A multi-target trajectory planning method and system for a mechanical arm based on digital twinning

Abstract

The present application relates to the field of mechanical arm motion planning and digital twin technology, especially relates to a kind of mechanical arm multi-objective trajectory planning method and system based on digital twin, for large-scale fast disordered feeding, mechanical arm continuously high-intensity grabbing, transport material, there is start-stop impact, easy to shake, production operation efficiency and service life reduction and other problems, through LNSGA-ⅡSolving the multi-objective function of "efficiency, impact, energy consumption", the joint trajectory of mechanical arm is optimized using 7-order B-spline curve, so that the joint angular displacement, angular velocity and angular acceleration motion curve of the mechanical arm is more smooth and continuous, can protect servo motor, and through MATLAB-CoppeliaSim entity mechanical arm, build digital twin platform, apply trajectory planning model in actual operation task of mechanical arm, monitor mechanical arm working condition, respond to factory task scene.

Description

Technical Field

[0001] This invention relates to the fields of robotic arm motion planning and digital twin technology, and in particular to a method and system for multi-objective trajectory planning of robotic arms based on digital twins. Background Technology

[0002] With the continuous improvement and development of modern industrial technology, the application scenarios of robotic arms in production have become increasingly widespread and in-depth. Under various complex working conditions and practical needs, single-objective trajectory planning algorithms can no longer meet the diversified, complex, and precise requirements of robotic arm production operations. Junsen Huang proposed a time-impact integrated optimal trajectory planning method for robotic arms, which interpolates trajectories in joint space using 5th-order B-splines and uses NSGA-II for multi-objective solution. In multi-objective trajectory planning for robotic arms, researchers mainly use linear weighting to convert multi-objective functions into single-objective functions for solution. However, due to the different dimensions between different objectives, it is impossible to accurately allocate weights. These methods cannot guarantee the continuity of joint acceleration and jerk, which may lead to hardware damage to high-speed robotic arms. Although these methods can achieve the purpose of trajectory planning, they are not ideal in multi-objective optimization.

[0003] Robotic arms are gradually replacing humans in repetitive, dangerous, or high-precision tasks, improving production efficiency and safety. At the same time, the structure and function of robotic arms are becoming increasingly complex, making data collection and processing more difficult. However, the emergence of digital twins effectively solves this problem. In actual production tasks, factory personnel typically set the path between materials and the control panel, controlling the robotic arm to grasp the target. However, the grasping path often only involves the three-dimensional coordinates of the robotic arm's working area, the material, and the control panel, only considering the completion of the grasping action, without considering the compliance of the servo motor driving the robotic arm.

[0004] To address the aforementioned issues, this patent proposes a multi-objective trajectory planning method and system for robotic arms based on digital twins. It solves the multi-objective function of "optimal efficiency, energy consumption, and impact" of the robotic arm through a multi-objective optimization algorithm and builds a digital twin platform to accelerate the digitalization and intelligentization of robotic arms. Summary of the Invention

[0005] In view of the problems existing in the prior art, the present invention is proposed.

[0006] Therefore, this invention provides a multi-objective trajectory planning method for robotic arms based on digital twins. This method addresses issues such as large start-stop impacts, vibration, reduced production efficiency and lifespan, and even servo motor damage caused by the continuous high-intensity grasping and transport of materials during large-scale, rapid, and disordered material handling. During the robotic arm's grasping process, necessary trajectory optimization can make the motion curves of multiple joints, such as angular displacement, angular velocity, and angular acceleration, smoother and more continuous, while also protecting the servo motors.

[0007] To address the aforementioned technical problems, this invention provides the following technical solution: a multi-objective trajectory planning method for a robotic arm based on digital twins, comprising: addressing the uneven randomization of initial individuals and susceptibility to iteration counts in elite non-dominated sorting genetic algorithms, proposing a mutational chaotic strategy and a dynamic goal-oriented development strategy to improve the LNSGA-II algorithm, and designing infeasibility measures to resolve the nonlinear constraints of the trajectory planning model; establishing a multi-objective function to improve robot operation efficiency, trajectory stability, and reduce robot energy consumption; optimizing the 7th-order B-spline curve node vector using the LNSGA-II algorithm based on the passage time and order of key points in the input motion path to complete the multi-objective trajectory planning of the robotic arm; and building a digital twin platform using MATLAB-CoppeliaSim-solid robotic arm to apply the trajectory planning model to the actual operation tasks of the robotic arm.

