CN116652936A - Continuous casting ladle mechanical arm track multi-objective optimization method based on snake optimization algorithm - Google Patents
Continuous casting ladle mechanical arm track multi-objective optimization method based on snake optimization algorithm Download PDFInfo
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Abstract
The application discloses a continuous casting ladle mechanical arm track multi-target optimization method based on a snake optimization algorithm, which belongs to the technical field of continuous casting production process informatization and comprises the following steps: constructing a coordinate space of the six-degree-of-freedom mechanical arm according to the field environment of the continuous casting ladle area, and determining a starting point, an environmental obstacle and a target point of a mechanical arm path; designing a path planning algorithm with obstacle avoidance by utilizing an RRT algorithm to obtain a shortest path; constructing a cubic B spline function, performing smoothing treatment on the path, and adding initial time information into a path point sequence to plan the track of the mechanical arm; and optimizing time information of the track point sequence of the mechanical arm through a multi-target snake optimizing algorithm, so as to realize time-energy-impact multi-target optimization of the track of the mechanical arm. According to the application, the track of the continuous casting ladle mechanical arm is optimized through the snake optimization algorithm, so that the running time of the track of the mechanical arm is shorter, the total energy consumption is lower, the track is smoother, and a good foundation is laid for efficient and safe continuous casting production.
Description
Technical Field
The application belongs to the technical field of informatization in a continuous casting production process, and particularly relates to a continuous casting ladle mechanical arm track multi-objective optimization method based on a snake optimization algorithm.
Background
With the rapid development of informatization and intellectualization in the steel industry, factory unmanned/less unmanned is an important direction of intelligent manufacturing development. Korean pump item steel, japan new day iron, national treasures group, south steel group, first steel transfer, and other steel enterprises, robots are being introduced successively to replace manual work to complete the functions of automatic loading and unloading of large ladle sliding gate hydraulic cylinders, tundish temperature measurement, sampling, covering agent addition, and the like, so that standardized and accurate operation is ensured, and dangerous post manual operation and repeated labor are reduced. At present, the automation degree of continuous casting is greatly improved, but certain difficulties still exist in achieving unmanned casting truly, and a large ladle sliding gate hydraulic cylinder is still needed to be assembled and disassembled manually sometimes. According to the ladle nozzle position environment and the water nozzle changing action flow, the six-degree-of-freedom mechanical arm is adopted to replace a manual loading and unloading ladle sliding nozzle hydraulic cylinder, so that the degree of automation and the production efficiency can be improved, the production risk can be reduced, and the guarantee of the life health safety of workers is enhanced. The mechanical arm is equipment for carrying heavy-duty materials, can meet complex environments such as high temperature, heat radiation, steel splash splashing, equipment layout height staggering and the like in a continuous casting area, can improve operation safety coefficient, effectively avoids safety accidents and improves site operation efficiency. The traditional track planning method adopting polynomial fitting cannot achieve the aim of avoiding obstacles, so that in order to replace the traditional mechanical arm track planning method, and from the aspects of improving efficiency, saving energy and safety and stability, a continuous casting bale mechanical arm track multi-target optimization method based on a snake optimization algorithm with the shortest time, the smallest energy and the smallest impact as targets can be adopted.
Disclosure of Invention
The application aims to provide a continuous casting ladle mechanical arm track multi-objective optimization method based on a snake optimization algorithm so as to solve the problems in the background technology.
In order to achieve the above purpose, the present application provides the following technical solutions:
a continuous casting ladle mechanical arm track multi-target optimization method based on a snake optimization algorithm comprises the following steps:
step 1, constructing a working space of a continuous casting ladle mechanical arm according to the actual process basic task of the continuous casting ladle mechanical arm and combining with the actual continuous casting site, and determining the positions of a starting point, an environmental obstacle and a target point of a mechanical arm path;
step 2, planning a path of the continuous casting ladle mechanical arm by utilizing an RRT algorithm with obstacle avoidance, and obtaining the shortest path from a starting point to a target point of the continuous casting ladle mechanical arm;
step 3, smoothing the shortest path of the obtained continuous casting ladle mechanical arm by adopting a cubic B spline function, and adding initial time information into a path point sequence to plan the track of the mechanical arm;
step 4, taking the speed, the acceleration and the jerk of each joint of the mechanical arm as constraints, and carrying out multi-objective optimization on the running time, the energy and the impact of the track of the mechanical arm based on a snake optimization algorithm to obtain an fitness function, the total track running time, the mechanical arm energy average value and the mechanical arm impact average value of the snake optimization algorithm; and updating time information of the control points in the B spline function to obtain the position, speed, acceleration and jerk curves of all joints of the optimized continuous casting ladle mechanical arm.
