Parallel robot trajectory optimization method based on improved dream optimization algorithm

Abstract

The invention discloses a parallel robot trajectory optimization method based on an improved dream optimization algorithm. The invention relates to the technical field of parallel robot trajectory optimization, and aims to obtain a smooth running trajectory of a robot in a high-speed running process and improve the motion performance of the parallel robot in the high-speed running process. The method comprises the following steps: constructing a target function according to total time and total impact required when a parallel robot operates according to a specified track; constructing constraint conditions according to the speed and acceleration operation requirements of the parallel robot; initializing a population of a dream optimization algorithm by means of a good point set and reverse learning; improving a dream sharing strategy by adopting a difference algorithm; and jumping out of the local optimization capability through the crossover variation improvement algorithm, thereby improving the quality of the solution and obtaining the optimal solution of the target function. The objective function considers the running time and impact of the robot, and the stability of the running process of the robot is guaranteed while the running speed of the robot is increased.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of parallel robot trajectory optimization, and particularly relates to a parallel robot trajectory optimization method based on an improved dream optimization algorithm. BACKGROUND

[0002] Delta parallel robots have the characteristics of fast moving speed, high repeat positioning accuracy, etc., and are widely used in food, electronics, pharmaceutical and other industries, and can complete fast material handling, packaging and sorting and other work. With the continuous improvement of the production efficiency requirement of modern industry, higher requirements are put forward for the running speed and accuracy of the Delta parallel robot. Using intelligent optimization algorithms such as particle swarm algorithm, genetic algorithm, whale algorithm, etc. to optimize the running trajectory of the robot is an important means to improve the running speed of the robot while ensuring the stability of its trajectory. However, the optimization results obtained by using intelligent optimization algorithms depend to a certain extent on the calculation accuracy and convergence speed of the algorithm itself. Therefore, exploring a new efficient trajectory optimization algorithm to obtain a smooth running trajectory of the robot in the high-speed running process has important theoretical and practical significance for improving the motion performance of the Delta parallel robot in the high-speed running process. SUMMARY

[0003] The purpose of the present application is to provide a parallel robot trajectory optimization method based on an improved dream optimization algorithm to obtain a smooth running trajectory of the robot in the high-speed running process and improve the motion performance of the parallel robot in the high-speed running process.

[0004] The present application provides a parallel robot trajectory optimization method based on an improved dream optimization algorithm, comprising: constructing a target function according to the total time and total impact required when the parallel robot runs according to a specified trajectory; setting a constraint condition according to the running requirements of the speed and acceleration of the parallel robot; determining the population parameters of the dream optimization algorithm, the population parameters including population size, iteration number, maximum value and minimum value, the population including a plurality of individuals, and each individual position representing a solution of the target function; initializing the population of the dream optimization algorithm by means of a good point set and a reverse learning strategy; exploring and developing the initialized population to obtain the optimal solution of the target function; wherein in the exploration stage, the individual positions are updated by using the memory strategy, forgetting and supplementing strategy of the dream optimization algorithm and the improved dream sharing strategy of introducing a global optimal individual; in the development stage, the individual positions are updated by using the memory strategy, forgetting and supplementing strategy of the dream optimization algorithm; the individual positions are disturbed by using a crossover and a polynomial mutation strategy to obtain a new optimal solution; If the set number of iterations is reached, the current optimal solution is output as the trajectory optimization parameters of the parallel robot; if not, the next optimization is continued in the exploration phase.

[0005] Further, the objective function is defined as follows: In the formula, is the objective function of the motion time, is the impact measurement index of the robot, is the time interval between two adjacent nodes, is the total time of the robot motion, is the angular displacement of the driving arm, i and j are the serial numbers of the control points on the NURBS spline curve, n is the total number of control points, and t is the time.

[0006] Further, in the good point set and reverse learning strategy, the process of introducing the good point set mapping is described as follows: In the formula, is the good point set mapping, and represents and some between , represents the good points uniformly distributed in the d-dimensional search space, t takes the minimum pixel point value of t≥ 2s +3, s represents the upper limit of the selected k value range, s is less than N, and N represents a positive integer.

[0007] Further, in the good point set and reverse learning strategy, the reverse learning is for a known solution in the target space, and the reverse solution thereof in the space is obtained by reverse learning, and the optimal solution of the two is selected as the current solution.