[0008] As a preferred embodiment of the multi-objective trajectory planning method for a robotic arm based on digital twins described in this invention, the multi-objective function is expressed as follows:

[0009]

[0010] Where f1 is the motion time, measuring the efficiency of the robotic arm; f2 is the average acceleration of the joint, measuring the energy consumption of the robotic arm; f3 is the joint jerkiness, measuring the smoothness of the robotic arm's motion; and the objective functions are, in order, optimal efficiency, optimal energy consumption, and optimal impact. s is the robotic arm's motion node, and t... s Let s represent the s-th time point of the robotic arm movement, m be the number of robotic arm joints, a be the joint acceleration, J be the joint impact pulsation, and T be the total joint movement time.

[0011] As a preferred embodiment of the multi-objective trajectory planning method for a robotic arm based on digital twins described in this invention, the passage time and sequence of key points on the motion path include: when the robotic arm moves from start point A to end point B in the task space, a series of key points are obtained through inverse kinematics calculations.

[0012] m Q s ={( m q s ,ts ),(m=1,2...,s=0,1...n)}

[0013] Where m is the number of joints in the robotic arm, s is the time node of the robotic arm movement, n is the total number of time nodes, and q is the joint movement angle. m q s It is the motion angle of the m-th joint at time s. m Q s These are the joint motion functions of the robotic arm, obtained through robotic arm trajectory planning.

[0014] m f(t) = m q s

[0015] Where f(t) represents the curve of the motion angle q of the m-th robotic arm joint as a function of time;

[0016] The motion trajectory of the robotic arm is constructed using a k-th degree B-spline curve. The B-spline curve is represented as follows:

[0017]

[0018] Where, d j These are the coordinates of the control points, F j,k B(t) is a k-th degree B-spline basis function, where B(t) represents the joint position at time t. By inversely finding the control vertices of the B-spline curve, each robotic arm joint passes through the key points. m q s Furthermore, the segmented connection points of the trajectory curve correspond to the key nodes, with the start and end points being consistent. The time node t is parameterized according to the cumulative chord length parameterization method. j Normalization yields the internal node values, Δt. k For the chord length,

[0019]

[0020] Δt k =t k+1 -t k k = 0, 1, ..., n-1

[0021] Among them, t s Let t represent the s-th time point of the robotic arm's movement. k Let Δt be the k-th time point of the robotic arm's movement. s Let t be the chord length of the s-th robotic arm movement time. s-1 Let s be the (s-1)th time node of the robotic arm movement. By normalizing the time nodes, n+1 equations that satisfy the interpolation conditions are established. Solving the equations yields the control nodes of the k-th B-spline curve.

[0022] As a preferred embodiment of the multi-objective trajectory planning method for a robotic arm based on digital twins described in this invention, the LNSGA-Ⅱ algorithm is expressed as follows: Δt k =t k+1 -t k To optimize variables, the iteration begins. A mutated chaotic strategy is used to initialize the individual positions in the population, and multi-objective functions f1, f2, and f3 are calculated. Based on the objective function values, the population undergoes fast non-dominated sorting and crowding calculation, and a dynamic adjustment factor r is calculated. When r ∈ (-1, 1), a dynamic goal-oriented development strategy is used to update the population positions; when r ≥ 1 or r ≤ -1, crossover and mutation are used to update the population positions. Infeasibility is calculated, and individuals far from the feasible region are removed. The multi-objective function values ​​are calculated, and the iteration continues until the maximum number of iterations is reached, at which point the iteration terminates. The optimal population position and objective function value are returned.

[0023] As a preferred embodiment of the multi-objective trajectory planning method for a robotic arm based on digital twins described in this invention, the mutated chaotic strategy is expressed as follows:

[0024]

[0025] in, It is the original sine mapping, mod is the modulo function, μ = 0.99. This is represented as a mutated chaotic strategy.

[0026] As a preferred embodiment of the multi-objective trajectory planning method for a robotic arm based on digital twins described in this invention, the dynamic target-oriented development strategy includes employing a dynamic adjustment factor r to ensure population diversity during crossover and mutation, and using target-oriented development to accelerate the algorithm's convergence speed.