The technical scheme of the application is further improved as follows: in the step 1, the basic process tasks of the continuous casting ladle mechanical arm are as follows: after a starting point, an environmental obstacle and a target point are actually set according to process requirements and sites, the continuous casting ladle mechanical arm firstly takes the process object from the starting point, bypasses the environmental obstacle and then places the process object to the target point.
The technical scheme of the application is further improved as follows: in the step 2, in the RRT algorithm, screening the next node of the current node by detecting an obstacle, reselecting a father node and the next path, and optimizing the target direction of the path to obtain the shortest path of the mechanical arm; in the path planning of the continuous casting ladle mechanical arm, the mechanical arm joint is equivalent to a cylinder enveloping object, the obstacle is equivalent to a spherical enveloping object, whether the cylinder and the sphere intersect or not is judged, the zone bit is set to 0 when no collision occurs, the zone bit is set to 1 when collision occurs, and if no collision occurs, the node is reserved.
The technical scheme of the application is further improved as follows: step 3, obtaining m path point sequences of the continuous casting ladle mechanical arm according to an RRT (remote radio unit) algorithm, smoothing the path by using a 5-time B spline curve, and adding time information into the path point sequences so as to convert a path planning problem into a track planning problem; the B spline function isWherein d i (i=0, 1,) N; n=m+3) is the control point coordinates, N i,k (i=0, 1,., n) is the basis function of a k-th order B-spline curve, k being taken as 5.
The technical scheme of the application is further improved as follows: in step 4, the adopted snake optimization algorithm is firstly initialized when algorithm parameters are set, the population number is determined to be N, and the threshold value of the food quantity Q is set to be Q 0 Setting the threshold of the temperature Temp as Temp 0 The individuals X in the population represent the time solutions corresponding to the path points of the B spline function; secondly, grouping all individuals, and equally dividing the individuals into males and females; then iteratively calculating the food quantity Q and the temperature Temp when Q<Q 0 When the search phase is entered, the snake searches for food only around it, searches for food by selecting any random location and updating their location relative to it, iteratively calculates the optimal male location X i,ma And an optimal female position X i,fe The method comprises the steps of carrying out a first treatment on the surface of the When Q is>Q 0 ,Temp>Temp 0 At the same time, the feeding mode is entered into the development stage, and in the case of food being available but at a high temperature, the snake is only concentrated on eating the available food, and at this time, the position X of the male or female individual is calculated iteratively i,j The method comprises the steps of carrying out a first treatment on the surface of the When Q is>Q 0 ,Temp<Temp 0 When the development stage is started, the mating mode is entered, the mating process is divided into a combat mode or a mating mode, in which each male fights against the best female, each female tries to select the best male, and at this time, the iterative calculation of X is performed i,ma And X i,fe In mating mode, the mating between each pair is related to the availability of the quantity of food, at which time the worst male position X is calculated worst,ma And the worst female position X worst,fe And iteratively calculate X i,ma And X i,fe 。
The optimization targets adopting the snake optimization algorithm are respectively set as the time S from the initial point to the target point 1 Energy S 2 Impact S 3 The definition is as follows:
wherein m represents the track point number, which is obtained by RRT algorithm, i represents the ith track point, t i (i=1, 2, …, m) represents the i-th trace point corresponding time, Δt i Represents the time taken for the ith track segment, a li Acceleration, j, representing the ith trajectory of the ith joint li The jerk of the ith track of the ith joint is represented, m=6, and the mechanical arm is six degrees of freedom;
the kinematic constraint conditions are the speeds, accelerations and jerks of the starting point, the middle path point and the target point of the motion track, and the speeds, accelerations and jerks remain continuous, and the definition constraint conditions are as follows:
|v li (t)|＝|P'(t)|<v max
|a li (t)|＝|P”(t)|<a max
|j li (t)|＝|P (3) (t)|＜j max
wherein t is [ t ] 1 ,t 2 ,…,t m ]，v max Is the maximum speed during the running of the joint, a max Is the maximum acceleration during the running process of the joint, j max Is the maximum jerk in the running process of the joint;
defining a penalty function by using an outlier penalty function method as follows:
wherein S is pun The initial value of (2) 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 At the time S pun Gradually increasing;
