Multi-objective optimization method for continuous casting ladle robot trajectory based on snake optimization algorithm

Abstract

The present invention discloses a multi-objective optimization method for the trajectory of a continuous casting ladle robot arm based on a snake optimization algorithm, which belongs to the field of information technology of continuous casting production process, and includes the following steps: constructing a coordinate space of a six-degree-of-freedom robot arm according to the on-site environment of the continuous casting ladle area, and determining the starting point, environmental obstacles and target point of the robot arm path; designing a path planning algorithm with obstacle avoidance using the RRT* algorithm to obtain the shortest path; constructing a quintic B-spline function to smooth the path, and adding initial time information to the path point sequence to plan the trajectory of the robot arm; optimizing the time information of the robot arm trajectory point sequence through a multi-objective snake optimization algorithm to achieve time-energy-impact multi-objective optimization of the robot arm trajectory. The present invention optimizes the trajectory of the continuous casting ladle robot arm through the snake optimization algorithm, so that the running time of the robot arm trajectory is shorter, the total energy consumption is lower, and the trajectory is smoother, which lays a good foundation for efficient and safe production of continuous casting.

Description

Technical Field

[0001] The invention belongs to the technical field of information technology of continuous casting production process, and specifically relates to a multi-objective optimization method for continuous casting ladle robot arm trajectory based on a snake optimization algorithm. Background Art

[0002] With the rapid development of informatization and intelligence in the steel industry, unmanned / less-manned factories have become an important direction for the development of intelligent manufacturing. Steel companies such as Posco in South Korea, Nippon Steel in Japan, Baowu Group, Nanjing Iron and Steel Group, and Shougang Qiangang in China are gradually introducing robots to replace manual labor to complete the automatic loading and unloading of the hydraulic cylinder of the sliding nozzle of the ladle, temperature measurement of the tundish, sampling, and addition of covering agents, ensuring standardized and precise operations and reducing manual operations and repetitive labor in dangerous positions. At present, the degree of automation of continuous casting has been greatly improved, but there are still certain difficulties in truly achieving unmanned casting. Sometimes manual loading and unloading of the hydraulic cylinder of the sliding nozzle of the ladle is still required. According to the location environment of the large ladle nozzle and the action process of the nozzle change, the use of a six-degree-of-freedom robotic arm to replace manual loading and unloading of the hydraulic cylinder of the sliding nozzle of the ladle can improve the degree of automation and production efficiency, while also reducing production risks and strengthening the protection of the life, health and safety of employees. The robotic arm is a heavy-duty material handling equipment that can meet the complex environment of high temperature, heat radiation, steel flower splashing, and high and low staggered equipment layout in the continuous casting area. It can improve the safety factor of the operation, effectively avoid safety accidents, and improve the efficiency of on-site operations. The traditional trajectory planning method using polynomial fitting often cannot achieve the purpose of obstacle avoidance. Therefore, in order to replace the traditional robot arm trajectory planning method and consider it from the perspective of improving efficiency, saving energy, and safety and stability, a multi-objective optimization method of the continuous casting ladle robot arm trajectory based on the snake optimization algorithm can be adopted with the goals of shortest time, minimum energy and minimum impact. Summary of the invention

[0003] The purpose of the present invention is to provide a multi-objective optimization method for the trajectory of a continuous casting ladle robot arm based on a snake optimization algorithm to solve the problems arising from the above-mentioned background technology.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A multi-objective optimization method for the trajectory of a continuous casting ladle robot arm based on a snake optimization algorithm, the method comprising the following steps:

[0006] Step 1: According to the basic tasks of the actual process of the continuous casting ladle robot arm and the actual situation of the continuous casting site, the working space of the continuous casting ladle robot arm is constructed, and the positions of the starting point of the robot arm path, environmental obstacles and target points are determined;

[0007] Step 2: Plan the path of the continuous casting ladle robot arm using the RRT* algorithm with obstacle avoidance to obtain the shortest path from the starting point to the target point of the continuous casting ladle robot arm;

[0008] Step 3: for the obtained shortest path of the continuous casting ladle robot arm, a quintic B-spline function is used to smooth it, and the initial time information is added to the path point sequence to plan the trajectory of the robot arm;

[0009] Step 4, taking the speed, acceleration and jerk of each joint of the robot as constraints, based on the snake optimization algorithm, multi-objective optimization is performed on the running time, energy and impact of the robot trajectory, and the fitness function of the snake optimization algorithm, the total trajectory running time, the mean energy of the robot, and the mean impact of the robot are obtained; the time information of the control point is updated in the B-spline function to obtain the position, speed, acceleration and jerk curves of each joint of the continuous casting ladle robot after optimization.

