Mechanical arm multi-target trajectory planning method and system based on digital twinning

Abstract

The invention relates to the technical field of mechanical arm motion planning and digital twinning, in particular to a mechanical arm multi-target trajectory planning method and system based on digital twinning, and aims to solve the problems that during large-scale rapid disordered feeding, a mechanical arm continuously grabs and transports materials with high strength, and the working efficiency is high. In order to solve the problems of large start-stop impact, easy shaking, reduced production operation efficiency, shortened service life and the like in the prior art, a multi-objective function of efficiency, impact and energy consumption is solved through LNSGA-II, and a seven-order B spline curve is utilized to optimize a joint track of the mechanical arm, so that angular displacement, angular velocity and angular acceleration motion curves of multiple joints of the mechanical arm are smoother and more continuous, a servo motor can be protected, and the mechanical arm is more stable in operation. And a digital twin platform is built through an MATLAB-AppeliaSim entity mechanical arm, the trajectory planning model is applied to an actual operation task of the mechanical arm, the working condition of the mechanical arm is monitored, and a factory task scene is coped with.

Description

Technical Field

[0001] The present invention relates to the field of robot arm motion planning and digital twin technology, and in particular to a robot arm multi-target trajectory planning method and system based on digital twin. Background Art

[0002] With the continuous improvement and development of modern industrial technology, the production application scenarios of robotic arms have become more extensive and in-depth. Under various complex working conditions and actual needs, the single-objective trajectory planning algorithm can no longer meet the diversified, complex and precise requirements of robotic arm production operations. Junsen Huang proposed a time-impact comprehensive optimal trajectory planning method for robotic arms, which interpolates the trajectory in the joint space through 5th-order B-splines and uses NSGA-Ⅱ for multi-objective solution. In the multi-objective trajectory planning of robotic arms, researchers mainly use linear weighting to convert multi-objective functions into single-objective functions for solution, but due to the different dimensions between different objectives, the weights cannot be accurately assigned. These methods cannot guarantee the continuity of joint acceleration and jerkiness, which may cause hardware damage to high-speed working 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 to complete repetitive, dangerous or high-precision work, improving production efficiency and safety. At the same time, the structure and function of the robotic arm have become more and more complex, and the collection and processing of robotic arm data has become more and more difficult, but the emergence of digital twins has effectively solved this problem. In actual production tasks, factory personnel usually set the path between the material and the operating table to control the robotic arm to grasp the target, but the grasping path often only involves the three-dimensional coordinates of the robotic arm's working area, the material and the operating table, and only considers the completion of the grasping action, without involving the flexibility of the servo motor driving the robotic arm.

[0004] In response to the above problems, this patent proposes a multi-objective trajectory planning method and system for a robotic arm based on digital twins. It solves the multi-objective function of "efficiency, energy consumption, and impact optimization" of the robotic arm through a multi-objective optimization algorithm, and builds a digital twin platform to accelerate the digitalization and intelligentization process of the robotic arm. Summary of the invention

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

[0006] Therefore, the present invention provides a multi-target trajectory planning method for a robotic arm based on digital twins, which can solve the problems of large start-stop impact, easy shaking, reduced production efficiency and service life when the robotic arm continuously grasps and transports materials in large-scale, rapid and disordered loading, and even damages the servo motor due to impact. During the robotic arm grasping process, the necessary trajectory optimization can make the motion curves of multiple joint angular displacements, angular velocities, angular accelerations, etc. of the robotic arm smoother and more continuous, while also protecting the servo motor.

[0007] In order to solve the above technical problems, the present invention provides the following technical solutions: a multi-objective trajectory planning method for a robotic arm based on digital twins, comprising: aiming at the uneven randomization of initial individuals of the elite non-dominated sorting genetic algorithm and susceptibility to the number of iterations, a mutation chaos strategy and a dynamic goal-oriented development strategy are proposed to improve and form LNSGA-Ⅱ, and the infeasibility is designed to solve the nonlinear constraints of the trajectory planning model; a multi-objective function is established to improve the robot's operating efficiency, the smoothness of the running trajectory and reduce the robot's energy consumption, and the LNSGA-Ⅱ algorithm is used to optimize the 7th-order B-spline curve node vector according to the passing time and sequence of the key points of the input motion path to complete the multi-objective trajectory planning of the robotic arm; a digital twin platform is built through MATLAB-CoppeliaSim-physical robotic arm, and the trajectory planning model is applied to the actual operation tasks of the robotic arm.

