Particle swarm optimization and Kepler optimization algorithm-based stacker crane trajectory optimization method

Abstract

The invention relates to a stacking machine track optimization method based on particle swarm optimization and Kepler optimization algorithms, and belongs to the technical field related to industrial robot control. The method comprises the following steps: iteratively searching optimal parameters of time and energy consumption by adopting an improved particle swarm algorithm, and storing the optimal parameters; in the trajectory optimization process, the speed, the acceleration, the maximum speed and the maximum acceleration of the stacker crane joint are considered; initializing parameters; establishing a trajectory interpolation function based on the path point coordinates; time optimization, energy consumption optimization and motion limitation of the mechanical arm are comprehensively considered, and the inertia weight is determined; an improved particle swarm algorithm is adopted to optimize time and energy consumption; updating the speed of each particle according to a particle swarm algorithm speed updating formula, and updating the position of each particle according to a particle swarm algorithm position updating formula; local optimization is performed in combination with a Kepler optimization algorithm, the convergence speed of the optimization process is increased, and the calculation efficiency is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to the control of industrial robots, and particularly relates to a palletizer trajectory optimization method based on particle swarm optimization and Kepler optimization algorithm. Background Technique

[0002] Palletizing robots are important components in industrial automation and intelligent logistics systems, and are widely used in fields such as warehousing, production lines, and logistics transportation. Their main task is to stack or handle goods in a specific manner according to the set trajectory and strategy. The core goal of palletizing robot trajectory optimization is to ensure a smooth and efficient trajectory, reduce energy consumption, and meet the operating requirements in complex environments at the same time.

[0003] Currently, the trajectory planning methods of palletizers mainly include polynomial interpolation, spline interpolation, and methods based on intelligent optimization algorithms (such as genetic algorithms, particle swarm optimization, etc.). However, these methods still have many deficiencies in practical applications:

[0004] Existing palletizer trajectory planning methods mainly focus on the feasibility of the path and the execution time, and do not fully consider the need to reduce energy consumption. Although the currently widely used polynomial interpolation method can generate a relatively smooth trajectory, it is not optimized for energy consumption, resulting in high energy consumption during the operation of the joint drive system and reducing the overall energy utilization rate of the equipment.

[0005] Intelligent optimization methods such as particle swarm are widely used in the field of trajectory optimization due to their strong global search ability. However, in complex path optimization tasks, traditional particle swarm methods are prone to falling into local optimal solutions, resulting in a slow convergence speed of the optimization process. In addition, due to the rapid decline of individual diversity, the particle swarm may have problems with unstable optimization quality during the search process, affecting the actual application effect.

[0006] Current trajectory optimization methods are difficult to simultaneously ensure the smoothness of the trajectory, the continuity of speed, and a low acceleration impact. For example, quintic polynomial interpolation can ensure the continuity of speed and acceleration, but its computational complexity is high, resulting in a large consumption of computational resources. Cubic polynomial interpolation, although computationally simple, cannot guarantee the smooth change of acceleration and may introduce large speed fluctuations during the trajectory transition process.

[0007] Existing palletizing robot trajectory optimization methods mostly optimize for specific tasks and lack universality, making it difficult to meet the trajectory planning requirements in different working environments. Traditional optimization methods often have limited optimization capabilities when facing complex environments (such as multiple obstacles, non-fixed palletizing tasks), affecting the applicable range of palletizing robots. Summary of the Invention

[0008] The object of the present invention is to solve the problems mentioned in the background art, and to provide a palletizer trajectory optimization method based on particle swarm optimization and Kepler optimization algorithm, so as to reduce the energy consumption of the palletizer and optimize the execution time.

[0009] To achieve the above object, the technical solution of the present invention is: A palletizer trajectory optimization method based on particle swarm optimization and Kepler optimization algorithm, comprising:

[0010] S1. Adopt an S-shaped trajectory for stacking goods in the cargo box;

[0011] S2. Adopt a U-shaped motion curve to ensure that the end of the robotic arm will not collide with the goods during operation;

[0012] S3. Use an improved particle swarm algorithm to iteratively search for the optimal parameters of time and energy consumption and save them; during the trajectory optimization process, consider the speed, acceleration, maximum speed, and maximum acceleration of the palletizer joints;

[0013] S4. Initialize parameters;

[0014] S5. Establish a trajectory interpolation function based on the path point coordinates;

[0015] S6. Comprehensively consider the time-optimal and energy-optimal and the motion constraints of the robotic arm to determine the inertia weight;