[0027]

[0028] r = 2·r c rand-r c

[0029] β s =|rand·β best (t)-β(t)|

[0030] β(t+1)=β best (t)-r c ·rand·β s ·cos(θ)

[0031] Where, β bestβ(t) is the individual ranked first in the t-th iteration, β(t) is the individual ranked lower and with higher crowding in the t-th iteration, θ is the angle randomly selected by the roulette wheel, and M... S These are user-defined constants. Iter and Max-iter refer to the current iteration number and the maximum iteration number, respectively. rand represents a random number between [0, 1], β(t+1) represents the position of an individual in the population at the (t+1)th iteration, and r... c Represented as adaptive iterative weights, β s This indicates that the selection of individual positions within the population is goal-oriented.

[0032] As a preferred embodiment of the multi-objective trajectory planning method for a robotic arm based on digital twins described in this invention, the calculation of infeasibility includes designing an infeasibility factor for the objective solution to handle constraints, defined as the sum of squares of all conflicting constraint values, expressed as...

[0033]

[0034] Where A and B are the number of constraints, and G is the number of constraints. a (x i ),T b (x i ) are equality constraints and inequality constraints, respectively, ψ(x) i The infeasibility degree is a metric that measures the distance between the current solution and the feasible region. When the infeasibility degree is 0, it indicates that the position x of an individual in the population is zero. i This is a feasible solution; as the infeasibility value increases, x... i It will gradually move away from the feasible region, while setting an infeasibility threshold to determine x. i Whether it is accepted or not determines whether to proceed to the next step of genetic manipulation.

[0035] As a preferred embodiment of the multi-target trajectory planning system for a robotic arm based on digital twins described in this invention, it includes: a data acquisition module, a calculation module, and a twin module;

[0036] The acquisition module, for industrial applications of robotic arms, such as grasping and transporting materials, collects joint angle data of the robotic arm's grasping path and inputs it into the calculation module.

[0037] The calculation module establishes a multi-objective function based on the obtained joint angle data of the robotic arm to improve the robot's work efficiency, track stability and reduce robot energy consumption. According to the passage time and order of the key points of the input motion path, the LNSGA-Ⅱ algorithm is used to optimize the node vector of the 7th order B-spline curve to complete the multi-objective trajectory planning of the robotic arm.

[0038] The twin module, through MATLAB-CoppeliaSim-physical robotic arm, builds a digital twin platform to form a virtual-real mapping, applies the trajectory planning model to the actual operation tasks of the robotic arm, and monitors the working status of the robotic arm through the twin module.

[0039] A computer device includes a memory and a processor, the memory storing a computer program, characterized in that the processor executes the computer program to implement the steps of any one of the methods in a digital twin-based multi-objective trajectory planning method for a robotic arm.

[0040] A computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it implements the steps of any one of the methods in a digital twin-based multi-objective trajectory planning method for a robotic arm.

[0041] The beneficial effects of this invention are as follows: This invention designs an infeasibility degree for the objective solution to handle constraints, defined as the sum of the squares of all conflicting constraint values. The infeasibility degree refers to the distance of the current solution from the feasible region; when the infeasibility degree is 0, then x... i A feasible solution is one that is infeasible; the greater the degree of infeasibility, the smaller x becomes. i The further away from the feasible region, the more infeasibility threshold is set to determine x. iWhether the algorithm is accepted determines the next step of the genetic operation. The original sinusoidal chaotic map has an uneven distribution of chaotic values ​​and exhibits boundary clustering. The mutated sinusoidal chaotic map has a better uniform distribution of random values, the boundary clustering disappears, and the initial individuals are randomized and homogenized. NSGA-II is greatly affected by the number of iterations and has timeliness issues. A dynamic goal-oriented development method is proposed to accelerate the evolution of NSGA-II individuals towards the Pareto front, speeding up the algorithm's computation time and reducing the number of iterations. Based on the passage time and order of key points in the input motion path, the LNSGA-II algorithm is used to optimize the node vector of the 7th-order B-spline curve to complete the multi-objective trajectory planning of the robotic arm. Compared with four multi-objective algorithms—Multi-objective Differential Evolution Algorithm (MODE), Multi-objective Particle Swarm Optimization Algorithm (MOPSO), Multi-objective Gray Wolf Algorithm (MOGWO), and Elite Non-dominated Sorting Genetic Algorithm (NSGA-II)—the results show that the velocity, acceleration, and jerk of each joint in the start and stop phases of the robotic arm are all 0, the overall joint motion trajectory is smooth and continuous, reducing robotic arm vibration and effectively protecting key components such as motors and reducers. Taking the UR16e as an example, a 3D virtual model of the UR16e robotic arm is established. Combined with the physical entity, a digital twin model interaction platform is constructed using MATLAB-CoppeliaSim-UR16e. A trajectory planning model is applied to solve problems such as large start-stop impact, easy vibration, and reduced production efficiency and service life of the robotic arm during large-scale, rapid, and disordered material feeding. In summary, this invention provides a multi-objective trajectory planning method for robotic arms based on digital twins. Based on the passage time and sequence of key points in the input motion path, the LNSGA-II algorithm is used to optimize the node vector of the 7th-order B-spline curve to complete the multi-objective trajectory planning of the robotic arm. A digital twin platform is built and applied to the actual grasping tasks of the robotic arm, accelerating the digitalization and intelligentization process of the robotic arm. Attached Figure Description

