CN117029859A - Robot path planning method and device, storage medium and robot controller - Google Patents
Robot path planning method and device, storage medium and robot controller Download PDFInfo
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Abstract
The application provides a robot path planning method, a device, a storage medium and a robot controller, wherein the method comprises the following steps: acquiring a given theoretical path, sequentially acquiring coordinates of a given plurality of model value points, and determining the number of the model value points; determining a node vector under a third parameterization expression based on the obtained coordinates of the plurality of model value points and the number of the plurality of model value points; determining a B-spline expression for performing the robot path planning based on the determined node vector; performing the robot path planning by using the determined B-spline expression; the third parameterization expression is determined according to a first parameterization expression and a second parameterization expression which are determined in advance, and a first parameter coefficient and a second parameter coefficient which are respectively introduced for the first parameterization and the second parameterization. The scheme provided by the application can dynamically adjust and improve the smoothness and fitting precision of the fitting path.
Description
Technical Field
The present application relates to the field of control, and in particular, to a robot path planning method, a device, a storage medium, and a robot controller.
Background
Along with the development of the age and the progress of technology, more and more complex curved surfaces are in the fields of household appliances, automobiles, aviation, mold manufacturing and the like, and for operation parts with curvature mutation or dense parts, a teaching programming method is often adopted for track planning. In the teaching process of the robot, misoperation problems are unavoidable due to insufficient experience of workers, a large amount of teaching information is required to be collected to optimize teaching tracks, working efficiency is greatly affected by the method, and an application scene is too single.
Based on the current situation of the industry, the B spline planning algorithm is mostly adopted to perform path fitting on complex curved surfaces in the current academic research, so that the path fitting effect can be greatly improved while the field operation requirement is met. The B spline planning algorithm formula comprises two core parameters, namely a control vertex and a node vector. In the related art, a uniform parameterization method, an accumulated chord length parameterization method or a centripetal parameterization method is often adopted to solve the node vector. The accumulated chord length parameterization method can cause the problem of larger curvature change of the B spline curve; centripetal parameterization can lead to a problem of greater "longitudinal" fitting errors of the B-spline curve. In order to ensure the fitting precision and the smoothness of the cubic B spline curve, the low longitudinal fitting error of the accumulated chord length parameter method and the low curvature of the centripetal parameter method are comprehensively considered.
Disclosure of Invention
The application aims to overcome the defects of the related art, and provides a robot path planning method, a device, a storage medium and a robot controller, so as to solve the problems of larger curvature change and larger longitudinal fitting error of a B spline curve of a parameterization method in the related art.
In one aspect, the present application provides a method for planning a path of a robot, including: acquiring a given theoretical path, sequentially acquiring coordinates of a given plurality of model value points, and determining the number of the model value points; determining a node vector under a third parameterization expression based on the obtained coordinates of the plurality of model value points and the number of the plurality of model value points; determining a B-spline expression for performing the robot path planning based on the determined node vector under the third parameterized expression; performing the robot path planning by using the determined B-spline expression to obtain discrete path points of the robot motion; the third parameterization expression is determined according to a first parameterization expression and a second parameterization expression which are determined in advance, and a first parameter coefficient and a second parameter coefficient which are respectively introduced for the first parameterization and the second parameterization.
Optionally, the first parameterized expression includes: accumulating a chord length parameterization expression; the second parameterized expression includes: centripetal parameterization expression.
Optionally, determining the node vector under the third parameterized expression based on the acquired coordinates of the plurality of model value points and the number of the plurality of model value points includes: calculating the sum of the plurality of model value points under the third parameterization expression according to the coordinates of the plurality of model value points and the number of the plurality of model value points; and calculating a node vector under the third parameterization expression according to the coordinates of the plurality of model value points, the number of the plurality of model value points, the preset spline order and the calculated sum of the plurality of model value points under the third parameterization expression.
Optionally, determining a B-spline expression for performing the robot path planning based on the determined node vector under the third parameterized expression comprises: solving a basis function of the B spline expression by using a preset recurrence formula according to the determined node vector under the third parameterized expression; and determining a B-spline expression for carrying out robot path planning according to the predetermined B-spline curve control vertex and the basis function obtained by solving.
