Ship narrow space robot welding track optimization method under multi-target constraint

Abstract

The invention belongs to the technical field of welding robots, and particularly relates to a ship narrow space robot welding trajectory optimization method under multi-target constraint, the optimization method considers multiple constraints in a narrow space and combines a genetic algorithm and a particle swarm optimization algorithm to optimize the trajectory, and the optimization algorithm not only has strong global search ability, but also has high reliability. And the method also has high local search efficiency. The inertia weight and the learning factor of the particle swarm algorithm and the mutation probability of the genetic algorithm are adjusted by introducing a self-adaptive mechanism, so that the search precision and the convergence speed of the algorithm are remarkably improved. The method provides favorable support for a narrow space welding task, and is suitable for being applied to welding in a complex environment under multi-target constraint.

Description

Technical Field

[0001] The invention belongs to the technical field of welding robots, and in particular to a method for optimizing welding trajectories of robots in a narrow space of a ship under multi-objective constraints. Background Art

[0002] Welding operations in the confined spaces of ships face significant challenges. The environment is complex and ever-changing, manual welding is laborious and inefficient, and quality consistency is poor. To drive the automation and intelligent development of my country's shipbuilding industry, the use of robots for welding tasks has become an inevitable trend. Portable robots, due to their flexibility and portability, can complete welding operations in complex environments, significantly improving welding efficiency and quality. However, optimizing the welding trajectory under multi-objective constraints to ensure the robot can complete the task accurately and efficiently is particularly important. Therefore, optimizing the welding trajectory through intelligent algorithms can ensure that robots can complete welding operations efficiently and quickly in confined spaces, while reducing operating costs and enhancing operational flexibility and intelligence.

[0003] Chinese patent application number 202211656986.9, titled "Robotic Welding Trajectory Planning Method and Welding Robot," only studies complex curved trajectory planning without optimizing the trajectory, resulting in a suboptimal welding trajectory. Optimizing the welding trajectory to obtain the optimal welding path when a robot performs welding tasks in complex environments has important theoretical significance and broad application value. This method is applicable not only to welding in confined spaces but also in other welding scenarios, demonstrating its versatility. Summary of the Invention

[0004] This invention aims to address the problems of high labor intensity, low efficiency and difficulty in ensuring stable welding quality in traditional manual welding methods during welding in a small space. It proposes a robot welding trajectory optimization under multi-objective constraints. The robot replaces manual labor to perform efficient and precise welding operations in a limited space, further optimizes the welding trajectory, and significantly improves welding efficiency.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] The present invention provides a method for optimizing welding trajectories of a robot in a narrow space of a ship under multi-objective constraints, the method comprising the following steps:

[0007] Step 1: Define the fitness function;

[0008] Determine the robot position, welding time, and welding reachability as sub-objective functions, and take the shortest welding time, the maximum welding reachability, and the optimal robot position as the goals. Considering the different importance of the three sub-objective functions under different working conditions, introduce the target weight and convert the three sub-objective functions into one objective function, Fitness.

[0009] Step 2: Calculate the fitness value of each particle and update the position and velocity of the particle according to the fitness value;

[0010] According to the objective function Fitness, the fitness value of each particle is calculated, and the individual optimal position and global optimal position of the particle are updated according to the fitness value;

[0011] Step 3: Perform crossover and mutation operations to generate new offspring particles and update the population;

[0012] Randomly select a pair of parent particles, perform a crossover operation according to the crossover probability Pc, and generate child particles. The parent particles are replaced by the child particles.

[0013] Perform mutation operations on individuals according to the mutation probability Pm, update the population, and replace the original particle individuals with the mutated particle individuals;

[0014] Step 4: Algorithm termination;

[0015] When the maximum number of iterations is reached or the fitness value meets the preset threshold, the iteration is stopped; under the termination condition, the welding path with the highest fitness value is output as the optimal solution.

[0016] As a further preferred solution, the fitness function is defined as:

[0017] Fitness=α*W time +β*R position +δ*(1-W accessibility )

[0018] Where: R position : Robot position, W time :Welding time, W accessibility : welding accessibility;

[0019] α, β, and δ are weight coefficients used to balance the importance of the three objectives.