[0008] As a preferred solution of the multi-objective trajectory planning method of a robotic arm based on digital twinning described in the present invention, wherein: the multi-objective function is expressed as,

[0009]

[0010] Among them, f1 is the movement time, which measures the efficiency of the robot, f2 is the average acceleration of the joint, which measures the energy consumption of the robot, f3 is the joint jerk, which measures the smoothness of the robot movement, and the objective functions are optimal efficiency, optimal energy consumption, and optimal impact, respectively. s is the robot movement node, t s It is represented as the s-th robot arm motion time node, m is the number of robot arm joints, a is the joint acceleration, J is the joint impact pulsation, and T is the total joint motion time.

[0011] As a preferred solution of the multi-objective trajectory planning method of a manipulator based on digital twins described in the present invention, wherein: the passing time and sequence of the key points of the motion path include: when the manipulator moves from the starting point A to the end point B in the task space, a series of key points are obtained by inverse kinematics calculation,

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

[0013] Among them, m is the number of robot joints, s is the robot movement time node, n is the total number of movement time nodes, q is the joint movement angle, m q s is the motion angle of the mth joint at time s, m Q s is the robot joint motion function, obtained through robot trajectory planning,

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

[0015] Where f(t) represents the curve of the motion angle q of the mth robot joint changing with time;

[0016] The k-order B-spline curve is used to construct the robot arm motion trajectory. The B-spline curve is expressed as:

[0017]

[0018] Among them, d j are the control point coordinates, F j,k (t) is the k-order B-spline basis function, B(t) represents the joint position at time t. By inversely solving the control vertices of the B-spline curve, each robot joint passes through the key point m q s , and the segmented connection points of the trajectory curve correspond to the key nodes, the starting point and the end point are consistent, and the time node t is calculated according to the cumulative chord length parameterization method. j Normalize to get the internal node value, Δt k is the chord length,

[0019]

[0020] Δt k =t k+1 -t k ,k=0,1...n-1

[0021] Among them, t s Represented as the s-th robot arm motion time node, t k Represented as the kth robot movement time node, Δt s It is expressed as the time chord length of the s-th robot arm movement, t s-1 It is represented as the s-1th robot arm motion time node. By normalizing the time nodes, n+1 equations that meet the interpolation conditions are established, and the control nodes of the k-order B-spline curve are obtained by solving the equations.

[0022] As a preferred solution of the multi-objective trajectory planning method of a digital twin-based manipulator described in the present invention, the LNSGA-Ⅱ algorithm is expressed as follows: k =t k+1 -t k To optimize the variables, the iteration begins, the mutation chaos strategy is used to initialize the individual positions of the population, and the multi-objective functions f1, f2, and f3 are calculated; according to the objective function value, the population performs fast non-dominated sorting and crowding calculation, and calculates the dynamic adjustment factor r; when r∈(-1, 1), the dynamic goal-oriented development strategy is used to update the population position, and when r≥1 or r≤-1, the crossover and mutation are used to update the population position; the infeasibility is calculated, and the population individuals far away from the feasible domain are deleted; the multi-objective function value is calculated, and the iteration is continued until the maximum number of iterations is reached, and the iteration is terminated; the optimal population position and the objective function value are returned.

[0023] As a preferred solution of the multi-objective trajectory planning method of a robotic arm based on digital twins described in the present invention, the variant chaos strategy is expressed as:

[0024]

[0025] in, is the original sine map, mod is the remainder function, μ=0.99, Represented as a mutated chaotic strategy.

[0026] As a preferred solution of the multi-objective trajectory planning method of a manipulator based on digital twins described in the present invention, the dynamic goal-oriented development strategy includes adopting a dynamic adjustment factor r to ensure the diversity of the crossover mutation population, and adopting goal-oriented development to accelerate the convergence speed of the algorithm.

[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] Among them, β best(t) is the individual ranked first at the tth iteration, β(t) is the individual ranked lower and with higher crowding at the tth iteration, θ is the angle randomly selected by the roulette wheel, M S is a custom constant, 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 the individual in the population at the t+1th iteration, and r c Represented as adaptive iterative weight, β s Represents the goal-oriented selection of individual positions of a population.