Another aspect of the present application provides a robot path planning apparatus, including: the system comprises an acquisition unit, a calculation unit and a calculation unit, wherein the acquisition unit is used for acquiring a given theoretical path, sequentially acquiring coordinates of a given plurality of model value points and determining the number of the model value points; a first determining unit configured to determine a node vector under a third parameterized expression based on the coordinates of the plurality of model value points and the number of the plurality of model value points acquired by the acquiring unit; a second determining unit configured to determine a B-spline expression for performing the robot path planning based on the node vector under the third parameterized expression determined by the first determining unit; a path planning unit, configured to perform path planning of the robot by using the B-spline expression determined by the second determining unit, so as to obtain discrete path points of the robot motion; the third parameterization expression is determined according to a first parameterization expression and a second parameterization expression which are determined in advance, and a first parameter coefficient and a second parameter coefficient which are respectively introduced for the first parameterization and the second parameterization.
Optionally, the first parameterized expression includes: accumulating a chord length parameterization expression; the second parameterized expression includes: centripetal parameterization expression.
Optionally, the first determining unit determines a node vector under a third parameterized expression based on the acquired coordinates of the plurality of model value points and the number of the plurality of model value points, including:
calculating the sum of the plurality of model value points under the third parameterization expression according to the coordinates of the plurality of model value points and the number of the plurality of model value points; and calculating a node vector under the third parameterization expression according to the coordinates of the plurality of model value points, the number of the plurality of model value points, the preset spline order and the calculated sum of the plurality of model value points under the third parameterization expression.
Optionally, the second determining unit determines a B-spline expression for performing the robot path planning based on the node vector under the third parameterized expression determined by the first determining unit, including: solving a basis function of the B spline expression by using a preset recurrence formula according to the determined node vector under the third parameterized expression; and determining a B-spline expression for carrying out robot path planning according to the predetermined B-spline curve control vertex and the basis function obtained by solving.
In a further aspect the application provides a storage medium having stored thereon a computer program which when executed by a processor performs the steps of any of the methods described above.
In a further aspect the application provides a robot controller comprising a processor, a memory and a computer program stored on the memory and executable on the processor, the processor implementing the steps of any of the methods described above when executing the program.
In a further aspect, the application provides a robot controller comprising a robot path planning device as described in any one of the preceding.
According to the technical scheme of the application, the parameter coefficient k is introduced 1 Post-accumulation chord length parameterization expression and introduced parameter coefficient k 2 The obtained centripetal parameterization expression is combined to obtain an improved parameterization expression, then a node vector is calculated, and then the overall fitting path of the B spline is determined, so that the overall fitting effect is improved; the improved parameterization expression is obtained by integrating the expression of the two parameterization methods by considering the improvement of the low 'longitudinal' fitting error of the accumulated chord length parameterization method and the low curvature property of the centripetal parameterization method.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1 is a schematic diagram of a method of an embodiment of a robot path planning method according to the present application;
FIG. 2 shows a schematic diagram of the improved principle of the improved parameterization method of the present application;
FIG. 3 shows the coordinates based on the plurality of model value points obtained and the number of the plurality of model value points;
FIG. 4 illustrates a flow diagram of one embodiment of the step of determining a B-spline expression for performing the robot path planning based on the determined node vector under the third parameterized expression;
FIG. 5 shows a theoretical path trajectory;
FIG. 6 shows a comparison of the fitting effect of the improved parameterization of the present application with the accumulated chord length parameterization and centripetal parameterization;
FIG. 7 shows a comparison of the X-direction local fitting effect of the improved parameterization of the present application with the accumulated chord length parameterization and centripetal parameterization;
FIG. 8 shows a longitudinal fit error comparison of the improved parameterization of the present application with accumulated chord length parameterization and centripetal parameterization;
FIG. 9 shows the curvature variation of the improved parameterization of the present application compared to the accumulated chord length parameterization and centripetal parameterization;
FIG. 10 is a method diagram of a robot path planning method according to an embodiment of the present application;
fig. 11 is a block diagram illustrating a robot path planning apparatus according to an embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be clearly and completely described below with reference to specific embodiments of the present application and corresponding drawings. It will be apparent that the described embodiments are only some, but not all, embodiments of the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
It should be noted that the terms "first," "second," and the like in the description and the claims of the present application and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the application described herein may be implemented in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Fig. 1 is a schematic diagram of a method of an embodiment of a robot path planning method according to the present application.