[0016] S7. Use an improved particle swarm algorithm to optimize time and energy consumption;

[0017] S8. Calculate the fitness value f(x[i]) of each particle, set the personal best position pBest[i]=x[i], and select the global best position gBest=min(f(pBest[i]));

[0018] S9. Update the speed of each particle according to the particle swarm algorithm speed update formula, and update the position of each particle according to the particle swarm algorithm position update formula;

[0019] S10. Calculate the distance between the planet and the sun, and adjust the orbital eccentricity and period according to the distance;

[0020] S11. According to the orbital parameters and the distance from the sun, the Kepler optimization algorithm adjusts the exploration (i.e., away from the sun) and exploitation (i.e., approaching the sun) intensity;

[0021] S12. Judge that the change amount of the fitness corresponding to the two optimization results before and after updating f(gBest) is less than the change threshold V, increment the update number ItemIter by 1, return to step S6 to continue iterative update until the maximum iteration number MaxIter is reached, and obtain the optimal optimization result x of the particle swarm algorithm and the Kepler optimization algorithm best 。

[0022] Furthermore, in step S4, the initialization parameters include the size parameters of the container and the goods and the parameters of the particle swarm. The size parameters of the container and the goods include the length, width, and height of the container and the goods, and the parameters of the particle swarm include the initial velocity and position of the particle swarm.

[0023] Furthermore, the robotic arm is a five-axis robotic arm, and its forward kinematic equation is:

[0024]

[0025] Among them, represents the transformation matrix from the i coordinate system to the i+1 coordinate system, n x / y / z , o x / y / z , a x / y / z respectively represent the unit vectors of the rotation transformation matrices n, o, and a on the x / y / z axes, and p x / y / z represents the translation vector on the x / y / z axes.

[0026] Furthermore, in step S5, the trajectory interpolation function is as follows:

[0027] θ k1 (t) = q k13 t 3 + q k12 t 2 + q k11 t + q k10

[0028] θ k2 (t) = q k25 t 5 + q k24 t 4 + q k23 t 3 + q k22 t 2 + q k21 t + q k20

[0029] θ k3 (t) = q k33 t 3 + q k32 t 2 + q k31 t + q k30

[0030] Among them, θ k1 , θ k2 , θ k3 respectively represent the first, second, and third trajectories of the 3-5-3 spline polynomial, q kijDenote the angle of interpolation of joint i, where i represents the joint number, i = 1, 2, 3, 4, 5, j represents the serial number of the interpolation point, j = 1, 2, 3, 4, t represents time, and k is used for character differentiation with no actual meaning.

[0031] Further, step S6 is specifically implemented as follows:

[0032] The objective function of time is:

[0033] S1 = t1 + t2 + t3

[0034] where t1, t2, and t3 respectively represent the time of the first, second, and third segments of the interpolation curve.

[0035] The optimal function of energy consumption is:

[0036]

[0037] where N is the total number of sampling points in the polynomial curve process, n is a sampling point, T is a period of the polynomial curve, and a t represents the acceleration during the operation of the robotic arm.

[0038] The motion limit of the robotic arm is:

[0039]

[0040] where ν k , a k are respectively the velocity and acceleration of joint k, ν max represents the maximum velocity of the joint, and a max represents the maximum acceleration of the joint;

[0041] The optimization objective function is:

[0042] f = ω1S 1norm + ω2S 2norm

[0043] where S 1norm , S 2norm are respectively the normalized total time cost and the normalized total energy consumption cost; the inertia weights of time and energy consumption are ω1 and ω2 respectively, and ω1 = ω2 = 0.5.

[0044] Further, step S7 is specifically implemented as follows:

[0045] The velocity update formula of the particle swarm algorithm:

[0046]

[0047] The position update formula of the particle swarm algorithm:

[0048]

[0049] Among them, is the velocity of the i-th particle at the n-th iteration in d dimensions, ω is the inertia weight factor, c1 is the individual experience weight factor, c2 is the swarm experience weight factor, r1 and r2 are random numbers in the interval [0,1], pbest id is the individual optimal value recorded when the i-th particle iterates to the n-th time, gbest id is the individual optimal value recorded when all particles iterate to the n-th time, is the position of the i-th particle at the n-th iteration in d dimensions.

[0050] Furthermore, step S10 is specifically implemented as follows:

[0051] Calculate the gravitational effect of the planet, and the formula is:

[0052]

[0053] Among them, G represents the gravitational parameter, usually set as G = 6.674*10 -11 , and dist[i] is the Euclidean distance between this position and the sun.

