CN117970813B - Robot polishing track offline planning method and system based on automobile gear - Google Patents
Robot polishing track offline planning method and system based on automobile gear Download PDFInfo
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Abstract
The application relates to a robot polishing track offline planning method and system based on an automobile gear, comprising the following steps: s100: discrete grinding of track points by using a three-dimensional model of the automobile gear; s200: constructing a polishing track quality multi-target comprehensive mathematical model, and quantitatively evaluating the track optimizing effect; s300: optimizing the polishing track points by utilizing a multi-target collaborative genetic algorithm to obtain an optimal sequence of the polishing track points; s400: acquiring a robot joint track by utilizing quintic B spline interpolation, and optimizing the robot joint track and the motion performance; s500: constructing a polishing track error model verification optimization effect, and obtaining a first verification result; s600: when the first verification result does not meet the error model, dispersing new track points and re-optimizing the polishing track; s700: and when the first verification result meets the error model, finishing track optimization, and outputting a planned polishing track. The application can realize the efficient offline planning and comprehensive optimization of the robot polishing track and improve the quality comprehensive performance of the robot polishing track.
Description
Technical Field
The application relates to the technical field of automobile gear polishing technology and industrial robot motion trail offline planning, in particular to an automobile gear-based robot polishing trail offline planning method and system.
Background
In recent years, industrial robots are gradually applied to various important industries by virtue of the characteristics of programmability, automation, high flexibility and the like, and the industrial robots have high flexibility and adaptability and are ideal choices for automatic polishing of a large number of parts with complex surfaces in various types. The traditional teaching programming can not meet the requirements of high efficiency, high precision and the like of the modern polishing process, and offline programming becomes a main programming mode of the polishing robot. The track planning is the core of offline programming of the polishing robot, and polishing track points are determined on the surface of an object by utilizing the three-dimensional digital model of the polished object, so that a polishing motion track of the robot is formed, and the robot is automatically polished.
Aiming at the discrete type combination optimization problem of the polishing track points of complex parts such as automobile gears, the core is to solve the optimal polishing track point sequence, because the number of the polishing track points is more, a larger combination optimization search space is needed, the general optimization algorithm is difficult to solve when facing large-scale and complicated iteration problems, and the phenomena of local convergence, insufficient searching reliability and the like are easy to occur, therefore, the multi-target collaborative genetic optimization algorithm is provided, the algorithm randomly performs multi-target clustering on an initial polishing track point set, and makes each polishing track point evolve towards an optimal solution through mutual collaborative dynamic cross variation of polishing track points of different targets so as to achieve the aim of collaborative evolution of the multi-target polishing track points in cooperation and competition. Meanwhile, the rationality of the joint track of the robot not only affects the motion performance of the robot, but also affects the tracking precision of the polishing track, thereby affecting the polishing thickness uniformity of the part, therefore, a five-time B spline interpolation algorithm of the joint track of the robot is provided, and the algorithm constructs the joint track with controllable starting and stopping parameters and continuous motion parameters by setting the starting and stopping parameter constraint of the robot.
With the rapid development of equipment manufacturing industry in China, the requirements on the polishing quality of automobile gears are higher and higher, and the difficulty of an automatic polishing technology is higher. Therefore, the offline planning method and system for the polishing track of the robot based on the automobile gear are researched, the rationality and the motion performance of the polishing track of the robot are optimized, more powerful technical support is provided for offline planning and comprehensive optimization of the polishing track of the robot for complex parts such as the automobile gear, the product quality and economic benefit of enterprises can be improved, the safe production rights and interests of workers can be effectively ensured, and meanwhile, the development trend of new and old kinetic energy conversion and the urgent requirements of manufacturing industry on high-quality development are met.
Disclosure of Invention
The invention aims to provide an offline planning method and system for a robot polishing track based on an automobile gear, and aims at the characteristics that the traditional polishing track planning method is serious in singleness and cannot fully consider the motion performance of a robot, and the comprehensive evaluation index of polishing track quality is not perfect, and the polishing track and joint motion track of the robot are optimized by combining a multi-target collaborative genetic algorithm and a quintic B-spline interpolation algorithm, so that the start and stop stability of the robot is improved, the motion impact is effectively reduced, the motion performance of the robot is ensured, and the accuracy and efficiency of offline planning of the polishing track are greatly improved.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
in a first aspect, the invention provides a robot polishing track offline planning method based on an automobile gear, which is used for offline planning and comprehensive optimization of the polishing track of the automobile gear, and comprises the following steps:
S100: pre-planning a robot polishing track by using a three-dimensional model of an automobile gear, and dispersing polishing track points;
S200: analyzing main influencing factors in the robot polishing track planning, constructing a polishing track quality multi-target comprehensive mathematical model, screening polishing track points, and quantitatively evaluating polishing track optimizing effects;
s300: optimizing the polished track points by utilizing a multi-target collaborative genetic algorithm in combination with the robot polished track planning information, and mutually collaborative dynamic cross variation of the polished track points to obtain an optimal sequence of polished track points;
S400: combining the robot joint motion information, acquiring a robot joint track by utilizing quintic B spline interpolation, and optimizing the robot joint track and the motion performance;
s500: constructing a polishing track error model to verify the optimization effect of the polishing track and the joint track of the robot, and obtaining a first verification result;
S600: when the first verification result does not meet the polishing track error model, dispersing new polishing track points and re-optimizing the polishing track;
s700: and when the first verification result meets the polishing track error model, finishing the collaborative optimization of the robot polishing track, and outputting the planned polishing track.
