A method, system and medium for trajectory planning of a planar robot arm in a stamping production line

Abstract

The present invention belongs to the technical field of planar robotic arms for stamping production lines, and specifically discloses a trajectory planning method, system and medium for planar robotic arms for stamping production lines, including: adopting a segmented optimization strategy according to the stamping working conditions, using quintic B-spline interpolation to construct a smooth motion trajectory, and setting motion constraints. The optimization process is divided into two stages: generating an initial population with high diversity and uniform distribution through chaotic-low-discrepancy sequence hybrid initialization. The weight parameters of Alpha, Beta and Delta in the gray wolf algorithm are dynamically adjusted, and at the same time, the change of parameter a in the gray wolf algorithm is controlled based on the dynamic adjustment of the cosine function, effectively balancing the global exploration and local development capabilities. The improved sparrow algorithm is introduced in the local optimization to dynamically adjust the ratio of discoverers and alerters. The fusion algorithm gives full play to the advantages of the two optimization algorithms, maximizes the operating efficiency, and effectively improves the performance of the robotic arms of the stamping production line.

Description

Technical Field

[0001] The present invention belongs to the technical field of planar robotic arms for stamping production lines, and in particular relates to a trajectory planning method, system and medium for planar robotic arms for stamping production lines. Background Art

[0002] With the continuous development of modern intelligent manufacturing technology, industrial robotic arms are widely used in industrial production scenarios such as palletizing, grinding, spraying, and stamping. In the stamping field, industrial robotic arms serve as the core execution unit, and their trajectory planning quality directly affects production efficiency and product quality.

[0003] In the field of robot trajectory planning, two technical approaches can be categorized based on the planning space: Cartesian space trajectory planning and joint space trajectory planning. In actual industrial applications, inverse kinematics is often used to convert Cartesian space path points into joint space for planning. Current mainstream methods for joint space planning include polynomial interpolation, mixed polynomial interpolation, and B-spline curves. However, polynomial interpolation suffers from the inherent flaw of oscillation and divergence of high-order derivatives (such as jerk), which can cause excessive oscillation of the robotic arm. While cubic B-splines can ensure acceleration continuity, their third-order derivatives (jerk) still exhibit step changes, making them incapable of meeting precision operation requirements. The seventh-order B-spline method can ensure continuity of high-order derivatives up to jerk, but its computational complexity increases exponentially, making it difficult to meet the real-time requirements of the production line. The present invention utilizes a fifth-order B-spline method, which ensures both jerk continuity and a relatively simple linear-logarithmic computational complexity.

[0004] Current research in trajectory optimization demonstrates that the choice of intelligent optimization algorithm directly impacts trajectory quality and computational efficiency. Extensive experiments have verified that different algorithms exhibit significant differences in their characteristics. The Gray Wolf Optimizer (GWO) algorithm performs well in the global search phase. Its hierarchical group collaboration mechanism achieves effective coverage of over 90% of the solution space, but suffers from a slow convergence rate in the later stages. The Sparrow Search Algorithm (SSA), through its multi-role division of labor among discoverers, followers, and sentinels, can achieve optimization accuracy of up to 10^-4 rad in localized, refined searches, but it is highly dependent on the initial population. Summary of the Invention

[0005] In response to the problems in the prior art, the present invention provides a method, system and medium for planning the trajectory of a planar robot arm in a stamping production line to solve the problems raised in the above background technology.

[0006] The technical solution adopted in the present invention is as follows:

[0007] In a first aspect, the present application provides a method for trajectory planning of a planar robot arm in a stamping production line, the method comprising the following steps:

[0008] Step S1: Based on the actual working conditions of the stamping production line, the robot arm motion trajectory is divided into three characteristic segments: an approach segment from the initial position to the material collection point, a transport segment from the material collection point to the material discharge point, and a return segment from the material discharge point back to the initial position;

[0009] Set intermediate transition points in each characteristic segment trajectory, and solve the joint space coordinates of the manipulator at the starting point, intermediate point and end point of each segment through inverse kinematics;

[0010] The quintic B-spline curve is used to interpolate the motion trajectory of each segment of the joint to construct a continuous joint space motion trajectory expression;

[0011] Step S2: applying multi-dimensional constraints of position, velocity, and acceleration to the quintic B-spline interpolation function to establish a trajectory curve function that satisfies kinematic constraints;

[0012] By performing first-order, second-order and third-order differential operations on the function, the corresponding velocity characteristic curve, acceleration characteristic curve and jerk characteristic curve are derived respectively, so as to realize trajectory planning including full kinematic parameter constraints and generate the optimized motion path;

[0013] Step S3, calculating the optimal time for each segment in the motion path based on the gray wolf-sparrow search fusion algorithm;

[0014] Step S4: Substitute the optimal time into the quintic B-spline interpolation function of each joint to obtain the position, velocity, acceleration and jerk of each joint, complete the trajectory optimization, and obtain the optimized motion path.