[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 The LNSGA-II method for multi-objective trajectory planning of a robotic arm based on digital twins, as provided in one embodiment of the present invention, demonstrates the multi-objective trajectory planning results on the Pareto front. Compared with five other algorithms, the optimized angle, velocity, acceleration, and jerk curves are shown, demonstrating the superiority and success of the LNSGA-II proposed in the present invention in multi-objective trajectory planning of robotic arms.

[0044] Figure 2This invention provides a method for establishing a digital twin model of a robotic arm based on digital twins for multi-objective trajectory planning, as an embodiment of the present invention.

[0045] Figure 3 This invention provides a method for multi-target trajectory planning of a robotic arm based on digital twins, showing the joint motion curves of the UR16e robotic arm in an actual grasping task, which is based on digital twins.

[0046] Figure 4 This invention provides a method for calculating joint motion trajectory curves using a multi-objective trajectory planning method for a robotic arm based on digital twins, as an embodiment of the present invention. Detailed Implementation

[0047] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0048] Example 1, referring to Figures 1-3 This is the first embodiment of the present invention, aiming to solve the problems of large start-stop impact, easy vibration, and reduced production efficiency and service life of robotic arms when continuously grasping and transporting materials at high intensity. A multi-objective trajectory planning method for robotic arms based on digital twins is proposed. Its main principles include the following steps:

[0049] S1: Elite Non-Dominated Sorting Genetic Algorithm (NSGA-II)

[0050] Deb et al. further improved the NSGA algorithm and proposed NSGA-II. In NSGA-II, a new non-dominated solution sorting method, elite selection strategy and crowding distance were used, and the computational complexity was reduced from the original O(MN3) to O(MN2), where M represents the number of targets and N represents the population size.

[0051] 1) Fast Non-Dominated Sort: First, find the optimal non-dominated solution in the current population and assign it to level 1; then remove individuals with level 1 from the population, find new non-dominated solutions among the remaining individuals, and assign them to level 2; repeat the fast non-dominated sorting process until all individuals in the population are assigned the corresponding level.

[0052] 2) Selection Operation: The selection process guides optimization towards the Pareto optimal solution and distributes the solutions evenly. The selection operator aims to avoid the loss of effective genes, ensuring that high-performing individuals survive with a higher probability, thereby improving global convergence and computational efficiency. After sorting and crowding distance calculation, each individual i in the population acquires two attributes: non-dominated order i. rank and crowded distance i d The operator is selected using a round-robin format, that is, two individuals are randomly selected, and when i... rank <j rank or i rank =j rank And i d >j d When the order of individuals is different, individual i is preferred over individual j. The meaning of the above formula is: if two individuals have different non-dominated rankings, the individual with the lower ranking number is selected (the individual separated first during hierarchical sorting); if two individuals are at the same level, individual i is selected. d >j d Individuals.

[0053] 3) Crossover and mutation: Crossover and mutation work together to give genetic algorithms good local and global search performance. Crossover is performed on the parent individuals with real-number encodings; that is, for a given random crossover point, the portions of the two parent individuals located on either side of the crossover point are swapped.