Further, the specific method of step S100 is as follows:
The optimal track distance is determined according to the space gesture change of the robot polishing device and the polishing track length, each polishing track is scattered according to the optimal track distance, and the generated discrete points are used as polishing track points. And if the length of the polishing track is smaller than the optimal track interval, generating discrete points according to the length of the polishing track.
Further, the specific method of step S200 is as follows:
S201: the main influencing factors in the polishing track planning of the analysis robot comprise: polishing efficiency, polishing track repeatability and polishing stability;
S202: analyzing the length of the polishing track, calculating the distance between the polishing track points, and constructing a polishing track point distance matrix Wherein, the method comprises the steps of, wherein,For sharpening the track points, n represents the number of track points,I and j are the distances between the i and j points；
S203: construction of the polishing track Length：Wherein, the method comprises the steps of, wherein,The length of the polishing track of the section b;
S204: the median length is used for representing the concentration trend of the length of the polishing track section, and the median length can be constructed by arranging the length of the polishing track section Wherein, the method comprises the steps of, wherein,Is thatTaking the remainder of 2;
s205: constructing a mathematical model of robot polishing efficiency ；
S206: constructing a polishing track repetition matrixWherein, the method comprises the steps of, wherein,In order to polish the collection of track segments,To polish track segmentsAndAnd (2) repeating the steps of；
S207: repeating the matrix according to the polishing trackConstruction of repeatability of the polished track segment；
S208: according to the repetition degree value sequence of the polished track segments, constructing the median repetition degree；
S209: to optimize the repetition of the grinding track, a total repetition function of the grinding track is constructed；
S210: constructing a robot polishing track repeatability mathematical model；
S211: to control the turning angle of the polishing track to ensure polishing stability, the turning point number of the polishing track is constructed：Wherein, the method comprises the steps of, wherein,For the degree of turning of the ith polished trace point,In order to grind the included angle between the trace point vectors,The included angle threshold value of the polishing track section is set;
S212: to quantify the bending degree of each polishing track section, an average turning degree of the polishing track is constructed Wherein, the method comprises the steps of, wherein,In order to grind the total number of track segments,Turning degree of the polishing track at the b-th section, and，Is the turning degree of the a polishing track point on the b section polishing track,The total number of polishing track points of the polishing track of the section b;
s213: constructing robot polishing stability mathematical model ；
S214: constructing a polishing track quality multi-target comprehensive mathematical model。
Further, the specific method of step S300 is as follows:
s301: randomly carrying out multi-target clustering on the polished track points, and maintaining an optimal solution in each generation of track points for searching the optimal polished track points in the evolution process;
S302: random initialization Scale Is the polishing track point of (1)The track point is at the firstThe objective function value after the iteration isWherein K is the maximum iteration number of the polishing track points;
S303: performing multi-objective clustering on the polished track points according to the objective function value, and finally generating A set of track points, the firstThe number of the trace point sets is，For the number of sets of trajectory points,Representing an upward rounding;
S304: dividing the track point set into a plurality of track point subsets in the process of the integrated evolution of the polished track point set, wherein each track point subset independently completes dynamic cross and variation, and the collaborative evolution of each track point subset leads to the multi-target dynamic optimization of the whole track point set;
S305: the track point subset is subjected to multi-target evolution, and the crossover probability and the mutation probability can be adjusted in a coordinated and dynamic manner. The dynamic intersection and dynamic variation probabilities of the polished track points are respectively as follows: wherein, the method comprises the steps of, wherein, AndThe probability of crossing and mutation of the mth polishing track point in the kth evolution is respectively,、And、The maximum and minimum values of crossover and mutation probabilities respectively,AndThe cross and variance scale factors are respectively defined,、、AndAnd respectively obtaining an average value, a minimum value, a maximum value and a fitness function value of the objective function of the polishing track point.