the fitness function of the snake optimization algorithm is taken as:
setting the penalty term coefficient in the fitness function as k pun A time coefficient of k t The energy coefficient is k mj A smoothness coefficient of k j Respectively assigned as k pun ＝400,k t ＝56,k mj ＝0.2,k j ＝1050；
Performing multi-objective optimization on the continuous casting ladle mechanical arm track by adopting a snake optimization algorithm, and performing iterative calculation to obtain an optimal male position X best,ma And an optimal female position X best,fe Comparing fitness of individuals in the population, and taking the individual position with the minimum fitness as the optimal individual position X food Judging whether the maximum iteration times are reached, if the maximum iteration times are not reached, adding 1 to the iteration times, returning to a main loop, iteratively calculating the food quantity Q and the temperature Temp, updating the next generation of individual positions and calculating the fitness; after the maximum iteration times are reached, obtaining an fitness function, a track running total time, a mechanical arm energy mean value and a mechanical arm impact mean value of a snake optimizing algorithm; and updating time information of the control points in the B spline function to obtain the position, speed, acceleration and jerk curves of all joints of the optimized continuous casting ladle mechanical arm.
The technical scheme of the application is further improved as follows: in the snake optimization algorithm, the threshold value of the food quantity Q is Q 0 =0.25, threshold of temperature Temp is Temp 0 ＝0.6。
By adopting the technical scheme, the application has the following technical progress:
the application performs path planning on the continuous casting ladle mechanical arm based on an RRT algorithm, and applies an obstacle detection model to obstacle avoidance judgment of the path planning algorithm to obtain a feasible obstacle avoidance path of the continuous casting ladle mechanical arm; and performing track planning on the mechanical arm in joint space based on a quintuple B spline function, solving all control points of the B spline curve according to the existing path point sequence and a boundary equation with the starting point and the speed and acceleration of the target point being 0, and constructing the quintuple B spline function to obtain smoother position, speed, acceleration and jerk curves of all joints of the mechanical arm of the continuous casting ladle.
The multi-objective optimization is carried out on the continuous casting ladle mechanical arm track based on the snake optimization algorithm, and the snake optimization algorithm has higher convergence speed and higher capability of jumping out of local optimization when carrying out mechanical arm track optimization. Selecting time, energy and impact as optimization targets, taking the kinematic constraint of the mechanical arm on speed, acceleration and jerk into consideration, establishing a punishment function by using an external point punishment function method, and obtaining the fitness function, the total track running time, the mechanical arm energy mean value and the mechanical arm impact mean value of a snake optimization algorithm after the maximum iteration times are reached; and updating time information in the B spline curve to obtain the optimized position, speed, acceleration and jerk curve of the continuous casting ladle mechanical arm.
According to the application, the off-line track planning is carried out on the continuous casting ladle mechanical arm, so that the safety of the debugging process is improved, the track points are easy to modify, and the debugging process is accelerated.
Drawings
FIG. 1 is a general flow chart of a continuous casting ladle mechanical arm track multi-objective optimization method based on a snake optimization algorithm;
fig. 2 is a path planning diagram of the RRT algorithm of the present application;
FIG. 3 is a plot of fitness function change for a snake optimization algorithm of the application;
FIG. 4 is a graph of the total time of track movement for the snake optimization algorithm of the application;
FIG. 5 is a graph of the energy mean change of the robotic arm of the snake optimization algorithm of the application;
FIG. 6 is a graph of the variation of the mean value of the impact of a mechanical arm of the snake optimizing algorithm of the application;
FIG. 7 is a graph of position, velocity, acceleration and jerk before and after trajectory optimization for joint 1;
FIG. 8 is a graph of position, velocity, acceleration and jerk before and after trajectory optimization for joint 2;
FIG. 9 is a graph of position, velocity, acceleration and jerk before and after trajectory optimization for joint 3;
FIG. 10 is a graph of position, velocity, acceleration and jerk before and after trajectory optimization for joint 4;
FIG. 11 is a graph of position, velocity, acceleration and jerk before and after trajectory optimization for joint 5;
fig. 12 is a graph of position, velocity, acceleration and jerk before and after trajectory optimization of joint 6.