[0015] Furthermore, step S3 includes the following steps:

[0016] Step S3-1: The duration t = [t1, t2, t3] of the robot arm completing each characteristic segment is used as the optimization variable, where t1, t2, and t3 correspond to the movement time of the approach segment, the transport segment, and the return segment, respectively. The initial population is constructed using a hybrid initialization strategy that combines chaotic mapping with low-discrepancy sequences.

[0017] Step S3-2: In the global search phase, according to the iteration mechanism of the Grey Wolf Algorithm, a convergence factor a dynamically adjusted by a cosine function is introduced, and the guidance weights of the Alpha, Beta, and Delta wolves are dynamically adjusted;

[0018] Step S3-3: In the local search phase, the optimal solution output by the Grey Wolf Algorithm is used as the initial guide, and the solution space is refined through the multi-strategy search mechanism of the Sparrow Algorithm, and the global optimal time solution is output through the two-way information interaction mechanism;

[0019] Step S3-4: Repeat steps S3-2 to S3-3 until the preset termination condition is met, and output the optimal time for each segment.

[0020] Furthermore, step S3-1 includes the following steps:

[0021] Step S3-1-1, generating 50% of the initial solutions based on the Logistic chaotic map;

[0022] Step S3-1-2: Generate the remaining 50% of initial solutions using the Halton low-discrepancy sequence;

[0023] Step S3-1-3, calculate the fitness value corresponding to each initial solution , and screen feasible solutions through constraint detection;

[0024] Step S3-1-4: Select three particles with the best fitness values ​​from the feasible solution set and mark them as Alpha, Beta and Delta particles in ascending order of fitness values.

[0025] Furthermore, Logistic is a specific chaotic map with the formula:

[0026] ;

[0027] Where r is the control parameter, usually 4; is the initial value, uniformly distributed between (0, 1), is a standard normal distribution;

[0028] Halton low discrepancy sequence formula is as follows:

[0029]

[0030] In the formula is the smallest prime number greater than or equal to dim+1; is the Weyl sequence coefficient of dimension j; For the kth individual in the The value of the dimension;

[0031] Map the generated chaotic sequences and low-discrepancy sequences to the actual solution space:

[0032]

[0033] Combine the populations generated by the two methods:

[0034] , where They are the populations generated by Logistic chaotic mapping and Halton low-discrepancy sequence respectively; are the upper and lower bound variables of each optimization variable respectively.

[0035] Furthermore, in step S3-2:

[0036] The cosine attenuation expression of the convergence factor is:

[0037]

[0038] In the formula is the current iteration number, ; is the initial value of the convergence factor, usually 2; is the final value of the convergence factor, usually 0; It is the attenuation curve adjustment exponent, used to control the convergence speed, usually set to 0.5; The maximum number of iterations, the first 50% of iterations use convex decay to strengthen global exploration, and the last 50% of iterations use concave decay to focus on local development;

[0039] Nonlinear adjustment of Alpha, Beta and Delta wolf guide weights:

[0040]

[0041] In the formula are the Alpha, Beta and Delta wolf guide weights, respectively, where the Alpha weight decreases with the number of iterations, the Beta weight increases with the number of iterations, and the Delta weight is constant;

[0042] According to the convergence factor And weight distribution, real-time calculation of the core parameters of the Grey Wolf Algorithm:

[0043] Random perturbation vector generation:

[0044]

[0045] In the formula Through the dynamic convergence factor Generated by linear combination of random numbers, the value range is ; Uniformly distributed random numbers are used to generate random perturbations in each dimension independently of the individual position vector; To optimize the variable dimension; rand (1, dim) is to generate a uniformly distributed random number between [0, 1];

[0046] Calculate the relative displacement for Alpha, Beta, and Delta wolves respectively:

[0047]

[0048] In the formula They are the current positions of the Alpha, Beta, and Delta wolf packs respectively. To be updated the location of the wolf pack;

[0049] Synthesize the guided candidate solutions of Alpha, Beta, and Delta wolves:

[0050]

[0051] In the formula They are the guided candidate solutions of Alpha, Beta, and Delta wolves respectively;

[0052] Weighted average based on dynamic weights:

[0053]

[0054] In the formula To update the new wolf pack, and The value of , used for local exploration in subsequent sparrow search.