Further, the specific method of step S400 is as follows:
s401: selecting a polishing track starting point, connecting points of different types of surfaces, a curvature change point of a processing surface and a tail end track speed change point from a three-dimensional model of the automobile gear as polishing track characteristic points of the robot;
s402: according to inverse kinematics of the robot, acquiring the polishing track characteristic points at actual nodes Corresponding joint angleAnd constructing a joint angle-time node sequenceWherein, the method comprises the steps of, wherein,The number of the track feature points; j is six joints of the robot;
S403: interpolation calculation of joint motion by adopting a cubic B spline method Wherein, the method comprises the steps of, wherein,For the joint angle at each node, u is the node of the B-spline,Is the control vertex of the B-spline curve,Is a basis function of a cubic B spline;
S404: five-degree B spline curve definition domain node vector The frequency number of the head and tail nodes u is 6, and the time nodes are normalized by using an accumulated chord length parameter methodWherein, the method comprises the steps of, wherein,As the time node interval value,；
S405: 4 constraint conditions can be obtained when the start-stop angular velocity and the angular acceleration are zero, so that n+5 quintic B spline interpolation equations are constructedWherein, the method comprises the steps of, wherein,AndThe angular velocity and the angular acceleration of the joint are respectively,And、AndAngular velocity and angular acceleration of track start-stop respectively, and will、、、All values are constrained to 0;
S406: constructing a robot joint track B spline interpolation track meeting joint angle-time node sequence constraint according to the quintic B spline interpolation equation to enable different joints to be different Moment of articulation angleSmooth movement toMoment of articulation angle。
Further, the specific method of step S500 is as follows:
S501: construction No. Chord error of segment theoretical track and feedback trackWherein, the method comprises the steps of, wherein,、The plumb heights between the maximum points of the Euclidean distance from the theoretical polishing track and the feedback polishing track to the characteristic point connecting line are respectively,Is the included angle of the normal plane,Is the ratio of the drop foot distance to the characteristic point distance;
s502: construction No. Polishing thickness error model of segment trackWhereinTo feed back the polished thickness profile of the trace,Theoretical polishing thickness;
S503: constructing a polishing track error model ；
S504: verifying and verifying the optimization effect of the polishing track and the joint track of the robot by using the polishing track error model, and setting a first stepChord error threshold for segment trajectoriesPolishing thickness error thresholdThe first verification result is obtained by comparing the error after polishing track optimization with the threshold value of the errorWhen (when)The chord error and the coating thickness error of the polishing track are both lower than the threshold values, the first verification result meets the polishing track error model at the moment, and otherwiseAnd at the moment, the first verification result does not meet the polishing track error model.
In a second aspect, the invention provides a robot polishing track offline planning system based on an automobile gear, which is characterized by comprising:
The model acquisition module is used for acquiring a three-dimensional digital model of the automobile gear;
The polishing track point discrete module is used for acquiring the robot polishing track and dispersing polishing track points;
the polishing track multi-target optimization module is used for constructing a polishing track quality multi-target comprehensive mathematical model to quantitatively evaluate a polishing track optimization effect, optimizing the polishing track points by utilizing the multi-target cooperative genetic algorithm, and acquiring an optimal sequence of the polishing track points to optimize the robot polishing track;
the joint track interpolation module is used for carrying out the five-time B spline interpolation to obtain a robot joint track and optimize the robot joint track and the motion performance;
The track error verification module is used for constructing the polishing track error model and verifying the optimization effect of the robot polishing track and the joint track to obtain a first verification result;
And the polishing track output module is used for finishing the collaborative optimization of the robot polishing track and outputting the planned polishing track program.
The beneficial technical effects of the invention are as follows: the grinding track quality optimization effect is evaluated by utilizing a multi-target comprehensive mathematical model, the co-evolution and balance relation among different track points is realized by utilizing a multi-target evolution and collaborative dynamic genetic strategy, the optimal set of the grinding track points is obtained, the full iteration and efficient mining of track point data information are realized, the defects of local convergence and insufficient searching reliability caused by single data iteration and no gradient information are reduced, and the accuracy of grinding track point data is effectively improved; establishing an optimal polishing track point sequence, constructing a five-time B spline interpolation of the robot joint track, and effectively improving the optimization precision of the robot joint motion track; the robot polishing track and the joint motion track are planned offline based on a multi-target collaborative genetic optimization algorithm and a quintic B-spline interpolation algorithm, and the polishing track and the joint track are comprehensively optimized, so that the polishing error quality is met, the collaborative optimization of the motion performance and the joint motion track of the robot is realized, and the track planning efficiency and accuracy are effectively improved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method of an embodiment of the present invention;
FIG. 2 is a flow chart of a multi-objective collaborative genetic optimization algorithm in accordance with an embodiment of the present invention;
FIG. 3 is a graph of a chord error model of a theoretical grinding track and a feedback grinding track in a grinding track error model in an embodiment of the invention;
FIG. 4 is a flowchart for comprehensively optimizing the polishing track and the joint track of the robot according to the embodiment of the invention;
FIG. 5 is a schematic diagram of a robot polishing track offline planning system based on an automobile gear, provided by the invention;
FIG. 6 is a simulation effect diagram of a robot polishing track offline planning method and system based on an automobile gear;
fig. 7 is an implementation effect diagram of a robot polishing track offline planning method and system based on an automobile gear.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than as described herein, and therefore the present invention is not limited to the specific embodiments disclosed below.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this application pertains. The terms "first," "second," and the like in the description and in the claims, are not used for any order, quantity, or importance, but are used for distinguishing between different elements. Likewise, the terms "a" or "an" and the like do not denote a limitation of quantity, but rather denote the presence of at least one. The terms "connected" or "connected," and the like, are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "upper", "lower", "left", "right", etc. are used merely to indicate a relative positional relationship, which changes accordingly when the absolute position of the object to be described changes.
As shown in fig. 1 to 4, in combination with a process of comprehensively optimizing a polishing track and a joint track of a robot, the embodiment provides an offline planning method for polishing tracks of a vehicle gear, which is used for offline planning and comprehensive optimization of polishing tracks of the vehicle gear, and comprises the following steps:
S100: pre-planning a robot polishing track by using a three-dimensional model of an automobile gear, and dispersing polishing track points; the specific method comprises the following steps:
The optimal track distance is determined according to the space gesture change of the robot polishing device and the polishing track length, each polishing track is scattered according to the optimal track distance, and the generated discrete points are used as polishing track points. And if the length of the polishing track is smaller than the optimal track interval, generating discrete points according to the length of the polishing track.
