Block alignment multi-target trajectory optimization method based on IWOA

Abstract

The invention provides a block alignment multi-target trajectory optimization method based on IWOA. The block alignment multi-target trajectory optimization method comprises the steps of 1, determining a ship block trajectory planning mode; 2, dynamic track parameters which need to be followed by the attitude adjusting trolley in different directions are obtained; 3, multi-target trajectory optimization of the block and the attitude adjusting trolley is achieved; 4, planning the attitude adjustment of the block, solving the optimal time within the constraint range, and solving the motion trail of the attitude adjustment trolley; 5, establishing a posture adjusting trolley block alignment model; and step 6, verifying the feasibility of block trajectory multi-objective optimization and the accuracy of block alignment trajectory planning. The method has the beneficial effects that efficient and accurate automatic alignment of the ship block is realized through automatic alignment system building, high-precision measurement system building, coordinate transformation model building, point set matching algorithm building, intelligent optimization algorithm building, trajectory planning algorithm building and ship block automatic alignment trajectory planning system building.

Description

Technical Field

[0001] The invention relates to a total section alignment multi-objective trajectory optimization method based on IWOA, and belongs to the technical field of shipbuilding. Background Art

[0002] With the continuous growth of the global economy and the strong demand in the shipping industry, driven by the independent research and development of new technologies by various shipbuilding powers, hull construction technology has achieved a huge leap, and the world's shipbuilding powers are forming a rapid response model for shipbuilding. At present, the block shipbuilding method is generally used in shipbuilding. The block shipbuilding method uses the ship block as the manufacturing unit, and uses cranes to move the block assembled in place A to place B to assemble it into a complete ship, so that the assembly facilities can be fully utilized to form a parallel batch production model for ship manufacturing in different locations. This model can reduce the workload of ship berth assembly and welding, and help shorten the ship construction cycle.

[0003] In this mode, the closure of the main section, as one of the key processes in the shipbuilding process, directly affects the overall efficiency and accuracy of shipbuilding. At present, the development of the main section shipbuilding method in China has not achieved the expected results. A major difficulty comes from the fact that the main section closure process is mostly based on manual visual inspection and manual operation and adjustment for alignment, which leads to low closure efficiency and poor accuracy, and it is difficult to achieve efficient and accurate closure in one go. When the traditional method is used for the alignment of the main section, the fixed main section must first be hoisted on the slipway, and then the subsequent main section must be hoisted. Then use the measuring instrument to measure the positional relationship between the main sections, and position the subsequent main sections twice to ensure the accuracy of the positioning. Under the traditional method, the alignment process requires multiple measurements and positioning to ensure the positional relationship between the main sections. The overall alignment process is cumbersome, inefficient, and has poor accuracy.

[0004] At present, the assembly process of the main section in domestic shipyards needs to occupy the core production equipment such as cranes for a long time, which easily forms a bottleneck in the shipbuilding process and is a great constraint on improving shipbuilding efficiency. When the crane lifts the main section for alignment, due to factors such as the deformation of the rope is difficult to detect and the force direction is variable, it often causes a huge alignment error. At the same time, with the increasing size and weight of the hull main section, the traditional visual method, marking method positioning operation and manual control method are gradually unable to ensure the efficiency and accuracy of the alignment operation. This not only introduces huge stress in the welding area of ​​the main section, but also has a negative impact on the construction quality of the ship and increases the safety risk during the operation of the ship. Under the modern main section shipbuilding model, achieving efficient and accurate alignment of the main section has become an extremely important step in the process of ship assembly.

[0005] At present, the rapid development of automatic alignment technology has made the block alignment process automated and digital, greatly reducing the labor burden, reducing the alignment time, and improving the alignment accuracy. The relevant technology is particularly evident in the assembly process of aircraft and aerospace equipment, while the research and application in the field of ship block alignment is currently in its infancy.

[0006] Although my country's shipbuilding industry ranks at the forefront of global production, there is still much room for improvement in quality. In terms of key block alignment technology, compared with the world's leading level, my country still has a certain gap to make up. The low efficiency and poor precision in block alignment seriously restrict the vigorous development of my country's shipbuilding industry. Therefore, introducing advanced technical concepts such as new generation information technology and artificial intelligence technology into the shipbuilding industry and promoting efficient and accurate automated alignment of ship blocks has become an inevitable choice for my country to develop automated, intelligent, and digital shipbuilding and accelerate the construction of a shipbuilding power. Summary of the invention

[0007] Purpose of the invention: In view of the shortcomings in the prior art, the present invention provides a multi-objective trajectory optimization method for section alignment based on IWOA, which realizes efficient and accurate automatic alignment of ship sections through the construction of an automated alignment system, a high-precision measurement system, a coordinate transformation model, a point set matching algorithm, an intelligent optimization algorithm, a trajectory planning algorithm and a ship section automatic alignment trajectory planning system.

[0008] Technical solution: A total segment alignment multi-objective trajectory optimization method based on IWOA, comprising the following steps:

[0009] Step 1: Select the alignment method based on the completed posture calculation results of the posture adjustment vehicle, adjust the position and posture of the hull section through the coordinated operation of the posture adjustment vehicle; and determine the trajectory planning method of the ship section according to the given task requirements;

[0010] Step 2: The overall section and the supporting attitude adjustment trolley are regarded as an automatic alignment parallel system with six degrees of freedom. The overall section serves as a mobile platform, and the multiple attitude adjustment trolleys constitute the power support of the system. By analyzing the inverse kinematics of the system, the dynamic trajectory parameters that the attitude adjustment trolley needs to follow in different directions are obtained;

[0011] Step 3: On the basis of determining the overall segment alignment method and trajectory planning method, combined with the speed constraint and acceleration constraint of the attitude adjustment vehicle, a time-energy consumption-impact degree multi-objective function is established, and the multi-objective optimization model is further solved by the improved whale algorithm to achieve multi-objective trajectory optimization of the overall segment and the attitude adjustment vehicle;

[0012] Step 4: Simulate and analyze the multi-objective optimization process. Also, according to the calculation results of the posture adjustment car in step 1, the posture adjustment of the total section is planned in combination with the speed constraint and acceleration constraint of the posture adjustment car. During the rotation and translation process of the total section, the dichotomy method is used to solve the optimal time within the constraint range. Based on the above multi-objective function, the improved whale algorithm is used to solve the objective function, thereby solving the rotation process and translation process time of the total section. The motion trajectory of the posture adjustment car is solved through the time parameter, the seventh-order polynomial trajectory planning method, the speed and acceleration constraints of the posture adjustment car.

[0013] Step 5: Under the condition that the basic motion mode and motion constraints of the posture adjustment trolley are consistent, simplify the design model of the posture adjustment trolley, and use ADAMS software to establish the overall segment alignment model of the posture adjustment trolley without the internal transmission system;

[0014] Boolean constraints and joint constraints are added to the established model. Multiple parts of the attitude adjustment car are combined into fewer parts through Boolean constraints to facilitate kinematic simulation. At the same time, the movement direction of the parts in the attitude adjustment car is determined through joint constraints. Then the overall segment alignment kinematic simulation is performed, and the accuracy of the trajectory planning is judged based on the simulation results.

[0015] Step 6: Conduct the overall segment multi-objective optimization experimental verification and the overall segment overall alignment experimental verification respectively to determine the feasibility of the overall segment trajectory multi-objective optimization and the accuracy of the overall segment alignment trajectory planning.

