of the first control vector; the prediction model is
Si＝f(d1i,d2i,βi)
In the formula, SiThe maximum offset corresponding to the turning point of the second-order Bezier curve is represented, i is more than or equal to 1 and is a natural number; d1iRepresenting a first pitch; d2iRepresenting a second pitch; beta is aiRepresenting a first included angle;
s3: constructing an evaluation function by using the prediction model; the evaluation function is
S4: loading an environment map to obtain a first path;
s5: extracting all control points in the first path to obtain a third set, wherein the third set comprises a starting point, an end point and all other turning points;
s6: identifying all turning points in the third set;
s7: selecting turning points in the third set one by one, and randomly acquiring control points on two sides sequentially adjacent to the turning points to form a fourth set;
s8: calculating first control vectors corresponding to all turning points in the fourth set to obtain a fifth set;
s9: inputting the fifth set into an evaluation function to obtain a first evaluation value;
s10: repeatedly executing S7-S9 to obtain a second evaluation value;
s11: comparing the first evaluation value with the second evaluation value, and keeping the smaller value of the first evaluation value and the second evaluation value and a corresponding fourth set, wherein the smaller value is used as the first evaluation value to continuously participate in the next comparison;
s12: repeatedly executing S10-S11 until a termination condition is reached to obtain a minimum evaluation value;
s13: acquiring a fourth set corresponding to the minimum evaluation value;
s14: selecting turning points in the fourth set corresponding to the minimum evaluation value and two side control points sequentially adjacent to the turning points one by one, and inputting a second-order Bezier curve function to obtain second-order Bezier curves corresponding to all the turning points;
s15: and sequentially connecting the second-order Bezier curves and the end points corresponding to all turning points from the initial point to obtain the optimized path.
2. The second-order Bezier curve-based robot continuous path optimization method according to claim 1, wherein the prediction model is constructed by using a BP neural network, and comprises an input layer, an output layer and a hidden layer, and the hidden layer comprises 60 neurons.
3. The second-order bezier curve-based robot continuous path optimization method according to claim 1, further comprising the following steps after step S7:
s71: taking the control points P which are adjacent in sequence in the fourth seti、Pi+1、Pi+2And Pi+3；
Wherein the control point is PiAnd Pi+3The control point P is two adjacent turning points in the first pathi+1、Pi+2To be located at PiAnd Pi+3Two second order bezier curve control points on the path between;
s72: comparison
And
if it is not
Then p isiWhen the fourth set is obtained, the fourth set is valid, and the next step is executed;
if it is not
Then p isiIf 1, the fourth set is invalid, and the process returns to step S7;
wherein, the
Is a turning point PiAnd Pi+3The spacing therebetween; the above-mentioned
Is a control point PiAnd Pi+1The spacing therebetween; the above-mentioned
Is a control point Pi+2And Pi+3Of p between p and piIs a distance penalty factor.
4. The second-order bezier curve-based robot continuous path optimization method according to claim 3, further comprising the following steps after step S72:
s73: selecting turning points P in the fourth set one by oneiAnd two side control points P sequentially adjacent theretoi-1And Pi+1Inputting a second-order Bezier curve function to obtain second-order Bezier curves corresponding to all turning points;
s74: respectively acquiring coordinates of all points on a second-order Bezier curve corresponding to all turning points to form a first coordinate set;
s75: respectively acquiring coordinates of all points on the edge of each obstacle in the environment map to form a second coordinate set;
s76: acquiring a distance between any point in the first coordinate set and any point in the second coordinate set to obtain a third distance set;
s77: acquiring a minimum distance in the third distance set;
s78: comparing the minimum distance with a minimum safe distance for the robot to travel,
if the minimum spacing is larger than or equal to the minimum safety spacing, ciWhen the fourth set is valid, the next step is executed;
if the minimum spacing is less than the minimum safety spacing, ciIf the fourth set is invalid, the process returns to step S7;
wherein, c isiIs a collision penalty factor.
5. The second-order bezier curve-based robot continuous path optimization method according to claim 4, further comprising the following steps after step S78:
s79: acquiring maximum curvatures on second-order Bezier curves corresponding to all turning points to form a first curvature set;
s710: obtaining a maximum curvature of the first curvature set;
s711: comparing the maximum curvature with a maximum curvature of the robot turn,
if the maximum curvature is less than or equal to the maximum curvature of the turning of the robot, riWhen the fourth set is valid, the next step is executed;
if the maximum curvature > maximum curvature of the robot turn, riIf the fourth set is invalid, the process returns to step S7;
wherein, r isiPenalizing factors for path feasibilityAnd (4) adding the active ingredients.
6. The second-order bezier curve-based robot continuous path optimization method according to claim 5, further comprising the following steps after step S711:
s712: acquiring the minimum critical speed on each second-order Bezier curve corresponding to all turning points to form a first speed set;
s713: acquiring a minimum speed in the first speed set;
s714: comparing the minimum speed with the robot running speed,
if the minimum speed is larger than or equal to the running speed of the robot, uiWhen the fourth set is valid, the next step is executed;
if the minimum speed < robot running speed, uiIf the fourth set is invalid, the process returns to step S7;
wherein u isiA penalty factor for the speed of movement.
7. The second-order bezier curve-based robot continuous path optimization method of claim 1, wherein a predetermined number of the first control vectors are obtained by a latin hypercube sampling method.
8. The second-order Bezier curve-based robot continuous path optimization method according to claim 6, wherein the algorithm for solving the optimized path comprises a genetic algorithm, a simulated annealing algorithm and a particle swarm algorithm.
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