As shown in fig. 1, the robot path planning method at least includes step S110, step S120, step S130, and step S140 according to one embodiment of the present application.
Step S110, acquiring a given theoretical path, sequentially acquiring coordinates of a given plurality of model value points, and determining the number of the model value points.
For example, a given theoretical path may be y=x (x-2); the model value point coordinates may be generated based on theoretical paths or corresponding paths may be determined based on three-dimensional drawing software, and then point coordinates may be extracted. For example, the coordinates of the model value points obtained on the theoretical route y=x (x-2) are shown in table 1.
TABLE 1
The number n of the model value points can be determined by acquiring the coordinates of the given model value points, for example, the number n=17 of the model value points in table 1. The more the number of the model value points is, the larger the calculated amount is, and the better the fitting effect is.
Step S120, determining a node vector under the third parameterization expression based on the obtained coordinates of the plurality of model value points and the number of the plurality of model value points.
Wherein the third parameterizationThe method expression is determined according to a first parameterized method expression and a second parameterized method expression which are determined in advance, and a first parameter coefficient and a second parameter coefficient which are respectively introduced for the first parameterized method and the second parameterized method. Specifically, a first parameter coefficient k introduced in a first parameterization method 1 Second parameter coefficient k introduced in second parameterization 2 Then a third parameterized expression f can be obtained 3 ：
f 3 ＝f 1 (X(i+1),X(i),Y(i+1),Y(i),k 1 )+f 2 (X(i+1),X(i),Y(i+1),Y(i),k 2 )
For example, the first parameterized expression f1, the second parameterized expression f2, and the modified third parameterized expression f3 are as follows:
first parameter coefficient k 1 And a second parameter coefficient k 2 Are all dynamic parameters between 0 and 1. In one embodiment, k can be based on 1 And k 2 Corresponding fitting error and smoothness training are used to determine the parameter k 1 And k 2 Based on the fitting error and the smoothness requirement of the actual process requirement to the processing path, a trained model is called to obtain a determined k 1 And k 2 。
In a specific embodiment, the first parameterized expression f 1 Comprising: cumulative chord length parameterization expression f 1 The method comprises the steps of carrying out a first treatment on the surface of the The second parameterized expression f 1 Comprising: centripetal parameterization expression f 2 。
The application introduces a first parameter coefficient k 1 And a second parameter coefficient k 2 The advantages and disadvantages of the first and second parameterization methods can be dynamically combined to obtain an improved parameterization expression, i.e. the third parameterization expression. For example, the cumulative chord length parameterization method has the advantages of high fitting precision and poor smoothness, so that a first parameter coefficient k is introduced 1 The method is involved in node vector calculation and used for adjusting fitting precision; the centripetal parameterization method has the advantages of better fairing property and low fitting precision, so the second parameter coefficient k is introduced 2 For adjusting the smoothness of the path fit; introducing a parameter coefficient k 1 Post-accumulation chord length parameterization expression and introduced parameter coefficient k 2 And combining the subsequent centripetal parameterization expression to obtain an improved parameterization expression.
The improved parameterized expression can dynamically adjust the parameter coefficient k based on the requirement of industry on the fitting path 1 And k 2 Therefore, under the condition of ensuring fitting precision, the smoothness of a fitting path is improved; or under the condition of ensuring the smoothness of the fitting path, the fitting accuracy of the fitting path is improved.
Fig. 2 shows a schematic diagram of the improved principle of the improved parameterization method of the present application. As shown in fig. 2, in the related art, the accumulated chord length parameterization method and the centripetal parameterization method are often used for the node vector calculation. The accumulated chord length method is to calculate a node vector based on adjacent chord value points; the method has the advantages of high fitting precision, small fitting error, large curvature change, poor fairing, and the centripetal parameterization method is based on centripetal parameters of adjacent chord value points to calculate node vectors; the method has the advantages of small curvature change, good smoothness, low fitting precision and large fitting error. Based on the two parameterization principles of the accumulated chord length parameterization method and the centripetal parameterization method, the defects of high fitting precision and poor smoothness of the accumulated chord length parameters are considered, and a parameter coefficient k1 is introduced to participate in node vector calculation for adjusting the fitting precision; considering the advantages of the centripetal parameter method, such as good smoothness and low fitting precision, the parameter coefficient k2 is introduced for adjusting the smoothness of the path fitting.