[0008] Further, the definition of reverse learning is shown in the following formula: In the formula, and are the upper and lower limits of the initial population, respectively, X is the initial population, is the reverse population of the initial population.

[0009] Further, the population of the dream optimization algorithm is initialized by means of the good point set and the reverse learning strategy, including: The individuals generated by the good point set are mixed with the individuals generated by the random method in the dream optimization algorithm to form new individuals, the mixed population is further processed by reverse learning, and the first N individuals with high fitness values are selected as the new population.

[0010] Further, the improved dream sharing strategy comprises: In the formula, is the value of the jth individual in the mth dimension before updating, is the value of the jth individual in the ith dimension after updating; is the value of the kth dimension of the randomly selected jth individual; is the value of the kth dimension of the global optimal individual; is a random value in [0, 1].

[0011] Further, the crossover and polynomial mutation strategy comprises: Select the first 10% and the last 10% of individuals to perform crossover and mutation between each other, compare the fitness of the compiled individuals with the original individuals, and leave the individuals with the best fitness to complete a crossover and mutation.

[0012] Further, the expression of crossover is: In the formula, , .

[0013] Further, the expression of polynomial mutation operation is: In the formula, is a mutation operator, and the expression is: , , u is a random number in the interval [0, 1], is a distribution index selected by a user, and are the upper and lower limits of the initial value of the population, respectively.

[0014] The application has the following beneficial effects: the parallel robot trajectory optimization method based on the improved dream optimization algorithm, according to the total time and total impact required when the parallel robot runs according to the specified trajectory, constructs a target function; according to the running requirements of the speed and acceleration of the parallel robot, a constraint condition is constructed; the population of the dream optimization algorithm is initialized by means of the best point set and reverse learning, and the uniformity of the population distribution is improved; the dream sharing strategy is improved by using the differential algorithm, and the global optimization ability of the algorithm is improved; the algorithm jumping out of local optimization ability is improved by crossover and mutation, so as to improve the quality of the solution and obtain the optimal solution of the target function. The target function takes into account the running time and impact of the robot, and improves the running speed of the robot while ensuring the stability of the running process.​ Attached Figure Description

[0015] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0016] Figure 1 Diagram showing population initialization; Figure 2 A diagram illustrating the dream optimization algorithm and its iterative process for improvement. Figure 3 This is a diagram of the gate-shaped picking trajectory of a parallel robot in the operating space, which is fitted using NURBS spline curves. Figure 4 The graphs show the motion parameters of each joint of the parallel robot before optimization; where (a) is the angular displacement curve of the driving arm, (b) is the angular velocity curve of the driving arm, (c) is the angular acceleration curve of the driving arm, and (d) is the angular jerk curve of the driving arm. Figure 5 The optimized door-type picking trajectory diagram is used to improve the dream optimization algorithm; Figure 6 The graphs of motion parameters of each joint of the parallel robot after the optimization of the dream optimization algorithm are shown. Among them, (a) is the angular displacement curve of the driving arm, (b) is the angular velocity curve of the driving arm, (c) is the angular acceleration curve of the driving arm, and (d) is the angular jerk curve of the driving arm. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. The technical solutions provided by various embodiments of this invention will be described in detail below with reference to the accompanying drawings.

[0018] This invention provides a method for optimizing the trajectory of a parallel robot based on an improved dream optimization algorithm, comprising: Step 1: Construct the objective function based on the total time and total impact required for the parallel robot to run along the specified trajectory.

[0019] Specifically, the objective function is defined as follows: In the formula, Let the objective function be the motion time. a measure of the impact on the robot, a time interval between two adjacent nodes, a total time of the robot movement, an angular displacement of the driving arm, i and j are serial numbers of control points on the NURBS spline curve, n is a total number of control points, and t is time.

[0020] Step two, setting a constraint condition according to a running requirement of velocity and acceleration of the parallel robot.

[0021] Step three, determining population parameters of the dream optimization algorithm, the population parameters including a population size, an iteration number, a maximum value and a minimum value, the population including a plurality of individuals, each individual position representing a solution of the objective function; initializing the population of the dream optimization algorithm by means of a good point set and a reverse learning strategy.