Detailed Description
According to the embodiment of the application, by providing the continuous casting ladle mechanical arm track multi-objective optimization method based on the snake optimization algorithm, the automation degree and the production efficiency in the process can be improved, the production risk is reduced, the manual operation and the repeated labor of dangerous posts are effectively reduced, and the guarantee of the life health safety of workers is enhanced. The general idea is as follows: the path planning of the continuous casting ladle mechanical arm is realized by utilizing an RRT algorithm, the path planning of the continuous casting ladle mechanical arm is realized by utilizing a quintic B spline function, the time-energy-impact multi-objective optimization of the continuous casting ladle mechanical arm path is realized by utilizing a snake optimization algorithm, and a solid foundation is laid for the efficient production of continuous casting and continuous rolling.
The application is described in further detail below with reference to the attached drawings and examples:
as shown in fig. 1, the continuous casting ladle mechanical arm track multi-objective optimization method based on the snake optimization algorithm comprises the following steps:
step 1, constructing a working space of a continuous casting ladle mechanical arm according to the actual process basic requirements of the continuous casting ladle mechanical arm and combining with the actual continuous casting site, and determining the positions of a hydraulic cylinder interface at a transfer table, a ladle bottom hydraulic cylinder tray and a preset environmental obstacle;
step 2, selecting a hydraulic cylinder interface at a middle rotary table as a starting point, and a hydraulic cylinder tray at the bottom of a ladle as a target point, and planning a path of a continuous casting ladle mechanical arm by utilizing an RRT (progressively optimal rapid expansion random tree, asymptotically Optimal Rapidly-Exploring Random Trees) algorithm with obstacle avoidance to obtain the shortest path of the continuous casting ladle mechanical arm (shown in figure 2);
step 3, smoothing the shortest path of the obtained continuous casting ladle mechanical arm by adopting a cubic B spline function, and adding initial time information into a path point sequence to plan the track of the mechanical arm;
step 4, taking the speed, the acceleration and the jerk of each joint of the mechanical arm as constraints, and carrying out multi-objective optimization on the running time, the energy and the impact of the track of the mechanical arm based on a snake optimization algorithm to obtain an fitness function, the total track running time, the mechanical arm energy average value and the mechanical arm impact average value of the snake optimization algorithm; and updating time information of the control points in the B spline function to obtain the position, speed, acceleration and jerk curves of all joints of the optimized continuous casting ladle mechanical arm.
Examples:
1. basic process task for determining continuous casting ladle mechanical arm
The basic process tasks of the continuous casting ladle mechanical arm are as follows: the continuous casting ladle mechanical arm firstly takes a hydraulic cylinder from a middle turntable tray, bypasses environmental barriers such as an oil gas medium coupler and the like of a continuous casting site, and then places the hydraulic cylinder on a ladle bottom hydraulic cylinder tray, wherein a hydraulic cylinder interface at the middle turntable is used as a starting point, and the ladle bottom hydraulic cylinder tray is used as a target point; the inverse task is as follows: the continuous casting ladle mechanical arm takes the hydraulic cylinder from the ladle bottom hydraulic cylinder tray, bypasses environmental barriers such as an oil gas medium coupler and the like of a continuous casting site, and then places the hydraulic cylinder on the hydraulic cylinder tray at the transfer station, wherein the ladle bottom hydraulic cylinder interface is used as a starting point, and the hydraulic cylinder tray at the transfer station is used as a target point.