[0010] A further improvement of the technical solution of the present invention is that in step 1, the basic process task of the continuous casting ladle robot arm is: after setting the starting point, environmental obstacles and target point according to process requirements and actual site conditions, the continuous casting ladle robot arm first takes the process object from the starting point, bypasses the environmental obstacles, and then places the process object at the target point.

[0011] The further improvement of the technical solution of the present invention is that: in step 2, in the RRT* algorithm, the next node of the current node is screened by detecting obstacles, the parent node and the next path are reselected, the target direction of the path is optimized, and the shortest path of the robot arm is obtained; in the path planning of the continuous casting ladle robot arm, the robot arm joints are equivalent to cylindrical envelopes, and the obstacles are equivalent to spherical envelopes. It is determined whether the cylinder and the sphere intersect, and the flag is set to 0 when there is no collision and to 1 when there is a collision. If there is no collision, the node is retained.

[0012] The further improvement of the technical solution of the present invention is that: in step 3, the m path point sequence of the continuous casting ladle robot arm is obtained according to the RRT* algorithm, the path is smoothed by using a 5th-order B-spline curve, and time information is added to the path point sequence, so as to transform the path planning problem into a trajectory planning problem; the B-spline function is Among them, d i (i=0,1,...,n;n=m+3) are the coordinates of the control points, N i,k (i=0,1,...,n) is the basis function of the k-order B-spline curve, and k is taken as 5.

[0013] A further improvement of the technical solution of the present invention lies in: in step 4, the snake optimization algorithm is adopted. When setting the algorithm parameters, first, the algorithm is initialized. The population size is determined to be N, the threshold of the food amount Q is set to Q0, the threshold of the temperature Temp is set to Temp0, and the individual X in the population represents the time solution corresponding to the path point of the B-spline function. Secondly, all individuals are grouped into males and females equally. Then, the food amount Q and the temperature Temp are iteratively calculated. When Q < Q0, it enters the exploration stage. In the exploration stage, the snake only searches for food around, searches for food by choosing any random position, and updates its position relative to it, and iteratively calculates the optimal male position X i,ma and the optimal female position X i,fe ; when Q > Q0 and Temp > Temp0, it enters the feeding mode in the exploitation stage. In the case where food is available but the temperature is high, the snake only focuses on eating the available food. At this time, the position X of the male or female individual is iteratively calculated i,j ; when Q > Q0 and Temp < Temp0, it enters the mating mode in the exploitation stage. The mating process is divided into a combat mode or a mating mode. In the combat mode, each male fights for the best female, and each female tries to choose the best male. At this time, X i,ma and X i,fe are iteratively calculated. In the mating mode, mating occurs between each pair and is related to the availability of the food quantity. At this time, the worst male position X worst,ma and the worst female position X worst,fe are calculated and X i,ma and X i,fe are iteratively calculated.

[0014] The optimization objectives of the snake optimization algorithm are respectively set as the time S1, energy S2, and shock S3 from the initial point to the target point, and are defined as follows:

[0015]

[0016]

[0017]

[0018] Among them, m represents the number of trajectory points, obtained by the RRT* algorithm, i represents the i-th trajectory point, t i (i = 1, 2, …, m) represents the time corresponding to the i-th trajectory point, Δt i represents the time used for the i-th segment of the trajectory, a li represents the acceleration of the l-th joint in the i-th segment of the trajectory, j li represents the jerk of the l-th joint in the i-th segment of the trajectory, and M = 6, indicating that the robotic arm has six degrees of freedom;

[0019] The kinematic constraints are the velocity, acceleration, and jerk of the starting point, intermediate path points, and target point of the motion trajectory, and the velocity, acceleration, and jerk are kept continuous. The constraints are defined as follows:

[0020] |v li (t)|=|P'(t)| <v max

[0021] |a li (t)|=|P”(t)| max

[0022] |j li (t)|=|P (3) (t)|<j max

[0023] where t∈[t1,t2,…,t m ],v max is the maximum speed of the joint during operation, a max is the maximum acceleration of the joint during operation, j max is the maximum jerk during joint operation;

[0024] Using the exterior point penalty function method, the penalty function is defined as:

[0025]

[0026] Among them, S pun The initial value is set to 0; when v li (t), a li (t) and j li (t) respectively exceeds the constraint value v max 、a max and j max When S pun gradually increase in size;