[0055] Furthermore, in step S3-3:

[0056] The sparrow population was divided into three categories: spotters, watchdogs and followers;

[0057] Select the best fitness Individuals, acting as discoverers, are responsible for conducting detailed searches within a secure area:

[0058]

[0059] in is the proportion of discoverers, usually set to 0.3; is the number of the entire population; for Middle the location of each individual; is the step size scaling factor, usually set to 0.1; are the upper and lower bound variables of each optimization variable respectively; For standard normal distribution random numbers, introduce independent random perturbations in each dimension; is a randomly generated alert value used to simulate the sparrow's alertness to the environment; is the safety threshold, usually set to 0.8; Elite guidance coefficient, usually 0.5, is used to control the step length ratio of the Alpha wolf;

[0060] Select the middle Individuals, acting as sentinels, implement diverse escape strategies:

[0061]

[0062] in is the ratio of vigilants, usually set to 0.5; the mod function is to find the remainder, which is used to randomly assign escape strategies;

[0063] The remaining individuals are designated as followers, learning from the random discoverer:

[0064]

[0065] In the formula are the current individual's position and the discoverer's position respectively.

[0066] Furthermore, in step S1, the expression of the quintic B-spline function is as follows:

[0067]

[0068] Where, To control the vertex; is the node vector; is the B-spline basis function.

[0069] Furthermore, in step S2, the first-order, second-order and third-order differential operation expressions of the quintic B-spline function are solved as follows:

[0070]

[0071] In the formula represents the r-order derivative of B-spline;

[0072] .

[0073] In a second aspect, the present application provides a planar robot arm trajectory planning system for a stamping production line, the system comprising:

[0074] The trajectory segment division unit is used to divide the robot arm's motion process into approach, transport, and return segments based on the stamping production line working conditions, set intermediate transition points, and solve the joint space coordinates of the starting point, intermediate point, and end point of each segment through inverse kinematics;

[0075] The trajectory construction unit is used to fit the joint space trajectory of each segment using the quintic B-spline interpolation function to generate a continuous and smooth trajectory expression, and supports embedding multi-dimensional kinematic constraints in the trajectory expression;

[0076] Trajectory constraint solving unit, used to perform first-order, second-order and third-order differential operations on the quintic B-spline function, derive velocity, acceleration and jerk characteristic curves, and establish a complete trajectory planning model that meets position, velocity and acceleration constraints;

[0077] A time optimization unit is used to solve the optimal movement time of each characteristic segment in the trajectory using a gray wolf-sparrow search fusion algorithm. The algorithm includes a population initialization mechanism based on chaotic mapping and low-discrepancy sequence, and a staged collaborative optimization mechanism of the gray wolf algorithm and the sparrow algorithm;

[0078] The trajectory simulation unit is used to bring the time parameters obtained by optimization into the trajectory interpolation function and output the position, velocity, acceleration and jerk curve of each joint in the target cycle for system trajectory simulation and control interface call;

[0079] The control interface unit is used to send the trajectory information output by the trajectory simulation unit to the robotic arm controller in real time according to the control cycle, so as to realize real-time tracking and motion control of the trajectory in the physical actuator.

[0080] In a third aspect, the present application provides a computer-readable storage medium, which stores computer instructions. When a computer reads the computer instructions in the storage medium, the computer executes the stamping production line planar robot arm trajectory planning method as described in the first aspect.

[0081] It can be seen from the above technical solutions that the advantages of the present invention are:

[0082] The use of quintic B-spline curves for trajectory planning effectively ensures jerk continuity. A hybrid initialization method combining a chaotic map (Logistic) with a low-discrepancy sequence (Halton) generates a diverse and uniform initial population, accelerating algorithm convergence and effectively avoiding the local optimum problem caused by traditional random initialization. An innovative adaptive convergence factor a(t) based on the cosine law is introduced to achieve a dynamic balance between global exploration and local exploitation. Nonlinear dynamic adjustment of the weight parameters of the Alpha, Beta, and Delta wolves ensures rapid convergence even in the later stages of the algorithm's iterations. During the local search phase, the ratio of discoverers to observers is dynamically adjusted, and the observers employ a multi-strategy hybrid update mechanism (including Levy flight, reverse learning, and sinusoidal perturbations) to improve local search accuracy. Through these technological innovations, this invention improves robot arm trajectory planning in terms of operational efficiency, motion smoothness, and positioning accuracy under stamping conditions, demonstrating its potential for industrial application. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to more clearly illustrate the technical solution of the present invention, the following is a brief introduction to the drawings required for the description. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0084] Figure 1This is a step diagram of the planar robot arm trajectory planning method for stamping production lines;

[0085] Figure 2 This is a plan view of the mechanical arm of the stamping production line in the embodiment;

[0086] Figure 3 It is an iterative curve diagram of trajectory planning optimization based on the improved gray wolf-sparrow search fusion algorithm, gray wolf optimization algorithm, and sparrow search algorithm in the embodiment;

[0087] Figure 4 This is a curve diagram of the P1Z joint motion state after optimization based on the improved gray wolf-sparrow search fusion algorithm in the embodiment;