[0016] The step 1 is specifically as follows:

[0017] A two-step alignment method is used as the overall segment posture adjustment alignment method, and the two-step alignment method is:

[0018] First, the roll, pitch and yaw angles of the ship's main section are adjusted to achieve angle alignment, and then fine position adjustments are made in the three main axis directions X, Y and Z to complete the entire alignment operation process;

[0019] The seventh-order polynomial is used to plan the trajectory of the ship section. The seventh-order polynomial planning expression is:

[0020] a(t)=at 7 +bt 6 +ct 5 +dt 4 +et 3 +ft 2 +gt+h

[0021] Assume that the initial time is t0=0 and the final time is t f , and its constraints are:

[0022]

[0023] Substituting the constraints in the above equation, we can solve the values ​​of each parameter:

[0024]

[0025] Let △a=a1-a0, we can get the motion trajectory of α:

[0026]

[0027] Similarly, the motion trajectory of the total segments x, y, z, β, γ can be obtained:

[0028]

[0029] The step 2 is specifically as follows:

[0030] Step 2.1, measure the center position of the rotating ball head of the posture adjustment trolley, and convert the measured data into the moving total segment coordinate system. The center position of the rotating ball head of each trolley in the moving total segment coordinate system is: M i (x i ,y i ,z i ),i=1,2,L n, where n represents the number of posture adjustment vehicles;

[0031] During the rotation of the total segment, the inverse kinematics of the posture adjustment trolley is solved through the rotation matrix; during the translation of the total segment, only four posture adjustment trolleys need to move simultaneously to achieve the translation of the total segment, so the trajectory of each trolley is consistent with the above-mentioned translation trajectory of the total segment;

[0032] The time for the total section rotation adjustment is t1, and the time for the total section translation adjustment is t2. Therefore, in the overall process of adjusting the total section of the ship, the relative displacement of the attitude adjustment car in the three degrees of freedom directions is:

[0033]

[0034] Where R(t) is:

[0035]

[0036]

[0037]

[0038] In the formula, a(t), β(t), and γ(t) are functions of angle and time. By taking the derivative of the above formula, we can get the expression of the velocity motion of each degree of freedom during the adjustment process of the total segment rotation:

[0039]

[0040] By taking the derivative of the above formula, we can get the expression of the acceleration motion of each degree of freedom of the total segment during the attitude adjustment process:

[0041]

[0042] By taking the derivative of the above formula, we can get the expression of the acceleration motion of each degree of freedom of the total segment during the attitude adjustment process:

[0043]

[0044] The step 2 is specifically as follows:

[0045] Step 2.2: Constrain the speed and acceleration of each posture adjustment vehicle. The constraints are:

[0046]

[0047] During the rotation of the whole segment, the maximum speed limit of each degree of freedom of the posture adjustment car is 10mm / s, and the acceleration limit is 2mm 2 / s; During the total segment translation process, the maximum speed limit of each degree of freedom of the posture adjustment car is 30mm / s, and the acceleration limit is 2mm 2 / s.

[0048] The step 3 is specifically as follows:

[0049] Step 3.1: Establish trajectory optimization objective function

[0050] Aiming at the problem of high energy consumption and large impact force in the process of attitude adjustment of large ship section automatic alignment system, multi-objective planning is carried out for each car in the process of overall attitude adjustment of the section, and the objective function is defined:

[0051]

[0052] Where st is the number of steps for total segment posture adjustment, st = 2; t i represents the time used in the i-th step; T is the running time of the posture adjustment car, N represents the number of cars, N = 4; a in 、j in are the total acceleration and total jerk of the nth posture adjustment car in three degrees of freedom in step i; f1 is the motion time of the entire posture adjustment process; f2 is an index to measure the energy consumption of all posture adjustment cars during the posture adjustment process; f3 is an index to measure the joint impact of all posture adjustment cars;

[0053] Step 3.2: Integral solution based on Simpson's method

[0054] Divide the integral interval [a, b] into 2n equal-width subintervals [x k , xk +1], the length of each small interval is h = (ba) / 2n, 2n is the number of subintervals, and n is a positive integer, then the corresponding complex Simpson integral formula is as follows:

[0055]

[0056] In the formula, a = 0; b = t1, which indicates the completion time of the first stage of the total segment;

[0057] The error formula is:

[0058]

[0059] In the formula, f (4) is the maximum value of the fourth-order derivative of f(x) in the interval [a, b], where η∈[a, b].

[0060] The step 3 is specifically as follows:

[0061] Step 3.3: Solve the multi-objective optimization model through the improved whale algorithm to achieve multi-objective trajectory optimization of the overall segment and the attitude adjustment vehicle. Specifically:

[0062] By improving the population initialization, weight, convergence factor and search ability in the whale optimization algorithm, an improved whale optimization algorithm is obtained;

[0063] The population initialization in the whale optimization algorithm is improved, and the initial distribution of the population is optimized by the Hammersley low-discrepancy sequence to promote the uniformity of the population distribution; the formula for the Hammersley sequence to generate the initial population is as follows:

[0064]

[0065] Where: x i is the position of the initial individual; X lb is the lower limit of individual variables; X up is the upper limit of the individual variable; H is a random number [0, 1] generated based on Hammersley;

[0066] Improve the population weight in the whale optimization algorithm, introduce the weight concept in the particle swarm algorithm into the whale algorithm, and propose an adaptive weight strategy to address the problem that the weight is generally a linear function and has poor convergence.

[0067]

[0068] After adding weights, the position update formula of the whale algorithm is:

[0069] x(t+1)=x rand (t)×wA×D rand,p<0.5,|A|>1

[0070] x(t+1)=x * (t)×wA×D1,p<0.5,|A|≤1

[0071] x(t+1)=D2e bl cos(2πl)+x * (t)×w,p≥0.5

[0072] Improve the convergence factor of the population in the whale optimization algorithm, change the decreasing method of a to nonlinear decreasing, and the updating formula of the nonlinear convergence factor is:

[0073]

[0074] Improve the search capability of the population in the whale optimization algorithm. In IWOA, Replace it with an isotropic Levy step, and the process is as follows:

[0075]

[0076] Where Levy is the step size extracted from the Levy distribution, Γ(λ) is the standard gamma function. U and V follow normal distributions with mean equal to zero, σ 2 u and σ 2 v is the variance.

[0077] The step 3 is specifically as follows:

[0078] Step 3.4: Solving the objective function based on IWOA

[0079] Before using the IWOA algorithm to solve the function of time-energy consumption-impact degree as the target, the target function is normalized to eliminate the dimension. The normalization formula is as follows:

[0080]

[0081] Where: f inew is the new dimensionless function after normalization of the i-th objective function; f i (x) min is the minimum function value of the i-th objective function within the range; f i (x) max is the maximum function value of the i-th objective function within the range;

[0082] In order to better formulate the weight of each target in the optimization, the normalized objective function is weighted, and the constructed normalized weighted objective function is as follows:

[0083]

[0084] In the formula, a1, a2, and a3 are weight coefficients, which define the importance of each target in the alignment of the ship's overall section. Different projects have different focuses and different weights. In order to find the most balanced value, this study uses an equal weight distribution method to take a1 = a2 = a3 = 1 / 3;

[0085] An external penalty factor is added to the objective function, so that the fitness corresponding to the parameters that are not within the constraint range is larger. When finding the minimum value of the objective function, the group optimal value update process is jumped out. The objective function after adding the penalty factor is:

[0086] F(x)=f(x)+K·T max g(x)

[0087] Where f(x) represents the unconstrained initial function; K is the penalty coefficient, and this study sets K = 1000; T max is the maximum number of iterations; g(x) is the constraint condition. When the constraint condition meets the requirements: g(x) = 0; when the constraint condition does not meet the requirements: g(x) = 1; by solving the above objective function and finding the two time periods corresponding to the minimum F(x) within the constraint range, the required time is the optimal solution under multi-objective equilibrium.

[0088] The step 4 is specifically as follows:

[0089] Under the premise of the above speed constraints and acceleration constraints, the overall segment attitude adjustment is planned. During the rotation and translation of the overall segment, the dichotomy method is used to solve the optimal time within the constraints.