[0027] The fitness function of the snake optimization algorithm is taken as:

[0028]

[0029] Set the penalty coefficient in the fitness function to k pun , the time coefficient is k t , the energy coefficient is k mj , the smoothness coefficient is k j , respectively assigned to k pun =400,k t =56,k mj =0.2,k j =1050;

[0030] ​The snake optimization algorithm is used to perform multi-objective optimization on the trajectory of the continuous casting ladle robot arm, and the optimal male position X is obtained by iterative calculation. best,ma and the optimal female position X best,fe , compare the fitness of individuals in the population, and take the individual position with the smallest fitness as the optimal individual position X food , determine whether the maximum number of iterations has been reached. If not, add 1 to the number of iterations and return to the main loop to iteratively calculate the amount of food Q and the temperature Temp, update the position of the next generation of individuals and calculate the fitness; after reaching the maximum number of iterations, obtain the fitness function of the snake optimization algorithm, the total trajectory running time, the mean energy of the robotic arm, and the mean impact of the robotic arm; update the time information of the control point in the B-spline function to obtain the position, velocity, acceleration, and jerk curves of each joint of the optimized continuous casting ladle robotic arm.

[0031] A further improvement of the technical solution of the present invention is that in the snake optimization algorithm, the threshold value of the food quantity Q is Q0=0.25, and the threshold value of the temperature Temp is Temp0=0.6.

[0032] Due to the adoption of the above technical solution, the technical progress achieved by the present invention is:

[0033] The present invention performs path planning for a continuous casting ladle robot arm based on an RRT* algorithm, applies an obstacle detection model to the obstacle avoidance judgment of the path planning algorithm, and obtains a feasible obstacle avoidance path for the continuous casting ladle robot arm; and performs trajectory planning for the robot arm in a joint space based on a quintic B-spline function, obtains all control points of the B-spline curve according to an existing path point sequence and boundary equations in which the velocities and accelerations of a starting point and a target point are added as zero, constructs a quintic B-spline function, and obtains relatively smooth position, velocity, acceleration and jerk curves of each joint of the continuous casting ladle robot arm.

[0034] The present invention performs multi-objective optimization on the trajectory of the continuous casting ladle robot based on the snake optimization algorithm. When the snake optimization algorithm is used to optimize the trajectory of the robot, the convergence speed is fast and the ability to jump out of the local optimum is strong. This paper selects time, energy and impact as optimization targets, considers the kinematic constraints of the robot on speed, acceleration and jerk, and uses the external point penalty function method to establish a penalty function. After reaching the maximum number of iterations, the fitness function of the snake optimization algorithm, the total trajectory running time, the mean energy value of the robot, and the mean impact value of the robot are obtained; the time information is updated in the B-spline curve, and the optimized position, speed, acceleration and jerk curves of the continuous casting ladle robot are obtained.

[0035] The present invention performs offline trajectory planning for the continuous casting ladle robot arm, thereby improving the safety of the debugging process, making it easy to modify trajectory points, and accelerating the debugging process. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a general flow chart of the multi-objective optimization method of the continuous casting ladle robot arm trajectory based on the snake optimization algorithm of the present invention;

[0037] Figure 2 is the path planning diagram of the RRT* algorithm of the present invention;

[0038] Figure 3 It is the fitness function variation curve of the snake optimization algorithm of the present invention;

[0039] Figure 4 It is the total time variation curve of the trajectory operation of the snake optimization algorithm of the present invention;

[0040] Figure 5 It is the mean value change curve of the mechanical arm energy of the snake optimization algorithm of the present invention;

[0041] Figure 6 It is the change curve of the mean impact value of the mechanical arm of the snake optimization algorithm of the present invention;

[0042] Figure 7 Position, velocity, acceleration and jerk curves before and after optimization of joint 1 trajectory;

[0043] Figure 8 Position, velocity, acceleration and jerk curves before and after optimization of joint 2 trajectory;

[0044] Fig. 9 Position, velocity, acceleration and jerk curves before and after optimization of joint 3 trajectory;

[0045] Fig.10 Position, velocity, acceleration and jerk curves before and after optimization of joint 4 trajectory;

[0046] Fig.11 Position, velocity, acceleration and jerk curves before and after optimization of joint 5 trajectory;

[0047] Fig.12 Position, velocity, acceleration, and jerk curves before and after optimization of joint 6 trajectory. DETAILED DESCRIPTION

[0048] The embodiment of the present application provides a multi-objective optimization method for the trajectory of the continuous casting ladle robot arm based on the snake optimization algorithm, which can improve the degree of automation and production efficiency in the process, reduce production risks, effectively reduce manual operations and repetitive labor in dangerous positions, and strengthen the protection of the life, health and safety of employees. The general idea is to use the RRT* algorithm to realize the path planning of the continuous casting ladle robot arm, use the quintic B-spline function to realize the trajectory planning of the continuous casting ladle robot arm, and use the snake optimization algorithm to realize the time-energy-impact multi-objective optimization of the trajectory of the continuous casting ladle robot arm, which lays a solid foundation for the efficient production of continuous casting and rolling.