[0054] 4) Elite Strategy: The elite strategy involves retaining superior individuals from the parent generation and directly introducing them into the offspring. This is a necessary condition for the genetic algorithm to converge with a probability of 1. The method employed is: ① Select the best individuals from the parent generation P... t and offspring Q t All individuals combine to form a unified population R t R t The number of individuals is 2N; ② The population R t Quickly sort non-dominated individuals and calculate the local crowding distance for each individual. Select individuals one by one according to their rank until the number of individuals reaches N, thus forming a new parent population P. t+1 ③ In the new parent population P t+1 Based on this, a new round of selection, crossover, and mutation begins, forming a new offspring population Q. t+1 .

[0055] S2: Improved multi-objective algorithm LNSGA-II

[0056] Although the traditional NSGA-II algorithm is significantly more efficient than NSGA in solving non-dominated scheduling problems, it still takes a considerable amount of time to solve large-scale scheduling problems with many targets.

[0057] 1) Infeasibility design: When dealing with constrained problems, the conventional method is to transform out-of-bounds solutions into boundary extreme points. This invention designs an infeasibility of the objective solution to handle constraints, which is defined as the sum of squares of all conflicting constraint values.

[0058]

[0059] Where A and B are the number of constraints, and G a (x i ),T b (x i These represent equality constraints and inequality constraints, respectively. Infeasibility degree refers to the distance from the current feasible region to the point of liberation. When the infeasibility degree is 0, then x... i A feasible solution is one that is infeasible; the greater the degree of infeasibility, the smaller x becomes. i The further away from the feasible region, the more infeasibility threshold is set to determine x. i Whether it is accepted or not determines whether to proceed to the next step of genetic manipulation.

[0060] 2) Mutant Chaotic Strategy: This invention proposes a mutant chaotic strategy to address the problems of poor initial population diversity and uneven distribution in NSGA-II. Where, It is the original sine mapping, mod is the modulo function, μ = 0.99. This is represented as a mutated chaotic strategy.

[0061]

[0062] 3) Dynamic Goal-Oriented Development: This invention proposes a dynamic goal-oriented development method to accelerate the evolution of NSGA-II individuals toward the Pareto front. A dynamic adjustment factor r is used to ensure population diversity during crossover mutations while simultaneously accelerating algorithm convergence through goal-oriented development. Where M... s These are user-defined constants. Iter and Max-iter refer to the current iteration number and the maximum iteration number, respectively.

[0063]

[0064] r = 2·r c rand-r c

[0065] β s =|rand·β best (t)-β(t)|

[0066] β(t+1)=β best (t)-r c ·rand·β s ·cos(θ)

[0067] Where, βbest β(t) is the individual ranked first in the current iteration, β(t) is the individual ranked lower and with higher crowding, and θ is the angle randomly selected by roulette.

[0068] In summary, a novel LNSGA-II algorithm is developed by first addressing the constraint problem through design infeasibility, then initializing the population using a mutated sinusoidal chaotic mapping, and finally accelerating iterative convergence of individuals through dynamic goal-oriented development. LNSGA-II is then applied to solve the multi-objective trajectory optimization problem for robotic arms.

[0069] S3: Trajectory Planning Model

[0070] 1) Construction of robotic arm joint trajectories

[0071] When the robotic arm moves from point A to point B in the task space, a series of key points are obtained through inverse kinematics calculations. m Q s ={( m q s ,t s ), (m=1,2...,s=0,1...n)}, where m is the number of robot arm joints, s is the number of robot arm motion nodes, n is the total number of motion nodes, and q is the joint motion angle, obtained through robot arm trajectory planning. m f(t) = m q s The robot arm's motion trajectory is constructed using k-order non-uniform rational B-splines (NURBS). The B-spline curve is as follows:

[0072]

[0073] Where, d j These are the coordinates of the control points, F j,k B(t) is a k-th degree B-spline basis function. B(t) refers to the joint position at time t. By inversely finding the control vertices of the B-spline curve, each robotic arm joint passes through the key points. m q s Furthermore, the segmented connection points of the trajectory curve correspond to the key nodes, and the start and end points are consistent. Based on the cumulative chord length parameterization method, the time node t... j Normalization yields the internal node values, where Δt k Let be the chord length.

[0074]

[0075] Δt k =t k+1 -t k k = 0, 1, ..., n-1

[0076] This yields n+1 equations that satisfy the interpolation conditions. Solving these equations yields the control nodes of the k-th degree B-spline curve. This patent uses a 7th degree B-spline curve to achieve trajectory planning for the robotic arm.