[0054] Update the particle position, and the formula is:

[0055]

[0056] Among them, F[i] is the planet gravitational correction vector, and the Kepler correction term is an adjustment term that combines factors including orbital eccentricity and period.

[0057] Furthermore, in step S11, according to the orbital parameters and the distance from the sun, the Kepler optimization algorithm adjusts the exploration (i.e., moving away from the sun) and exploitation (i.e., moving closer to the sun) intensities, and the specific formula is:

[0058]

[0059] Among them is the optimal position discovered by the sun at time t + 1, is the optimal position at time t, represents the best position of the sun discovered so far, and represents a solution randomly selected from the overall population at time t, h is the adaptive operator, represents the numerical value 0 or 1. If the randomly generated numerical value is greater than the given numerical value, it is 0, otherwise it is 1.

[0060] The present invention also provides a palletizer trajectory optimization system based on the particle swarm optimization and Kepler optimization algorithms, including a memory, a processor, and computer program instructions stored on the memory and executable by the processor. When the processor runs the computer program instructions, the method steps described in any of the above can be implemented.

[0061] The present invention also provides a computer-readable storage medium, on which computer program instructions executable by a processor are stored. When the processor runs the computer program instructions, the method steps described in any of the above can be implemented.

[0062] Compared with the prior art, the present invention has the following beneficial effects: The method of the present invention has significant advantages: By optimizing the trajectory, the power consumption of the joint driver is effectively reduced, and the energy consumption is reduced; By combining the particle swarm algorithm and the Kepler optimization algorithm, the execution time of the palletizer trajectory is significantly shortened, and the operation efficiency is greatly improved; The optimized trajectory ensures the continuous movement of each joint of the palletizer, avoids drastic speed and acceleration changes, and enhances the trajectory smoothness; At the same time, local optimization is carried out by combining the Kepler optimization algorithm, which speeds up the convergence rate of the optimization process and improves the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is the robot used in the present invention;

[0064] Figure 2 is a schematic cross-sectional view of the stacking of 45-inch cargo boxes;

[0065] Figure 3 is a flow chart of the trajectory optimization of the particle swarm algorithm combined with the Kepler optimization algorithm;

[0066] Figure 4 is a comparison chart of the time optimization of the particle swarm algorithm combined with the Kepler optimization algorithm and other algorithms;

[0067] Figure 5 is the speed and acceleration diagram of the optimized robotic arm. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0068] To make the above objects, features, and advantages of the present invention more clearly understood, taking the time and energy consumption optimization of a five-axis palletizing robotic arm as an example, which is mainly applied to the palletizing of carton-like goods in containers. The present invention will be further described in detail in conjunction with the accompanying drawings and specific embodiments.

[0069] Figure 1 is the robot of the five-axis robotic arm used in the present invention; Figure 2 is a schematic cross-sectional view of the stacking of 45-inch cargo boxes, as Figure 3 shown, a palletizer trajectory optimization method based on the particle swarm optimization and Kepler optimization algorithms for a five-axis robotic arm of the present invention includes the following steps:

[0070] S1. Adopt an S-shaped trajectory for stacking goods in the cargo box;

[0071] S2. Adopt a U-shaped motion curve to ensure that the end of the robotic arm will not collide with the goods during operation;

[0072] S3. Use an improved particle swarm algorithm to iteratively search for and save the optimal parameters of time and energy consumption; during the trajectory optimization process, consider the speed, acceleration, maximum speed, and maximum acceleration of the joints of the palletizing robot;

[0073] S4. Initialize the parameters, including:

[0074] Initialize the size parameters of the container and the goods, and the parameters include the length, width, and height of the container and the goods;

[0075] Initialize the parameters of the particle swarm, and the parameters include the initial velocity and position of the particle swarm;

[0076] For a five-axis robotic arm, the forward kinematic equation is:

[0077]

[0078] Among them, represents the transformation matrix from the i coordinate system to the i+1 coordinate system, n x / y / z , o x / y / z , a x / y / z respectively represent the unit vectors of the rotation transformation matrices n, o, a on the x / y / z axes, and p x / y / z represents the translation vector on the x / y / z axes.