[0049] The present invention is further described in detail below with reference to the accompanying drawings and embodiments:

[0050] like Figure 1 As shown in the figure, the multi-objective optimization method of the trajectory of the continuous casting ladle robot arm based on the snake optimization algorithm includes the following steps:

[0051] Step 1: According to the basic requirements of the actual process of the continuous casting ladle robot arm and the actual situation of the continuous casting site, the working space of the continuous casting ladle robot arm is constructed, and the positions of the hydraulic cylinder interface at the transfer table, the hydraulic cylinder tray at the bottom of the ladle, and the preset environmental obstacles are determined;

[0052] Step 2: Select the hydraulic cylinder interface at the transfer table as the starting point and the hydraulic cylinder tray at the bottom of the ladle as the target point. Use the RRT* (Asymptotically Optimal Rapidly-Exploring Random Trees) algorithm with obstacle avoidance to plan the path of the continuous casting ladle robot arm and obtain the shortest path of the continuous casting ladle robot arm (such as Figure 2 shown);

[0053] Step 3: for the obtained shortest path of the continuous casting ladle robot arm, a quintic B-spline function is used to smooth it, and the initial time information is added to the path point sequence to plan the trajectory of the robot arm;

[0054] Step 4, taking the speed, acceleration and jerk of each joint of the robot as constraints, based on the snake optimization algorithm, multi-objective optimization is performed on the running time, energy and impact of the robot trajectory, and the fitness function of the snake optimization algorithm, the total trajectory running time, the mean energy of the robot, and the mean impact of the robot are obtained; the time information of the control point is updated in the B-spline function to obtain the position, speed, acceleration and jerk curves of each joint of the continuous casting ladle robot after optimization.

[0055] Example:

[0056] 1. Determine the basic process tasks of the continuous casting ladle robot arm

[0057] The basic process task of the continuous casting ladle robotic arm is: the continuous casting ladle robotic arm first takes the hydraulic cylinder from the turntable tray, bypasses environmental obstacles such as the oil-gas medium coupler at the continuous casting site, and then places the hydraulic cylinder on the hydraulic cylinder tray at the bottom of the ladle, wherein the hydraulic cylinder interface at the turntable is the starting point, and the hydraulic cylinder tray at the bottom of the ladle is the target point; its inverse task is: the continuous casting ladle robotic arm takes the hydraulic cylinder from the hydraulic cylinder tray at the bottom of the ladle, bypasses environmental obstacles such as the oil-gas medium coupler at the continuous casting site, and then places the hydraulic cylinder on the hydraulic cylinder tray at the turntable, wherein the hydraulic cylinder interface at the bottom of the ladle is the starting point, and the hydraulic cylinder tray at the turntable is the target point.

[0058] 2. Construct the working space of the continuous casting ladle robot

[0059] According to the basic requirements of the actual process of the continuous casting ladle robot arm and the actual situation of the continuous casting site, the working space of the continuous casting ladle robot arm is constructed, and the positions of the hydraulic cylinder interface at the transfer table, the hydraulic cylinder tray at the bottom of the ladle, and the preset environmental obstacles are determined;

[0060] 3. Path planning for continuous casting ladle robot arm

[0061] The hydraulic cylinder interface at the transfer table is selected as the starting point, and the hydraulic cylinder tray at the bottom of the ladle is selected as the target point. The RRT* algorithm with obstacle avoidance is used to plan the path of the continuous casting ladle robot arm to achieve the purpose of shortest path planning. The RRT* algorithm process is as follows:

[0062] (1) Set the boundary space and use the uniform random distribution function to generate a global random node x rand ;

[0063] (2) Find the distance from the random point to each node on the tree and find the distance from x rand The closest node x near And along x rand to x near Direction expands the new node x with a fixed step size L new , expand the new node x new The formula is as follows:

[0064]

[0065] (3) The idea of ​​obstacle detection in the path planning of the continuous casting ladle robot arm is to treat the robot arm joint as a cylindrical envelope and the obstacle as a spherical envelope, and to determine whether the cylinder and the sphere intersect. The flag is set to 0 when there is no collision and to 1 when there is a collision. If there is no collision, the node is retained.