[0032] As a preferred solution of the multi-objective trajectory planning method of a manipulator based on digital twinning described in the present invention, wherein: the calculation of the infeasibility includes designing an infeasibility of a target solution to handle constraints, which is defined as the sum of the squares of all conflicting constraint values, expressed as,

[0033]

[0034] Among them, A, B are the number of constraints, G a (x i ),T b (x i ) are equality constraints and inequality constraints respectively, ψ(x i ) is the infeasibility degree, which is an indicator to measure the distance between the current solution and the feasible domain. When the infeasibility degree is 0, it means that the position x of the individual in the population i is a feasible solution; as the infeasibility value increases, x i will gradually move away from the feasible region, and at the same time set an infeasibility threshold to judge x i Whether it is accepted, proceed to the next genetic operation.

[0035] As a preferred solution of a multi-target trajectory planning system for a robotic arm based on digital twinning described in the present invention, it includes: an acquisition module, a calculation module, and a twinning module;

[0036] The acquisition module collects the joint angle data of the robot arm's grasping path for industrial application scenarios of the robot arm, such as grasping and transporting materials, and inputs it into the calculation module;

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

[0038] The twin module builds a digital twin platform through MATLAB-CoppeliaSim-physical robotic arm to form a virtual-reality 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 comprises a memory and a processor, wherein the memory stores a computer program, and is characterized in that when the processor executes the computer program, the steps of any one of the methods for multi-objective trajectory planning of a robotic arm based on digital twins are implemented.

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

[0041] Beneficial effects of the present invention: The present invention designs an infeasibility degree of the target solution to handle constraints, which is defined as the sum of the squares of all conflicting constraint values. The infeasibility degree refers to the distance from the current solution to the feasible domain. When the infeasibility degree is 0, then x i is a feasible solution; the larger the infeasibility, the greater the x i The farther away from the feasible region, the lower the probability of failure. iWhether it is accepted, the next genetic operation is carried out. The original sinusoidal chaotic map has uneven distribution of chaotic values ​​and there is a boundary aggregation phenomenon. The mutated sinusoidal chaotic map has better uniformly distributed random values, and the boundary aggregation phenomenon disappears, making the initialization individual randomized and uniform. NSGA-Ⅱ is greatly affected by the number of iterations and has timeliness problems. A dynamic goal-oriented development method is proposed to accelerate the evolution of NSGA-Ⅱ individuals to the Pareto frontier, speed up the calculation time of the algorithm and reduce the number of iterations. According to the passing time and sequence 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 robot. Compared with the four multi-objective algorithms of multi-objective differential evolution algorithm (MODE), multi-objective particle swarm algorithm (MOPSO), multi-objective grey wolf algorithm (MOGWO), and elite non-dominated sorting genetic algorithm (NSGA-Ⅱ), the speed, acceleration and jerk of each joint of the robot in the start and stop phase are all 0, the overall joint motion trajectory is smooth and continuous, the vibration of the robot is reduced, and the key components such as the motor and reducer are effectively protected. 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 interactive platform is constructed through MATLAB-CoppeliaSim-UR16e, and a trajectory planning model is applied to solve the problems of large start-stop impact, easy shaking, reduced production efficiency and service life of the robotic arm in the process of large-scale rapid and disordered feeding. In summary, the present invention provides a multi-target trajectory planning method for a robotic arm based on digital twins. According to the passing time and sequence 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, complete the multi-target trajectory planning of the robotic arm, build a digital twin platform, and apply it to the actual grasping task of the robotic arm to accelerate the digitalization and intelligentization process of the robotic arm. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0043] Figure 1 The multi-objective trajectory planning results of LNSGA-Ⅱ on the Pareto front surface of a multi-objective trajectory planning method for a robotic arm based on digital twin provided in one embodiment of the present invention are compared with the other five algorithms, and the optimized angle, speed, acceleration and jerk curves are respectively displayed, demonstrating the superiority and success of LNSGA-Ⅱ proposed in the present invention in the multi-objective trajectory planning of the robotic arm.

[0044] Figure 2A process for establishing a digital twin model of a robotic arm based on a digital twin multi-objective trajectory planning method for a robotic arm is provided as an embodiment of the present invention.