[0077] 2) Multi-objective function:

[0078] To improve robot operation efficiency, trajectory stability, and reduce robot energy consumption, a multi-objective function is established and solved using the LNSGA-II algorithm. Based on the passage time and sequence of key points in the input motion path, and considering path and joint constraints, a 7th-order B-spline curve is optimized to complete the multi-objective trajectory planning of the robotic arm.

[0079] f1 is the motion time, measuring the efficiency of the robotic arm. f2 is the average acceleration of the joints, measuring the energy consumption of the robotic arm. f3 is the joint jerkiness, measuring the smoothness of the robotic arm's motion. The objective functions are, in order, optimal efficiency, optimal energy consumption, and optimal impact. Here, s is the time sequence of the current non-uniform rational B-spline, m is the number of robotic arm joints, a is the joint acceleration, and J is the joint impact pulsation.

[0080]

[0081] S4: LNSGA-II Algorithm Solution Flow

[0082] With Δt k =t k+1 -t k To optimize variables, the iteration begins. A mutated chaotic strategy is used to initialize the individual positions in the population, and multi-objective functions f1-f3 are calculated. Based on the objective function values, the population undergoes fast non-dominated sorting and crowding calculation, and a dynamic adjustment factor r is calculated. When r∈(-1, 1), a dynamic goal-oriented development strategy is used to update the population positions; otherwise, selection, crossover, and mutation are used to update the population positions when r≥1 or r≤-1. Infeasibility is calculated, and individuals far from the feasible region are removed. The multi-objective function values ​​are calculated, and the iteration continues until the maximum number of iterations is reached, at which point the iteration terminates. The optimal population position and objective function value are returned. The flowchart of the LNSGA-Ⅱ algorithm is attached. Figure 1 As shown.

[0083] S5: Using MATLAB-CoppeliaSim-UR16e, a digital twin platform is built to apply the trajectory planning model to the actual operation tasks of the robotic arm.

[0084] Taking UR16e as an example, a three-dimensional virtual model of the UR16e robotic arm is established. Combined with the physical entity, a digital twin model interaction platform is constructed using MATLAB-CoppeliaSim-UR16e. The trajectory planning model is solved by applying LNSGA-Ⅱ to obtain the robotic arm motion trajectory that satisfies multiple objectives. This solves problems such as large start-stop impact, easy shaking, reduced production efficiency and service life of the robotic arm during large-scale, rapid and disordered material feeding.

[0085] The present invention will now be described in detail with reference to the accompanying drawings and experimental results. Figures 1 to 4 As shown, the specific advantages of this invention are:

[0086] Figure 1 This is a flowchart of the LNSGA-Ⅱ algorithm solution process.

[0087] Figure 2 The results of five algorithms for multi-objective trajectory planning on the Pareto front are shown, displaying the optimized angle, velocity, acceleration, and jerk curves. Here, Time represents time, Angle, Velocity, Acceleration, and Jerk represent the angle, velocity, acceleration, and jerk curves of the robotic arm joints, respectively, and joint1-6 represent joints 1-6. The following conclusions can be drawn from the figures:

[0088] (1) From Figure 2 Looking at the angle curves in column 1, (a) and (i) show that the angle curves of MODE and MOPSO are not smooth enough, and there are inflection points in the motion angle, which causes jitter during the movement of the robotic arm. The angle curves of the other three algorithms are all smooth and continuous.

[0089] (2) In Figure 2 In columns 2-4, the velocity, acceleration, and jerk curves of MOPSO, NSGA-II, and LNSGA-II all meet the basic requirements for robotic arm joint trajectory planning: uniformity, smoothness, and continuity. Although the velocity, acceleration, and jerk curves of MOPSO and NSGA-II meet the basic requirements, their multi-objective functions lag far behind LNSGA-II, failing to more accurately achieve the "efficiency-energy-impact optimization" objective.

[0090] (3) From Figure 2 In (b)-(d), the speed, acceleration and jerk curves of MODE all have sharp corners, and the changes are abrupt at the inflection points, which can easily cause impact fluctuations in the robotic arm and lead to motor damage.