[0090] The seventh-order polynomial fitting trajectory method is used, and the dichotomy method is used to solve the time as follows:

[0091]

[0092] Where t f is the total segment alignment time;

[0093] Considering the actual engineering situation, the movement speed and working stroke of the three-dimensional adjustable car must meet certain constraints:

[0094]

[0095] In the formula, v max Indicates the maximum moving speed of the three-dimensional adjustable car; S xmax , S ymax , S zmax Respectively represent the maximum working stroke of the three-dimensional adjustable trolley in the x, y, and z directions; i=1, 2, 3, 4 represent each adjustable trolley;

[0096] Combined with the kinematic equations summarized above, by selecting the appropriate total segment alignment time for the above formula, the motion trajectory of each three-dimensional adjustable car in each direction that meets the constraint conditions can be obtained; considering that in actual engineering, we generally require the total segment alignment time to be as small as possible, so we use the minimum total segment alignment time as the goal of motion trajectory planning, and the mathematical model is as follows:

[0097] Target

[0098] mint f

[0099] constraint

[0100]

[0101] For the above optimization problem, the binary method is used to solve it. The specific steps are as follows:

[0102] Step (1): According to the initial position and target position of the hull section and the maximum speed requirements of the three-dimensional adjustable vehicle in each direction, a range of the alignment time of the section [t1, t2] is preliminarily given, and t f =t1,t f = t2 when the total segment position trajectory equation is:

[0103]

[0104] Step (2): Calculate t according to the trajectory equation and kinematic equation of the above total segment posture. f =t1,t f = t2, the maximum movement speed of each three-dimensional adjustable car in the x, y, and z directions;

[0105] It should be noted that it is very complicated to directly calculate the movement speed of each direction of the three-dimensional adjustable car by analytical methods. A simple method is to discretize the total segment alignment time. The smaller the discrete time interval, the better. Generally, it can be taken out to be the same as the sampling period of the actual control system, that is, it is approximately assumed that the movement speed of the three-dimensional adjustable car in each direction changes linearly within a sampling period. Then calculate the movement speed of the three-dimensional adjustable car in each direction at each time point, and then get the maximum movement speed of the three-dimensional adjustable car in each direction under the current total segment alignment time.

[0106] Step (3), if t f =t1,t f = t2 does not satisfy the constraint condition, which means that the values ​​of t1 and t2 are incorrect. In this case, return to step (1) and reset the range of the total segment docking time.

[0107] Step (4), if t f =t1,tf = f2 does not satisfy the constraint condition, then the optimal total segment alignment time t opt =t1, calculation ends;

[0108] Step (5), if t f =t1 does not satisfy the constraint condition, and t f = t2 satisfies the constraint condition, then let

[0109] Step (6), if t f = t3 satisfies the constraint condition, then let t2 = t3, otherwise let t1 = t3; then repeat the solution of step 5 until t2-t1≤δ, then t opt =t1 is the optimal total segment alignment time;

[0110] Step (7), get t f =t opt The total segment docking trajectory equation at :

[0111]

[0112] Combined with the kinematic equation, the displacement, velocity and acceleration of the sphere center of each three-dimensional adjustable trolley process joint in the X, Y and Z directions at each moment can be obtained respectively, and the data can be output and saved to complete the calculation.

[0113] Beneficial effects: This invention aims to solve the problem of high cost and large error caused by traditional total segment closing trajectory planning, which only considers time optimization but ignores energy consumption and impact degree. Firstly, a total segment alignment trajectory planning strategy based on seventh-order polynomial is proposed; secondly, a multi-objective trajectory optimization model is established with time-energy consumption-impact degree as the target, and the model solution is realized based on IWOA. Finally, trajectory planning simulation analysis is carried out based on MATLAB and ADAMS software and experimental verification is carried out.

[0114] The seventh-order polynomial realizes the optimization of impact degree when the whole section is aligned step by step; the improved whale algorithm has faster iteration speed and higher accuracy than other algorithms. The experimental results show that the multi-objective trajectory optimization based on IWOA realizes the multi-objective balanced optimization of time-energy consumption-impact degree of the whole section alignment trajectory; the final alignment error of the key measurement points of the whole section is within 2.5mm, which meets the alignment requirements of the whole section of the ship.

[0115] The time-energy-impact multi-objective trajectory optimization based on IWOA was realized. First, a time-energy-impact multi-objective parameter model was established; secondly, based on the constraints, the multi-objective function was simplified through normalization and weight concepts, and then IWOA was used to solve the objective function to solve the time-energy-impact equilibrium trajectory; then, the overall section alignment trajectory was verified based on ADAMS. The simulation results show that the planned trajectory can well realize the precise alignment of the ship's overall section; finally, the overall section alignment trajectory optimization experiment was carried out. The experimental results show that although the optimized trajectory is extended in time, the energy consumption and impact performance indicators are reduced. And the final alignment accuracy of the overall section is maintained within 2.5mm, which meets the requirements of alignment accuracy in the overall section closing process. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0117] Figure 1 This is a flow chart of multi-objective trajectory optimization of the present invention.

[0118] Figure 2 Generate individual distribution graphs for the random method and Hammersley sequence of the present invention.

[0119] Figure 3 It is a schematic diagram of the initial state during the overall segment alignment process of the present invention.

[0120] Figure 4 It is a schematic diagram of the rotation of the total section during the total section alignment process of the present invention.

[0121] Figure 5 It is a schematic diagram of the translation of the total section during the total section alignment process of the present invention.

[0122] Figure 6 This is a trajectory diagram of key measurement points of the present invention.

[0123] Figure 7 This is the Euclidean distance error diagram of the key measurement points of the present invention.

[0124] Figure 8 The sensor distribution diagram of a single trolley of the present invention (left) and the sensor distribution diagram of the overall alignment system (right).

[0125] Fig. 9 The diagram is a comparison chart of the energy consumption index (left) and the comparison chart of the impact index (right) of the present invention.

[0126] Fig.10 This is the automatic alignment completion diagram of the overall section of the present invention.

[0127] Fig.11 The XYZ direction error (left) and the Euclidean distance error (right) of the key measurement points of the present invention. DETAILED DESCRIPTION

[0128] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0129] In the description of the present invention, it is necessary to understand that the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship are based on the orientation or position relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0130] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may include that the first and second features are in direct contact, or may include that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, a first feature being "above", "above" and "above" a second feature includes that the first feature is directly above and obliquely above the second feature, or simply indicates that the first feature is higher in level than the second feature. A first feature being "below", "below" and "below" a second feature includes that the first feature is directly below and obliquely below the second feature, or simply indicates that the first feature is lower in level than the second feature.

[0131] A total segment alignment multi-objective trajectory optimization method based on IWOA, comprising the following steps:

[0132] Step 1. Select the alignment method according to the completed posture calculation result of the posture adjustment car. In the present invention, the posture calculation result is: formulate the original posture around its own coordinate system by rotating 1.5°, 2°, -1.15° in XYZ respectively, moving 200mm, -1000mm, -100mm in XYZ direction, and converting to the target posture.

[0133] The position and attitude of the ship section are adjusted through the coordinated operation of the attitude adjustment vehicle; and the trajectory planning method of the ship section is determined according to the given mission requirements;

[0134] Step 2: The overall section and the supporting attitude adjustment trolley are regarded as an automatic alignment parallel system with six degrees of freedom. The overall section serves as a mobile platform, and the multiple attitude adjustment trolleys constitute the power support of the system. By analyzing the inverse kinematics of the system, the dynamic trajectory parameters that the attitude adjustment trolley needs to follow in different directions are obtained;

[0135] Step 3: On the basis of determining the overall segment alignment method and trajectory planning method, combined with the speed constraint and acceleration constraint of the attitude adjustment vehicle, a time-energy consumption-impact degree multi-objective function is established, and the multi-objective optimization model is further solved by the improved whale algorithm to achieve multi-objective trajectory optimization of the overall segment and the attitude adjustment vehicle;

[0136] Step 4: Simulate and analyze the multi-objective optimization process. Also, according to the calculation results of the attitude adjustment car in step 1, the attitude adjustment of the total segment is planned in combination with the speed constraint and acceleration constraint of the attitude adjustment car. During the rotation and translation process of the total segment, the dichotomy method is used to solve the optimal time within the constraint range.