[0020] As a further optimization scheme, in order to ensure that the three sub-objective functions have a similar influence on the objective function Fitness, the three sub-objective functions are normalized to unify the order of magnitude of the variables so that the variables have a similar influence on the objective function Fitness. The constraints of α, β, and δ are:

[0021]

[0022] As a further preferred solution, in step 2, after calculating the fitness value, compare the current fitness value with the previously recorded individual optimal position P ij If the current fitness is better, update it to the current position and update the corresponding fitness value;

[0023] Among the individual optimal positions of all particles, find the position with the best fitness as the global optimal position p gj ;

[0024] According to the updated individual optimal position P ij and the global optimal position P gj Update the particle's velocity and position.

[0025] As a further preferred solution, in step 2, each particle represents a welding path, and the particle speed update formula is:

[0026] v ij (t+1)=ω·v ij (t)+c1r1(t)[p ij (t)-x ij (t)]+c2r2(t)[p gj (t)-x ij (t)]

[0027] Where, v ij (t) represents the velocity of particle i at the current time t; ω is the inertia weight; c1 and c2 are learning factors; r1 and r2 are random numbers between 0 and 1; p ij (t) represents the individual optimal position of particle i; x ij (t) represents the current position of particle i; p gj (t) is the global optimal position.

[0028] As a further preferred solution, an adaptive mechanism is added to the inertia weight in the particle velocity update formula to ensure that the algorithm has global search capabilities in the early stage and local convergence capabilities in the later stage;

[0029] The inertia weight ω should be large in the early stage of evolution to ensure that each particle can fully search the space. It should be small in the later stage to learn from other particles and move closer to the overall optimum. The inertia weight ω should be dynamically adjusted according to the current iteration situation.

[0030] An adaptive mechanism is introduced, which includes two parts: linear decrease and exponential decrease, and the final weight coefficient is calculated by these two parts;

[0031] Linear decrease:

[0032]

[0033] In the formula: iterations: the current number of iterations, iterations max : Maximum number of iterations, that is, the total number of iterations the algorithm will run, ω max : Initial maximum inertia weight, ω min : minimum inertia weight in the later stage;

[0034] Exponential Decrease:

[0035]

[0036] Add the linear decrease and exponential decrease parts to get the preliminary weight value:

[0037] ω=ω1+ω2

[0038] Where ω=max(ω max ,min(ω max ,ω)); Use max and min functions to ensure that the final weight value is within ω min and ω max between.

[0039] As a further optimization solution, an adaptive mechanism is added to the learning factor in the particle velocity update formula to ensure that the algorithm searches globally in the early stage and converges locally faster in the later stage.

[0040] The learning factor c1 is larger in the early stage and c2 is larger in the later stage, which can balance the global search ability and local search ability of the particle; the parameters c1 and c2 are dynamically adjusted according to the current iteration situation;

[0041] Introducing an adaptive mechanism, divided into exploration phase, development phase and convergence phase;

[0042] Learning factor exploration phase:

[0043]

[0044] Where: c 1max is the maximum value of c1; c 2min is the minimum value of c2;

[0045] Learning factor development stage:

[0046]

[0047] Where: c 1min is the minimum value of c1; c 2max is the maximum value of c2;

[0048] Learning factor convergence stage:

[0049]

[0050] As a further preferred solution, in step 2, each particle represents a welding path, and the particle position update formula is:

[0051] x ij (t+1)=x ij (t)+v ij (t+1)

[0052] Where, v ij (t+1) represents the velocity of particle i at the next moment calculated according to the velocity formula.

[0053] As a further preferred solution, in step three:

[0054] In the crossover operation, after the parent particle is replaced by the child particle, the position and velocity update formulas of the child particle are as follows:

[0055]

[0056]

[0057] Where p is a random number between [0,1]; are the position vector and velocity vector of the Dimensions dimension respectively; parent(x) and parent(v) are the position vector and velocity vector of the parent individual; child(x) and child(v) are the position vector and velocity vector of the child particle respectively; subscripts 1 and 2 represent different particles.