[0079] Obtain Figure 2 The three-dimensional coordinates of the path points 25-26 in

[0080] Table 1

[0081] Path coordinate points θ1 (°) θ2 (°) d3 (m) θ4 (°) θ5 (°) <![CDATA[P1]]> 11.7285 -84.6496 4.7186 84.6496 -11.7285 <![CDATA[P2]]> 11.7533 -84.6384 4.7089 84.6384 -11.7533 <![CDATA[P3]]> 14.0656 -85.6493 4.7455 85.6493 -14.0656 <![CDATA[P4]]> 14.0362 -85.6582 4.7552 85.6582 -14.0362

[0082] Among them, θ1, θ2, d3, θ4, θ5 respectively represent the joint angles or displacements of axes 1, 2, 3, 4, and 5.

[0083] S5. Establish a trajectory interpolation function based on the path point coordinates, and the formula is as follows:

[0084] θ k1 (t) = q k13 t 3 + q k12 t 2 + q k11 t + q k10

[0085] θk2 \(\theta(t)=q\) k25 \(t\) 5 \( + q\) k24 \(t\) 4 \( + q\) k23 \(t\) 3 \( + q\) k22 \(t\) 2 \( + q\) k21 \(t + q\) k20

[0086] \(\theta\) k3 \(\theta(t)=q\) k33 \(t\) 3 \( + q\) k32 \(t\) 2 \( + q\) k31 \(t + q\) k30

[0087] Among them, \(\theta\) k1 , \(\theta\) k2 , \(\theta\) k3 respectively represent the first, second, and third trajectories of the 3-5-3 spline polynomial, \(q\) kij represents the angle of interpolation of joint \(i\), where \(i\) represents the joint number, \(i = 1, 2, 3, 4, 5\), \(j\) represents the serial number of the interpolation point, \(j = 1, 2, 3, 4\), \(t\) represents time, and \(k\) is used for character distinction and has no practical meaning.

[0088] S6. Considering the time-optimal, energy-optimal, and motion limitations of the robotic arm comprehensively, determine the inertia weight, and the specific implementation is as follows:

[0089] The objective function of time is:

[0090] \(S1=t1 + t2 + t3\)

[0091] Among them, \(t1\), \(t2\), and \(t3\) respectively represent the time of the first, second, and third segments of the interpolation curve.

[0092] The optimal function of energy consumption is:

[0093]

[0094] Among them, \(N\) is the total number of sampling points in the polynomial curve process, \(n\) is a sampling point, \(T\) is a period of the polynomial curve, and \(a\) t represents the acceleration during the operation of the robotic arm.

[0095] The motion limitations of the robotic arm are:

[0096]

[0097] Among them, \(\nu\) k , \(a\) k are respectively the velocity and acceleration of joint \(k\), \(\nu\)max Denotes the maximum joint speed, a max Denotes the maximum joint acceleration;

[0098] The optimization objective function is:

[0099] f = ω1S 1norm +ω2S 2norm

[0100] where S 1norm , S 2norm are the normalized total time cost and the normalized total energy consumption cost respectively; the inertia weights of time and energy consumption are ω1 and ω2 respectively, and ω1 = ω2 = 0.5.

[0101] S7. Adopt an improved particle swarm optimization algorithm to optimize time and energy consumption. The specific implementation is as follows:

[0102] Particle swarm optimization algorithm velocity update formula:

[0103]

[0104] Particle swarm optimization algorithm position update formula:

[0105]

[0106] where is the velocity of the i-th particle at the n-th iteration in the d-th dimension, ω is the inertia weight factor, c1 is the individual experience weight factor, c2 is the swarm experience weight factor, r1 and r2 are random numbers in the interval [0, 1], pbest id is the individual best value recorded by the i-th particle when iterating to the n-th time, gbest id is the individual best value recorded by all particles when iterating to the n-th time, is the position of the i-th particle at the n-th iteration in the d-th dimension.

[0107] S8. Calculate the fitness value f(x[i]) of each particle, set the personal best position pBest[i] = x[i], and select the global best position gBest = min(f(pBest[i]));

[0108] S9. Update the velocity of each particle according to the particle swarm optimization algorithm velocity update formula, and update the position of each particle according to the particle swarm optimization algorithm position update formula;

[0109] S10. Calculate the distance between the planet and the sun, and adjust the orbital eccentricity and period according to the distance. The specific implementation is as follows:

[0110] Calculate the gravitational effect of the planet. The formula is:

[0111]

[0112] Among them, G represents the gravitational parameter, usually set as G = 6.674 * 10 -11 , and dist[i] is the Euclidean distance between this position and the sun.

[0113] Update the particle position, and the formula is:

[0114]

[0115] Among them, F[i] is the planetary gravitational correction vector, and the Kepler correction term is an adjustment term that combines factors including orbital eccentricity and period.