[0045] Figure 3 A digital twin-based robotic arm multi-objective trajectory planning method is provided in one embodiment of the present invention, and a joint motion curve of an actual grasping task of a digital twin-based robotic arm UR16e.

[0046] Figure 4 A joint motion trajectory curve calculated by a multi-objective trajectory planning method for a robotic arm based on digital twinning is provided in one embodiment of the present invention. DETAILED DESCRIPTION

[0047] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0048] Example 1, reference Figure 1-Figure 3 , which is the first embodiment of the present invention, aims to solve the problems of large start-stop impact, easy shaking, reduced production efficiency and service life of the robot arm when it continuously grabs and transports materials with high intensity. A multi-objective trajectory planning method for the robot arm based on digital twin is proposed. Its main principle includes 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. The computational complexity was also reduced from the original O(MN3) to O(MN2), where M represents the number of targets and N represents the size of the population.

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

[0052] 2) Selection operation: The selection process makes the optimization proceed in the direction of the Pareto optimal solution and makes the solution evenly distributed. The selection operator is to avoid the loss of effective genes and make high-performance individuals survive with a greater probability, thereby improving global convergence and computational efficiency. After sorting and crowding distance calculation, each individual i in the population obtains two attributes: non-dominated order i rank and crowding distance i d The round-robin selection operator is used, that is, 2 individuals are randomly selected. rank <j rank or rank =j rank And i d >j d The meaning of the above formula is: if the non-dominated rankings of two individuals are different, the individual with the lower number is selected (the individual that is separated first in hierarchical sorting); if the two individuals are at the same level, the i individual is selected. d >j d of individuals.

[0053] 3) Crossover and mutation: Crossover and mutation work together to give the genetic algorithm good local and global search performance. Perform a crossover operation on the real-number-coded parent individuals, that is, for a given random crossover point, exchange the parts of the two parent individuals on both sides of the crossover point.

[0054] 4) Elite strategy: The elite strategy is to retain the excellent individuals in the parent generation and directly enter the offspring. It is a necessary condition for the genetic algorithm to converge with probability 1. The method used is: ① The parent generation P t and offspring Q t All individuals are combined into a unified population R t , R t The number of individuals is 2N; ② The population R t Quickly sort the non-dominated population and calculate the local crowding distance of each individual. Select individuals one by one according to their level until the number of individuals reaches N, forming a new parent population P. t+1 ,③In the new parent population P t+1 On this basis, a new round of selection, crossover and mutation begins to form a new offspring population Q t+1 .

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

[0056] Although the traditional NSGA-II algorithm has greatly improved the efficiency of sorting non-dominated solutions compared with NSGA, it still takes a lot of time for scheduling problems with large scale and many targets.

[0057] 1) Infeasibility design: When dealing with constraint problems, the conventional method is to convert out-of-bounds solutions into boundary extreme points. The present invention designs an infeasibility degree of the target solution to deal with constraints, which is defined as the sum of the squares of all conflicting constraint values.

[0058]

[0059] Among them, A, B are the number of constraints, G a (x i ),T b (x i ) are equality constraints and inequality constraints respectively. The infeasibility degree refers to the distance from the current feasible domain. When the infeasibility degree is 0, x i is a feasible solution; the larger the infeasibility, the greater the x i The farther away from the feasible region, the lower the probability of failure. i Whether it is accepted, proceed to the next genetic operation.

[0060] 2) Mutation Chaos Strategy: This paper proposes a mutation chaos strategy to solve the problem of poor initial population diversity and uneven distribution of NSGA-Ⅱ. is the original sine map, mod is the remainder function, μ=0.99, Represented as a mutated chaotic strategy.

[0061]

[0062] 3) Dynamic goal-oriented development: This paper proposes a method of dynamic goal-oriented development to accelerate the evolution of individuals in NSGA-Ⅱ to the Pareto frontier. A dynamic adjustment factor r is used to ensure the diversity of the crossover mutation population and to accelerate the convergence of the algorithm by using goal-oriented development. s Iter and Max-iter refer to the current number of iterations and the maximum number of iterations 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] Among them, βbest (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 the roulette wheel.

[0068] In summary, the constraint problem is first solved by designing the infeasibility degree, then the mutated sinusoidal chaotic mapping is used to initialize the population individuals, and finally the dynamic goal-oriented development is used to accelerate the individual iteration convergence to form a new LNSGA-Ⅱ algorithm. LNSGA-Ⅱ is used to solve the multi-objective trajectory optimization problem of the robotic arm.