[0058] As a further preferred solution, in step 3: in the mutation operation, the mutated particle individual replaces the original particle individual, and the current iterative formula of the mutation probability is:

[0059]

[0060] Where, P m (t) is the mutation probability of the current iteration, is the initial mutation probability, k is the exponent that controls the nonlinear attenuation rate, f(t) is the optimal fitness of the current population, f min is the initial optimal fitness, and σ is the parameter that controls the decay rate.

[0061] Beneficial Effects: The combination of a genetic algorithm and a particle swarm algorithm in trajectory optimization provides not only powerful global search capabilities but also efficient local search efficiency. The introduction of an adaptive mechanism to adjust the particle swarm algorithm's inertia weight and learning factor significantly improves the algorithm's convergence speed and search accuracy. Simultaneously, the genetic algorithm updates and adaptively adjusts the crossover and mutation operations. Initially, the mutation probability is increased to ensure that particles fill the entire space as much as possible, while later, the probability is increased to ensure that particles converge more quickly. This achieves an organic combination of extensive early-stage search and rapid late-stage convergence. This algorithm can more efficiently optimize welding trajectories, improving the quality and efficiency of welding operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is the overall model of the portable robot;

[0063] Figure 2 This is a schematic diagram of the robot welding scene;

[0064] Figure 3 This is a schematic diagram of the scene weld;

[0065] Figure 4 Schematic diagram of the steps to improve the genetic particle algorithm;

[0066] Figure 5 Schematic diagram of the change of weight coefficient with the number of iterations;

[0067] Figure 6 Schematic diagram of the change of learning factor with the number of iterations;

[0068] Figure 7 Schematic diagram of the change of mutation probability with the number of iterations;

[0069] Figure 8 The following is a comparison chart of the performance tests of four algorithms. DETAILED DESCRIPTION

[0070] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0071] (1) Select the welding scene in a narrow space of a ship.

[0072] Typical examples of confined spaces on ships include, but are not limited to, the double bottom of a container ship, the hopper and topside tanks of a bulk carrier, the engine room of an oil tanker, and the longitudinal bulkhead tanks of an oil tanker. These environments are often narrow and complex, requiring robots to perform welding operations efficiently and accurately.

[0073] (2) Determine the portable robot model.

[0074] Since the welding scene is a small space on a ship, the welding robot model is configured as a portable robot. Figure 1 This is a portable robot model. Workers can carry the robot to perform welding tasks in the narrow space of the ship.

[0075] (3) In a complex and narrow space, multiple constraints need to be considered: such as welding process (W process ), robot position (R position )、Welding time(W time ), welding accessibility (W accessibility ), number of welding heads (N StartingWeldHeads ), welding efficiency (W efficiency )wait.

[0076] Among them, W process Refers to the process requirements that need to be followed during welding; R position Refers to the position of the robot in the welding scene; W time Refers to the time required to complete the welding task; W accessibility Refers to the robot's accessibility in a small space; W efficiency Refers to the overall efficiency of the welding task; N StartingWeldHeads Refers to the number of times the robot starts welding. Due to the requirements of the welding process, the weld cannot be completed in one go. The fewer the number of welding heads, the less auxiliary time, and the higher the robot welding efficiency.

[0077] like Figure 2 For the robot welding scene on the double bottom of a container ship, the robot is placed in each grid (grid-17, grid-18, grid-19) to perform welding tasks. According to the welding process requirements, the welds that the robot needs to weld in grid-18 are detailed in Figure 3 , involving the welds between T-section-5 and rib-6, the welds between bottom plate-8 and rib-6, the welds between T-section-5 and filler plate-7, and the welds between rib-6 and filler plate-7. The welding sequence should be followed, first vertical welding, then horizontal welding. The vertical welding process uses a bottom-up welding method, while the horizontal welding process uses a method of welding from the middle to the ends, thus forming a wrap angle on both sides and the top, so Figure 3 The middle weld 2 is divided into two sections for welding.