S200: analyzing main influencing factors in the robot polishing track planning, constructing a polishing track quality multi-target comprehensive mathematical model, screening polishing track points, and quantitatively evaluating polishing track optimizing effects; the specific method comprises the following steps:
S201: the main influencing factors in the polishing track planning of the analysis robot comprise: polishing efficiency, polishing track repeatability and polishing stability;
S202: analyzing the length of the polishing track, calculating the distance between the polishing track points, and constructing a polishing track point distance matrix ：
（1）
In the formula (1), the components are as follows,For sharpening the track points, n represents the number of track points,I and j are the distances between the i and j points；
S203: in the formula (1)In the time-course of which the first and second contact surfaces,Construction of the polishing track length：
（2）
In the formula (2), the amino acid sequence of the compound,For the length of the segment b grinding track,The smaller the robot polishing efficiency is, the higher the robot polishing efficiency is;
S204: the median length is used for representing the concentration trend of the length of the polishing track section, and the median length can be constructed by arranging the length of the polishing track section ：
（3）
In the formula (3), the amino acid sequence of the compound,Is thatThe remainder is taken for 2 and the remainder is taken,The larger the track section with larger polishing track section length is, the more the track section occupies, the fewer the number of the spatial gesture changes of the robot polishing device are, and the polishing efficiency of the robot is improved;
s205: according to the formula (2) and the formula (3), constructing a robot polishing efficiency mathematical model:
（4）
In the formula (4), the amino acid sequence of the compound, The smaller the value is, the higher the robot polishing efficiency is;
S206: to quantify the repeatability between the grinding track segments, a grinding track repetition matrix is constructed ：
（5）
In the formula (5), the amino acid sequence of the compound,In order to polish the collection of track segments,To polish track segmentsAndAnd (2) repeating the steps of；
S207: construction of the repetition of the polished track segment according to (5)：
（6）
In the formula (6), whenWhen the grinding track of the section b is not repeated, the tooth top grinding quality is good, and whenWhen the polishing track of the section b is repeated for a plurality of times, the polishing quality of the tooth tops is poorer;
S208: according to the repetition degree value sequence of the polished track segments, constructing the median repetition degree ：
（7）
In the formula (7), the amino acid sequence of the compound,The larger the value, the more serious the polishing track is repeated;
s209: to optimize the repetition of the grinding track, a total repetition function of the grinding track is constructed ：
（8）
In the formula (8), the amino acid sequence of the compound,The smaller the value is, the better the optimization effect of the repeated condition of the polishing track is;
S210: constructing a robot polishing track repeatability mathematical model according to the formula (7) and the formula (8):
（9）
in the formula (9), when When the polishing track is in a polishing track section, the repeated condition does not occur, and the polishing track optimization effect is obvious; when (when)When the polishing track is in heavy repeated polishing, the polishing quality of tooth tops is reduced;
s211: to control the turning angle of the polishing track to ensure polishing stability, the turning point number of the polishing track is constructed ：
（10）
In the formula (10), the amino acid sequence of the compound,For the degree of turning of the ith polished trace point,In order to grind the included angle between the trace point vectors,For polishing the included angle threshold of the track segment, whenAt this timeThe polishing track is not turned here; when (when)In the time-course of which the first and second contact surfaces,The polishing track is turned and the polishing track point is recorded as the turning point,In order to polish the number of trace turning points,The larger the value is, the more turning points of the polishing track are, and the poorer the polishing stability of the robot is;
S212: to quantify the bending degree of each polishing track section, an average turning degree of the polishing track is constructed ：
（11）
In the formula (11), the amino acid sequence of the compound,In order to grind the total number of track segments,Turning degree of the polishing track at the b-th section, and，Is the turning degree of the a polishing track point on the b section polishing track,The total number of polishing track points of the polishing track of the b section is thatThe polishing track has only two polishing track points; if it isThe more polishing track points among the polishing track sections and the smaller the turning angle among the polishing track points, the higher the polishing stability of the robot;
S213: according to the formula (10) and the formula (11), constructing a robot polishing stability mathematical model:
（12）
In the formula (12), the amino acid sequence of the compound, The smaller the value is, the better the robot polishing stability is;
s214: constructing a grinding track quality multi-target comprehensive mathematical model according to the formula (4), the formula (9) and the formula (12) 。
S300: optimizing the polished track points by utilizing a multi-target collaborative genetic algorithm in combination with the robot polished track planning information, and mutually collaborative dynamic cross variation of the polished track points to obtain an optimal sequence of polished track points; the specific method comprises the following steps:
s301: randomly carrying out multi-target clustering on the polished track points, and maintaining an optimal solution in each generation of track points for searching the optimal polished track points in the evolution process;
S302: random initialization Scale Is the polishing track point of (1)The track point is at the firstThe objective function value after the iteration isWherein K is the maximum iteration number of the polishing track points;
S303: performing multi-objective clustering on the polished track points according to the objective function value, and finally generating A set of track points, the firstThe number of the trace point sets is，For the number of sets of trajectory points,Representing an upward rounding;
S304: dividing the track point set into a plurality of track point subsets in the process of the integrated evolution of the polished track point set, wherein each track point subset independently completes dynamic cross and variation, and the collaborative evolution of each track point subset leads to the multi-target dynamic optimization of the whole track point set;
S305: the track point subset is subjected to multi-target evolution, and the crossover probability and the mutation probability can be adjusted in a coordinated and dynamic manner. The dynamic intersection and dynamic variation probabilities of the polished track points are respectively as follows:
（13）
（14）
in the formulas (13) and (14), AndThe probability of crossing and mutation of the mth polishing track point in the kth evolution is respectively,、And、The maximum and minimum values of crossover and mutation probabilities respectively,AndThe cross and variance scale factors are respectively defined,、、AndAnd respectively obtaining an average value, a minimum value, a maximum value and a fitness function value of the objective function of the polishing track point.