[0069] S3: Trajectory Planning Model

[0070] 1) Construction of robot arm joint trajectory

[0071] When the robot moves from the starting point A to the end point B in the task space, a series of key points are obtained through inverse kinematics calculation. m Q s ={( m q s ,t s ),(m=1,2...,s=0,1...n)}, m is the number of robot joints, s is the robot motion node, n is the total number of motion nodes, q is the joint motion angle, which is obtained through robot trajectory planning. m f(t)= m q s The k-order non-uniform rational B-spline (NURBS) is used to construct the robot motion trajectory. The B-spline curve is:

[0072]

[0073] Among them, d j are the control point coordinates, F j,k (t) is the k-order B-spline basis function. B(t) refers to the joint position at time t. By inversely solving the control vertices of the B-spline curve, each robot joint passes through the key point m q s , and the segmented connection points of the trajectory curve correspond to the key nodes, and the starting point and the end point are consistent. According to the cumulative chord length parameterization method, the time node t j Normalize to get the internal node value, where Δt k is the string length.

[0074]

[0075] Δt k =t k+1 -t k ,k=0,1...n-1

[0076] Thus, n+1 equations satisfying the interpolation condition are obtained, and the control nodes of the k-order B-spline curve are obtained by solving the equations. This patent uses the 7-order B-spline curve to realize the trajectory planning of the robot arm.

[0077] 2) Multi-objective function:

[0078] In order to improve the robot's operating efficiency, smoothness of running trajectory and reduce the robot's energy consumption, a multi-objective function was established and solved using the LNSGA-Ⅱ algorithm. According to the passing time and sequence of the key points of the input motion path, the 7th-order B-spline curve was optimized to complete the multi-objective trajectory planning of the robotic arm while considering the path and joint constraints.

[0079] f1 is the movement time, which measures the efficiency of the robot. f2 is the average acceleration of the joint, which measures the energy consumption of the robot. f3 is the joint jerk, which measures the smoothness of the robot's movement. The objective functions are optimal efficiency, optimal energy consumption, and optimal impact. Among them, s is the time node sequence of the current non-uniform rational B-spline, m is the number of robot joints, a is the joint acceleration, and J is the joint impact pulsation.

[0080]

[0081] S4: LNSGA-Ⅱ algorithm solution process

[0082] With Δt k =t k+1 -t k To optimize the variables, the iteration begins, the mutation chaos strategy is used to initialize the position of the individual population, and the multi-objective function f1-f3 is calculated; according to the objective function value, the population performs fast non-dominated sorting and crowding calculation, and calculates the dynamic adjustment factor r; when r∈(-1, 1), the dynamic goal-oriented development strategy is used to update the population position, otherwise when r≥1 or r≤-1, the selection operation, crossover and mutation are used to update the population position; the infeasibility is calculated, and the population individuals far away from the feasible domain are deleted; the multi-objective function value is calculated, and the iteration is continued until the maximum number of iterations is reached, and the iteration is terminated; the optimal population position and the objective function value are returned. The LNSGA-Ⅱ algorithm solution flow chart is shown in the attached figure. Figure 1 shown.

[0083] S5: Use MATLAB-CoppeliaSim-UR16e to build a digital twin platform and 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 was established. Combined with the physical entity, a digital twin model interactive platform was constructed through MATLAB-CoppeliaSim-UR16e, and LNSGA-Ⅱ was used to solve the trajectory planning model to obtain the robotic arm motion trajectory that meets multiple objectives, thereby solving the problems of large start-stop impact, easy jitter, reduced production efficiency and service life of the robotic arm during large-scale, rapid and disordered loading.

[0085] The present invention is described in detail below in conjunction with the accompanying drawings and experimental results. Figures 1 to 4 As shown, the specific advantages of the present invention are:

[0086] Figure 1 This is the solution flow chart of LNSGA-Ⅱ algorithm.