[0078] According to the welding process requirements, the specific welding sequence of Grid-18 is point 9 → point 10 → point 11 → point 12 → point 10 → point 9 → point 13 → point 14 → point 15 → point 16 → point 12 → point 13 → point 9.

[0079] The robot position is the position of the robot in the welding scene, such as Figure 2This is a scenario where a robot welds the double bottom of a container ship. The welding process dictates that welding only occurs along the y- and z-axes of the scene, not along the x-axis. Considering obstacles and accessibility within a confined space, the robot's position within the scene is crucial. Displacement toward x+, x-, y+, or y- will not only affect welding accessibility but also cause collisions. Therefore, selecting the appropriate welding position maximizes welding accessibility without causing collisions. Therefore, the robot's position is set between 550 and 650 mm from rib-6 and between 350 and 550 mm from both sides of the T-section-5.

[0080] Among the many constraints, the target constraint is: the robot position (R position )、Welding time(W time ), welding accessibility (W accessibility ). Others are normal constraints.

[0081] (4) Overview of welding path optimization algorithm: Combining genetic algorithm and particle swarm algorithm, and introducing adaptive mechanism, it can find the spatial distribution of the optimal solution in the global scope and quickly converge to the optimal solution. Figure 4 This is the step of improving the genetic particle algorithm. The specific steps are as follows:

[0082] a. Define the fitness function.

[0083] With the shortest welding time, the maximum welding accessibility and the optimal robot position as the goals, considering the different importance of the three sub-goals under different working conditions, the target weight is introduced to convert the sub-objective functions F1, F2, and F3 into an objective function Fitness. Its advantage is that the welder can flexibly adjust the optimization coefficient, and then effectively adjust the welding optimization goal to meet the needs of different scenarios (for example: shortest welding time, maximum welding accessibility, etc.). In order to ensure that the sub-objective functions F1, F2, and F3 have the same weight of influence on the objective function Fitness, the sub-objective functions are normalized, the order of magnitude of the variables is unified, and the degree of influence of the variables on the objective function Fitness is the same. Define the fitness function:

[0084] Fitness=α*W time +β*R position +δ*(1-W accessibility )

[0085] Where: α, β and δ are weight coefficients used to balance the importance of the three objectives.

[0086]

[0087] That is: according to the objective function Fitness, calculate the fitness value of each particle, and update the individual optimal position Pij and the global optimal position Pgj;

[0088] Compare its current fitness value with the fitness value of the previously recorded individual optimal position Pij. If the current fitness is better, update it to the current position and update the corresponding fitness value. Among the individual optimal positions of all particles, find the position with the best fitness and use it as the global optimal position pgj.

[0089] Update the particle speed and position according to the updated individual optimal position Pij and the global optimal position Pgj.

[0090] b. Initialize the parameters of particle swarm and genetic algorithm.

[0091] Initial particle position and velocity. Num is the number of particles, and Dimensions is the dimension of each particle. Set the parameters in the fitness function, including weight coefficients (α, β, δ), number of particles (Num), dimensions (Dimensions), inertia weight (ω), learning factors (c1, c2), random numbers (r1, r2), crossover probability (Pc), nonlinear decay exponent (k), fitness influence parameter (σ), etc.

[0092] c. Calculate the fitness value of each particle and update the position and velocity of the particle according to the fitness value.

[0093] An adaptive mechanism is added to the inertia weight and learning factor to ensure that the algorithm has global search capabilities in the early stage and local convergence capabilities in the later stage.

[0094] Each particle represents a welding path, and the particle speed and position update formula is:

[0095] v ij (t+1)=ω·v ij (t)+c1r1(t)[p ij (t)-x ij (t)]+c2r2(t)[p gj (t)-x ij (t)]

[0096] x ij (t+1)=x ij (t)+v ij (t+1)

[0097] Where, v ij (t) represents the velocity of particle i at the current time t; ω is the inertia weight; c1 and c2 are learning factors; r1 and r2 are random numbers between 0 and 1; p ij(t) represents the individual optimal position of particle i; x ij (t) represents the current position of particle i; p gj (t) is the global optimal position. ij (t+1) represents the velocity of particle i at the next moment calculated according to the velocity formula.