[0066] (4) Taking node x new As the center of the circle, set the proximity threshold and search for x within the distance range. new The adjacent node is used as a replacement x new Alternative parent node of ;

[0067] (5) To further reduce the path cost, rewire the random tree and update the relationships of other nodes in the neighborhood;

[0068] (6) Set the distance threshold disToFind. If the distance between the current path point and the target point is greater than disToFind, jump to step (2) and continue the above process. If it is less than disToFind, the target point is found, the search is terminated, and the number of path points m and the position vector P of each joint at the m optimal path points after obstacle avoidance are obtained.i =(p 1i ,p 2i ,p 3i ,p 4i ,p 5i ,p 6i )(i=1,2,…,m)(e.g. Figure 2 shown).

[0069] 4. Trajectory planning for continuous casting ladle robot arm

[0070] Using P i =(p 1i ,p 2i ,p 3i ,p 4i ,p 5i ,p 6i )(i=1,2,…,m) constructs the equation of the 5th-order B-spline curve, and considers the four boundary conditions of the velocity and acceleration being 0 at the start and end times, obtains the coordinates of the n+1 (where n=m+3) control points of the B-spline curve, and introduces the initial time series to plan the trajectory curve of the robot. The specific process is as follows: The 5th-order B-spline curve is:

[0071]

[0072] where d i (i=0,1,...,n) are the coordinates of the control points, N i,k (i=0,1,...,n) is the basis function of the k-order (here k=5) B-spline curve, which is composed of a sequence U of non-decreasing parameters u called knot vectors: u0≤u1≤...≤u n+k+1 Determine the k-th degree piecewise polynomial.

[0073] N i,k (u) can be obtained by the DeBoer formula:

[0074]

[0075] Introduce the initial time series [t1, t2, …, t m ], the position-time series of each joint is,

[0076] R=(P i ,t i )i=1,2,...,m

[0077] P i =P(u) is substituted into the fifth-order B-spline function formula, m equations are constructed, and 4 boundary conditions at the start and end times are added, that is, the velocity and acceleration of the start and target points are zero, and a total of m+4 equations are constructed to obtain the control point d iThe unique solution for (i=0,1,...,n).

[0078] When P(u) is used as the joint position vector, It represents the curve of the joint position. Since the B-spline curve has C k-1 The continuous property is that we only need to differentiate both sides of the formula to obtain the velocity, acceleration and jerk curves of each joint, which are respectively related to the α-order derivative P of the B-spline curve. α (u)(α=1,2,3) corresponds to P α (u) are as follows:

[0079]

[0080] According to the De Boer formula, we can get:

[0081]

[0082] 5. Use the snake optimization algorithm to perform time-energy-impact multi-objective optimization on the trajectory of the continuous casting ladle robot arm. The snake optimization algorithm is used to optimize the quintic B-spline curve. The main steps of the snake optimization algorithm are as follows:

[0083] (1) Initialize the snake optimization algorithm population and set the algorithm parameters:

[0084] In the snake optimization algorithm, the individual X in the population represents the time solution corresponding to the path point of the B-spline function; first, the snake optimization algorithm is initialized, and the population number of the snake optimization algorithm is set to N = 50, the threshold of food Q is Q0 = 0.25, the threshold of temperature Temp is Temp0 = 0.6, and the maximum number of iterations is q max = 100. The position formula of the initial population individuals is as follows:

[0085] X i =X min +r×(X max -X min )

[0086] Among them, X i (i=1,2,...,N) represents the position of individual i in the population, r represents a random number between 0 and 1, X min represents the lower bound of the individual position in the algorithm, X min =min(Δt i )(i=1,2,...,m-1),X max represents the upper bound of the individual position in the algorithm, X max =max(Δt i )(i=1,2,...,m-1).

[0087] (2) All individuals are divided into males and females. The grouping formula is as follows:

[0088] N ma =round(N / 2)

[0089] N fe =NN ma

[0090] Among them, N ma Represents the number of male individuals, N fe represents the number of female individuals, and the round(·) function represents rounding.

[0091] (3) Determine the ambient temperature and food quantity of the snake optimization algorithm. The calculation formulas for temperature Temp and food quantity Q are as follows:

[0092]

[0093]

[0094] Wherein, q represents the current number of iterations, c1 is a constant, and c1=0.5 is taken.