The multi-target collaborative genetic optimization algorithm optimizes the polishing track by adopting a multi-target optimization and collaborative dynamic cross variation strategy, and each polishing track point set carries out multi-target collaborative dynamic genetics so as to stimulate the polishing track points to evolve in a competitive and coordinated mode, and finally, the optimal polishing track points are obtained. FIG. 2 is a flow chart of a multi-objective collaborative genetic optimization algorithm in accordance with an embodiment of the present invention; the method comprises the following specific steps:
The first step: and determining parameters of the multi-objective collaborative genetic optimization algorithm. Setting the scale of polishing track point set Maximum iteration number K and target track point numberCross scale factorScale factor of variationAnd the like.
And a second step of: and initializing a grinding track point set. For polishing track point sequenceRandom initialization, and setting the evolution algebra of the track point sequence。
And a third step of: and grinding the track point multi-target clusters. Calculating a trajectory point objective function valueAnd performing multi-objective clustering according to the objective function value, and finally generatingAnd (3) target track points.
Fourth step: the target track point sequence co-evolves.The principle of independent collaborative parallelism is required to be kept in the evolution process of each track point set so as to ensure the diversity of the track point sets and the optimization efficiency of the algorithm.
Fifth step: dynamic crossover variation. Determination of the maximum of the objective functionMinimum valueAnd mean valueCalculating dynamic cross probability of track pointsProbability of dynamic variationAnd finishing the collaborative dynamic crossover and mutation operation.
Sixth step: and eliminating the preferential judgment. And (5) eliminating the repeated track points after the cross mutation operation is completed. At the same time ifAll track points can be judged to finish cross variation, and the optimal sequence set of each track point can be selected and shared after multiple evolutions; otherwise, jumping to step 3.
Seventh step: and (5) iterating and outputting judgment. And judging the values of the current iteration times K and the maximum iteration times K. If it isOutputting an optimal solution sequence corresponding to each polishing track point, and finishing comprehensive optimization of the robot polishing track; otherwise, jumping to step 3.
S400: combining the robot joint motion information, acquiring a robot joint track by utilizing quintic B spline interpolation, and optimizing the robot joint track and the motion performance; the specific method comprises the following steps:
S401: in order to select characteristic points which are enough to represent the grinding track, so as to reduce interpolation times and improve joint track interpolation efficiency, selecting a grinding track starting point, connecting points of different types of surfaces, a machining surface curvature change point and a tail end track speed change point from a three-dimensional model of the automobile gear as the grinding track characteristic points of the robot;
s402: according to inverse kinematics of the robot, acquiring the polishing track characteristic points at actual nodes Corresponding joint angleAnd constructing a joint angle-time node sequence A:
（15）
In the formula (15), the amino acid sequence of the compound, The number of the track feature points; j is six joints of the robot;
S403: in order to ensure that the start-stop speed and acceleration of the robot joint are controllable, the track is gentle and has no mutation in the motion process of the robot, and interpolation calculation is carried out on the joint motion by adopting a cubic B spline method:
（16）
in the formula (16), the amino acid sequence of the compound, For the joint angle at each node, u is the node of the B-spline,Is the control vertex of the B-spline curve,Is a basis function of a cubic B spline;
S404: five-degree B spline curve definition domain node vector The frequency number of the head and tail nodes u is 6, and the time nodes are normalized by using an accumulated chord length parameter method:
（17）
in the formula (17), the amino acid sequence of the compound, As the time node interval value,；
S405: 4 constraint conditions can be obtained when the start-stop angular velocity and the angular acceleration are zero, so that n+5 quintic B spline interpolation equations are constructed:
（18）
In the formula (18), the amino acid sequence of the compound, AndThe angular velocity and the angular acceleration of the joint are respectively,And、AndAngular velocity and angular acceleration of track start-stop respectively, and will、、、All values are constrained to 0;
s406: constructing a robot joint track B spline interpolation track meeting joint angle-time node sequence constraint according to the quintic B spline interpolation equation in the formula (18) so as to enable different joints to be different Moment of articulation angleSmooth movement toMoment of articulation angle。
S500: constructing a polishing track error model to verify the optimization effect of the polishing track and the joint track of the robot, and obtaining a first verification result; the specific method comprises the following steps:
s501: constructing a first chord error model diagram according to the theoretical grinding track and the feedback grinding track in the grinding track error model of fig. 3 Chord error of segment theoretical trajectory and feedback trajectory:
（19）
In the formula (19), the amino acid sequence of the compound, 、The plumb heights between the maximum points of the Euclidean distance from the theoretical polishing track and the feedback polishing track to the characteristic point connecting line are respectively,Is the included angle of the normal plane,Is the ratio of the drop foot distance to the characteristic point distance;
S502: the polishing thickness uniformity can be measured by the average value of polishing thickness errors, the larger the average value is, the worse the polishing thickness uniformity of the feedback track is, and the first structure is constructed Polishing thickness error model of the segment track;
（20）
in the formula (20), the amino acid sequence of the compound, To feed back the polished thickness profile of the trace,Theoretical polishing thickness;
S503: constructing a grinding track error model according to the formula (19) and the formula (20):
（21）
in the formula (21), the amino acid sequence of the amino acid, Represent the firstA polishing track error between the segment feedback track and the theoretical track;
s504: verifying and verifying the optimization effect of the polishing track and the joint track of the robot according to the polishing track error model of the formula (21), and setting the first step Chord error threshold for segment trajectoriesPolishing thickness error thresholdAnd obtaining the first verification result by comparing the error after polishing track optimization with the threshold value of the error:
（22）
when the Boolean quantity is obtained according to the formula (22) The chord error and the coating thickness error of the polishing track are both lower than the threshold values, which indicates that the polishing track error between the characteristic points is smaller, and the first verification result meets the polishing track error model at the moment, otherwise, whenAnd at the moment, the first verification result does not meet the polishing track error model.