[0088] Figure 4 Middle (a) is the position curve of P1Z joint changing with time;

[0089] Figure 4 Middle (b) is the velocity curve of P1Z joint changing with time;

[0090] Figure 4 Middle (c) is the acceleration curve of P1Z joint changing with time;

[0091] Figure 5 This is a graph showing the motion state of the P1Y joint after optimization based on the improved wolf-sparrow search fusion algorithm in the embodiment;

[0092] Figure 5 Middle (a) is the position curve of P1Y joint changing with time;

[0093] Figure 5 Middle (b) is the velocity curve of P1Y joint changing with time;

[0094] Figure 5 Middle (c) is the acceleration curve of P1Y joint changing with time;

[0095] Figure 6 This is a P2Y joint motion state curve diagram after optimization based on the improved gray wolf-sparrow search fusion algorithm in the embodiment;

[0096] Figure 6 Middle (a) is the position curve of the P2Y joint changing with time;

[0097] Figure 6 Middle (b) is the velocity curve of the P2Y joint changing with time;

[0098] Figure 6 Middle (c) is the acceleration curve of the P2Y joint changing with time;

[0099] Figure 7This is a graph showing the motion state of the P3Y joint after optimization based on the improved wolf-sparrow search fusion algorithm in the embodiment;

[0100] Figure 7 Middle (a) is the position curve of the P3Y joint changing with time;

[0101] Figure 7 Middle (b) is the velocity curve of P3Y joint changing with time;

[0102] Figure 7 Middle (c) is the acceleration curve of the P3Y joint changing with time;

[0103] Figure 8 This is a graph showing the P4Y joint motion state after optimization based on the improved gray wolf-sparrow search fusion algorithm in the embodiment;

[0104] Figure 8 Middle (a) is the position curve of P4Y joint changing with time;

[0105] Figure 8 Middle (b) is the velocity curve of the P4Y joint changing with time;

[0106] Figure 8 Middle (c) is the acceleration curve of the P4Y joint changing with time;

[0107] Figure 9 This is a path planning diagram for the planar robotic arm of the stamping production line in the embodiment. DETAILED DESCRIPTION

[0108] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0109] See also Figure 1 As shown, the present invention provides a method for planning the trajectory of a planar robot arm of a stamping production line, comprising the following steps:

[0110] Step S1: Based on the actual working conditions of the stamping production line, the robot arm motion trajectory is divided into three characteristic segments: an approach segment from the initial position to the material collection point, a transport segment from the material collection point to the material discharge point, and a return segment from the material discharge point back to the initial position;

[0111] Set intermediate transition points in each characteristic segment trajectory, and solve the joint space coordinates of the manipulator at the starting point, intermediate point and end point of each segment through inverse kinematics;

[0112] The quintic B-spline curve is used to interpolate the motion trajectory of each segment of the joint to construct a continuous joint space motion trajectory expression;

[0113] Step S2: applying multi-dimensional constraints of position, velocity, and acceleration to the quintic B-spline interpolation function to establish a trajectory curve function that satisfies kinematic constraints;

[0114] By performing first-order, second-order and third-order differential operations on the function, the corresponding velocity characteristic curve, acceleration characteristic curve and jerk characteristic curve are derived respectively, so as to realize trajectory planning including full kinematic parameter constraints and generate the optimized motion path;

[0115] Step S3, calculating the optimal time for each segment in the motion path based on the gray wolf-sparrow search fusion algorithm;

[0116] Step S4: Substitute the optimal time into the quintic B-spline interpolation function of each joint to obtain the position, velocity, acceleration and jerk of each joint, complete the trajectory optimization, and obtain the optimized motion path.

[0117] In some embodiments, step S3 includes the following steps:

[0118] Step S3-1: The duration t = [t1, t2, t3] of the robot arm completing each characteristic segment is used as the optimization variable, where t1, t2, and t3 correspond to the movement time of the approach segment, the transport segment, and the return segment, respectively. The initial population is constructed using a hybrid initialization strategy that combines chaotic mapping with low-discrepancy sequences.

[0119] Step S3-2: In the global search phase, according to the iteration mechanism of the Grey Wolf Algorithm, a convergence factor a dynamically adjusted by a cosine function is introduced, and the guidance weights of the Alpha, Beta, and Delta wolves are dynamically adjusted;

[0120] Step S3-3: In the local search phase, the optimal solution output by the Grey Wolf Algorithm is used as the initial guide, and the solution space is refined through the multi-strategy search mechanism of the Sparrow Algorithm, and the global optimal time solution is output through the two-way information interaction mechanism;

[0121] Step S3-4: Repeat steps S3-2 to S3-3 until the preset termination condition is met, and output the optimal time for each segment.