FIG. 3 is a flow chart of one embodiment of the step of determining a node vector under a third parameterized expression based on the acquired coordinates of the plurality of model points and the number of the plurality of model points. As shown in fig. 3, step S120 may specifically include: step S121 and step S122.
Step S121, calculating a sum of the plurality of model value points under the third parameterization expression according to the coordinates of the plurality of model value points and the number of the plurality of model value points.
Specifically, the Sum of the plurality of model value points under the third parameterization expression can be obtained according to the coordinates X (i), Y (i) of the plurality of model value points and the number n of the plurality of model value points:
step S122, calculating a node vector under the third parameterization expression according to the coordinates of the plurality of model value points, the number of the plurality of model value points, the preset spline order, and the calculated sum of the plurality of model value points under the third parameterization expression.
Specifically, from the coordinates X (i), Y (i) of the plurality of model value points, the number n of the plurality of model value points, and the spline order k (for example, with cubic B-spline, spline order k=3), the node vector U (i) under the third parameterized expression may be obtained:
as shown in table 2, table 2 shows a comparison of the modified parameterization with the node vectors of the other two parameterizations.
TABLE 2
And step S130, determining a B-spline expression for carrying out the robot path planning based on the determined node vector under the third parameterized expression.
FIG. 4 shows a flow diagram of one embodiment of the step of determining a B-spline expression for performing the robot path planning based on the determined node vector under the third parameterized expression. As shown in fig. 4, step S130 may specifically include: step S131 and step S132.
Step S131, solving the basis function of the B spline expression by using a preset recurrence formula according to the determined node vector under the third parameterized expression.
Specifically, the basis functions of the B-spline expression can be solved using the Cox-De Boor recurrence formula from the calculated node vector U (i).
And S132, determining a B spline expression for carrying out the robot path planning according to the predetermined B spline curve control vertex and the basis function obtained by solving.
Specifically, a B-spline expression for performing the robot path planning can be determined according to the control vertex and the basis function obtained by solving.
And step S140, performing path planning of the robot by using the determined B-spline expression to obtain discrete path points of the motion of the robot.
Specifically, a robot path is planned using the determined B-spline expression to obtain discrete path points for the robot motion.
Fig. 5 shows a theoretical path trajectory. FIG. 6 shows a comparison of the fitting effect of the improved parameterization of the present application with the accumulated chord length parameterization and centripetal parameterization; fig. 7 shows the X-direction local fitting effect comparison of the improved parameterization of the present application with the accumulated chord length parameterization and centripetal parameterization.
From fig. 6, it can be seen that the improved parameterization of the present application almost coincides with the fitting curves of the cumulative chord length parameterization and the centripetal parameterization. As can be seen from fig. 7, the effect of the local fitting in the X direction by the improved parameterization method of the present application is closer to the theoretical curve, which indicates that the effect of the local fitting in the X direction by the improved parameterization method of the present application is better.
And verifying and analyzing the fitting effect of the improved parameterization method. First, the cumulative chord length parameterization function f is plotted 1 Centripetal parameterization function f 2 Improved parameterization function f 3 And (3) corresponding fitting curves, comparing the fitting curves with theoretical curves respectively, and solving the longitudinal fitting errors and the curvature of the curves corresponding to different parameterization methods.
Figure 8 shows a comparison of the longitudinal fitting error of the improved parameterization of the present application with the accumulated chord length parameterization and centripetal parameterization. Fig. 9 shows the curvature variation of the improved parameterization of the present application compared to the accumulated chord length parameterization and centripetal parameterization. As shown in fig. 8 and 9, the "longitudinal" fitting error is processed and analyzed based on the minimum error absolute value, the maximum error absolute value and the average error absolute value, so that the fitting accuracy of the improved parameterization method can be improved obviously, and the fitting errors of the improved parameterization method, the accumulated chord length parameterization method and the centripetal parameterization method are shown in table 3. The curvature graph of the curve can intuitively reflect the smoothness of the fitted curve by three parameterization methods.
TABLE 3 Table 3
In order to clearly illustrate the technical scheme of the present application, a specific embodiment is used to describe the execution flow of the robot path planning method provided by the present application.
Fig. 10 is a schematic diagram of a method of a robot path planning method according to an embodiment of the present application. The embodiment shown in fig. 10 includes steps S1 to S5.
