Parallel robot trajectory optimization method based on improved dream optimization algorithm

Abstract

The application discloses a trajectory optimization method for a parallel robot based on an improved dream optimization algorithm, and relates to the technical field of trajectory optimization of parallel robots, aiming 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 application constructs a target function according to the total time and total impact required when the parallel robot runs according to a specified trajectory, constructs a constraint condition according to the running requirements of the speed and acceleration of the parallel robot, initializes a population of the dream optimization algorithm by means of a good point set and reverse learning, improves a dream sharing strategy by adopting a differential algorithm, and improves the local optimization ability of a crossover mutation algorithm, thereby improving the quality of a solution and obtaining an optimal solution of the target function.The target function takes into account the running time and impact of the robot, improves the running speed of the robot, and guarantees the stability of the running process of the robot.

Description

TECHNICAL FIELD

[0001] The 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 high moving speed, high repeat positioning accuracy, etc., are widely applied to food, electronic, pharmaceutical and other industries, and can complete rapid material carrying, packaging and sorting and other work. With the continuous improvement of the requirement of modern industrial level on production efficiency, higher requirements are put forward for the operation speed and accuracy of the Delta parallel robot. Using intelligent optimization algorithms such as particle swarm algorithm, genetic algorithm and whale algorithm to optimize the operation trajectory of the robot is an important means to improve the operation speed of the robot while ensuring the stability of the trajectory. However, the optimization result obtained by using the intelligent optimization algorithm depends on the calculation accuracy and convergence speed of the algorithm itself to a certain extent. Therefore, exploring a new efficient trajectory optimization algorithm to obtain a smooth operation trajectory of the robot in the high-speed operation process has important theoretical and practical significance for improving the motion performance of the Delta parallel robot in the high-speed operation process. SUMMARY

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

[0004] The application provides a parallel robot trajectory optimization method based on an improved dream optimization algorithm, which comprises the following steps:

[0005] A target function is constructed according to the total time and total impact required when the parallel robot runs according to a specified trajectory;

[0006] Constraint conditions are set according to the operation requirements of the speed and acceleration of the parallel robot;

[0007] Population parameters of the dream optimization algorithm are determined, the population parameters comprise population size, iteration number, maximum value and minimum value, the population comprises a plurality of individuals, and each individual position represents 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;

[0008] The initialized population is explored and developed to obtain the optimal solution of the target function; in the exploration stage, the memory strategy, forgetting and supplement strategy of the dream optimization algorithm and the improved dream sharing strategy of introducing the global optimal individual are used to update the individual position; in the development stage, the memory strategy, forgetting and supplement strategy of the dream optimization algorithm are used to update the individual position; the individual position is disturbed by using the crossover and polynomial mutation strategy to obtain a new optimal solution;

[0009] It is judged whether the set iteration number is reached at present, if yes, 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.

[0010] Further, the target function is defined as follows:

[0011]

[0012] In the formula, is the target function of the motion time, is the measurement index of the robot impact, is the time interval of 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.

[0013] Further, in the good point set and the reverse learning strategy, the process of introducing the good point set mapping is described as follows:

[0014]

[0015] In the formula, is the good point set mapping, and represents and between them, , represents the good points uniformly distributed in the d-dimensional search space, t takes the minimum pixel point 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.

[0016] Further, in the good point set and the reverse learning strategy, the reverse learning is for a known solution in the target space, and the reverse solution thereof is obtained by reverse learning, and the optimal solution of the two is selected as the current solution.

[0017] Further, the definition of reverse learning is shown in the following formula:

[0018]

[0019] In the formula, and Here, X represents the upper and lower bounds of the initial population value, respectively, where X is the initial population. This is the reverse population of the initial population.

[0020] Furthermore, the population for the dream optimization algorithm is initialized using a set of optimal points and a reverse learning strategy, including:

[0021] Individuals generated from the best point set are mixed with individuals generated by the random method in the dream optimization algorithm to form a new population. The mixed population is further processed using back learning, and the top N individuals with high fitness values ​​are selected as the new population.

[0022] Furthermore, the improved dream-sharing strategy includes:

[0023]

[0024] In the formula, It is the value of the j-th individual in the m-th dimension before the update. It is the updated value of the j-th individual in the i-th dimension; It is a randomly selected number The value of an individual in the k-th dimension; It is the value of the globally optimal individual in the k-th dimension; It is a random value in the range [0,1].

[0025] Furthermore, the crossover and polynomial mutation strategy includes:

[0026] The top 10% and bottom 10% of individuals are selected for pairwise crossover mutation. The fitness of the compiled individuals is compared with that of the original individuals, and the individual with the best fitness is retained, thus completing one crossover mutation.