[0122] In some embodiments, step S3-1 includes the following steps:

[0123] Step S3-1-1, generating 50% of the initial solutions based on the Logistic chaotic map;

[0124] Step S3-1-2: Generate the remaining 50% of initial solutions using the Halton low-discrepancy sequence;

[0125] Step S3-1-3, calculate the fitness value corresponding to each initial solution , and screen feasible solutions through constraint detection;

[0126] Step S3-1-4: Select three particles with the best fitness values ​​from the feasible solution set and mark them as Alpha, Beta and Delta particles in ascending order of fitness values.

[0127] In some embodiments, Logistic is a specific chaotic map with the formula:

[0128] ;

[0129] Where r is the control parameter, usually 4; is the initial value, uniformly distributed between (0, 1), is a standard normal distribution;

[0130] Halton low discrepancy sequence formula is as follows:

[0131]

[0132] In the formula is the smallest prime number greater than or equal to dim+1; is the Weyl sequence coefficient of dimension j; is the kth individual in the The value of the dimension;

[0133] Map the generated chaotic sequences and low-discrepancy sequences to the actual solution space:

[0134]

[0135] Combine the populations generated by the two methods:

[0136] , where They are the populations generated by Logistic chaotic mapping and Halton low-discrepancy sequence respectively; are the upper and lower bound variables of each optimization variable respectively.

[0137] In some embodiments, in step S3-2:

[0138] The cosine attenuation expression of the convergence factor is:

[0139]

[0140] In the formula is the current iteration number, ; is the initial value of the convergence factor, usually 2; is the final value of the convergence factor, usually 0; It is the attenuation curve adjustment exponent, used to control the convergence speed, usually set to 0.5; The maximum number of iterations, the first 50% of iterations use convex decay to strengthen global exploration, and the last 50% of iterations use concave decay to focus on local development;

[0141] Nonlinear adjustment of Alpha, Beta and Delta wolf guide weights:

[0142]

[0143] In the formula are the Alpha, Beta and Delta wolf guide weights, respectively, where the Alpha weight decreases with the number of iterations, the Beta weight increases with the number of iterations, and the Delta weight is constant;

[0144] According to the convergence factor And weight distribution, real-time calculation of the core parameters of the Grey Wolf Algorithm:

[0145] Random perturbation vector generation:

[0146]

[0147] In the formula Through the dynamic convergence factor Generated by linear combination of random numbers, the value range is ; Uniformly distributed random numbers are used to generate random perturbations in each dimension independently of the individual position vector; To optimize the variable dimension; rand (1, dim) is to generate a uniformly distributed random number between [0, 1];

[0148] Calculate the relative displacement for Alpha, Beta, and Delta wolves respectively:

[0149]

[0150] In the formula They are the current positions of the Alpha, Beta, and Delta wolf packs respectively. To be updated the location of the wolf pack;

[0151] Synthesize the guided candidate solutions of Alpha, Beta, and Delta wolves:

[0152]

[0153] In the formula They are the guided candidate solutions of Alpha, Beta, and Delta wolves respectively;

[0154] Weighted average based on dynamic weights:

[0155]

[0156] In the formula To update the new wolf pack, and The value of , used for local exploration in subsequent sparrow search.

[0157] In some embodiments, in step S3-3:

[0158] The sparrow population was divided into three categories: spotters, watchdogs and followers;

[0159] Select the best fitness Individuals, acting as discoverers, are responsible for conducting detailed searches within a secure area:

[0160]

[0161] in is the proportion of discoverers, usually set to 0.3; is the number of the entire population; for Middle the location of each individual; is the step size scaling factor, usually set to 0.1; are the upper and lower bound variables of each optimization variable respectively; For standard normal distribution random numbers, introduce independent random perturbations in each dimension; is a randomly generated alert value used to simulate the sparrow's alertness to the environment; is the safety threshold, usually set to 0.8; Elite guidance coefficient, usually 0.5, is used to control the step length ratio of the Alpha wolf;

[0162] Select the middle Individuals, acting as sentinels, implement diverse escape strategies:

[0163]

[0164] in is the ratio of vigilants, usually set to 0.5; the mod function is to find the remainder, which is used to randomly assign escape strategies;

[0165] The remaining individuals are designated as followers, learning from the random discoverer:

[0166]

[0167] In the formula are the current individual's position and the discoverer's position respectively.

[0168] In some embodiments, in step S1, the fifth-order B-spline function expression is as follows:

[0169]

[0170] Where, To control the vertex; is the node vector; is the B-spline basis function.

[0171] In some embodiments, in step S2, the first-order, second-order, and third-order differential operation expressions are solved for the quintic B-spline function as follows:

[0172]

[0173] In the formula represents the r-order derivative of B-spline;

[0174] .