S600: when the first verification result does not meet the polishing track error model of the formula (21), in the first stepDispersing new polishing track points in the section track, inserting new characteristic points at the same time, and re-optimizing and generating the polishing track to reduce the error of the spraying track;
S700: and when the first verification result meets the polishing track error model in the formula (21), according to the comprehensive optimization flow chart of the robot polishing track and the joint track shown in fig. 4, the collaborative optimization of the robot polishing track and the joint track is finished, and the planned polishing track is output.
According to the embodiment of the invention, polishing error detection can be realized in the offline planning and comprehensive optimization stages of the polishing track of the robot, and if the first verification result does not meet the polishing track error model of the formula (21), the polishing track is unreasonably planned, so that unreasonable polishing tracks can be timely found before the robot starts to polish the automobile gear, and the polishing quality can be guaranteed. Compared with a single optimization method for only the robot polishing track or the joint track, the track planning method for the robot polishing track and the joint motion track collaborative optimization improves the accuracy and the speed of polishing track offline planning. The grinding track quality optimization effect is evaluated by utilizing a multi-target comprehensive mathematical model, the co-evolution and balance relation among different track points is realized by utilizing a multi-target evolution and collaborative dynamic genetic strategy, the optimal set of the grinding track points is obtained, the full iteration and efficient mining of track point data information are realized, the defects of local convergence and insufficient searching reliability caused by single data iteration and no gradient information are reduced, and the accuracy of grinding track point data is effectively improved; establishing an optimal polishing track point sequence, constructing a five-time B spline interpolation of the robot joint track, and effectively improving the optimization precision of the robot joint motion track; and the polishing track and the joint motion track of the robot are planned offline based on a multi-target collaborative genetic optimization algorithm and a quintic B-spline interpolation algorithm, and the polishing track and the joint track are comprehensively optimized, so that the polishing error quality is met, the collaborative comprehensive optimization of the motion performance and the joint motion track of the robot is realized, the efficiency and the accuracy of the offline track planning are effectively improved, and the economic and resource loss of the polishing operation of the robot due to the track error is reduced.
As shown in fig. 5, the present embodiment proposes a robot polishing track offline planning system based on an automobile gear, the system includes:
the model acquisition module 501 is used for acquiring a three-dimensional digital model of the automobile gear;
the polishing track point discrete module 502 is used for acquiring the polishing track of the robot and dispersing polishing track points;
The polishing track multi-target optimization module 503 is configured to construct the polishing track quality multi-target comprehensive mathematical model, screen polishing track points, quantitatively evaluate polishing track optimization effects, optimize the polishing track points by using the multi-target collaborative genetic algorithm, mutually collaborate and dynamically change the polishing track points in a crossing manner, and obtain an optimal sequence of the polishing track points to optimize the robot polishing track;
The joint track interpolation module 504 is configured to perform the five-time B-spline interpolation to obtain a robot joint track, obtain robot joint angle information, and optimize the robot joint track and the motion performance;
the track error verification module 505 is configured to construct the polishing track error model, verify the optimization effects of the robot polishing track and the joint track, obtain a first verification result, and when the first verification result does not meet the polishing track error model, discrete new polishing track points and re-optimize the polishing track;
And the polishing track output module 506 is used for outputting the planned polishing track program after the robot polishing track collaborative optimization is finished when the first verification result meets the polishing track error model.
According to the robot polishing track offline planning system based on the automobile gears, provided by the embodiment of the invention, different types of automobile gear polishing tracks can be planned out of line automatically according to the collaborative optimization method of the robot polishing track and the joint movement track through different types of automobile gear three-dimensional models, so that the defects of discontinuous polishing track and rough polishing surface of manual teaching are effectively avoided; the rationality of the automobile gear polishing track can be judged by combining the offline planning of the robot polishing track and the polishing error detection result in the comprehensive optimization stage, the unreasonable polishing track can be found in time, the polishing quality is ensured, and the automation and the intellectualization of the automobile gear polishing work are realized.