[0027] Furthermore, the expression for the intersection is:

[0028]

[0029] In the formula, , .

[0030] Furthermore, the expression for the polynomial mutation operation is:

[0031]

[0032] In the formula, The mutation operator is expressed as:

[0033]

[0034] , , u is a random number in the interval [0, 1], is a distribution index selected by a user, and are upper and lower limits of initial values of the population, respectively.

[0035] The application has the following beneficial effects: the parallel robot trajectory optimization method based on the improved dream optimization algorithm has the following beneficial effects: the target function is constructed according to the total time and total impact required when the parallel robot runs according to the specified trajectory; the constraint condition is constructed according to the running requirements of the speed and acceleration of the parallel robot; the population of the dream optimization algorithm is initialized by means of the good point set and the 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 crossing and mutation, so that the quality of the solution is improved, and the optimal solution of the target function is obtained. The target function takes into account the running time and impact of the robot, and ensures the stability of the running process while improving the running speed of the robot. BRIEF DESCRIPTION OF DRAWINGS

[0036] In order to more clearly illustrate the technical solutions of the present application, the drawings needed in the embodiments will be briefly introduced as follows: obviously, for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0037] Figure 1 It is a population initialization schematic diagram;

[0038] Figure 2 It is an iteration diagram of the dream optimization algorithm and the improved dream optimization algorithm;

[0039] Figure 3 It is a door-shaped picking trajectory diagram of the parallel robot in the operation space fitted by the NURBS spline curve;

[0040] Figure 4 It is a curve diagram of the motion parameters of each joint of the parallel robot before optimization; wherein, (a) is a driving arm angular displacement curve, (b) is a driving arm angular velocity curve, (c) is a driving arm angular acceleration curve, and (d) is a driving arm angular jerk curve;

[0041] Figure 5 It is a door-shaped picking trajectory diagram after optimization by the improved dream optimization algorithm;

[0042] Figure 6In order to improve the motion parameter curve diagram of each joint of the parallel robot optimized by the dream optimization algorithm, wherein (a) is a driving arm angular displacement curve, (b) is a driving arm angular velocity curve, (c) is a driving arm angular acceleration curve, and (d) is a driving arm angular jerk curve. DETAILED DESCRIPTION

[0043] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions of the present application will be described below in connection with the specific embodiments of the present application and corresponding drawings. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the protection scope of the present application. The technical solutions provided by the embodiments of the present application will be described in detail below in connection with the drawings.

[0044] The parallel robot trajectory optimization method based on the improved dream optimization algorithm provided by the embodiment of the present application comprises:

[0045] Step one, constructing a target function according to the total time and total impact required when the parallel robot runs according to a specified trajectory.

[0046] Specifically, the target function is defined as follows:

[0047]

[0048] In the formula, is a target function of motion time, is a measurement index of robot impact, is a time interval of two adjacent nodes, is the total time of robot motion, is the angular displacement of the driving arm, i and 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.

[0049] Step two, setting a constraint condition according to the running requirements of the speed and acceleration of the parallel robot.

[0050] Step three, determining the population parameters of the dream optimization algorithm, wherein the population parameters comprise population size, iteration number, maximum value and minimum value, the population comprises a plurality of individuals, and each individual position represents 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.

[0051] Step four, exploration and development are carried out on the initialized population to obtain the optimal solution of the target function; wherein in the exploration stage, the memory strategy, forgetting and supplement strategy of dream optimization algorithm and the improved dream sharing strategy of introducing global optimal individual are used to update the individual position; in the development stage, the memory strategy, forgetting and supplement strategy of dream optimization algorithm are used to update the individual position; the individual position is disturbed by using the crossover and polynomial mutation strategy to obtain a new optimal solution.

[0052] Specifically, the population initialization strategy based on the good point set and reverse learning is used to disturb the initial position of the population through the good point set mapping, improve the uneven distribution of the initial solution, and make the population have high-quality initial solution. The good point set is a theory that can generate a uniformly distributed and non-repeated point set in a multi-dimensional cubic space. The introduction of the good point set into the population initialization is beneficial to increase the diversity of favorable solutions and avoid 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:

[0053]

[0054] In the formula, is the good point set mapping, and represents and some between , represents a good point uniformly distributed in a 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.

[0055] Reverse learning is to obtain the inverse solution of a known solution in the target space through reverse learning, and select the optimal solution of the two as the current solution.

[0056] The definition of reverse learning is shown in the following formula:

[0057]

[0058] In the formula, and are the upper and lower limits of the initial population value, X is the initial population, is the reverse population of the initial population.

[0059] The individual generated by the good point set is mixed with the individual generated by the random method in the dream optimization algorithm (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 (Improved Dream Optimization Algorithm, IDOA) of the application is improved based on the good point set and the population initialization of reverse learning, and the initial population and the improved population are selected to form a new initial 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.