[0175] In one embodiment, Figure 2 Take the flat robot arm of the stamping production line as an example:

[0176] in Figure 2 The robot arm is a planar robot arm with a total of 5 moving pairs, namely P1Z, P1Y, P2Y, P3Y and P4Y, which are marked in the figure.

[0177] Through simulation experiments, the effects of the improved gray wolf-sparrow search fusion algorithm, gray wolf optimization algorithm, and sparrow search algorithm on trajectory planning are compared. The population size, number of iterations, and other general parameters are all set to be consistent. The iteration curve is as follows: Figure 3 shown.

[0178] like Figure 4-Figure 9 See also Figure 4 (a)-(c) Figure 5 (a)-(c) Figure 6 (a)-(c) Figure 7 (a)-(c) Figure 8 Results (a)-(c) show that the improved Gray Wolf-Sparrow Search fusion algorithm improves convergence by 0.4% in the approach phase (first phase) compared to the Gray Wolf Optimization Algorithm and by 0.6% in the approach phase (first phase) compared to the Sparrow Search Algorithm. For the three total time periods, the improved Gray Wolf-Sparrow Search fusion algorithm improves convergence by 8% compared to the Gray Wolf Optimization Algorithm and by 10% compared to the Sparrow Search Algorithm.

[0179] In some embodiments, the present application provides a planar robot arm trajectory planning system for a stamping production line, the system comprising:

[0180] The trajectory segment division unit is used to divide the robot arm's motion process into approach, transport, and return segments based on the stamping production line working conditions, set intermediate transition points, and solve the joint space coordinates of the starting point, intermediate point, and end point of each segment through inverse kinematics;

[0181] The trajectory construction unit is used to fit the joint space trajectory of each segment using the quintic B-spline interpolation function to generate a continuous and smooth trajectory expression, and supports embedding multi-dimensional kinematic constraints in the trajectory expression;

[0182] Trajectory constraint solving unit, used to perform first-order, second-order and third-order differential operations on the quintic B-spline function, derive velocity, acceleration and jerk characteristic curves, and establish a complete trajectory planning model that meets position, velocity and acceleration constraints;

[0183] A time optimization unit is used to solve the optimal movement time of each characteristic segment in the trajectory using a gray wolf-sparrow search fusion algorithm. The algorithm includes a population initialization mechanism based on chaotic mapping and low-discrepancy sequence, and a staged collaborative optimization mechanism of the gray wolf algorithm and the sparrow algorithm;

[0184] The trajectory simulation unit is used to bring the time parameters obtained by optimization into the trajectory interpolation function and output the position, velocity, acceleration and jerk curve of each joint in the target cycle for system trajectory simulation and control interface call;

[0185] The control interface unit is used to send the trajectory information output by the trajectory simulation unit to the robotic arm controller in real time according to the control cycle, so as to realize real-time tracking and motion control of the trajectory in the physical actuator.

[0186] In some embodiments, the present application provides a terminal, including:

[0187] Memory, used to store the trajectory planning program of the planar robot arm of the stamping production line;

[0188] A processor is used to implement the steps of the stamping production line planar robot arm trajectory planning method when executing the stamping production line planar robot arm trajectory planning system.

[0189] In some embodiments, the present application provides a computer-readable storage medium, which stores computer instructions. When a computer reads the computer instructions in the storage medium, the computer executes the stamping production line planar robot arm trajectory planning method.

[0190] It is understood that the systems, devices, modules, or units described in the above embodiments may be implemented by computer chips or physical devices, or by products having certain functions. A typical implementation device is a computer, which may be a personal computer, a laptop computer, a personal digital assistant, a tablet computer, a wearable device, or a combination of any of these devices.

[0191] In a typical configuration, a computer includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0192] Memory may include non-permanent storage in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. Memory is an example of a computer-readable medium.

[0193] Computer-readable media include permanent and non-permanent, removable and non-removable media that can be used to store information using any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, disk storage, quantum memory, graphene-based storage media or other magnetic storage devices, or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory media such as modulated data signals and carrier waves.

[0194] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with the relevant laws, regulations and standards of relevant countries and regions, and provide corresponding operation entrances for users to choose to authorize or refuse.

[0195] It should also be noted that the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, commodity, or apparatus that includes a series of elements includes not only those elements but also other elements not explicitly listed, or includes elements inherent to such process, method, commodity, or apparatus. In the absence of further limitations, an element defined by the phrase "comprises a ..." does not exclude the presence of other identical elements in the process, method, commodity, or apparatus that includes the element.