[0087] Figure 2 The multi-objective trajectory planning results of the five algorithms on the Pareto frontier surface show the optimized angle, velocity, acceleration and jerk curves respectively. Time represents time, Angle, Velocity, Acceleration, and Jerk represent the angle, velocity, acceleration, and jerk of the robot joint motion respectively, and joint1-6 represents joints 1-6. The following conclusions can be drawn from the figure:

[0088] (1) From Figure 2 From the angle curves in the first column, (a)(i) shows that the angle curves of MODE and MOPSO are not smooth enough, there are inflection points in the motion angle, and the robot arm will jitter during the motion. The angle curves of the other three algorithms are smooth and continuous.

[0089] (2) Figure 2 In the velocity, acceleration and jerk curves of columns 2 to 4, MOPSO, NSGA-Ⅱ and LNSGA-Ⅱ all meet the basic requirements of robot arm joint trajectory planning: uniform, smooth and continuous. Although the velocity, acceleration and jerk curves of MOPSO and NSGA-Ⅱ meet the basic requirements, the multi-objective function is far behind LNSGA-Ⅱ, and it is impossible to achieve the optimization goal of "efficiency-energy-impact optimization" more accurately.

[0090] (3) From Figures (b)-(d), the velocity, acceleration, and jerk curves of MODE all have sharp corners and change drastically at the turning points, which can easily cause impact fluctuations in the robot arm and lead to motor damage.

[0091] (4) Figures (f)-(h) show that MOGWO has small changes in speed, acceleration, and jerk in the early stage of trajectory planning, but the curve fluctuates sharply in the 6th second, causing sharp changes in the speed, acceleration, and jerk of the robot arm. This is because when MOGWO optimizes the node variables of the B-spline curve, the subsequent time nodes are too compact and the changes are small.

[0092] The 7th-order B-spline curve is used for trajectory planning, and LNSGA-Ⅱ is used for multi-objective solution to optimize the node vector of the B-spline curve. The speed, acceleration and jerk of each joint of the robot arm in the start and stop stages are all 0. The overall joint motion trajectory is smooth and continuous, which reduces the vibration of the robot arm and effectively protects key components such as the motor and reducer.

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

[0094] Figure 4 It is the joint motion trajectory curve calculated by the present invention when the robot arm UR16e grabs the end cap, worm and bevel gear, that is, the command for the robot arm motion control. Where time is time, joint1-6 represents joints 1-6, v, a, j represent speed (° / s), acceleration (° / s) respectively. 2 ) and jerk (° / s 3 ).

[0095] Embodiment 2, the second embodiment of the present invention, is different from the previous embodiment in that:

[0096] If the functions are implemented in the form of 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 the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program codes.

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

[0098] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0099] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0100] Embodiment 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 an acquisition module, a calculation module, and a twin module;

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

[0102] The calculation module, based on the obtained robot arm joint angle data, establishes a multi-objective function to improve the robot's operating efficiency, the smoothness of the running trajectory and reduce the robot's energy consumption, uses the LNSGA-Ⅱ algorithm to solve, and optimizes the 7th-order B-spline curve to complete the multi-objective trajectory planning of the robot arm under the consideration of path and joint constraints;

[0103] The twin module builds a digital twin platform through MATLAB-CoppeliaSim-physical robotic arm to form a virtual-reality 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 are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A multi-objective trajectory planning method for a robotic arm based on digital twin, characterized by: include, A multi-objective function is established. According to the passing time and sequence 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 robot arm. Through MATLAB-CoppeliaSim-physical robotic arm, a digital twin platform is built, and the trajectory planning model is applied to the actual operation tasks of the robotic arm.

2. A multi-objective trajectory planning method for a robotic arm based on digital twinning as claimed in claim 1, characterized in that: The multi-objective function is expressed as, Among them, f1 is the movement time, which measures the efficiency of the robot, f2 is the average acceleration of the joint, which measures the energy consumption of the robot, and f3 is the joint jerk, which measures the smoothness of the robot movement. The objective functions are optimal efficiency, optimal energy consumption, and optimal impact, respectively. s is the time node of the robot movement, and t s It is represented as the s-th robot arm motion time node, q is the joint motion angle, m is the number of robot arm joints, a is the joint acceleration, J is the joint impact pulsation, and T is represented as the total joint motion time.