[0137] Based on the above multi-objective function, the improved whale algorithm is used to solve the objective function, so as to solve the total segment rotation process and translation process time. Through the time parameter, the seventh-order polynomial trajectory planning method, the speed and acceleration constraints of the attitude adjustment car, the motion trajectory of the attitude adjustment car is solved;

[0138] Step 5: Under the condition that the basic motion mode and motion constraints of the posture adjustment trolley are consistent, simplify the design model of the posture adjustment trolley, and use ADAMS software to establish the overall segment alignment model of the posture adjustment trolley without the internal transmission system;

[0139] Boolean constraints and joint constraints are added to the established model. Multiple parts of the attitude adjustment car are combined into fewer parts through Boolean constraints to facilitate kinematic simulation. At the same time, the movement direction of the parts in the attitude adjustment car is determined through joint constraints. Then the overall segment alignment kinematic simulation is performed, and the accuracy of the trajectory planning is judged based on the simulation results.

[0140] Step 6: Conduct the overall segment multi-objective optimization experimental verification and the overall segment overall alignment experimental verification respectively to determine the feasibility of the overall segment trajectory multi-objective optimization and the accuracy of the overall segment alignment trajectory planning.

[0141] The step 1 is specifically as follows:

[0142] In the process of automatic alignment of the hull section, that is, after the position and attitude calculation is completed, the position and attitude of the hull section are adjusted through the coordinated operation of the attitude adjustment vehicle. There are three alignment methods in this process: four-stage alignment method, one-step alignment method and two-step alignment method.

[0143] In engineering practice, it is often difficult to achieve high-precision requirements with a single alignment. In addition, when performing overall segment alignment, the coordinates of key measurement points and the movement of the attitude adjustment vehicle may introduce errors. Directly using a one-time alignment strategy may cause conflicts between the overall segment to be aligned and the fixed part due to errors. Therefore, a two-step alignment strategy came into being. This method first adjusts the roll, pitch, and yaw angles of the overall segment to achieve angle alignment, and then performs fine position adjustments in the three main axis directions X, Y, and Z to complete the entire alignment operation. This paper selects the two-step attitude adjustment method as the overall segment attitude alignment method.

[0144] Trajectory planning mainly defines the changes in the position, velocity, and acceleration of an object along its trajectory. It is based on the current posture of the object and the kinematic principles of the system to design a suitable path that ensures that the object moves according to the predetermined kinematic characteristics to achieve the desired position and posture. In simple terms, the purpose of trajectory planning is to develop an ideal movement route that complies with kinematic and geometric constraints based on given task requirements.

[0145] There are many methods for automatic alignment trajectory planning of hull sections. In engineering, polynomial fitting methods are generally used for planning. This paper mainly analyzes three trajectory fitting technologies: cubic, quintic and septic polynomials. The purpose is to determine the most suitable trajectory planning strategy according to the specific requirements of hull section alignment. Assume that the initial position of the moving section is: The target pose is The overall trajectory planning method is analyzed.

[0146] The seventh-order polynomial is used to plan the trajectory of the ship section. The seventh-order polynomial planning expression is:

[0147] a(t)=at 7 +bt 6 +ct 5 +dt 4 +et 3 +ft 2 +gt+h

[0148] Assume that the initial time is t0=0 and the end time is t f , and its constraints are:

[0149]

[0150] Substituting the constraints in the above equation, we can solve the values ​​of each parameter:

[0151]

[0152] Let △a=a1-a0, we can get the motion trajectory of α:

[0153]

[0154] Similarly, the motion trajectory of the total segments x, y, z, β, γ can be obtained:

[0155]

[0156] The seventh-order polynomial fitting takes into account the more balanced distribution of force at the contact point with the adjustment device, reducing the risk of deformation and damage to the overall segment. Therefore, it is particularly important to use the seventh-order polynomial for trajectory design to ensure the safety and stability of the overall segment during automatic alignment.

[0157] The step 2 is specifically as follows:

[0158] Although the ideal motion path of the total segment has been determined, in actual operation requirements, the dynamic parameters of the four attitude adjustment trolleys must be accurately calculated, and the precise actions of the attitude adjustment trolleys must be controlled based on these data to ensure that the total segment can move along the preset trajectory. The total segment and the supporting attitude adjustment trolleys are considered to be an automatic alignment parallel system with six degrees of freedom, in which the total segment serves as a mobile platform and each attitude adjustment trolley serves as the power support of the system. By analyzing the inverse kinematics of the system, the dynamic trajectory parameters that the attitude adjustment trolleys need to follow in different directions can be solved.

[0159] Step 2.1, measure the center position of the rotating ball head of the posture adjustment trolley, and convert the measured data into the moving total segment coordinate system. The center position of the rotating ball head of each trolley in the moving total segment coordinate system is: M i (x i ,y i ,z i ),i=1,2,L n, where n represents the number of posture adjustment vehicles;

[0160] During the rotation of the total segment, the inverse kinematics of the posture adjustment trolley is solved through the rotation matrix; during the translation of the total segment, only four posture adjustment trolleys need to move simultaneously to achieve the translation of the total segment, so the trajectory of each trolley is consistent with the above-mentioned translation trajectory of the total segment;

[0161] The time for the total section rotation adjustment is t1, and the time for the total section translation adjustment is t2. Therefore, in the overall process of adjusting the total section of the ship, the relative displacement of the attitude adjustment car in the three degrees of freedom directions is:

[0162]

[0163] Where R(t) is:

[0164]

[0165]

[0166]

[0167] In the formula, a(t), β(t), and γ(t) are functions of angle and time. By taking the derivative of the above formula, we can get the expression of the velocity motion of each degree of freedom during the adjustment process of the total segment rotation:

[0168]

[0169] By taking the derivative of the above formula, we can get the expression of the acceleration motion of each degree of freedom of the total segment during the attitude adjustment process:

[0170]

[0171] By taking the derivative of the above formula, we can get the expression of the acceleration motion of each degree of freedom of the total segment during the attitude adjustment process:

[0172]

[0173] Step 2.2: Constrain the speed and acceleration of each posture adjustment vehicle. The constraints are:

[0174]

[0175] During the rotation of the whole segment, the maximum speed limit of each degree of freedom of the posture adjustment car is 10mm / s, and the acceleration limit is 2mm 2 / s; During the total segment translation process, the maximum speed limit of each degree of freedom of the posture adjustment car is 30mm / s, and the acceleration limit is 2mm 2 / s.

[0176] The step 3 is specifically as follows:

[0177] The optimal time trajectory of the attitude adjustment trolley under the constraints of speed and acceleration is solved by the dichotomy method. Only the time is considered. However, in the actual process of the ship section alignment, many trolleys are required to perform linkage and attitude adjustment, which consumes a lot of energy and has a high cost. Therefore, the optimization of energy consumption is particularly important. Secondly, if the impact of the attitude adjustment trolley is too large, on the one hand, it will cause slight deformation of the bottom plane of the ship, and on the other hand, it will increase the vibration of the attitude adjustment trolley during the movement process, thereby shortening the service life of the attitude adjustment trolley and causing a large alignment error. Therefore, the influence of energy consumption and impact degree should also be taken into account in the actual process. Therefore, the trajectory of the attitude adjustment trolley is optimized with multiple objectives. The specific process is as follows: Figure 1 shown.

[0178] Firstly, on the basis of determining the overall segment alignment method and trajectory planning method, combined with the constraints, a time-energy consumption-impact degree multi-objective function is established, and the multi-objective optimization model is further solved through the improved whale algorithm, thereby realizing the multi-objective trajectory optimization of the overall segment and the attitude adjustment vehicle.

[0179] Step 3.1: Establish trajectory optimization objective function

[0180] Aiming at the problem of high energy consumption and large impact force in the process of attitude adjustment of large ship section automatic alignment system, multi-objective planning is carried out for each car in the process of overall attitude adjustment of the section, and the objective function is defined:

[0181]

[0182] Where st is the number of steps for total segment posture adjustment, st = 2; t i represents the time used in the i-th step; T is the running time of the posture adjustment car, N represents the number of cars, N = 4; a in 、j in are the total acceleration and total jerk of the nth posture adjustment car in three degrees of freedom in step i; f1 is the motion time of the entire posture adjustment process; f2 is an index to measure the energy consumption of all posture adjustment cars during the posture adjustment process; f3 is an index to measure the joint impact of all posture adjustment cars;

[0183] Step 3.2: Integral solution based on Simpson's method

[0184] Divide the integral interval [a, b] into 2n equal-width subintervals [x k , x k +1], the length of each small interval is h = (ba) / 2n, 2n is the number of subintervals, and n is a positive integer, then the corresponding complex Simpson integral formula is as follows:

[0185]

[0186] In the formula, a = 0; b = t1, which indicates the completion time of the first stage of the total segment;

[0187] The error formula is:

[0188]

[0189] In the formula, f (4) is the maximum value of the fourth-order derivative of f(x) in the interval [a, b], where η∈[a, b]. (4) There is no solution set close to 0, so f (4) It is approximately determined to be the maximum value of the fourth-order derivative of f(x) in the interval [1, b], and the subinterval n is set to 400.