[0116] Step S11: According to the orbital parameters and the distance from the sun, the Kepler optimization algorithm adjusts the exploration (i.e., moving away from the sun) and exploitation (i.e., moving closer to the sun) intensities. The specific formula is:

[0117]

[0118] Among them is the optimal position discovered by the sun at time t + 1, is the optimal position at time t, represents the best position of the sun discovered so far, and represent a solution randomly selected from the overall population at time t. h is the adaptive operator, represents the numerical value 0 or 1. If the randomly generated numerical value is greater than the given numerical value, it is 0, otherwise it is 1.

[0119] S12: Judge whether the change amount of the fitness corresponding to the two optimization results before and after updating f(gBest) is less than the change threshold V. Increment the update number ItemIter by 1, and return to step S6 to continue the iteration until the maximum iteration number MaxIter is reached, and obtain the optimal optimization result x of the particle swarm algorithm and the Kepler optimization algorithm best .

[0120] Through the above optimization process, we can obtain Figure 4 the comparison graph of the particle swarm algorithm combined with the Kepler optimization algorithm and other algorithms in terms of time optimization and Figure 5 the velocity and acceleration graphs of the optimized robotic arm. The trajectory optimization method of the present invention can effectively improve the working efficiency of the palletizing robot, reduce energy consumption, and ensure the smoothness of trajectory execution.

[0121] The present invention also provides a trajectory optimization system for a palletizer based on a particle swarm optimization and a Kepler optimization algorithm, including a memory, a processor, and computer program instructions stored on the memory and capable of being run by the processor. When the processor runs the computer program instructions, the method steps described in any of the above can be implemented.

[0122] The present invention also provides a computer-readable storage medium, on which computer program instructions capable of being run by a processor are stored. When the processor runs the computer program instructions, the method steps described in any of the above can be implemented.

[0123] The above are the preferred embodiments of the present invention. All changes made according to the technical solutions of the present invention, when the functions and effects produced do not exceed the scope of the technical solutions of the present invention, fall within the protection scope of the present invention.

Claims

1. A palletizer trajectory optimization method based on particle swarm optimization and Kepler optimization algorithm, characterized in that, Including: S1. Adopt an S-shaped trajectory for stacking goods in the cargo box; S2. Adopt a U-shaped motion curve to ensure that the end of the robotic arm will not collide with the goods during operation; S3. Adopt an improved particle swarm optimization algorithm to iteratively search for the optimal parameters of time and energy consumption and save them; during the trajectory optimization process, consider the speed, acceleration, maximum speed, and maximum acceleration of the joints of the palletizing robot; S4. Initialize parameters; S5. Establish a trajectory interpolation function based on the path point coordinates; S6. Comprehensively consider the time optimality, energy consumption optimality, and motion limitations of the robotic arm to determine the inertia weight; S7. Adopt an improved particle swarm optimization algorithm to optimize time and energy consumption; S8. Calculate the fitness value f(x[i]) of each particle, set the personal best position pBest[i]=x[i], and select the global best position gBest = min(f(pBest[i])); S9. Update the velocity of each particle according to the velocity update formula of the particle swarm optimization algorithm, and update the position of each particle according to the position update formula of the particle swarm optimization algorithm; S10. Calculate the distance between the planet and the sun, and adjust the orbital eccentricity and period according to the distance; S11. According to the orbital parameters and the distance from the sun, the Kepler optimization algorithm adjusts the exploration (i.e., moving away from the sun) and exploitation (i.e., moving closer to the sun) intensities; S12. Determine whether the change in fitness corresponding to the two optimization results before and after updating f(gBest) is less than the change threshold V. Increment the update count ItemIter by 1, and return to step S6 to continue iterating until the maximum number of iterations MaxIter is reached, obtaining the optimal optimization result x of the particle swarm algorithm and the Kepler optimization algorithm best .

2. A palletizer trajectory optimization method based on particle swarm optimization and Kepler optimization algorithm according to claim 1, characterized in that In step S4, initialize the parameters, including initializing the size parameters of the container and the goods and the parameters of the particle swarm. The size parameters of the container and the goods include the length, width, and height of the container and the goods, and the parameters of the particle swarm include the initial velocity and position of the particle swarm.