As shown in fig. 6 and fig. 7, according to the simulation effect diagram and the implementation effect diagram provided by the method and the system for offline planning of the polishing track of the robot based on the automobile gear, the output polishing track of the automobile gear has better stability, polishing precision and production efficiency, and the optimization effect of the polishing track of the robot gear is better.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. The robot polishing track offline planning method based on the automobile gear is used for performing offline planning and comprehensive optimization on the robot polishing track and is characterized by comprising the following steps of:
S100: pre-planning a robot polishing track by using a three-dimensional model of an automobile gear, and dispersing polishing track points;
s200: the main influencing factors in the polishing track planning of the analysis robot comprise: the method comprises the steps of constructing a robot polishing efficiency mathematical model by constructing a polishing track length and a median length, constructing a robot polishing track repeatability mathematical model by constructing a polishing track total repeatability and a median repeatability, constructing a robot polishing stability mathematical model by constructing a polishing track turning point number and a polishing track average turning degree, and finally constructing a polishing track quality multi-target comprehensive mathematical model by utilizing the robot polishing efficiency mathematical model, the polishing track repeatability mathematical model and the polishing stability mathematical model to screen polishing track points and quantitatively evaluate polishing track optimization effects;
S300: combining with robot polishing track planning information, randomly carrying out multi-target clustering on polishing track points, maintaining an optimal solution in each generation of track points for searching for optimal polishing track points in the evolution process, optimizing the polishing track points by utilizing a multi-target collaborative genetic algorithm, namely dividing a track point set into a plurality of track point subsets in the integrated evolution process of the polishing track points, independently completing dynamic cross and variation of each track point subset, carrying out collaborative multi-target evolution on each track point subset to lead to multi-target dynamic optimization of the whole track point set, and mutually collaborative dynamic cross variation of the polishing track points to obtain an optimal sequence of the polishing track points;
S400: combining the robot joint motion information, acquiring a robot joint track by utilizing quintic B spline interpolation, and optimizing the robot joint track and the motion performance;
S500: constructing a polishing track error model by utilizing the chord error characteristics and the polishing thickness error model of the theoretical polishing track and the feedback polishing track, and verifying the optimization effects of the robot polishing track and the joint track according to the polishing track error model to obtain a first verification result;
S600: when the first verification result does not meet the polishing track error model, dispersing new polishing track points and re-optimizing the polishing track;
s700: and when the first verification result meets the polishing track error model, finishing the collaborative optimization of the robot polishing track, and outputting the planned polishing track.
2. The method for offline planning of the polishing track of the robot based on the automobile gear according to claim 1, wherein the specific method in step S100 is as follows:
Determining an optimal track distance according to the space posture change of the robot polishing device and the polishing track length, dispersing each polishing track according to the optimal track distance, taking the generated discrete points as polishing track points, and generating the discrete points according to the polishing track length if the polishing track length is smaller than the optimal track distance.
3. The method for offline planning of the polishing track of the robot based on the automobile gear according to claim 1 or 2, wherein the specific method in step S200 is as follows:
S201: the main influencing factors in the polishing track planning of the analysis robot comprise: polishing efficiency, polishing track repeatability and polishing stability;
S202: analyzing the length of the polishing track, calculating the distance between the polishing track points, and constructing a polishing track point distance matrix Wherein, the method comprises the steps of, wherein,For sharpening the track points, n represents the number of track points,Is the firstPoint and the firstThe distance between the points is such that,AndIs that；
S203: construction of the polishing track Length：Wherein, the method comprises the steps of, wherein,Is the firstThe length of the segment polishing track;
S204: the median length is used for representing the concentration trend of the length of the polishing track section, and the median length can be constructed by arranging the length of the polishing track section Wherein, the method comprises the steps of, wherein,Is thatTaking the remainder of 2;
s205: constructing a mathematical model of robot polishing efficiency ；
S206: constructing a polishing track repetition matrixWherein, the method comprises the steps of, wherein,In order to polish the collection of track segments,To polish track segmentsAndAnd (2) repeating the steps of；
S207: repeating the matrix according to the polishing trackConstruction of repeatability of the polished track segment；
S208: according to the repetition degree value sequence of the polished track segments, constructing the median repetition degree；
S209: to optimize the repetition of the grinding track, a total repetition function of the grinding track is constructed；
S210: constructing a robot polishing track repeatability mathematical model；
S211: to control the turning angle of the polishing track to ensure polishing stability, the turning point number of the polishing track is constructed：Wherein, the method comprises the steps of, wherein,Is the firstThe turning degree of each polishing track point,In order to grind the included angle between the trace point vectors,The included angle threshold value of the polishing track section is set;
S212: to quantify the bending degree of each polishing track section, an average turning degree of the polishing track is constructed Wherein, the method comprises the steps of, wherein,In order to grind the total number of track segments,Is the firstTurning degree of segment polishing track, and，Is the firstTurning degree of the a-th polishing track point on the segment polishing track,Is the firstThe total number of polishing track points of the segment polishing track;
s213: constructing robot polishing stability mathematical model ；
S214: constructing a polishing track quality multi-target comprehensive mathematical model。
4. The method for offline planning of the polishing track of the robot based on the automobile gear according to claim 1, wherein the specific method in step S300 is as follows:
s301: randomly carrying out multi-target clustering on the polished track points, and maintaining an optimal solution in each generation of track points for searching the optimal polished track points in the evolution process;
S302: random initialization Scale Is the polishing track point of (1)The track point is at the firstThe objective function value after the iteration isWherein，，The maximum iteration number of the polishing track points is the maximum iteration number;
S303: performing multi-objective clustering on the polished track points according to the objective function value, and finally generating A set of track points, the firstThe number of the trace point sets isWherein，For the number of sets of trajectory points,Representing an upward rounding;
S304: dividing the track point set into a plurality of track point subsets in the process of the integrated evolution of the polished track point set, wherein each track point subset independently completes dynamic cross and variation, and the collaborative evolution of each track point subset leads to the multi-target dynamic optimization of the whole track point set;
S305: the track point subset is subjected to multi-target evolution, the crossing and variation probabilities can be adjusted cooperatively and dynamically, and the dynamic crossing and dynamic variation probabilities of the polished track points are respectively as follows: Wherein, the method comprises the steps of, wherein, AndRespectively the firstThe polishing track points are at the firstThe probability of crossover and mutation at the time of secondary evolution,、And、The maximum and minimum values of crossover and mutation probabilities respectively,AndThe cross and variance scale factors are respectively defined,、、AndAnd respectively obtaining an average value, a minimum value, a maximum value and a fitness function value of the objective function of the polishing track point.