[0022] Step four, exploring and developing the initialized population to obtain an optimal solution of the objective function; wherein, in the exploration stage, updating the individual position by means of a memory strategy, a forgetting and supplement strategy and an improved dream sharing strategy of introducing a global optimal individual of the dream optimization algorithm; in the development stage, updating the individual position by means of the memory strategy, the forgetting and supplement strategy of the dream optimization algorithm; disturbing the individual position by means of a crossover and a polynomial mutation strategy to obtain a new optimal solution.

[0023] Specifically, the population initialization strategy based on the good point set and the reverse learning is to disturb the initial position of the population by the good point set mapping, improve the uneven distribution of the initial solution, and make the population have high-quality initial solutions. The good point set is a theory that can generate a uniformly distributed and non-repeated point set in a multi-dimensional cubic space. Introducing the good point set into the population initialization is conducive to increasing the diversity of favorable solutions and avoiding being attracted by local extreme values. The uniform distribution is used for optimization in a d-dimensional exploration space. The process of introducing the good point set mapping is described as follows: In the formula, is the good point set mapping, and represents and a certain one between , represents a good point uniformly distributed in a d-dimensional search space, t takes a minimum pixel point of t≥ 2s +3, s represents an upper limit of a selected k value range, s is less than N, and N represents a positive integer.

[0024] The reverse learning is to obtain a reverse solution of a known solution in a target space by reverse learning, and select a better solution of the two as a current solution.

[0025] The definition of reverse learning is shown in the following formula: In the formula, And are the upper and lower limits of the initial population, X is the initial population, is the reverse population of the initial population.

[0026] The individual generated by the good point set is mixed with the individual generated by the random method in the dream optimization algorithm (DOA) to form a new individual, the mixed population is further processed by reverse learning, and the first N individuals with high fitness values are selected as the new population. The original dream optimization algorithm adopts a random initial population generation method, the improved dream optimization algorithm (IDOA) of the application is improved based on the good point set and the reverse learning population initialization, and the new initial population is selected from the initial population and the improved population with higher fitness values. As shown in Figure 1 After the reverse learning initialization, the population distribution is more uniform, which is conducive to the optimization of the algorithm.

[0027] The dream sharing strategy of the dream optimization algorithm adopts a new random individual selection method with strong randomness, which can explore the search space to a certain extent, but lacks the use of good solutions currently searched, which may cause the algorithm to wander around the local optimal solution and be difficult to converge to the global optimal solution. The global optimal individual sbest(in(h)) is introduced as a reference, which is updated by formula, so that the update of the current individual not only considers the information of the randomly selected individual, but also combines the information of the global optimal individual. The introduction of the random factor can increase the randomness of the search, which is helpful to explore new areas; and the introduction of the global optimal individual guides the algorithm to develop in the direction of the global optimal solution, so as to better balance the exploration and development ability of the algorithm.

[0028] Specifically, the improved dream sharing strategy comprises: In the formula, is the value of the jth individual in the mth dimension before updating, is the value of the jth individual in the ith dimension after updating; is the value of the kth individual in the kth dimension randomly selected; is the value of the kth individual in the kth dimension randomly selected; is the value of the kth individual in the kth dimension randomly selected; is a random value in [0, 1].

[0029] To enhance the dream optimization algorithm's ability to escape local optima, this invention utilizes the crossover and mutation method from genetic algorithms. It selects the top 10% and bottom 10% of individuals and performs pairwise crossover and mutation. The resulting individuals are then compared with the original individuals in terms of fitness, and the individual with the best fitness is retained, thus completing one crossover and mutation cycle. The expression for crossover is: In the formula, , .

[0030] Furthermore, the expression for the polynomial mutation operation is: In the formula, The mutation operator is expressed as: , u is a random number in the interval [0,1]. It is a distribution index selected by the user. and These are the upper and lower limits of the initial population value, respectively.

[0031] from Figure 2 As can be seen, the improved dream optimization algorithm with the three improvements has a faster iteration speed and a smaller optimal value, which has certain advantages.

[0032] Step 5: Determine if the set number of iterations has been reached. If it has, exit and output the current optimal solution as the trajectory optimization parameters for the parallel robot. If it has not been reached, return to the exploration phase to continue the next optimization.

[0033] The following are application examples of this invention in the trajectory optimization of Delta high-speed parallel robots.