[0190] The step 3 is specifically as follows:

[0191] (1) Whale Optimization Algorithm

[0192] The whale optimization algorithm is an intelligent algorithm that imitates the foraging behavior of whales. This algorithm has the advantages of fewer parameters and fast convergence speed. The main process of the algorithm is:

[0193] Searching for prey, in the whale optimization algorithm, the whale group first determines the location of the prey and updates its own position based on the current optimal position. Based on the exploration behavior of the tth round, when |A| is greater than 1, the whale will adjust its t+1th exploration behavior. The specific process is described as follows:

[0194] x(t+1)=x rand -A.D rand

[0195] Where: D rand =|c·x rand -x(t)| is the distance between the whale and the food; t is the current iteration number; A and c are coefficient vectors; x rand is the optimal whale position; x(t) is the current whale position. The coefficient vectors A and c can be expressed by equations (4.33) and (4.34).

[0196] A=2ar-a

[0197] c=2r

[0198] Where: r represents a random number between 0 and 1, a = 2-2t / T max , t represents the current iteration round, and Tmax is the maximum iteration round set. Parameter a gradually decreases linearly from 2 to 0, and parameter A will also decrease accordingly as a decreases. When parameter |A| decreases to 1 or below, the optimization algorithm will transition from the stage of searching for prey to the stage of encircling prey.

[0199] As the iteration process progresses, when the value of |A| drops to 1 or below, the algorithm enters the stage of surrounding the prey. At this time, the remaining whales will update their positions based on the currently known optimal position information, gradually narrow the encirclement to approach the prey, and finally determine the target position for capture.

[0200] x(t+1)=x * (t)-A·D1

[0201] Where D1 = |c·x * (t)-x(t)|, x*(t) is the optimal solution for each iteration. When A∈[-1,1] is a random value, x(t+1) is iteratively updated from x(t) to x*(t), gradually approaching the optimal solution.

[0202] Bubble hunting, whales show their unique hunting skills, that is, they swim upward in a spiral while blowing bubbles, which can gradually surround the prey and push it to the surface of the sea for the most effective capture. This unique behavior of attacking through bubbles can be described by the following mathematical model:

[0203] x(t+1)=D2e bl cos(2πl)+x*(t)

[0204] Where: b is the constant coefficient of the spiral equation, and in this study b = 1. D2 = |x * (t)-x(t)| represents the distance to the best whale. l is a random number in the interval [-1, 1].

[0205] In order to simulate the whale's simultaneous execution of the tightening encirclement and bubble hunting strategies, random probability is used to determine its position update strategy. This means that the probability of selecting both the encirclement contraction and bubble attack hunting methods is set to 50%. Based on this, the whale's position update can be calculated and expressed by the following formula,

[0206]

[0207] Step 3.3: Solve the multi-objective optimization model through the improved whale algorithm to achieve multi-objective trajectory optimization of the overall segment and the attitude adjustment vehicle. Specifically:

[0208] By improving the population initialization, weight, convergence factor and search ability in the whale optimization algorithm, an improved whale optimization algorithm is obtained;

[0209] The population layout in the initial stage of the algorithm is directly related to its ability to search for the optimal solution and its fast convergence performance. Among them, a balanced initial population is particularly critical to improving the overall efficiency of the algorithm. In traditional applications, the Whale Optimization Algorithm (WOA) uses a randomization method to achieve the initial configuration of the population, which may lead to an uneven distribution of the population.

[0210] Improve the initialization of the population in the whale optimization algorithm, and optimize the initial distribution of the population through the Hammersley low-discrepancy sequence to promote the uniformity of the population distribution; however, individuals in the random distribution initial population have a probability of appearing near the optimal value, so a judgment mechanism is added: if the initial random distribution population has a better value in the first solution, the random distribution population is used as the initial value. In order to show the difference in spatial distribution between random distribution and random numbers generated by Hammersley sequence, a population of 100 individuals is generated in the interval [0, 1], and the graphical comparison of these two distribution methods is shown in Figure 2The population distribution generated by the Hammersley sequence shows higher uniformity and more comprehensive coverage of the solution space. The formula for the Hammersley sequence to generate the initial population is as follows:

[0211]

[0212] Where: x i is the position of the initial individual; X lb is the lower limit of individual variables; X up is the upper limit of the individual variable; H is a random number [0, 1] generated based on Hammersley;

[0213] Improve the population weight in the whale optimization algorithm, introduce the weight concept in the particle swarm algorithm into the whale algorithm, and propose an adaptive weight strategy to address the problem that the weight is generally a linear function and has poor convergence.

[0214]

[0215] The adaptive weight proposed in the present invention shows a nonlinear decreasing trend as the iteration increases. The weight is relatively large in the early stage, which is conducive to the algorithm jumping out of the local optimum. After adding the weight, the position update formula of the whale algorithm is:

[0216] x(t+1)=x rand (t)×wA×D rand ,p<0.5,|A|>1

[0217] x(t+1)=x * (t)×wA×D1,p<0.5,|A|≤1

[0218] x(t+1)=D2e bl cos(2πl)+x * (t)×w,p≥0.5

[0219] Improve the convergence factor of the population in the whale optimization algorithm. In the whale optimization strategy (WOA), adjusting the parameter A significantly affects the balance between the exploration and exploitation phases, which is mainly controlled by the convergence factor a. By default, as the number of iterations increases, the a parameter will experience a linear decrease. This decreasing trend may lead to insufficient exploration in the early stages of the algorithm, and at the same time, the algorithm converges too slowly in the stage approaching the end. In order to achieve the algorithm focusing on global search in the early stages of iteration and local search in the later stages, the decrease method of a is changed to nonlinear decrease. The nonlinear convergence factor update formula is:

[0220]

[0221] Improve the search capability of the population in the whale optimization algorithm. The Levy flight trajectory mechanism is conducive to expanding the population diversity of the algorithm and can better balance the local search and global search capabilities of the algorithm. In IWOA, Replace it with an isotropic Levy step, and the process is as follows:

[0222]

[0223] Where Levy is the step size extracted from the Levy distribution, Γ(λ) is the standard gamma function. U and V follow normal distributions with mean equal to zero, σ 2 u and σ 2 v is the variance.

[0224] The step 3 is specifically as follows:

[0225] Step 3.4: Solving the objective function based on IWOA

[0226] Before using the IWOA algorithm to solve the function of time-energy consumption-impact degree as the target, the target function is normalized to eliminate the dimension. The normalization formula is as follows:

[0227]

[0228] Where: f inew is the new dimensionless function after normalization of the i-th objective function; f i (x) min is the minimum function value of the i-th objective function within the range; f i (x) max is the maximum function value of the i-th objective function within the range;

[0229] In this study, the total segment rotation adjustment time range is [0, 150], and the translation time is [0, 150]. The maximum and minimum values ​​of each objective function in the above interval (from optimal time to maximum set time) are the values ​​required by the above functions.

[0230] In order to better formulate the weight of each target in the optimization, the normalized objective function is weighted, and the constructed normalized weighted objective function is as follows:

[0231]

[0232] In the formula, a1, a2, and a3 are weight coefficients, which define the importance of each target in the alignment of the ship's overall section. Different projects have different focuses and different weights. In order to find the most balanced value, this study uses an equal weight distribution method to take a1 = a2 = a3 = 1 / 3;

[0233] The optimal time for the total segment rotation and translation process is usually solved by bisection. The present invention uses the optimal time that satisfies the constraints solved by the bisection method as the minimum time f1(x) of the objective function f1 interval. min , the maximum time set is f1(x) max ; The above objective function f2(x) min 、f2(x) max 、f3(x) min 、f3(x) max The numerical value can be solved by the maximum time and minimum time parameters of the trajectory, thereby solving the normalized objective function.