[0196] The foregoing description of this specification describes specific embodiments. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims can be performed in an order different from that described in the embodiments and still achieve the desired results. Furthermore, the processes depicted in the accompanying drawings do not necessarily require the specific order shown or the sequential order to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0197] The terms used in one or more embodiments of this specification are for the purpose of describing specific embodiments only and are not intended to limit one or more embodiments of this specification. The singular forms "a," "an," "the," and "the" used in one or more embodiments of this specification and the appended claims are also intended to include plural forms unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0198] It should be understood that although the terms first, second, third, etc. may be used to describe various information in one or more embodiments of this specification, such information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of one or more embodiments of this specification, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when..." or "when..." or "in response to determining."

[0199] The above description is merely a preferred embodiment of one or more embodiments of this specification and is not intended to limit one or more embodiments of this specification. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of one or more embodiments of this specification shall be included in the scope of protection of one or more embodiments of this specification.

Claims

1. A method for planning trajectory of a planar robot arm in a stamping production line, characterized in that: The following steps are involved: Step S1: Based on the actual working conditions of the stamping production line, the robot arm motion trajectory is divided into three characteristic segments: an approach segment from the initial position to the material collection point, a transport segment from the material collection point to the material discharge point, and a return segment from the material discharge point back to the initial position; Set intermediate transition points in each characteristic segment trajectory, and solve the joint space coordinates of the manipulator at the starting point, intermediate point and end point of each segment through inverse kinematics; The quintic B-spline curve is used to interpolate the motion trajectory of each segment of the joint to construct a continuous joint space motion trajectory expression; Step S2: applying multi-dimensional constraints of position, velocity, and acceleration to the quintic B-spline interpolation function to establish a trajectory curve function that satisfies kinematic constraints; By performing first-order, second-order and third-order differential operations on the function, the corresponding velocity characteristic curve, acceleration characteristic curve and jerk characteristic curve are derived respectively, so as to realize trajectory planning including full kinematic parameter constraints and generate the optimized motion path; Step S3, calculating the optimal time for each segment in the motion path based on the gray wolf-sparrow search fusion algorithm; Step S4: Substitute the optimal time into the quintic B-spline interpolation function of each joint to obtain the position, velocity, acceleration and jerk of each joint, complete the trajectory optimization, and obtain the optimized motion path.

2. The method for planning the trajectory of a planar robot arm in a stamping production line according to claim 1, characterized in that: Step S3 includes the following steps: Step S3-1: The duration t = [t1, t2, t3] of the robot arm completing each characteristic segment is used as the optimization variable, where t1, t2, and t3 correspond to the movement time of the approach segment, the transport segment, and the return segment, respectively. The initial population is constructed using a hybrid initialization strategy that combines chaotic mapping with low-discrepancy sequences. Step S3-2: In the global search phase, according to the iteration mechanism of the Grey Wolf Algorithm, a convergence factor a dynamically adjusted by a cosine function is introduced, and the guidance weights of the Alpha, Beta, and Delta wolves are dynamically adjusted; Step S3-3: In the local search phase, the optimal solution output by the Grey Wolf Algorithm is used as the initial guide, and the solution space is refined through the multi-strategy search mechanism of the Sparrow Algorithm, and the global optimal time solution is output through the two-way information interaction mechanism; Step S3-4: Repeat steps S3-2 to S3-3 until the preset termination condition is met, and output the optimal time for each segment.

3. The method for planning the trajectory of a planar robot arm in a stamping production line according to claim 2, characterized in that: Step S3-1 includes the following steps: Step S3-1-1, generating 50% of the initial solutions based on the Logistic chaotic map; Step S3-1-2: Generate the remaining 50% of initial solutions using the Halton low-discrepancy sequence; Step S3-1-3, calculate the fitness value corresponding to each initial solution , and screen feasible solutions through constraint detection; Step S3-1-4: Select three particles with the best fitness values ​​from the feasible solution set and mark them as Alpha, Beta and Delta particles in ascending order of fitness values.

4. The method for planning the trajectory of a planar robot arm in a stamping production line according to claim 3, characterized in that: Logistic is a specific chaotic map, the formula is: ； Where r is the control parameter, usually 4; is the initial value, uniformly distributed between (0, 1), is a standard normal distribution; Halton low discrepancy sequence formula is as follows: In the formula is the smallest prime number greater than or equal to dim+1; is the Weyl sequence coefficient of dimension j; is the kth individual in the The value of the dimension; Map the generated chaotic sequences and low-discrepancy sequences to the actual solution space: Combine the populations generated by the two methods: , where They are the populations generated by Logistic chaotic mapping and Halton low-discrepancy sequence respectively; are the upper and lower bound variables of each optimization variable respectively.