3. A multi-objective trajectory planning method for a robotic arm based on digital twinning as claimed in claim 2, characterized in that: The passing time and sequence of the key points of the motion path include: when the robot moves from the starting point A to the end point B in the task space, the key points are obtained by inverse kinematics calculation, m Q s ={( m q s ,t s ),(m=1,2...,s=0,1...n)} Where n is the total number of motion time nodes, m q s is the motion angle of the mth joint at time s, m Q s is the robot joint motion function, obtained through robot trajectory planning, m f(t)= m q s in, m f(t) represents the curve of the motion angle q of the m-th robot joint changing with time; The k-order B-spline curve is used to construct the robot arm motion trajectory. The B-spline curve is expressed as: Among them, d j are the control point coordinates, F j,k (t) is the k-order B-spline basis function, B(t) represents the joint position at time t. By inversely solving the control vertices of the B-spline curve, each robot joint passes through the key point m q s , and the segmented connection points of the trajectory curve correspond to the key nodes, the starting point and the end point are consistent, and the time node t is calculated according to the cumulative chord length parameterization method. j Normalize to get the internal node value, Δt k is the chord length, Δt k =t k+1 -t k ,k=0,1...n-1 Among them, t k Represented as the kth robot movement time node, Δt s It is expressed as the time chord length of the s-th robot arm movement, t s-1 It is represented as the s-1th robot arm motion time node. By normalizing the time nodes, n+1 equations that meet the interpolation conditions are established, and the control nodes of the k-order B-spline curve are obtained by solving the equations.

4. A multi-objective trajectory planning method for a robotic arm based on digital twinning as claimed in claim 3, characterized in that: The LNSGA-Ⅱ algorithm is expressed as, with Δt k =t k+1 -t k To optimize the variables, the iteration begins, the mutation chaos strategy is used to initialize the individual positions of the population, and the multi-objective functions f1, f2, and f3 are calculated; according to the objective function values, the population performs fast non-dominated sorting and crowding calculation, and calculates the dynamic adjustment factor r; when r∈(-1, 1), the dynamic goal-oriented development strategy is used to update the population position, and when r≥1 or r≤-1, the selection operation, crossover, and mutation are used to update the population position; Calculate the infeasibility and delete the individuals in the population that are far away from the feasible region; calculate the value of the multi-objective function and continue to iterate until the maximum number of iterations is reached and the iteration is terminated; Return the best population position and objective function value; Among them, t k+1 Represented as the k+1th robot arm movement time node.

5. A multi-objective trajectory planning method for a robotic arm based on digital twinning as claimed in claim 4, characterized in that: The mutation chaos strategy is expressed as: in, is the original sine map, mod is the remainder function, μ=0.99, Represented as a mutated chaotic strategy.

6. A method for multi-objective trajectory planning of a robotic arm based on digital twinning as claimed in claim 5, characterized in that: The dynamic goal-oriented development strategy is expressed as, 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) Among them, β best (t) is the individual ranked first at the tth iteration, β(t) is the individual ranked lower and with higher crowding at the tth iteration, θ is the angle randomly selected by the roulette wheel, and M S is a custom constant, 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 the individual in the population at the t+1th iteration, and r c Represented as adaptive iterative weight, β s It represents the goal-oriented selection of individual positions of a population.

7. A multi-objective trajectory planning method for a robotic arm based on digital twinning as claimed in claim 6, characterized in that: The computational infeasibility is expressed as, Among them, A, B are the number of constraints, G a (x i ),T b (x i ) are equality constraints and inequality constraints respectively, ψ(x i ) is the infeasibility degree. When the infeasibility degree is 0, it means that the position x of the individual in the population i is a feasible solution; as the infeasibility value increases, x i Will gradually move away from the feasible region, set the threshold of infeasibility, and judge x i Whether it is accepted, proceed to the next genetic operation.

8. A system for a multi-objective trajectory planning method for a robotic arm based on digital twinning according to any one of claims 1 to 7, characterized in that: Including acquisition module, calculation module and twin module; The acquisition module collects the joint angle data of the grasping path of the robotic arm for the industrial application scenario of the robotic arm, and inputs it into the calculation module; The calculation module establishes a multi-objective function based on the obtained robot arm joint angle data, and uses the LNSGA-Ⅱ algorithm to optimize the 7th-order B-spline curve node vector according to the passing time and sequence of the key points of the input motion path to complete the multi-objective trajectory planning of the robot arm; The twin module builds a digital twin platform through MATLAB-CoppeliaSim-physical robotic arm to form a virtual-reality 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.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

Images