5. The offline planning method for the polishing track of the robot based on the automobile gear according to claim 1, wherein the specific method in the step S400 is as follows:
s401: selecting a polishing track starting point, connecting points of different types of surfaces, a curvature change point of a processing surface and a tail end track speed change point from a three-dimensional model of the automobile gear as polishing track characteristic points of the robot;
s402: according to inverse kinematics of the robot, acquiring the polishing track characteristic points at actual nodes Corresponding joint angleAnd constructing a joint angle-time node sequenceWhereinThe number of the track feature points;， Six joints of the robot;
S403: interpolation calculation of joint motion by adopting a cubic B spline method WhereinFor the joint angle at each node,Is the node of the B-spline curve,Is the control vertex of the B-spline curve,Is a basis function of a cubic B spline;
S404: five-degree B spline curve definition domain node vector Head-tail nodeFrequency number of (6), normalizing time node by cumulative chord parameter methodWhereinAs the time node interval value,，；
S405: 4 constraint conditions can be obtained when the start-stop angular velocity and the angular acceleration are both zero, thereby constructingFive times B spline interpolation equationWhereinAndThe angular velocity and the angular acceleration of the joint are respectively,And、AndAngular velocity and angular acceleration of track start-stop respectively, and will、、、All values are constrained to 0;
S406: constructing a robot joint track B spline interpolation track meeting joint angle-time node sequence constraint according to the quintic B spline interpolation equation to enable different joints to be different Moment of articulation angleSmooth movement toMoment of articulation angle。
6. The offline planning method for the polishing track of the robot based on the automobile gear according to claim 1, wherein the specific method in the step S500 is as follows:
S501: construction No. Chord error of segment theoretical track and feedback trackWherein、The plumb heights between the maximum points of the Euclidean distance from the theoretical polishing track and the feedback polishing track to the characteristic point connecting line are respectively,Is the included angle of the normal plane,Is the ratio of the drop foot distance to the characteristic point distance, wherein；
S502: construction No.Polishing thickness error model of segment trackWhereinTo feed back the polished thickness profile of the trace,Theoretical polishing thickness;
S503: constructing a polishing track error model ；
S504: verifying and verifying the optimization effect of the polishing track and the joint track of the robot by using the polishing track error model, and setting a first stepChord error threshold for segment trajectoriesPolishing thickness error thresholdThe first verification result is obtained by comparing the error after polishing track optimization with the threshold value of the errorWhen (when)The chord error and the coating thickness error of the polishing track are both lower than the threshold values, the first verification result meets the polishing track error model at the moment, and otherwiseAnd at the moment, the first verification result does not meet the polishing track error model.
7. An offline planning system for a robot polishing track based on an automobile gear, for implementing the offline planning method for a robot polishing track based on an automobile gear as claimed in claim 1 or 2 or 3 or 4 or 5 or 6, the system comprising:
The model acquisition module is used for acquiring a three-dimensional digital model of the automobile gear;
The polishing track point discrete module is used for acquiring the robot polishing track and dispersing polishing track points;
the polishing track multi-target optimization module is used for constructing a polishing track quality multi-target comprehensive mathematical model to quantitatively evaluate a polishing track optimization effect, optimizing the polishing track points by utilizing the multi-target cooperative genetic algorithm, and acquiring an optimal sequence of the polishing track points to optimize the robot polishing track;
The joint track interpolation module is used for carrying out B spline interpolation for five times to obtain a robot joint track and optimize the robot joint track and the motion performance;
The track error verification module is used for constructing the polishing track error model and verifying the optimization effect of the robot polishing track and the joint track to obtain a first verification result;
And the polishing track output module is used for finishing the collaborative optimization of the robot polishing track and outputting the planned polishing track program.
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