[0091] (4) Figure 2As explained in (f)-(h), MOGWO exhibits relatively small changes in velocity, acceleration, and jerkiness in the early stages of trajectory planning, but a sharp fluctuation occurs in the curve at the 6s mark, causing acute changes in the robot arm's velocity, acceleration, and jerkiness. This is because MOGWO optimizes the nodal variables of the B-spline curve with subsequent time nodes being too compact, resulting in small changes.

[0092] The trajectory planning is performed using a 7th-order B-spline curve, and multi-objective solution is performed using LNSGA-Ⅱ. The node vector of the B-spline curve is optimized to obtain that the velocity, acceleration and jerk of each joint of the robot arm are all 0 during the start and stop phases. The overall joint motion trajectory is smooth and continuous, reducing the vibration of the robot arm and effectively protecting key components such as motors and reducers.

[0093] Figure 3 It is the process of establishing a digital twin model of the robotic arm, as described in S5. Figure 2 Matlab and Coppeliasim are two computer software programs.

[0094] Figure 4 This invention calculates the joint motion trajectory curves when the UR16e robotic arm grasps three mechanical parts: an end cap, a worm gear, and a helical gear. These curves represent the commands for controlling the robotic arm's motion. Here, `time` represents time, `joint1-6` represents joints 1-6, and `v`, `a`, and `j` represent velocity (° / s), acceleration (° / s), and acceleration (° / s), respectively. 2 ) and jerk (° / s) 3 ).

[0095] Example 2, the second embodiment of the present invention, differs from the previous embodiment in that:

[0096] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0097] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0098] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0099] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0100] Example 3 is the third embodiment of the present invention. This embodiment provides a multi-target trajectory planning system for a robotic arm based on digital twins, characterized in that it includes a data acquisition module, a calculation module, and a twin module.

[0101] The data acquisition module collects joint angle data of the robotic arm's grasping path for industrial applications such as grasping and transporting materials, and inputs it into the calculation module.

[0102] The calculation module establishes a multi-objective function based on the obtained joint angle data of the robotic arm to improve the robot's operation efficiency, trajectory stability and reduce energy consumption. It solves the function using the LNSGA-Ⅱ algorithm and optimizes the 7th order B-spline curve to complete the multi-objective trajectory planning of the robotic arm under the consideration of path and joint constraints.

[0103] The twin module, through MATLAB-CoppeliaSim-physical robotic arm, builds a digital twin platform to form a virtual-real mapping, applies the trajectory planning model to the actual operation tasks of the robotic arm, and monitors the working status of the robotic arm through the twin module.

[0104] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A multi-objective trajectory planning method for a robotic arm based on digital twins, characterized in that: include, A multi-objective function is established, and the LNSGA-Ⅱ algorithm is used to optimize the node vector of the 7th order B-spline curve based on the passage time and order of the key points of the input motion path to complete the multi-objective trajectory planning of the robotic arm. A digital twin platform was built using MATLAB-CoppeliaSim-physical robotic arm, and the trajectory planning model was applied to the actual operation tasks of the robotic arm. The multi-objective function is expressed as follows: Where f1 is the motion time, measuring the efficiency of the robotic arm; f2 is the average acceleration of the joints, measuring the energy consumption of the robotic arm; f3 is the joint jerkiness, measuring the smoothness of the robotic arm's motion; and the objective functions are, in order, optimal efficiency, optimal energy consumption, and optimal impact. s is the time node of the robotic arm's motion, and t... s Let s be the time node of the s-th robotic arm movement, q be the joint movement angle, m be the number of robotic arm joints, a be the joint acceleration, J be the joint impact pulsation, and T be the total joint movement time. The passage time and sequence of key points in the motion path include key points obtained through inverse kinematics calculations as the robotic arm moves from start point A to end point B in the task space. m Q s ={( m q s ,t s ),(m=1,2...,s=0,1...n)} Where n is the total number of motion time points. m q s It is the motion angle of the m-th joint at time s. m Q s These are the joint motion functions of the robotic arm, obtained through robotic arm trajectory planning. m f(t)= m q s in, m f(t) represents the curve of the motion angle q of the m-th robotic arm joint as a function of time; The motion trajectory of the robotic arm is constructed using a k-th degree B-spline curve, which is represented as follows: Where, d j These are the coordinates of the control points, F j,k B(t) is a k-th degree B-spline basis function, where B(t) represents the joint position at time t. By inversely finding the control vertices of the B-spline curve, each robotic arm joint passes through the key points. m q s Furthermore, the segmented connection points of the trajectory curve correspond to the key nodes, with the start and end points being consistent. The time node t is parameterized according to the cumulative chord length parameterization method. j Normalization yields the internal node values, Δt. k For the chord length, Δt k =t k+1 -t k ,k=0,1...n-1 Among them, t k Let Δt be the k-th time point of the robotic arm's movement. s Let t be the chord length of the s-th robotic arm movement time. s-1 Let s be the (s-1)th time node of the robotic arm movement. By normalizing the time nodes, n+1 equations that satisfy the interpolation conditions are established. Solving the equations yields the control nodes of the k-th B-spline curve.