Step S1: and giving a theoretical path, and sequentially determining the coordinates of the model value points.
For example, the coordinates of the model value points obtained on the theoretical route y=x (x-2) are shown in table 1.
Step S2: based on the step 1, determining and inputting the number n of the model value points; the more the number of the model value points is, the larger the calculated amount is, and the better the fitting effect is.
Step S3: according to a function expression U (i) of the node vector and an accumulated chord length parameterization expression f 1 Centripetal parameterization expression f 2 The abscissa X (i) and the ordinate Y (i) of each value point, the first parameter coefficient k introduced in the accumulated chord length parameterization method 1 Second parameter coefficient k introduced in centripetal parameterization 2 Determining an improved parameterization expression f by using the number n of model value points and the spline order k 3 Improved parameterization method f 3 Sum and node vector U (i) at different type value points: can obtain an improved parameterization expression f3 and an improved parameterization f 3 The Sum and node vector U (i) at the different type value points are as follows:
f 3 ＝f 1 (X(i+1),X(i),Y(i+1),Y(i),k 1 )+f 2 (X(i+1),X(i),Y(i+1),Y(i),k 2 )
combining the medium value point coordinates in the step S1, a node vector U (i) under the improved parameterization method can be calculated, for example, as shown in table 2; table 2 shows a comparison of the modified parameterization with the node vectors of the other two parameterizations.
Step S4: introducing an end point tangential condition, and solving a control vertex in a back calculation mode.
Step S5: the two core parameters of the cubic B spline curve are a control vertex and a base function respectively, wherein the control vertex is solved in the step S4, and the expression of the cubic B spline can be determined only by solving the base function according to a Cox-DeBoor recurrence formula;
step S6: and introducing a speed plan to obtain a series of discrete path points.
Fig. 11 is a block diagram illustrating a robot path planning apparatus according to an embodiment of the present application. As shown in fig. 11, the robot path planning apparatus 100 includes an acquisition unit 110, a first determination unit 120, a second determination unit 130, and a path planning unit 140.
The obtaining unit 110 is configured to obtain a given theoretical path, sequentially obtain coordinates of a given plurality of model value points, and determine the number of the plurality of model value points.
For example, a given theoretical path may be y=x (x-2); the model value point coordinates may be generated based on theoretical paths or corresponding paths may be determined based on three-dimensional drawing software, and then point coordinates may be extracted. For example, the coordinates of the model value points obtained on the theoretical route y=x (x-2) are shown in table 1.
TABLE 1
The number n of the model value points can be determined by acquiring the coordinates of the given model value points, for example, the number n=17 of the model value points in table 1. The more the number of the model value points is, the larger the calculated amount is, and the better the fitting effect is.
A first determining unit 120, configured to determine a node vector under a third parameterized expression based on the coordinates of the plurality of model value points and the number of the plurality of model value points acquired by the acquiring unit.
The third parameterization expression is determined according to a first parameterization expression and a second parameterization expression which are determined in advance, and a first parameter coefficient and a second parameter coefficient which are respectively introduced for the first parameterization and the second parameterization. Specifically, a first parameter coefficient k introduced in a first parameterization method 1 Second parameter coefficient k introduced in second parameterization 2 Then a third parameterized expression f can be obtained 3 ：
f 3 ＝f 1 (X(i+1),X(i),Y(i+1),Y(i),k 1 )+f 2 (X(i+1),X(i),Y(i+1),Y(i),k 2 )
For example, the first parameterized expression f1, the second parameterized expression f2, and the modified third parameterized expression f3 are as follows:
first parameter coefficient k 1 And a second parameter coefficient k 2 Are all dynamic parameters between 0 and 1. In one embodiment, k can be based on 1 And k 2 Corresponding fitting error and smoothness training are used to determine the parameter k 1 And k 2 Based on the fitting error and the smoothness requirement of the actual process requirement to the processing path, a trained model is called to obtain a determined k 1 And k 2 。
In a specific embodiment, the first parameterized expression f 1 Comprising: cumulative chord length parameterization expression f 1 The method comprises the steps of carrying out a first treatment on the surface of the The second parameterized expression f 1 Comprising: centripetal parameterization expression f 2 。
The application introduces a first parameter coefficient k 1 And a second parameter coefficient k 2 The advantages and disadvantages of the first and second parameterization methods can be dynamically combined to obtain an improved parameterization expression, i.e. the third parameterization expression. For example, the cumulative chord length parameterization method has the advantages of high fitting precision and poor smoothness, so that a first parameter coefficient k is introduced 1 The method is involved in node vector calculation and used for adjusting fitting precision; the centripetal parameterization method has the advantages of better fairing property and low fitting precision, so the second parameter coefficient k is introduced 2 For adjusting the smoothness of the path fit; handleIntroducing a parameter coefficient k 1 Post-accumulation chord length parameterization expression and introduced parameter coefficient k 2 And combining the subsequent centripetal parameterization expression to obtain an improved parameterization expression. The improved parameterized expression can dynamically adjust the parameter coefficient k based on the requirement of industry on the fitting path 1 And k 2 Therefore, under the condition of ensuring fitting precision, the smoothness of a fitting path is improved; or under the condition of ensuring the smoothness of the fitting path, the fitting accuracy of the fitting path is improved.