[0234] The normalized weight concept can be used to convert multiple objectives into a single objective, but this single objective is also a more complex function. Conventional solution methods take a long time and require a lot of calculations. Using intelligent algorithms can solve the objective function faster and more accurately. Therefore, the present invention combines the above-mentioned improved whale algorithm optimization algorithm to solve the final objective function.

[0235] Before using the IWOA algorithm to solve the function with time-energy consumption-impact as the target, it is also necessary to pay attention to the constraints such as trajectory speed and acceleration when performing multi-objective optimization. Therefore, it is necessary to exclude the situations that do not meet the constraints during the IWOA update iteration process, and add an external penalty factor to the objective function, so that the fitness corresponding to the parameters that are not within the constraint range is larger. When looking for the minimum value of the objective function, jump out of the group optimal value update process. The objective function after adding the penalty factor is:

[0236] F(x)=f(x)+K·T max g(x)

[0237] Where f(x) represents the unconstrained initial function; K is the penalty coefficient, and this study sets K = 1000; T max is the maximum number of iterations; g(x) is the constraint condition. When the constraint condition meets the requirements: g(x) = 0; when the constraint condition does not meet the requirements: g(x) = 1; by solving the above objective function and finding the two time periods corresponding to the minimum F(x) within the constraint range, the required time is the optimal solution under multi-objective equilibrium.

[0238] The step 4 is specifically as follows:

[0239] Under the premise of the above speed constraints and acceleration constraints, the overall segment attitude adjustment is planned. During the rotation and translation of the overall segment, the dichotomy method is used to solve the optimal time within the constraints.

[0240] The seventh-order polynomial fitting trajectory method is used, and the dichotomy method is used to solve the time as follows:

[0241]

[0242] Where t f is the total segment alignment time;

[0243] Considering the actual engineering situation, the movement speed and working stroke of the three-dimensional adjustable car must meet certain constraints:

[0244]

[0245] In the formula, v max Indicates the maximum moving speed of the three-dimensional adjustable car; S xmax , S ymax , S zmax Respectively represent the maximum working stroke of the three-dimensional adjustable trolley in the x, y, and z directions; i=1, 2, 3, 4 represent each adjustable trolley;

[0246] Combined with the kinematic equations summarized above, by selecting the appropriate total segment alignment time for the above formula, the motion trajectory of each three-dimensional adjustable car in each direction that meets the constraint conditions can be obtained; considering that in actual engineering, we generally require the total segment alignment time to be as small as possible, so we use the minimum total segment alignment time as the goal of motion trajectory planning, and the mathematical model is as follows:

[0247] Target

[0248] mint f

[0249] constraint

[0250]

[0251] For the above optimization problem, the binary method is used to solve it. The specific steps are as follows:

[0252] Step (1): According to the initial position and target position of the hull section and the maximum speed requirements of the three-dimensional adjustable vehicle in each direction, a range of the alignment time of the section [t1, t2] is preliminarily given, and t f =t1,t f = t2 when the total segment position trajectory equation is:

[0253]

[0254]

[0255] Step (2): Calculate t according to the trajectory equation and kinematic equation of the above total segment posture. f =t1,t f = t2, the maximum movement speed of each three-dimensional adjustable car in the x, y, and z directions;

[0256] It should be noted that it is very complicated to directly calculate the movement speed of each direction of the three-dimensional adjustable car by analytical methods. A simple method is to discretize the total segment alignment time. The smaller the discrete time interval, the better. Generally, it can be taken out to be the same as the sampling period of the actual control system, that is, it is approximately assumed that the movement speed of the three-dimensional adjustable car in each direction changes linearly within a sampling period. Then calculate the movement speed of the three-dimensional adjustable car in each direction at each time point, and then get the maximum movement speed of the three-dimensional adjustable car in each direction under the current total segment alignment time.

[0257] Step (3), if t f =t1,t f = t2 does not satisfy the constraint condition, which means that the values ​​of t1 and t2 are incorrect. In this case, return to step (1) and reset the range of the total segment docking time.

[0258] Step (4), if t f =t1,t f = f2 does not satisfy the constraint condition, then the optimal total segment alignment time t opt =t1, calculation ends;

[0259] Step (5), if t f =t1 does not satisfy the constraint condition, and t f = t2 satisfies the constraint condition, then let

[0260] Step (6), if t f = t3 satisfies the constraint condition, then let t2 = t3, otherwise let t1 = t3; then repeat the solution of step 5 until t2-t1≤δ, then t opt =t1 is the optimal total segment alignment time;

[0261] Step (7), get t f =t opt The total segment docking trajectory equation at :

[0262]

[0263] Combined with the kinematic equation, the displacement, velocity and acceleration of the sphere center of each three-dimensional adjustable trolley process joint in the X, Y and Z directions at each moment can be obtained respectively, and the data can be output and saved to complete the calculation.

[0264] The step 5 is specifically as follows:

[0265] Boolean constraints and joint constraints are added to the established model. Multiple parts of the attitude adjustment car are combined into fewer parts through Boolean constraints to facilitate kinematic simulation. At the same time, the movement direction of the parts in the attitude adjustment car is determined through joint constraints. Then the overall segment alignment kinematic simulation is performed, and the accuracy of the trajectory planning is judged based on the simulation results.

[0266] Step 5.1 Set up joint constraints

[0267] ①Fixed secondary constraint

[0268] The structures that do not participate in the movement are fixedly connected to the ground through fixed pairs. The components that do not participate in the movement include four supporting piers, fixed sections and four tracks. The ball head of the attitude adjustment trolley should be fixed as a separate part instead of performing Boolean operations with the telescopic rod of the jacking mechanism. The reason is that in the subsequent process of constraining the ball head, it is easier to find the coordinates of the ball center of the ball head. Therefore, the jacking mechanism and the trolley ball head are fixed in the form of fixed pair constraints.

[0269] ②Movement constraint

[0270] In order to simplify the movement of the mechanism, the movement of the wheel hub guide rail at the bottom of the posture adjustment trolley is approximately regarded as plane movement, and a moving pair is added to make the bottom platform slide on the track; similarly, a moving pair is set for the middle platform and the bottom platform of the posture adjustment trolley to simplify the movement of the ball screw of the middle platform. For the lifting movement of the posture adjustment trolley, it can be directly regarded as a cylindrical pair.

[0271] ③ Ball joint constraint

[0272] During the attitude adjustment process, the ship's main section needs to rotate around the ball head on the top of the attitude adjustment trolley. Therefore, it is necessary to add a ball joint to the ball head structure of the attitude adjustment trolley so that the ball head and the ball head base have passive rotation constraints.

[0273] Step 5.2: Perform kinematic simulation of the overall segment alignment

[0274] (1) Driver settings

[0275] Add drive to the moving pair that needs active motion. The direction of the XYZ drive of the posture adjustment car must be consistent with the XYZ direction of the global coordinate system. The ball pair is not set to drive, and the ball pair is used as a passive mechanism. Add drive to the moving pair in the XYZ direction on the car. The above drive curves are the displacement curves derived after the software calculation. By selecting "Experimental Data", each car curve can be imported, and each car drive curve can be established through the CUBSPL function.

[0276] (2) Overall kinematics simulation analysis

[0277] After each drive is established, 35 pairs of points are established for the fixed segment and the moving segment, and the Euclidean distance between the corresponding points is measured by the position measurement function. The total time is set to 178.21s, and kinematic simulation is performed based on the theoretical pose data of the pose solution part. The initial state is as follows Figure 3 As shown, the rotation is completed as Figure 4 As shown, the overall alignment is completed as Figure 5 shown.