2. The multi-objective trajectory planning method for a robotic arm based on digital twins as described in claim 1, characterized in that: The LNSGA-Ⅱ algorithm is expressed as follows, with Δt k =t k+1 -t k To optimize variables, the iteration begins. A mutated chaotic strategy is used to initialize the individual positions of the population, and multi-objective functions f1, f2, and f3 are calculated. Based on the objective function values, the population undergoes fast non-dominated sorting and crowding calculation, and a dynamic adjustment factor r is calculated. When r ∈ (-1, 1), a dynamic goal-oriented development strategy is used to update the population positions. When r ≥ 1 or r ≤ -1, selection, crossover, and mutation operations are used to update the population positions. Calculate the infeasibility degree and remove individuals from the population that are far from the feasible region; calculate the multi-objective function value and continue iterating until the maximum number of iterations is reached, then terminate the iteration. Return the optimal population location and the objective function value; Among them, t k+1 This is represented as the (k+1)th time node of the robotic arm's movement.

3. The multi-objective trajectory planning method for a robotic arm based on digital twins as described in claim 2, characterized in that: The mutated chaotic strategy is expressed as follows: in, It is the original sine mapping, mod is the modulo function, μ = 0.

99. This is represented as a mutated chaotic strategy.

4. The multi-objective trajectory planning method for a robotic arm based on digital twins as described in claim 3, characterized in that: The dynamic goal-oriented development strategy is expressed as follows: r=2·r c ·rand-r c b s =|rand·β best (t)-β(t)| β(t+1)=β best (t)-r c ·rand·b s ·cos(θ) Where, β best β(t) is the individual ranked first in the t-th iteration, β(t) is the individual ranked lower and with higher crowding in the t-th iteration, θ is the angle randomly selected by the roulette wheel, and M... S These are user-defined constants. Iter and Max-iter refer to the current iteration number and the maximum iteration number, respectively. rand represents a random number between [0, 1], β(t+1) represents the position of an individual in the population at the (t+1)th iteration, and r... c Represented as adaptive iterative weights, β s This indicates that the selection of individual positions within the population is goal-oriented.

5. The multi-objective trajectory planning method for a robotic arm based on digital twins as described in claim 4, characterized in that: The computational infeasibility degree is expressed as follows: Where A and B are the number of constraints, and G is the number of constraints. a (x i ),T b (x i ) are equality constraints and inequality constraints, respectively, ψ(x) i The infeasibility degree is represented by 0, indicating the position of an individual in the population. i This is a feasible solution; as the infeasibility value increases, x... i It will gradually move away from the feasible region, set an infeasibility threshold, and determine x. i Whether it is accepted or not determines whether to proceed to the next step of genetic manipulation.

6. A system based on the multi-objective trajectory planning method for a robotic arm based on digital twins as described in any one of claims 1-5, characterized in that: This includes a data acquisition module, a computing module, and a twin module; The acquisition module, designed for industrial applications of robotic arms, collects joint angle data along the grasping path of the robotic arm and inputs it into the calculation module. The calculation module establishes a multi-objective function based on the obtained joint angle data of the robotic arm, and optimizes the node vector of the 7th order B-spline curve using the LNSGA-Ⅱ algorithm according to the passage time and order of the key points of the input motion path, so as to complete the multi-objective trajectory planning of the robotic arm. The twin module, through MATLAB-CoppeliaSim-physical robotic arm, builds a digital twin platform to form a virtual-real mapping, applies the trajectory planning model to the actual operation tasks of the robotic arm, and monitors the working status of the robotic arm through the twin module.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 5.

Images