2. Working space for constructing continuous casting ladle mechanical arm
According to the basic requirements of the actual process of the continuous casting ladle mechanical arm, combining with the actual continuous casting site, constructing the working space of the continuous casting ladle mechanical arm, and determining the positions of a hydraulic cylinder interface at a transfer table, a ladle bottom hydraulic cylinder tray and a preset environmental obstacle;
3. path planning is carried out on the continuous casting ladle mechanical arm
And selecting a hydraulic cylinder interface at the position of the transfer platform as a starting point, and planning a path of the continuous casting ladle mechanical arm by using an RRT algorithm with obstacle avoidance by using a ladle bottom hydraulic cylinder tray as a target point so as to achieve the aim of planning the shortest path. The RRT algorithm flow is as follows:
(1) Setting a boundary space, and generating a global random node x by using a uniform random distribution function rand ；
(2) Solving the distance from the random point to each node on the tree, finding the distance from the random point to x rand Node x closest to near And along x rand To x near Direction expanding new node x with fixed step L new Expanding new node x new The formula of (2) is as follows:
(3) The method comprises the following steps of in the path planning of a continuous casting large ladle mechanical arm, enabling a mechanical arm joint to be equivalent to a cylindrical enveloping object, enabling the obstacle to be equivalent to a spherical enveloping object, judging whether the cylindrical object and the spherical object are intersected, setting a zone bit to be 0 when the mechanical arm is not collided, setting the zone bit to be 1 when the mechanical arm is collided, and reserving the node if the mechanical arm is not collided;
(4) With node x new Setting a proximity threshold for the center of a circle, and searching x in a distance range new Adjacent nodes as alternatives x new Is an alternative to the parent node of (a);
(5) To further reduce path cost, rewiring the random tree, and updating the relationship of other nodes in the neighborhood;
(6) Setting a distance threshold disToFind, if the distance between the current path point and the target point is greater than disToFind, jumping to the step (2) to continue the process; if the number of the target points is smaller than disToFind, finding out the target points, and stopping searching to obtain the number m of the path points and the position vector P of each joint at m optimal path points after obstacle avoidance i ＝(p 1i ,p 2i ,p 3i ,p 4i ,p 5i ,p 6i ) (i=1, 2, …, m) (as shown in fig. 2).
4. Track planning is carried out on the continuous casting ladle mechanical arm
By P i ＝(p 1i ,p 2i ,p 3i ,p 4i ,p 5i ,p 6i ) (i=1, 2, …, m) constructing a 5-degree B-spline curve equation, taking 4 boundary conditions that the speed and the acceleration at the starting and ending moments are 0 into consideration, solving n+1 (where n=m+3) control point coordinates of the B-spline curve, and introducing an initial time sequence to plan a track curve of the mechanical arm. The specific process is as follows: the 5 th order B-spline curve is:
wherein d is i (i=0, 1,) N is control point coordinates, N i,k (i=0, 1,., n) is the basis function of a k-th-order (here taken as k=5-th-order) B-spline curve, which is a sequence U: U of a non-decreasing parameter U called a node vector 0 ≤u 1 ≤...≤u n+k+1 The determined k th order piecewise polynomials.
N i,k (u) can be found by the Deboolean formula:
introducing an initial time sequence t 1 ,t 2 ,…,t m ]The position-time sequence of each joint is that,
R＝(P i ,t i )i＝1,2,...,m
will P i Substituting P (u) into the 5-degree B spline function formula to construct m equations, and adding 4 boundary conditions of starting and ending moments, i.e. the speeds and accelerations of the starting point and the target point are zero, constructing m+4 equations altogether, and obtaining a control point d i (i=0, 1,) and n).
When P (u) is the joint position vector,the curve representing the joint position is due to the B-sampleWith a curve C k-1 The continuous property can be obtained by respectively deriving the two sides of the formula to obtain the speed, acceleration and jerk curves of each joint, which are respectively matched with the alpha derivative P of the B spline curve α (u) (α=1, 2, 3), P α (u) the following:
the Deboolean formula can be used to find:
5. the continuous casting ladle mechanical arm track is subjected to time-energy-impact multi-objective optimization by using a snake optimization algorithm, a quintic B spline curve is optimized by using the snake optimization algorithm, and the main steps of the snake optimization algorithm are as follows:
(1) Initializing a snake optimization algorithm population and setting algorithm parameters:
in the snake optimization algorithm, individual X in the population represents a time solution corresponding to a path point of a B spline function; firstly, initializing a snake optimizing algorithm, setting the population number of the snake optimizing algorithm as N=50, and setting the threshold value of food Q as Q 0 Threshold value of temperature temp=0.25 is Temp 0 =0.6, maximum number of iterations q max =100. The positional formula for initializing population individuals is as follows:
X i ＝X min +r×(X max -X min )
wherein X is i (i=1, 2,., N) represents the position of the individual i in the population, r represents a random number between 0 and 1, X min Representing the lower bound, X, of the individual position in the algorithm min ＝min(Δt i )(i＝1,2,...,m-1)，X max Representing the upper bound, X, of the individual position in the algorithm max ＝max(Δt i )(i＝1,2,...,m-1)。
(2) All individuals were grouped and split equally into males and females. The grouping formula is as follows:
N ma ＝round(N/2)
N fe ＝N-N ma
wherein N is ma Represents the number of male individuals, N fe Representing female number of individuals, the round (·) function represents rounded rounding.