[0034] The three-degree-of-freedom Delta high-speed parallel robot mainly consists of a fixed static platform, a flexibly movable end effector platform, and three identical parallelogram branches. It is typically used for high-speed material sorting, packing, and assembly, and can achieve translational motion in the X, Y, and Z directions. Each branch includes a drive arm, a driven arm, and a ball joint. The drive arms are evenly distributed at 120° intervals on the static platform. During operation, the three servo motors start simultaneously, coordinating to control the drive arm to rotate a specific angle. Since the drive arm and driven arm are connected by ball joints, when the drive arm rotates, the parallelogram driven arm moves accordingly through the ball joints. The driven arms of the three branches work together to propel the end effector platform to complete translational motion in the X, Y, and Z directions, achieving precise and efficient operation.

[0035] In the operation process of the Delta high-speed parallel robot, three servo motors respectively drive corresponding driving arms to rotate, each driving arm drives three parallelogram driven arms to rotate through a spherical hinge mechanism, and then drives the end moving platform by the synchronous movement of the driven arms, so as to ensure the positioning ability of the end effector, i.e. the moving platform, in the three-dimensional space.

[0036] Delta robot NURBS trajectory planning. The operation space trajectory is constructed by means of a quintic NURBS function, and Table 1 lists the numerical values of the six path key points of the preset door-shaped trajectory. During each picking movement, the trajectory of the end moving platform is: uplink interval to p1→p2→p3, horizontal transition interval p3→p4, and downlink phase trajectory p4→p5→p6; and during the placement movement, the trajectory is: uplink phase p6→p5→p4, horizontal movement interval p4→p3, and downlink phase p3→p2→p1.

[0037] Table 1 Key points of door-shaped trajectory The kinematic constraint conditions of the selected Delta high-speed parallel robot are shown in Table 2.

[0038] Table 2 Kinematic constraints of Delta high-speed parallel robot The door-shaped picking trajectory of the robot in the operation space is obtained by using a quintic NURBS curve interpolation as shown in Figure 3 The specific process of obtaining the trajectory is a prior art, which will not be described here.

[0039] After completing the quintic non-uniform rational B-spline (NURBS) motion trajectory planning in the operation space, the angular displacement, angular velocity, angular acceleration and angular jerk curves of the three driving arms of the Delta parallel robot in the joint space are further obtained by the inverse kinematics method. As shown in Figure 4 It is found through analysis that the change process of the angular displacement, angular velocity and angular acceleration curves generated by the quintic non-uniform rational B-spline curve interpolation is relatively smooth. However, the angular jerk curve has obvious mutation points, and the sharp change in the numerical value indicates that the robot will bear a large motion impact during operation, which may affect the stability and service life of the equipment, and subsequent targeted optimization and improvement are needed.

[0040] When the time-impact optimal trajectory planning is implemented for the Delta parallel robot, the IDOA algorithm is adopted, all simulations are carried out in the MATLAB2024a environment, the algorithm population size is set to 30, the maximum iteration number is set to 100 times, in practical application, the weight coefficients are distributed according to the scene, in this case, the time weight coefficient and the impact weight coefficient are consistent, both are 0.5. The optimized robot grabbing trajectory is shown as Figure 5 .

[0041] After the improved dream optimization algorithm is optimized, the angular displacement, angular velocity, angular acceleration and angular jerk change curves of the three driving joints in the grabbing trajectory are shown as Figure 6 From the figure, it can be seen that within the set constraint range, the time required for completing a set trajectory before optimization is 0.7s, and the time required for completing a set trajectory after optimization is 0.4695s, which is reduced by 0.2305s compared with before optimization, the robot grabbing efficiency is improved by 32.92%, the maximum values of each joint of the driving arm before and after optimization are not more than deg / s3 and deg / s3, the mutation phenomenon of the angular jerk curve is significantly improved, the motion impact is effectively suppressed, and the impact is obviously reduced. The results show that the IDOA algorithm successfully realizes the optimal trajectory planning of the Delta parallel robot under the double targets of time and impact, which not only ensures the efficient operation of the robot, but also greatly reduces the mechanical impact in the motion process, effectively prolongs the service life of the equipment.

[0042] The above-mentioned embodiments of the application do not constitute a limitation on the protection scope of the application.