Fig. 2 shows a schematic diagram of the improved principle of the improved parameterization method of the present application. As shown in fig. 2, in the related art, the accumulated chord length parameterization method and the centripetal parameterization method are often used for the node vector calculation. The accumulated chord length method is to calculate a node vector based on adjacent chord value points; the method has the advantages of high fitting precision, small fitting error, large curvature change, poor fairing, and the centripetal parameterization method is based on centripetal parameters of adjacent chord value points to calculate node vectors; the method has the advantages of small curvature change, good smoothness, low fitting precision and large fitting error.
Based on the two parameterization principles of the accumulated chord length parameterization method and the centripetal parameterization method, the defects of high fitting precision and poor smoothness of the accumulated chord length parameters are considered, and a parameter coefficient k1 is introduced to participate in node vector calculation for adjusting the fitting precision; considering the advantages of the centripetal parameter method, such as good smoothness and low fitting precision, the parameter coefficient k2 is introduced for adjusting the smoothness of the path fitting.
In one embodiment, the first determining unit 120 determines a node vector under a third parameterized expression based on the obtained coordinates of the plurality of model value points and the number of the plurality of model value points, including: calculating the sum of the plurality of model value points under the third parameterization expression according to the coordinates of the plurality of model value points and the number of the plurality of model value points; and calculating a node vector under the third parameterization expression according to the coordinates of the plurality of model value points, the number of the plurality of model value points, the preset spline order and the calculated sum of the plurality of model value points under the third parameterization expression.
Specifically, the Sum of the plurality of model value points under the third parameterization expression can be obtained according to the coordinates X (i), Y (i) of the plurality of model value points and the number n of the plurality of model value points:
from the coordinates X (i), Y (i) of the plurality of model value points, the number n of the plurality of model value points, and the spline order k (for example, when three B-splines are used, the spline order k=3), the node vector U (i) under the third parameterized expression may be obtained:
as shown in table 2, table 2 shows a comparison of the modified parameterization with the node vectors of the other two parameterizations.
TABLE 2
A second determining unit 130, configured to determine a B-spline expression for performing the robot path planning based on the node vector under the third parameterized expression determined by the first determining unit.
In one specific embodiment, the second determining unit determines a B-spline expression for performing the robot path planning based on the node vector under the third parameterized expression determined by the first determining unit, and includes: solving a basis function of the B spline expression by using a preset recurrence formula according to the determined node vector under the third parameterized expression; and determining a B-spline expression for carrying out robot path planning according to the predetermined B-spline curve control vertex and the basis function obtained by solving.
Specifically, an endpoint tangent vector condition is introduced, a control vertex is solved in a back calculation mode, and a basis function of a B spline expression is solved by utilizing a Cox-De Boor recurrence formula according to a calculated node vector U (i). And determining the B-spline expression for carrying out the robot path planning according to the control vertex and the basis function obtained by solving.
A path planning unit 140, configured to perform the path planning of the robot by using the B-spline expression determined by the second determining unit 130, so as to obtain discrete path points of the motion of the robot.
Specifically, a robot path is planned using the determined B-spline expression to obtain discrete path points for the robot motion.