3. A palletizer trajectory optimization method based on particle swarm optimization and Kepler optimization algorithm according to claim 1, characterized in that, The robotic arm adopts a five-axis robotic arm, and its forward kinematic equation is: Among them, represents the transformation matrix from the i coordinate system to the i+1 coordinate system, n x / y / z , o x / y / z , a x / y / z respectively represent the unit vectors of the rotation transformation matrices n, o, a on the x / y / z axes, and p x / y / z represents the translation vector on the x / y / z axes.

4. A palletizer trajectory optimization method based on particle swarm optimization and Kepler optimization algorithm according to claim 1, characterized in that, In step S5, the trajectory interpolation function is as follows: θ k1 (t) = q k13 t 3 + q k12 t 2 + q k11 t + q k10 θ k2 (t) = q k25 t 5 + q k24 t 4 + q k23 t 3 + q k22 t 2 + q k21 t + q k20 θ k3 (t) = q k33 t 3 + q k32 t 2 + q k31 t + q k30 Among them, θ k1 , θ k2 , θ k3 represent the first, second, and third trajectories of the 3-5-3 spline polynomial respectively, q kij represents the angle of interpolation of joint i, where i represents the joint number, i = 1, 2, 3, 4, 5, j represents the serial number of the interpolation point, j = 1, 2, 3, 4, t represents time, and k is used for character distinction.

5. A palletizer trajectory optimization method based on particle swarm optimization and Kepler optimization algorithm according to claim 1, characterized in that, Step S6 is specifically implemented as follows: The objective function of time is: S1 = t1 + t2 + t3 where t1, t2, and t3 respectively represent the time of the first, second, and third segments of the interpolation curve; The optimal function of energy consumption is: Among them, N is the total number of sampling points in the polynomial curve process, n is the nth sampling point in N, T is a period of the polynomial curve, a t represents the acceleration during the operation of the robotic arm, and t represents time; The motion limitations of the robotic arm are: where, ν k and a k are the velocity and acceleration of joint k respectively, ν max represents the maximum velocity of the joint, and a max represents the maximum acceleration of the joint; The optimization objective function is: f = ω1S 1norm + ω2S 2norm Among them, S 1norm , S 2norm are the normalized total time cost and the normalized total energy consumption cost respectively; the inertia weights of time and energy consumption are ω1 and ω2 respectively, and ω1 = ω2 = 0.

5.

6. A palletizer trajectory optimization method based on particle swarm optimization and Kepler optimization algorithm according to claim 1, characterized in that, Step S7 is specifically implemented as follows: Particle swarm optimization algorithm velocity update formula: Particle swarm optimization algorithm position update formula: Among them, is the velocity of the i-th particle at the n-th iteration in d dimensions, ω is the inertia weight factor, c1 is the individual experience weight factor, c2 is the swarm experience weight factor, r1 and r2 are random numbers in the interval [0, 1], pbest id is the individual best value recorded when the i-th particle iterates to the n-th time, gbest id is the individual best value recorded when all particles iterate to the n-th time, is the position of the i-th particle at the n-th iteration in d dimensions.

7. A palletizer trajectory optimization method based on particle swarm optimization and Kepler optimization algorithm according to claim 6, characterized in that Step S10 is specifically implemented as follows: Calculate the gravitational force of the planet, and the formula is: where G is the gravitational parameter and dist[i] is the Euclidean distance between the corresponding position and the sun; Update the particle position, and the formula is: where F[i] is the planetary gravity correction vector, and the Kepler correction term is an adjustment term that combines factors including orbital eccentricity and period.

8. A palletizer trajectory optimization method based on particle swarm optimization and Kepler optimization algorithm according to claim 1, characterized in that In step S11, according to the orbital parameters and the distance from the sun, the Kepler optimization algorithm adjusts the exploration (i.e., moving away from the sun) and exploitation (i.e., moving closer to the sun) intensities, and the specific formula is: Among them, is the optimal position of the sun found at time t+1, is the optimal position at time t, represents the best position of the sun found so far, and represents a solution randomly selected from the population at time t, h is an adaptive operator, is represented as the numerical value 0 or 1. If the randomly generated numerical value is greater than the given numerical value, it is 0, otherwise it is 1.

9. A palletizer trajectory optimization system based on particle swarm optimization and Kepler optimization algorithm, characterized in that, Including a memory, a processor, and computer program instructions stored on the memory and capable of being run by the processor. When the processor runs the computer program instructions, it can implement the method steps described in any one of claims 1-8.

10. A computer-readable storage medium, on which computer program instructions capable of being run by the processor are stored. When the processor runs the computer program instructions, it can implement the method steps described in any one of claims 1-8.

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