Claims

1. A trajectory optimization method for parallel robots based on improved dream optimization algorithm, characterized in that, The application relates to a trajectory optimization method for a parallel robot. A target function is constructed according to the total time and total impact required when the parallel robot runs along a specified trajectory; Constraint conditions are set according to the running requirements of the speed and acceleration of the parallel robot; Population parameters of a dream optimization algorithm are determined, the population parameters including population size, iteration number, maximum value and minimum value, the population including multiple individuals, and each individual position representing a solution of the target function; The population of the dream optimization algorithm is initialized by means of a good point set and a reverse learning strategy; The initialized population is explored and developed to obtain an optimal solution of the target function; in the exploration stage, individual positions are updated by using a memory strategy, a forgetting and supplement strategy and an improved dream sharing strategy of the dream optimization algorithm; in the development stage, individual positions are updated by using the memory strategy, the forgetting and supplement strategy of the dream optimization algorithm; new optimal solutions are obtained by disturbing the individual positions by using a crossover and polynomial mutation strategy; It is judged whether the set iteration number is reached, if yes, the optimization is exited, and the current optimal solution is output as the trajectory optimization parameter of the parallel robot; if not, the exploration stage is returned to continue the next optimization.

2. The improved dream optimization algorithm based trajectory optimization method for parallel robots as claimed in claim 1 wherein, The target function is defined as follows: wherein is a target function of motion time, is a measure of robot impact, is a time interval between two adjacent nodes, is the total time of robot motion, is the angular displacement of the driven arm, i, j are the serial numbers of control points on the NURBS spline curve, n is the total number of control points, and t is time.

3. The improved dream optimization algorithm based trajectory optimization method for parallel robots as claimed in claim 1 wherein, In the good point set and the reverse learning strategy, the mapping process of the good point set is described as follows: In the formula, is a good point set mapping, and represents and between some one, , represents a good point uniformly distributed in a d-dimensional search space, t takes a minimum pixel point value t≥2s+3, s represents an upper limit of the selected k value range, s is less than N, and N represents a positive integer.

4. The improved dream optimization algorithm based trajectory optimization method for parallel robots as claimed in claim 3 wherein, In the good point set and the reverse learning strategy, the reverse learning is performed on a known solution in a target space, a reverse solution of the known solution in the space is obtained by the reverse learning, and the optimal solution of the known solution and the reverse solution is selected as a current solution.

5. The improved dream optimization algorithm based trajectory optimization method for parallel robots as claimed in claim 4 wherein, The definition of the reverse learning is shown in the following formula: wherein and are the upper and lower limits of the initial population, respectively, X is the initial population, is the inverse population of the initial population.

6. The improved dream optimization algorithm based trajectory optimization method for parallel robots as claimed in claim 5 wherein, The population of the dream optimization algorithm is initialized by means of the good point set and the reverse learning strategy, including: Individuals generated by the good point set and individuals generated by a random method in the dream optimization algorithm are mixed into new individuals, the mixed population is further processed by using the reverse learning, and the first N individuals with high fitness values are selected as the new population.

7. The improved dream optimization algorithm based trajectory optimization method for parallel robots as claimed in claim 1 wherein, The improved dream sharing strategy includes: wherein, is the value of the jth individual in the mth dimension before updating, is the value of the jth individual in the ith dimension after updating; is the value of the kth individual randomly selected in the kth dimension; is the value of the kth individual randomly selected in the kth dimension; is the value of the global optimal individual in the kth dimension; is a random value in [0, 1].

8. The improved dream optimization algorithm based trajectory optimization method for parallel robots as claimed in claim 1 wherein, The crossover and polynomial mutation strategy includes: Individuals in the first 10% and the last 10% are crossed and mutated, the fitness of the compiled individuals is compared with that of the original individuals, the individuals with the best fitness are reserved, and one-time crossover and mutation are completed.

9. The improved dream optimization algorithm based trajectory optimization method for parallel robots as claimed in claim 8, wherein, The expression of the crossover is as follows: In the formulae, , .

10. The improved dream optimization algorithm based trajectory optimization method for parallel robots as claimed in claim 9, wherein, The expression of the polynomial mutation operation is as follows: wherein is a mutation operator, and the expression is: , , u is a random number in the interval [0, 1], is the distribution index selected by the user, and are the upper and lower limits of the initial value of the population, respectively.

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