[0098] Adaptive mechanism: The inertia weight ω should be larger in the early stage of evolution to ensure that each particle can fully search the space. It should be smaller in the later stage to learn more from other particles and move closer to the overall optimal state. The parameter ω is dynamically adjusted according to the current iteration situation. The specific changes of ω with the number of iterations are as follows: Figure 5 As shown in the figure, the adaptive mechanism is introduced, which is divided into two parts: linear decrease and exponential decrease. The final weight coefficient is calculated from these two parts.

[0099] Linear decrease:

[0100]

[0101] Where: iterations: the current number of iterations. max : Maximum number of iterations, that is, the total number of iterations the algorithm will run. max : Initial maximum inertia weight. ω min : Minimum inertia weight in the later stage.

[0102] Exponential Decrease:

[0103]

[0104] Add the linear decrease and exponential decrease parts to get the preliminary weight value:

[0105] ω=ω1+ω2

[0106] Where ω=max(ω max ,min(ω max ,ω)). Use max and min functions to ensure that the final weight value is within ω min and ω max This is necessary because previous calculations may produce weight values ​​outside this range.

[0107] The learning factor c1 is larger in the early stage and c2 is larger in the later stage, which can balance the global search ability and local search ability of the particle. The parameters c1 and c2 are dynamically adjusted according to the current iteration situation. The specific changes with the number of iterations are as follows: Figure 6 As shown in the figure, an adaptive mechanism is introduced, which is divided into the exploration phase, the development phase and the convergence phase.

[0108] Learning factor exploration phase:

[0109]

[0110] Where: c 1max is the maximum value of c1; c 2min is the minimum value of c2.

[0111] Learning factor development stage:

[0112]

[0113] Where: c 1min is the minimum value of c1; c 2max is the maximum value of c2.

[0114] Learning factor convergence stage:

[0115]

[0116] d. Perform crossover and mutation operations to generate new offspring particles and update the population.

[0117] The mutation probability is adjusted through an adaptive mechanism to ensure that the algorithm can escape from the local optimal solution and stably converge to the global optimal solution.

[0118] A pair of parent particles is randomly selected and a crossover operation is performed based on the crossover probability Pc to generate a child particle. The parent particle is replaced by the child particle. The position and velocity update formula of the child particle is as follows:

[0119]

[0120] Where p is a random number between [0,1]; are the position and velocity vectors for the Dimensions dimension, respectively; parent(x) and parent(v) are the position and velocity vectors for the parent individual; child(x) and child(v) are the position and velocity vectors for the child particle, respectively. After the particle swarm updates its velocity and position, the child particles generated by the crossover operation on randomly selected particles must replace their parent particles to maintain a fixed swarm size.

[0121] Perform mutation operations on individuals according to the mutation probability Pm. Update the population, and the mutated particle individuals replace the original particle individuals.

[0122] By introducing an adaptive mutation probability mechanism, the algorithm increases the mutation probability in the early stages of the optimization process to enhance global search capabilities, while reducing it in the later stages to improve local search and convergence capabilities. This method, which combines nonlinear adjustment with fitness adjustment, effectively balances exploration and exploitation, thereby improving the performance of the optimization algorithm.

[0123]

[0124] Where, P m (t) is the mutation probability of the current iteration; is the initial mutation probability; k is the exponent that controls the nonlinear attenuation speed, which can be a value greater than 1 to achieve nonlinear attenuation; f(t) is the optimal fitness of the current population, f min is the initial optimal fitness, and σ is the parameter that controls the decay rate. The specific changes of its mutation probability with the number of iterations are as follows: Figure 7 shown.

[0125] Mutation operations include nonlinear adjustment and fitness adjustment. By adjusting the number of iterations nonlinearly, the mutation probability changes significantly in the early stages and gradually decreases in the later stages. Based on the current population's optimal fitness, the mutation probability is dynamically adjusted to ensure that the mutation probability is reduced when the fitness is good, thereby promoting convergence.