Fig. 5 shows a theoretical path trajectory. FIG. 6 shows a comparison of the fitting effect of the improved parameterization of the present application with the accumulated chord length parameterization and centripetal parameterization; fig. 7 shows the X-direction local fitting effect comparison of the improved parameterization of the present application with the accumulated chord length parameterization and centripetal parameterization. From fig. 6, it can be seen that the improved parameterization of the present application almost coincides with the fitting curves of the cumulative chord length parameterization and the centripetal parameterization. As can be seen from fig. 7, the effect of the local fitting in the X direction by the improved parameterization method of the present application is closer to the theoretical curve, which indicates that the effect of the local fitting in the X direction by the improved parameterization method of the present application is better.
And verifying and analyzing the fitting effect of the improved parameterization method. First, the cumulative chord length parameterization function f is plotted 1 Centripetal parameterization function f 2 Improved parameterization function f 3 And (3) corresponding fitting curves, comparing the fitting curves with theoretical curves respectively, and solving the longitudinal fitting errors and the curvature of the curves corresponding to different parameterization methods. Figure 8 shows a comparison of the longitudinal fitting error of the improved parameterization of the present application with the accumulated chord length parameterization and centripetal parameterization. Fig. 9 shows the curvature variation of the improved parameterization of the present application compared to the accumulated chord length parameterization and centripetal parameterization. As shown in FIG. 8 and FIG. 9, the "longitudinal" fitting error is based on the minimum error absolute value, the maximum error absolute value, and the average errorThe absolute value is subjected to data processing and analysis, so that the fitting precision of the improved parameterization method can be highlighted to be better, and the fitting errors of the improved parameterization method, the accumulated chord length parameterization method and the centripetal parameterization method are shown in the table 3. The curvature graph of the curve can intuitively reflect the smoothness of the fitted curve by three parameterization methods.
TABLE 3 Table 3
The application also provides a storage medium corresponding to the robot path planning method, on which a computer program is stored, which program, when being executed by a processor, implements the steps of any of the methods described above.
The application also provides a robot controller corresponding to the robot path planning method, comprising a processor, a memory and a computer program stored on the memory and executable on the processor, the processor executing the program to implement the steps of any of the methods described above.
The application also provides a robot controller corresponding to the robot path planning device, which comprises any one of the robot path planning devices.
Accordingly, the scheme provided by the application introduces the parameter coefficient k 1 Post-accumulation chord length parameterization expression and introduced parameter coefficient k 2 The obtained centripetal parameterization expression is combined to obtain an improved parameterization expression, then a node vector is calculated, and then the overall fitting path of the B spline is determined, so that the overall fitting effect is improved; the improved parameterization expression is obtained by integrating the expression of the two parameterization methods by considering the improvement of the low 'longitudinal' fitting error of the accumulated chord length parameterization method and the low curvature property of the centripetal parameterization method.
According to the technical scheme, compared with an accumulated chord length parameterization method, the curvature change is reduced, and the smoothness of a B spline fitting curve is improved; compared with a centripetal parameterization method, the method reduces the 'longitudinal' fitting error and improves the precision of the B spline fitting curve;
according to the technical scheme, parameters can be dynamically adjusted based on the requirements of the process on the fitting precision and the fitting curve smoothness, so that the smoothness of curve fitting is improved on the premise of meeting the fitting precision, and the fitting precision of the curve is improved on the premise of meeting the curve smoothness.
The functions described herein may be implemented in hardware, software executed by a processor, firmware, or any combination thereof. If implemented in software that is executed by a processor, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Other examples and implementations are within the scope and spirit of the application and the appended claims. For example, due to the nature of software, the functions described above may be implemented using software executed by a processor, hardware, firmware, hardwired, or a combination of any of these. In addition, each functional unit may be integrated in one processing unit, each unit may exist alone physically, or two or more units may be integrated in one unit.
In the several embodiments provided in the present application, it should be understood that the disclosed technology may be implemented in other manners. The above-described embodiments of the apparatus are merely exemplary, and the division of the units, for example, may be a logic function division, and may be implemented in another manner, for example, a plurality of units or components may be combined or may be integrated into another system, or some features may be omitted, or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed with each other may be through some interfaces, units or modules, or may be in electrical or other forms.
The units described as separate components may or may not be physically separate, and components as control devices may or may not be physical units, may be located in one place, or may be distributed over a plurality of units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present application may be embodied in essence or a part contributing to the related art or all or part of the technical solution, in the form of a software product stored in a storage medium, including several instructions for causing a computer device (which may be a personal computer, a server or a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a removable hard disk, a magnetic disk, or an optical disk, or other various media capable of storing program codes.