[0278] Through the above simulation analysis, it can be clearly seen that after the rotation of the total segment, the angular deviation of the total segment has been adjusted, and after the translation of the total segment, the alignment of the surface has been completed. The 35 pairs of key measurement points of the alignment surface of the total segment are measured, such as Figure 6 As shown, the Euclidean distance error of each key measurement point is measured simultaneously The Euclidean distance error curve is obtained as Figure 7 shown.

[0279] pass Figure 6 It can be seen that as time goes by, the distance differences of the 35 pairs of key measurement points are close to 0, and the final error value is Figure 7 It can be seen that the errors of the 35 pairs of key measurement points are very small, with the error value within 0.012mm, which shows the feasibility and accuracy of trajectory planning, and meets the alignment requirements of the overall section in the project.

[0280] Step 6: Conduct the overall segment multi-objective optimization experimental verification and the overall segment overall alignment experimental verification respectively to determine the feasibility of the overall segment trajectory multi-objective optimization and the accuracy of the overall segment alignment trajectory planning.

[0281] Step 6.1: Experimental verification of multi-objective optimization of the overall segment

[0282] First, the experimental platform is built by using sensor equipment. Speed ​​measurement sensors are set on each attitude adjustment vehicle. By measuring the speed, the energy consumption and impact degree are calculated. The sensors are distributed as follows: Figure 8 The distribution of sensors on a single attitude adjustment vehicle is as follows. Figure 8 As shown in the middle left figure, the left sensor is used to measure the acceleration of the posture adjustment car, and the right sensor indirectly measures the speed of the posture adjustment car through the integration method, both using the RS485 communication protocol. Figure 8 As shown in the middle right figure, by measuring the speed and acceleration of each attitude adjustment vehicle and substituting them into the multi-objective objective function, the relevant energy consumption index and impact index can be calculated.

[0283] Under the condition that the alignment method and trajectory planning placement are the same, the optimization method with the optimal time as the goal is used as the control group, and 10 groups of experiments are carried out respectively. The values ​​of energy consumption index and impact index in each group of experiments are recorded. The energy consumption index is as follows: Fig. 9 As shown in the middle left figure, the impact index is Fig. 9 As shown in the middle right picture.

[0284] It can be seen that the energy consumption and impact performance indicators are reduced, and after calculation, the average value of the original energy consumption index experimental data is 9.65, and the average value of the energy consumption index after optimization is 2.35; the average value of the original impact index experimental data is 2.01, and the average value of the impact index after optimization is 0.18, indicating that the energy consumption and impact of the optimized trajectory have different degrees of reduction, which proves the correctness of the multi-objective optimization of the trajectory in this chapter.

[0285] Step 6.2: Overall alignment test verification

[0286] On the basis of the above-mentioned total segment data measurement and posture solution experiment, the trajectory planning content of this study is applied to the total segment posture adjustment experiment to verify the total segment alignment. After the posture adjustment is completed, the total segment alignment is as follows: Fig.10 shown.

[0287] As can be seen from the figure above, the end faces of the total section have reached the state of alignment. The relative measurement points on the outside of the total section are measured by two total stations, and the errors of the 35 pairs of points on the alignment surface in the XYZ direction are calculated through the relative relationship. Fig.11 As shown in the middle left figure. The Euclidean distance error is Fig.11 As shown in the middle right picture.

[0288] From the above experiments, it can be seen that the error of the key measurement points on the alignment surface in the XYZ direction is within ±2mm, and the Euclidean distance error is within 2.5mm, which meets the technical requirements for precise alignment of the overall section.

[0289] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0290] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-objective trajectory optimization method for total segment alignment based on IWOA, characterized in that: The following steps are involved: Step 1: Select the alignment method based on the completed posture calculation results of the posture adjustment vehicle, adjust the position and posture of the hull section through the coordinated operation of the posture adjustment vehicle; and determine the trajectory planning method of the ship section according to the given task requirements; Step 2: The overall section and the supporting attitude adjustment trolley are regarded as an automatic alignment parallel system with six degrees of freedom. The overall section serves as a mobile platform, and the multiple attitude adjustment trolleys constitute the power support of the system. By analyzing the inverse kinematics of the system, the dynamic trajectory parameters that the attitude adjustment trolley needs to follow in different directions are obtained; Step 3: On the basis of determining the overall segment alignment method and trajectory planning method, combined with the speed constraint and acceleration constraint of the attitude adjustment vehicle, a time-energy consumption-impact degree multi-objective function is established, and the multi-objective optimization model is further solved by the improved whale algorithm to achieve multi-objective trajectory optimization of the overall segment and the attitude adjustment vehicle; Step 4: Simulate and analyze the multi-objective optimization process. Also, according to the calculation results of the attitude adjustment car in step 1, the attitude adjustment of the total segment is planned in combination with the speed constraint and acceleration constraint of the attitude adjustment car. During the rotation and translation process of the total segment, the dichotomy method is used to solve the optimal time within the constraint range. Based on the above multi-objective function, the improved whale algorithm is used to solve the objective function, so as to solve the total segment rotation process and translation process time. Through the time parameter, the seventh-order polynomial trajectory planning method, the speed and acceleration constraints of the attitude adjustment car, the motion trajectory of the attitude adjustment car is solved; Step 5: Under the condition that the basic motion mode and motion constraints of the posture adjustment trolley are consistent, simplify the design model of the posture adjustment trolley, and use ADAMS software to establish the overall segment alignment model of the posture adjustment trolley without the internal transmission system; Boolean constraints and joint constraints are added to the established model. Multiple parts of the attitude adjustment car are combined into fewer parts through Boolean constraints to facilitate kinematic simulation. At the same time, the movement direction of the parts in the attitude adjustment car is determined through joint constraints. Then the overall segment alignment kinematic simulation is performed, and the accuracy of the trajectory planning is judged based on the simulation results. Step 6: Conduct the overall segment multi-objective optimization experimental verification and the overall segment overall alignment experimental verification respectively to determine the feasibility of the overall segment trajectory multi-objective optimization and the accuracy of the overall segment alignment trajectory planning.

2. The IWOA-based total segment alignment multi-objective trajectory optimization method according to claim 1 is characterized in that: The step 1 is specifically as follows: A two-step alignment method is used as the overall segment posture adjustment alignment method, and the two-step alignment method is: First, the roll, pitch and yaw angles of the ship's main section are adjusted to achieve angle alignment, and then fine position adjustments are made in the three main axis directions X, Y and Z to complete the entire alignment operation process; The seventh-order polynomial is used to plan the trajectory of the ship section. The seventh-order polynomial planning expression is: a(t)=at 7 +bt 6 +ct 5 +dt 4 +et 3 +ft 2 +gt+h Assume that the initial time is t0=0 and the final time is t f , and its constraints are: Substituting the constraints in the above equation, we can solve the values ​​of each parameter: Let △a=a1-a0, we can get the motion trajectory of α: Similarly, the motion trajectory of the total segments x, y, z, β, γ can be obtained:

3. The IWOA-based total segment alignment multi-objective trajectory optimization method according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2.1, measure the center position of the rotating ball head of the posture adjustment trolley, and convert the measured data into the moving total segment coordinate system. The center position of the rotating ball head of each trolley in the moving total segment coordinate system is: M i (x i ,y i ,z i ),i=1,2,L n, where n represents the number of posture adjustment vehicles; During the rotation of the total segment, the inverse kinematics of the posture adjustment trolley is solved through the rotation matrix; during the translation of the total segment, only four posture adjustment trolleys need to move simultaneously to achieve the translation of the total segment, so the trajectory of each trolley is consistent with the above-mentioned translation trajectory of the total segment; The time for the total section rotation adjustment is t1, and the time for the total section translation adjustment is t2. Therefore, in the overall process of adjusting the total section of the ship, the relative displacement of the attitude adjustment car in the three degrees of freedom directions is: Where R(t) is: In the formula, a(t), β(t), and γ(t) are functions of angle and time. By taking the derivative of the above formula, we can get the expression of the velocity motion of each degree of freedom during the adjustment process of the total segment rotation: By taking the derivative of the above formula, we can get the expression of the acceleration motion of each degree of freedom of the total segment during the attitude adjustment process: By taking the derivative of the above formula, we can get the expression of the acceleration motion of each degree of freedom of the total segment during the attitude adjustment process:

4. The IWOA-based total segment alignment multi-objective trajectory optimization method according to claim 3 is characterized in that: The step 2 is specifically as follows: Step 2.2: Constrain the speed and acceleration of each posture adjustment vehicle. The constraints are: During the rotation of the whole segment, the maximum speed limit of each degree of freedom of the posture adjustment car is 10mm / s, and the acceleration limit is 2mm 2 / s; During the total segment translation process, the maximum speed limit of each degree of freedom of the posture adjustment car is 30mm / s, and the acceleration limit is 2mm 2 / s.