[0095] (4) When Q<0.25, it enters the exploration phase, which represents environmental factors, namely cold places and food. If the temperature is below Q0 and there is enough food, mating will occur, otherwise the snake will only look for food or eat the remaining food. The snake optimization algorithm searches for food by selecting any random position and updating their position relative to it. The random search formula is:

[0096] X i,ma (q+1)=X rand1,ma (q)±c2×A ma ×((X max -X min )×rand(·)+X min )

[0097]

[0098] X i,fe (q+1)=X rand1,fe (q)±c2×A fe ×((X max -X min )×rand(·)+X min )

[0099]

[0100] Among them, X i,ma and X i,fedenote the position of individual i in the male and female populations, respectively, and denote the positions of random males and females in the population, respectively. rand(·) is a random function between 0 and 1. A ma and A fe represent the ability of males and females to find food, respectively, rand1,ma express The fitness of express The fitness, f i,ma and f i,fe Represent the fitness of individual i in the male and female populations respectively, c2 is a constant, and c2=0.05 is taken.

[0101] (5) When Q>0.25, Temp>0.6, the snake enters the development stage of approaching food mode. When food is available but the temperature is high, the snake will only focus on eating the available food. The position update formula is as follows:

[0102] X i,j (q+1)=X food ±c3×Temp×rand(·)×(X food -X i,j (q))

[0103] Among them, X i,j Indicates the position of male or female individuals, X food represents the position of the optimal individual, c3 is a constant, and c3=2.

[0104] (6) When Q>0.25, Temp<0.6, if food is available and the area is cold, the mating process will occur; the mating process is divided into fighting mode or mating mode. In the fighting mode, each male will fight for the best female, and each female will try to choose the best male. The fighting mode update formula is as follows:

[0105] X i,ma (q+1)=X i,ma (q)+c3×F ma ×rand(·)×(Q×X best,fe -X i,ma (q))

[0106] X i,fe (q+1)=X i,fe (q)+c3×F fe ×rand(·)×(Q×X best,ma -X i,fe (q))

[0107]

[0108]

[0109] Among them, X best,ma and X best,fe Represent the positions of the best individuals in the male and female populations, respectively, and F ma and F fe Represents the fighting ability of males and females, respectively, i represents the fitness of individuals in the population, f best,ma and f best,fe Represent the fitness of the best individuals in the male and female populations respectively.

[0110] (7) In the mating mode, the occurrence of mating between each pair is related to the availability of food. The mating mode update formula is as follows:

[0111] X i,ma (q+1)=X i,ma (q)+c3×M ma ×rand(·)×(Q×X i,fe (t)-X i,ma (q))

[0112] X i,fe (q+1)=X i,fe (q)+c3×M fe ×rand(·)×(Q×X i,ma (q)-X i,fe (q))

[0113]

[0114]

[0115] X worst,ma =X min +rand(·)×(X max -X min )

[0116] X worst,fe =X min +rand(·)×(X max -X min )

[0117] Among them, M ma and M fe represent the mating ability of males and females, respectively, X worst,ma and X worst,fe Represents the position of the worst individuals in the male and female populations, respectively.

[0118] The optimization targets of the snake optimization algorithm are set as time S1, energy S2, and impact S3. By optimizing the time target, the working efficiency of the robot arm is improved; by optimizing the energy index, the energy consumption of the robot arm is reduced; by optimizing the impact index, the smoothness of the trajectory is improved. The specific definitions are as follows:

[0119]

[0120]

[0121]

[0122] Where m represents the number of trajectory points (obtained by the RRT* algorithm), i represents the i-th trajectory point, and t i (i=1,2,…,m) represents the time corresponding to the i-th trajectory point, Δt i represents the time taken for the i-th trajectory; M = 6, represents the number of degrees of freedom of the robot arm, a li represents the acceleration of the i-th trajectory of the l-th joint, j li Represents the jerk of the i-th trajectory of the l-th joint.

[0123] The kinematic constraints are the velocity, acceleration, and jerk of the starting point, intermediate path points, and target point of the motion trajectory, and the velocity, acceleration, and jerk are kept continuous. The constraints are defined as follows:

[0124] |v li (t)|=|P'(t)| <v max

[0125] |a li (t)|=|P”(t)| max

[0126] |j li (t)|=|P (3) (t)|<j max

[0127] where t∈[t1,t2,…,t m ],v max is the maximum speed of the joint during operation, here we take v max =100° / s, a max is the maximum acceleration of the joint during operation, here we take a max =100° / s 2 , j max is the maximum jerk of the joint during operation, where j is taken max =400° / s 3 .