[0060] 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 better 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, and the current individual 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.

[0061] Specifically, the improved dream sharing strategy comprises:

[0062]

[0063] 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 selected randomly; is the value of the kth individual in the kth dimension selected randomly; is the value of the kth individual in the kth dimension selected randomly; is a random value in [0, 1].

[0064] In order to enhance the ability of the dream optimization algorithm to jump out of the local optimum, based on the crossover and mutation method in the genetic algorithm, the first 10% and the last 10% of individuals are selected to perform crossover and mutation between each other, and the fitness of the compiled individual and the original individual is compared, and the individual with the best fitness is left, which completes a crossover and mutation. The expression of the crossover is:

[0065]

[0066] In the formula, , .

[0067] Further, the polynomial mutation operation expression is:

[0068]

[0069] In the formula, is a mutation operator, and the expression is:

[0070]

[0071] , u is a random number in the interval [0, 1], is a distribution index selected by a user, and are respectively upper and lower limits of initial values of the population.

[0072] As can be seen from Figure 2 , the improved dream optimization algorithm after implementing the three improvements has a faster iteration speed and a smaller optimal value, and has certain superiority.

[0073] Step five, it is judged whether the set iteration number is reached at present, if yes, then the current optimal solution is output as the trajectory optimization parameter of the parallel robot and the process is exited, if not, then the exploration stage is returned to continue the next optimization.

[0074] The following is an application example of the application in the trajectory optimization of a Delta high-speed parallel robot.

[0075] The three-degree-of-freedom Delta high-speed parallel robot mainly comprises a fixed static platform, a movable terminal movable platform which can be flexibly moved, and three parallel four-bar chains which are the same in structure, is usually used for realizing high-speed sorting, boxing, assembling and other fields of materials, and can achieve translational motion in the space X, Y and Z directions. Each chain comprises a driving arm, a driven arm and a spherical hinge, wherein the driving arms are uniformly distributed at 120° on the static platform. In the actual working process, three servo motors are started at the same time to cooperatively control the driving arms to rotate by a specific angle. Since the driving arm and the driven arm are connected through the spherical hinge, when the driving arm rotates, the parallel four-bar driven arm is driven to move through the spherical hinge. The driven arms of the three chains jointly exert force, and finally push the terminal movable platform to complete the translational motion in the X, Y and Z directions in the space, so as to realize precise and efficient operation.

[0076] 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.

[0077] 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.

[0078] Table 1 Key points of the door-shaped trajectory

[0079]

[0080] The kinematic constraint conditions of the selected Delta high-speed parallel robot are shown in Table 2.

[0081] Table 2 Kinematic constraints of the Delta high-speed parallel robot

[0082]

[0083] 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, and will not be described here.

[0084] 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.

[0085] 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 .

[0086] 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.

[0087] 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 the dream optimization algorithm are determined, the population parameters including population size, iteration number, maximum value and minimum value, and the population including multiple individuals, 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, the individual positions are updated by using 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, the individual positions are updated by using the memory strategy, the forgetting and supplement strategy of the dream optimization algorithm; the individual positions are disturbed by using a crossover and polynomial mutation strategy to obtain a new optimal solution; The improved dream sharing strategy comprises the following steps: In the formula, It is the value of the j-th individual in the m-th dimension before the update. It is the updated value of the j-th individual in the i-th dimension; It is a randomly selected number The value of an individual in the k-th dimension; It is the value of the globally optimal individual in the k-th dimension; A random value in the range [0,1]. The crossover and polynomial mutation strategy comprises the following steps: The first 10% and the last 10% of individuals are selected to be crossed and mutated, the fitness of the compiled individuals is compared with that of the original individuals, the individual with the best fitness is left, one-time crossover and mutation are completed, and the expression of the crossover is as follows: In the formulae, , ; 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 is the serial number of the control point on the NURBS spline curve, n is the total number of control points, t is the 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 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 a certain one between and , represents a good point uniformly distributed in a d-dimensional search space, t is the minimum pixel point with a value of t ≥ 2 s +3, s represents the upper limit of the value range of the selected k , s is less than N , 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 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 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 as shown in the following formula: wherein with 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 a good point set and a reverse learning strategy, which comprises the following steps: Individuals generated from the optimal point set are mixed with individuals randomly generated in the dream optimization algorithm to form a new population. Backward learning is then used to further process the mixed population, and individuals with high fitness values ​​are selected. N This is a new population.

7. The improved dream optimization algorithm based trajectory optimization method for parallel robots as claimed in claim 1 wherein, The expression of the polynomial mutation operation is as follows: wherein is the 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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