5. The IWOA-based total segment alignment multi-objective trajectory optimization method according to claim 1, characterized in that: The step 3 is specifically as follows: Step 3.1: Establish trajectory optimization objective function Aiming at the problem of high energy consumption and large impact force in the process of attitude adjustment of large ship section automatic alignment system, multi-objective planning is carried out for each car in the process of overall attitude adjustment of the section, and the objective function is defined: Where st is the number of steps for total segment posture adjustment, st = 2; t i represents the time taken in the i-th step; T is the running time of the posture adjustment trolley, N is the number of trolleys, N = 4; a in 、j in are the total acceleration and total jerk of the nth posture adjustment car in three degrees of freedom in step i; f1 is the motion time of the entire posture adjustment process; f2 is an index to measure the energy consumption of all posture adjustment cars during the posture adjustment process; f3 is an index to measure the joint impact of all posture adjustment cars; Step 3.2: Integral solution based on Simpson's method Divide the integral interval [a, b] into 2n equal-width subintervals [x k , x k +1], the length of each small interval is h = (ba) / 2n, 2n is the number of subintervals, and n is a positive integer, then the corresponding complex Simpson integral formula is as follows: In the formula, a = 0; b = t1, which indicates the completion time of the first stage of the total segment; The error formula is: In the formula, f (4) is the maximum value of the fourth-order derivative of f(x) in the interval [a, b], where η∈[a, b].

6. The IWOA-based total segment alignment multi-objective trajectory optimization method according to claim 1, characterized in that: The step 3 is specifically as follows: Step 3.3: Solve the multi-objective optimization model through the improved whale algorithm to achieve multi-objective trajectory optimization of the overall segment and the attitude adjustment vehicle. Specifically: By improving the population initialization, weight, convergence factor and search ability in the whale optimization algorithm, an improved whale optimization algorithm is obtained; The population initialization in the whale optimization algorithm is improved, and the initial distribution of the population is optimized by the Hammersley low-discrepancy sequence to promote the uniformity of the population distribution; the formula for the Hammersley sequence to generate the initial population is as follows: Where: x i is the position of the initial individual; X lb is the lower limit of individual variables; X up is the upper limit of the individual variable; H is a random number [0, 1] generated based on Hammersley; Improve the population weight in the whale optimization algorithm, introduce the weight concept in the particle swarm algorithm into the whale algorithm, and propose an adaptive weight strategy to address the problem that the weight is generally a linear function and has poor convergence. After adding weights, the position update formula of the whale algorithm is: x(t+1)=x rand (t)×w-A×D rand ,p<0.5,|A|>1 x(t+1)=x * (t)×w-A×D1,p<0.5,|A|≤1 x(t+1)=D2e bl cos(2πl)+x * (t)×w,p≥0.5 Improve the convergence factor of the population in the whale optimization algorithm, change the decreasing method of a to nonlinear decreasing, and the updating formula of the nonlinear convergence factor is: Improve the search capability of the population in the whale optimization algorithm. In IWOA, Replace it with an isotropic Levy step size, and the process is as follows: Where Levy is the step size extracted from the Levy distribution, Γ(λ) is the standard gamma function. U and V follow normal distributions with mean equal to zero, σ 2 u and σ 2 v is the variance.

7. The IWOA-based total segment alignment multi-objective trajectory optimization method according to claim 6 is characterized in that: The step 3 is specifically as follows: Step 3.4: Solving the objective function based on IWOA Before using the IWOA algorithm to solve the function of time-energy consumption-impact degree as the target, the target function is normalized to eliminate the dimension. The normalization formula is as follows: Where: f inew is the new dimensionless function after normalization of the i-th objective function; f i (x) min is the minimum function value of the i-th objective function within the range; f i (x) max is the maximum function value of the i-th objective function within the range; In order to better formulate the weight of each target in the optimization, the normalized objective function is weighted, and the constructed normalized weighted objective function is as follows: In the formula, a1, a2, and a3 are weight coefficients, which define the importance of each target in the alignment of the ship's overall section. Different projects have different focuses and different weights. In order to find the most balanced value, this study uses an equal weight distribution method to take a1 = a2 = a3 = 1 / 3; An external penalty factor is added to the objective function, so that the fitness corresponding to the parameters that are not within the constraint range is larger. When finding the minimum value of the objective function, the group optimal value update process is jumped out. The objective function after adding the penalty factor is: F(x)=f(x)+K·T max ·g(x) Where f(x) represents the unconstrained initial function; K is the penalty coefficient, and this study sets K = 1000; T max is the maximum number of iterations; g(x) is the constraint condition. When the constraint condition meets the requirements: g(x) = 0; when the constraint condition does not meet the requirements: g(x) = 1; by solving the above objective function and finding the two time periods corresponding to the minimum F(x) within the constraint range, the required time is the optimal solution under multi-objective equilibrium.

8. The IWOA-based total segment alignment multi-objective trajectory optimization method according to claim 1, characterized in that: The step 4 is specifically as follows: Under the premise of the above speed constraints and acceleration constraints, the overall segment attitude adjustment is planned. During the rotation and translation of the overall segment, the dichotomy method is used to solve the optimal time within the constraints. The seventh-order polynomial fitting trajectory method is used, and the dichotomy method is used to solve the time as follows: Where t f is the total segment alignment time; Considering the actual engineering situation, the movement speed and working stroke of the three-dimensional adjustable car must meet certain constraints: In the formula, v max Indicates the maximum moving speed of the three-dimensional adjustable car; S xmax , S ymax , S zmax Respectively represent the maximum working stroke of the three-dimensional adjustable trolley in the x, y, and z directions; i = 1, 2, 3, 4 represents each adjustable trolley; Combined with the kinematic equations summarized above, by selecting the appropriate total segment alignment time for the above formula, the motion trajectory of each three-dimensional adjustable car in each direction that meets the constraint conditions can be obtained; considering that in actual engineering, we generally require the total segment alignment time to be as small as possible, so we use the minimum total segment alignment time as the goal of motion trajectory planning, and the mathematical model is as follows: Target as f constraint For the above optimization problem, the binary method is used to solve it. The specific steps are as follows: Step (1): According to the initial position and target position of the hull section and the maximum speed requirements of the three-dimensional adjustable vehicle in each direction, a range of the alignment time of the section [t1, t2] is preliminarily given, and t f =t1,t f = t2 when the total segment position trajectory equation is: Step (2): Calculate t according to the trajectory equation and kinematic equation of the above total segment posture. f =t1,t f = t2, the maximum movement speed of each three-dimensional adjustable car in the x, y, and z directions; Step (3), if t f =t1,t f = t2 does not satisfy the constraint condition, which means that the values ​​of t1 and t2 are incorrect. In this case, return to step (1) and reset the range of the total segment docking time. Step (4), if t f =t1,t f = f2 does not satisfy the constraint condition, then the optimal total segment alignment time t opt =t1, calculation ends; Step (5), if t f =t1 does not satisfy the constraint condition, and t f = t2 satisfies the constraint condition, then let Step (6), if t f = t3 satisfies the constraint condition, then let t2 = t3, otherwise let t1 = t3; then repeat the solution of step 5 until t2-t1≤δ, then t opt =t1 is the optimal total segment alignment time; Step (7), get t f =t opt The total segment docking trajectory equation at : Combined with the kinematic equation, the displacement, velocity and acceleration of the sphere center of each three-dimensional adjustable trolley process joint in the X, Y and Z directions at each moment can be obtained respectively, and the data can be output and saved to complete the calculation.

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