[0128] ​Using the exterior point penalty function method, the penalty function is defined as:

[0129]

[0130] Among them, S pun The initial value is set to 0; when v li (t), a li (t) and j li (t) respectively exceeds the constraint value v max 、a max and j max When S pun Gradually increase.

[0131] The fitness function of the snake optimization algorithm is taken as:

[0132]

[0133] Set the penalty coefficient in the fitness function to k pun , the time coefficient is k t , the energy coefficient is k mj , the smoothness coefficient is k j , respectively assigned to k pun =400,k t =56,k mj =0.2,k j =1050.

[0134] The snake optimization algorithm is used to perform multi-objective optimization on the trajectory of the continuous casting ladle robot arm, and the optimal male position X is obtained by iterative calculation. best,ma and the optimal female position X best,fe , compare the fitness of individuals in the population, and take the individual position with the smallest fitness as the optimal individual position X food , determine whether the maximum number of iterations has been reached. If not, the number of iterations q = q + 1, return to step (3), repeat the main loop, iteratively calculate the amount of food Q and the temperature Temp, update the position of the next generation of individuals and calculate the fitness; after reaching the maximum number of iterations, the fitness function change curve, the trajectory running total time change curve, the robot arm energy mean change curve, and the robot arm impact mean change curve of the snake optimization algorithm are obtained, respectively as follows: Figure 3-6 As shown; update the time information in the B-spline curve to obtain the optimized position, speed, acceleration and jerk curves of each joint of the continuous casting ladle robot arm, as shown Figure 7-12 As shown in the figure, the final optimized trajectory of the continuous casting ladle robot arm shortened the total time by 6.6%, reduced the energy mean by 43.4%, and reduced the impact mean by 1.3%.

[0135] The technical solutions of the present invention can also be appropriately combined to form other implementation plans that can be understood by those skilled in the art. All equivalent changes made according to the claims of this patent are within the protection scope of the claims of this application.

[0136] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective optimization method for the trajectory of a continuous casting ladle robot based on a snake optimization algorithm, characterized in that The following steps are involved: Step 1: According to the basic tasks of the actual process of the continuous casting ladle robot arm and the actual situation of the continuous casting site, the working space of the continuous casting ladle robot arm is constructed, and the positions of the starting point of the robot arm path, environmental obstacles and target points are determined; Step 2: Plan the path of the continuous casting ladle robot arm using the RRT* algorithm with obstacle avoidance to obtain the shortest path from the starting point to the target point of the continuous casting ladle robot arm; Step 3: for the obtained shortest path of the continuous casting ladle robot arm, a quintic B-spline function is used to smooth it, and the initial time information is added to the path point sequence to plan the trajectory of the robot arm; Step 4, taking the speed, acceleration and jerk of each joint of the robot as constraints, based on the snake optimization algorithm, multi-objective optimization is performed on the running time, energy and impact of the robot trajectory, and the fitness function of the snake optimization algorithm, the total trajectory running time, the mean energy of the robot, and the mean impact of the robot are obtained; the time information of the control point is updated in the B-spline function to obtain the position, speed, acceleration and jerk curves of each joint of the continuous casting ladle robot after optimization.

2. The multi-objective optimization method for continuous casting ladle robot arm trajectory based on snake optimization algorithm according to claim 1 is characterized in that: In step 1, the basic process task of the continuous casting ladle robot arm is: after setting the starting point, environmental obstacles and target point according to the process requirements and actual site conditions, the continuous casting ladle robot arm first takes the process object from the starting point, bypasses the environmental obstacles, and then places the process object at the target point.

3. The multi-objective optimization method for continuous casting ladle robot arm trajectory based on snake optimization algorithm according to claim 1 is characterized in that: In step 2, in the RRT* algorithm, the next node of the current node is screened by detecting obstacles, the parent node and the next path are reselected, the target direction of the path is optimized, and the shortest path of the robot arm is obtained; in the path planning of the continuous casting ladle robot arm, the robot arm joints are equivalent to cylindrical envelopes, and the obstacles are equivalent to spherical envelopes. It is determined whether the cylinder and the sphere intersect, and the flag is set to 0 when there is no collision and to 1 when there is a collision. If there is no collision, the node is retained.