[0126] Mutation is a key step in this method, helping to increase population diversity and prevent the algorithm from falling into local optima. Nonlinear adjustment and fitness adjustment are two strategies for optimizing mutation. They dynamically adjust the mutation probability in different ways, thereby better balancing the algorithm's global and local search capabilities during the search process.

[0127] e. The algorithm terminates.

[0128] When the maximum number of iterations is reached or the fitness value meets the preset threshold, the iteration stops. Under the termination condition, the welding path with the highest fitness value is output as the optimal solution.

[0129] (5) Algorithm performance testing.

[0130] The algorithm performance of four functions was tested using the standard GA algorithm, the standard PSO algorithm GA-PSO algorithm and the algorithm of the present invention (IGA-PSO).

[0131] like Figure 8 As shown in (a), f1 (Rastrigin function): minf = 20 + (x12-10cos(2πx1)) + (x22-10cos(2πx2)), xi∈[-5.12,5.12], the function has a global minimum value of 0 at x1=x2=0.

[0132] like Figure 8 As shown in (b), f2 (Ackley function):

[0133] xi∈[-32.768,32.768], the function has a global minimum value of 0 at x1=0 and x2=0.

[0134] like Figure 8 As shown in (c), f3 (Rosenbrock function): minf = (1-x1)2 + 100(x2-x12)2, xi∈[-5,10], the function has a minimum value at x1=1 and x2=1.

[0135] like Figure 8 As shown in (d), f4 (Schwefel function):

[0136] xi∈[-32.768,32.768], the function has a global minimum value of 0 at x1=x2=420.9687.

[0137] The test results are as follows Figure 8 The results show that the proposed algorithm has strong optimization capabilities and fast computational speed. Its advantages are particularly significant when processing high-dimensional functions. When processing other functions, the algorithm converges quickly within the first 50 iterations, fully demonstrating its high efficiency.

[0138] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for optimizing welding trajectories of robots in narrow ship spaces under multi-objective constraints, characterized in that: The optimization method comprises the following steps: Step 1: Define the fitness function; Determine the robot position, welding time, and welding reachability as sub-objective functions, and take the shortest welding time, the maximum welding reachability, and the optimal robot position as the goals. Considering the different importance of the three sub-objective functions under different working conditions, introduce the target weight and convert the three sub-objective functions into one objective function, Fitness. Step 2: Calculate the fitness value of each particle and update the position and velocity of the particle according to the fitness value; According to the objective function Fitness, the fitness value of each particle is calculated, and the individual optimal position and global optimal position of the particle are updated according to the fitness value; Step 3: Perform crossover and mutation operations to generate new offspring particles and update the population; Randomly select a pair of parent particles, perform a crossover operation according to the crossover probability Pc, and generate child particles. The parent particles are replaced by the child particles. Perform mutation operations on individuals according to the mutation probability Pm, update the population, and replace the original particle individuals with the mutated particle individuals; Step 4: Algorithm termination; When the maximum number of iterations is reached or the fitness value meets the preset threshold, the iteration is stopped; under the termination condition, the welding path with the highest fitness value is output as the optimal solution.

2. The method for optimizing welding trajectories of a robot in a narrow space of a ship under multi-objective constraints according to claim 1 is characterized by: Define the fitness function: Fitness=α*W time +β*R position +δ*(1-W accessibility ) Where: R position : Robot position, W time :Welding time, W accessibility : welding accessibility; α, β, and δ are weight coefficients used to balance the importance of the three objectives.

3. The method for optimizing welding trajectories of a robot in a narrow space of a ship under multi-objective constraints according to claim 2 is characterized by: To ensure that the three sub-objective functions have a similar impact on the objective function Fitness, the three sub-objective functions are normalized to unify the magnitude of the variables so that the variables have a similar impact on the objective function Fitness. The constraints of α, β, and δ are:

4. The method for optimizing welding trajectories of a robot in a narrow space of a ship under multi-objective constraints according to claim 1 is characterized by: In step 2, after calculating the fitness value, compare the current fitness value with the previously recorded individual optimal position P ij If the current fitness is better, update it to the current position and update the corresponding fitness value; Among the individual optimal positions of all particles, find the position with the best fitness as the global optimal position p gj ; According to the updated individual optimal position P ij and the global optimal position P gj Update the particle's velocity and position.