The above description is only an example of the present application and is not intended to limit the present application, but various modifications and variations can be made to the present application by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.
Claims (10)
1. A robot path planning method, comprising:
acquiring a given theoretical path, sequentially acquiring coordinates of a given plurality of model value points, and determining the number of the model value points;
determining a node vector under a third parameterization expression based on the obtained coordinates of the plurality of model value points and the number of the plurality of model value points;
determining a B-spline expression for performing the robot path planning based on the determined node vector under the third parameterized expression;
performing the robot path planning by using the determined B-spline expression to obtain discrete path points of the robot motion;
the third parameterization expression is determined according to a first parameterization expression and a second parameterization expression which are determined in advance, and a first parameter coefficient and a second parameter coefficient which are respectively introduced for the first parameterization and the second parameterization.
2. The method of claim 1, wherein the first parameterized expression comprises: accumulating a chord length parameterization expression; the second parameterized expression includes: centripetal parameterization expression.
3. The method according to claim 1 or 2, wherein determining a node vector under a third parameterized expression based on the acquired coordinates of the plurality of model value points and the number of the plurality of model value points comprises:
calculating the sum of the plurality of model value points under the third parameterization expression according to the coordinates of the plurality of model value points and the number of the plurality of model value points;
and calculating a node vector under the third parameterization expression according to the coordinates of the plurality of model value points, the number of the plurality of model value points, the preset spline order and the calculated sum of the plurality of model value points under the third parameterization expression.
4. The method according to claim 1 or 2, wherein determining a B-spline expression for performing the robot path planning based on the determined node vector under the third parameterized expression comprises:
solving a basis function of the B spline expression by using a preset recurrence formula according to the determined node vector under the third parameterized expression;
and determining a B-spline expression for carrying out robot path planning according to the predetermined B-spline curve control vertex and the basis function obtained by solving.
5. A robot path planning apparatus, comprising:
the system comprises an acquisition unit, a calculation unit and a calculation unit, wherein the acquisition unit is used for acquiring a given theoretical path, sequentially acquiring coordinates of a given plurality of model value points and determining the number of the model value points;
a first determining unit configured to determine a node vector under a third parameterized expression based on the coordinates of the plurality of model value points and the number of the plurality of model value points acquired by the acquiring unit;
a second determining unit configured to determine a B-spline expression for performing the robot path planning based on the node vector under the third parameterized expression determined by the first determining unit;
a path planning unit, configured to perform path planning of the robot by using the B-spline expression determined by the second determining unit, so as to obtain discrete path points of the robot motion;
the third parameterization expression is determined according to a first parameterization expression and a second parameterization expression which are determined in advance, and a first parameter coefficient and a second parameter coefficient which are respectively introduced for the first parameterization and the second parameterization.
6. The apparatus of claim 5, wherein the first parameterized expression comprises: accumulating a chord length parameterization expression; the second parameterized expression includes: centripetal parameterization expression.
7. The apparatus according to claim 5 or 6, wherein the first determining unit determines a node vector under a third parameterized expression based on the acquired coordinates of the plurality of model value points and the number of the plurality of model value points, comprising:
calculating the sum of the plurality of model value points under the third parameterization expression according to the coordinates of the plurality of model value points and the number of the plurality of model value points;
and calculating a node vector under the third parameterization expression according to the coordinates of the plurality of model value points, the number of the plurality of model value points, the preset spline order and the calculated sum of the plurality of model value points under the third parameterization expression.
8. The apparatus according to claim 5 or 6, wherein the second determination unit determines a B-spline expression for performing the robot path planning based on a node vector under the third parameterized expression determined by the first determination unit, comprising:
solving a basis function of the B spline expression by using a preset recurrence formula according to the determined node vector under the third parameterized expression;
and determining a B-spline expression for carrying out robot path planning according to the predetermined B-spline curve control vertex and the basis function obtained by solving.
9. A storage medium having stored thereon a computer program which when executed by a processor performs the steps of the method of any of claims 1-4.
10. A robot controller comprising a processor, a memory and a computer program stored on the memory and executable on the processor, when executing the program, implementing the steps of the method of any of claims 1-4, comprising the robot path planning apparatus of any of claims 5-8.
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