4. The multi-objective optimization method for continuous casting ladle robot arm trajectory based on snake optimization algorithm according to claim 1 is characterized in that: In step 3, based on the m path point sequence of the continuous casting ladle robot obtained by the above RRT* algorithm, the path is smoothed using a 5th-order B-spline curve, and time information is added to the path point sequence, thereby converting the path planning problem into a trajectory planning problem; the B-spline function is Among them, d i (i=0,1,...,n;n=m+3) are the coordinates of the control points, N i,k (i=0,1,...,n) is the basis function of the i-th k-order B-spline curve, and k is taken as 5.

5. The multi-objective optimization method for continuous casting ladle robot trajectory based on snake optimization algorithm according to claim 1 is characterized in that: In step 4, the snake optimization algorithm is adopted. When setting the algorithm parameters, first, the algorithm is initialized. The population size is determined as N, the threshold of the food quantity Q is set as Q0, and the threshold of the temperature Temp is set as Temp0. The individual X in the population represents the time solution corresponding to the path points of the B-spline function. Secondly, all individuals are grouped into males and females evenly. Then, the food quantity Q and the temperature Temp are iteratively calculated. When Q < Q0, it enters the exploration stage. In the exploration stage, the snake only searches for food around, searches for food by choosing any random position, and updates their positions relative to it, and iteratively calculates the optimal male position X i,ma and the optimal female position X i,fe ; when Q > Q0 and Temp > Temp0, it enters the feeding mode in the exploitation stage. In the case where food is available but the temperature is high, the snake only focuses on eating the available food. At this time, the position X of male or female individuals is iteratively calculated i,j ; when Q > Q0 and Temp < Temp0, it enters the mating mode in the exploitation stage. The mating process is divided into a battle mode or a mating mode. In the battle mode, each male fights for the best female, and each female tries to choose the best male. At this time, X i,ma and X i,fe are iteratively calculated. In the mating mode, mating occurs between each pair and is related to the availability of the food quantity. At this time, the worst male position X worst,ma and the worst female position X worst,fe are calculated and X i,ma and X i,fe are iteratively calculated; The optimization objectives of the snake optimization algorithm are set as the time S1, energy S2, and impact S3 from the initial point to the target point, which are defined as follows: Where m represents the number of trajectory points, obtained by the RRT* algorithm, i represents the i-th trajectory point, and t i (i=1,2,…,m) represents the time corresponding to the i-th trajectory point, Δt i represents the time taken for the i-th trajectory, a li represents the acceleration of the i-th trajectory of the l-th joint, j li represents the jerk of the i-th trajectory of the l-th joint, M = 6, indicating that the robot arm has six degrees of freedom; The kinematic constraints are the velocity, acceleration, and jerk of the starting point, intermediate path points, and target point of the motion trajectory, and the velocity, acceleration, and jerk are kept continuous. The constraints are defined as follows: |v li (t)|=|P'(t)|<v max |a li (t)|=|P”(t)|<a max |j li (t)|=|P (3) (t)|<j max where t∈[t1,t2,…,t m ],v max is the maximum speed of the joint during operation, a max is the maximum acceleration of the joint during operation, j max is the maximum jerk during joint operation; Using the exterior point penalty function method, the penalty function is defined as: Among them, S pun The initial value is set to 0; when v li (t), a li (t) and j li (t) respectively exceeds the constraint value v max 、a max and j max When S pun gradually increase in size; The fitness function of the snake optimization algorithm is taken as: Set the penalty coefficient in the fitness function to k pun , the time coefficient is k t , the energy coefficient is k mj , the smoothness coefficient is k j , respectively assigned to k pun =400,k t =56,k mj =0.2,k j =1050; The snake optimization algorithm is used to perform multi-objective optimization on the trajectory of the continuous casting ladle robot arm, and the optimal male position X is obtained by iterative calculation. best,ma and the optimal female position X best,fe , compare the fitness of individuals in the population, and take the individual position with the smallest fitness as the optimal individual position X food , determine whether the maximum number of iterations has been reached. If not, add 1 to the number of iterations and return to the main loop to iteratively calculate the amount of food Q and the temperature Temp, update the position of the next generation of individuals and calculate the fitness; after reaching the maximum number of iterations, obtain the fitness function of the snake optimization algorithm, the total trajectory running time, the mean energy of the robotic arm, and the mean impact of the robotic arm; update the time information of the control point in the B-spline function to obtain the position, velocity, acceleration, and jerk curves of each joint of the optimized continuous casting ladle robotic arm.

6. The multi-objective optimization method for continuous casting ladle robot trajectory based on snake optimization algorithm according to claim 5 is characterized in that: In the snake optimization algorithm, the threshold of food quantity Q is Q0=0.25, and the threshold of temperature Temp is Temp0=0.6.

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