5. The method for optimizing welding trajectories of a robot in a narrow space of a ship under multi-objective constraints according to claim 1 is characterized in that: In step 2, each particle represents a welding path, and the particle speed update formula is: v ij (t+1)=ω·v ij (t)+c1r1(t)[p ij (t)-x ij (t)]+c2r2(t)[p gj (t)-x ij (t)] Where, v ij (t) represents the velocity of particle i at the current time t; ω is the inertia weight; c1 and c2 are learning factors; r1 and r2 are random numbers between 0 and 1; p ij (t) represents the individual optimal position of particle i; x ij (t) represents the current position of particle i; p gj (t) is the global optimal position.

6. The method for optimizing welding trajectories of a robot in a narrow space of a ship under multi-objective constraints according to claim 5, characterized in that: An adaptive mechanism is added to the inertia weight in the particle velocity update formula to ensure that the algorithm has global search capabilities in the early stage and local convergence capabilities in the later stage; The inertia weight ω should be large in the early stage of evolution to ensure that each particle can fully search the space. It should be small in the later stage to learn from other particles and move closer to the overall optimum. The inertia weight ω should be dynamically adjusted according to the current iteration situation. An adaptive mechanism is introduced, which includes two parts: linear decrease and exponential decrease, and the final weight coefficient is calculated by these two parts; Linear decrease: In the formula: iterations: the current number of iterations, iterations max : Maximum number of iterations, that is, the total number of iterations the algorithm will run, ω max : Initial maximum inertia weight, ω min : minimum inertia weight in the later stage; Exponential Decrease: Add the linear decrease and exponential decrease parts to get the preliminary weight value: ω=ω1+ω2 Where ω=max(ω max ,min(ω max ,ω)); Use max and min functions to ensure that the final weight value is within ω min and ω max between.

7. The method for optimizing welding trajectories of a robot in a narrow space of a ship under multi-objective constraints according to claim 5, characterized in that: Add an adaptive mechanism to the learning factor in the particle velocity update formula to ensure that the algorithm searches globally in the early stage and converges locally faster in the later stage; The learning factor c1 is larger in the early stage and c2 is larger in the later stage, which can balance the global search ability and local search ability of the particle; the parameters c1 and c2 are dynamically adjusted according to the current iteration situation; Introducing an adaptive mechanism, divided into exploration phase, development phase and convergence phase; Learning factor exploration phase: Where: c 1max is the maximum value of c1; c 2min is the minimum value of c2; Learning factor development stage: Where: c 1min is the minimum value of c1; c 2max is the maximum value of c2; Learning factor convergence stage:

8. The method for optimizing welding trajectories of a robot in a narrow space of a ship under multi-objective constraints according to claim 1 is characterized by: In step 2, each particle represents a welding path, and the particle position update formula is: x ij (t+1)=x ij (t)+v ij (t+1) Where, v ij (t+1) represents the velocity of particle i at the next moment calculated according to the velocity formula.

9. The method for optimizing welding trajectories of a robot in a narrow space of a ship under multi-objective constraints according to claim 1, characterized in that: In the step three: In the crossover operation, after the parent particle is replaced by the child particle, the position and velocity update formulas of the child particle are as follows: Where p is a random number between [0,1]; are the position vector and velocity vector of the Dimensions dimension respectively; parent(x) and parent(v) are the position vector and velocity vector of the parent individual; child(x) and child(v) are the position vector and velocity vector of the child particle respectively; subscripts 1 and 2 represent different particles.

10. The method for optimizing welding trajectories of a robot in a narrow space of a ship under multi-objective constraints according to claim 1, characterized in that: In step 3: in the mutation operation, the mutated particle individual replaces the original particle individual, and the current iterative formula of the mutation probability is: Where, P m (t) is the mutation probability of the current iteration, is the initial mutation probability, k is the exponent that controls the nonlinear attenuation rate, f(t) is the optimal fitness of the current population, f min is the initial optimal fitness, and σ is the parameter that controls the decay rate.

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