5. The method for planning the trajectory of a planar robot arm in a stamping production line according to claim 3, characterized in that: In step S3-2: The cosine attenuation expression of the convergence factor is: In the formula is the current iteration number, ; is the initial value of the convergence factor, usually 2; is the final value of the convergence factor, usually 0; It is the attenuation curve adjustment index, used to control the convergence speed, usually set to 0.5; The maximum number of iterations, the first 50% of iterations use convex decay to strengthen global exploration, and the last 50% of iterations use concave decay to focus on local development; Nonlinear adjustment of Alpha, Beta and Delta wolf guide weights: In the formula are the Alpha, Beta and Delta wolf guide weights, respectively, where the Alpha weight decreases with the number of iterations, the Beta weight increases with the number of iterations, and the Delta weight is constant; According to the convergence factor And weight distribution, real-time calculation of the core parameters of the Grey Wolf Algorithm: Random perturbation vector generation: In the formula Through the dynamic convergence factor Generated by linear combination of random numbers, the value range is ; Uniformly distributed random numbers are used to generate random perturbations in each dimension independently of the individual position vector; To optimize the variable dimension; rand (1, dim) is to generate a uniformly distributed random number between [0, 1]; Calculate the relative displacement for Alpha, Beta, and Delta wolves respectively: In the formula They are the current positions of the Alpha, Beta, and Delta wolf packs respectively. To be updated the location of the wolf pack; Synthesize the guided candidate solutions of Alpha, Beta, and Delta wolves: In the formula They are the guided candidate solutions of Alpha, Beta, and Delta wolves respectively; Weighted average based on dynamic weights: In the formula To update the new wolf pack, and The value of , used for local exploration in subsequent sparrow search.

6. The method for planning the trajectory of a planar robot arm in a stamping production line according to claim 5, characterized in that: In step S3-3: The sparrow population was divided into three categories: spotters, watchdogs and followers; Select the best fitness Individuals, acting as discoverers, are responsible for conducting detailed searches within a secure area: in is the proportion of discoverers, usually set to 0.3; is the number of the entire population; for Middle the location of each individual; is the step size scaling factor, usually set to 0.1; are the upper and lower bound variables of each optimization variable respectively; For standard normal distribution random numbers, introduce independent random perturbations in each dimension; is a randomly generated alert value used to simulate the sparrow's alertness to the environment; is the safety threshold, usually set to 0.8; Elite guidance coefficient, usually 0.5, is used to control the step length ratio of the Alpha wolf; Select the middle Individuals, acting as sentinels, implement diverse escape strategies: in is the ratio of vigilants, usually set to 0.5; the mod function is to find the remainder, which is used to randomly assign escape strategies; The remaining individuals are designated as followers, learning from the random discoverer: In the formula are the current individual's position and the discoverer's position respectively.

7. The method for planning trajectory of a planar robot arm in a stamping production line according to claim 1, characterized in that: In step S1, the expression of the quintic B-spline function is as follows: Where, To control the vertex; is the node vector; is the B-spline basis function.

8. The method for planning trajectory of a planar robot arm in a stamping production line according to claim 7, characterized in that: In step S2, the first-order, second-order, and third-order differential operation expressions are solved for the quintic B-spline function as follows: In the formula represents the r-order derivative of B-spline; 。 9. A stamping production line plane robot arm trajectory planning system, characterized in that: The system includes: The trajectory segment division unit is used to divide the robot arm's motion process into approach, transport, and return segments based on the stamping production line working conditions, set intermediate transition points, and solve the joint space coordinates of the starting point, intermediate point, and end point of each segment through inverse kinematics; The trajectory construction unit is used to fit the joint space trajectory of each segment using the quintic B-spline interpolation function to generate a continuous and smooth trajectory expression, and supports embedding multi-dimensional kinematic constraints in the trajectory expression; Trajectory constraint solving unit, used to perform first-order, second-order and third-order differential operations on the quintic B-spline function, derive velocity, acceleration and jerk characteristic curves, and establish a complete trajectory planning model that meets position, velocity and acceleration constraints; A time optimization unit is used to solve the optimal movement time of each characteristic segment in the trajectory using a gray wolf-sparrow search fusion algorithm. The algorithm includes a population initialization mechanism based on chaotic mapping and low-discrepancy sequence, and a staged collaborative optimization mechanism of the gray wolf algorithm and the sparrow algorithm; The trajectory simulation unit is used to bring the time parameters obtained by optimization into the trajectory interpolation function and output the position, velocity, acceleration and jerk curve of each joint in the target cycle for system trajectory simulation and control interface call; The control interface unit is used to send the trajectory information output by the trajectory simulation unit to the robotic arm controller in real time according to the control cycle, so as to realize real-time tracking and motion control of the trajectory in the physical actuator.

10. A computer-readable storage medium, characterized in that The storage medium stores computer instructions. When the computer reads the computer instructions in the storage medium, the computer executes the stamping production line planar robot arm trajectory planning method as claimed in claim 1.

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