(3) The environmental temperature and the food quantity of the snake optimizing algorithm are determined, and the calculation formulas of the temperature Temp and the food quantity Q are as follows:
where q represents the current iteration number, c 1 Taking c as a constant 1 ＝0.5。
(4) When Q is<0.25, the exploration phase is entered, which represents environmental factors, i.e. cold places and foods, if the temperature is lower than Q 0 Mating can occur if the food is sufficient, otherwise the snake will only look for food or eat the rest of the food. The snake optimization algorithm searches for food and updates their position relative to it by selecting any random position, the random search formula:
X i,ma (q+1)＝X rand1,ma (q)±c 2 ×A ma ×((X max -X min )×rand(·)+X min )
X i,fe (q+1)＝X rand1,fe (q)±c 2 ×A fe ×((X max -X min )×rand(·)+X min )
wherein X is i,ma And X i,fe The positions of individuals i in the male and female populations are indicated respectively,and->Respectively representing the positions of random male individuals and random female individuals in the population, wherein the rand (·) is a random function between 0 and 1, A ma And A fe Indicating the ability of male and female, respectively, to find food, f rand1,ma Representation->Is adaptive to->Representation->Adaptation degree f of (f) i,ma And f i,fe Respectively representing the fitness of individuals i in male and female populations, c 2 Taking c as a constant 2 ＝0.05。
(5) When Q >0.25, temp >0.6, enter the near food mode of the development phase, where the snake will only concentrate on eating the available food, but at a high temperature, the location update formula is as follows:
X i,j (q+1)＝X food ±c 3 ×Temp×rand(·)×(X food -X i,j (q))
wherein X is i,j Represents the position of a male or female individual, X food Representing the position of the optimal individual, c 3 Taking c as a constant 3 ＝2。
(6) When Q >0.25, temp <0.6, if food is available and the area is cold, this can lead to mating process occurring; the mating process is classified into a combat mode or a mating mode. In combat mode, each male fights for the best female, each female tries to select the best male, and the combat mode update formula is as follows:
X i,ma (q+1)＝X i,ma (q)+c 3 ×F ma ×rand(·)×(Q×X best,fe -X i,ma (q))
X i,fe (q+1)＝X i,fe (q)+c 3 ×F fe ×rand(·)×(Q×X best,ma -X i,fe (q))
wherein X is best,ma And X best,fe Representing the location of the optimal individual in the male and female populations, respectively, F ma And F fe Respectively represent the combat competence of male and female, f i Representing fitness of individuals in the population, f best,ma And f best,fe Indicating fitness of the optimal individuals in the male and female populations, respectively.
(7) In mating mode, the occurrence of mating between each pair of pairs is related to the availability of the number of foods, and the mating mode update formula is as follows:
X i,ma (q+1)＝X i,ma (q)+c 3 ×M ma ×rand(·)×(Q×X i,fe (t)-X i,ma (q))
X i,fe (q+1)＝X i,fe (q)+c 3 ×M fe ×rand(·)×(Q×X i,ma (q)-X i,fe (q))
X worst,ma ＝X min +rand(·)×(X max -X min )
X worst,fe ＝X min +rand(·)×(X max -X min )
wherein M is ma And M fe Respectively represents mating ability of male and female, X worst,ma And X worst,fe The position of the worst individual in the male and female populations, respectively.
Setting optimization targets of the snake optimization algorithm as time S respectively 1 Energy S 2 Impact S 3 The working efficiency of the mechanical arm is improved by optimizing the time target; the energy consumption of the mechanical arm is reduced by optimizing the energy index; by optimizing the impact index, the smoothness of the track is improved. The specific definition is as follows:
where m represents the number of track points (obtained by RRT algorithm), i represents the ith track point, t i (i=1, 2, …, m) represents the i-th trace point corresponding time, Δt i Representing the time taken by the ith track; m=6, the number of degrees of freedom of the mechanical arm, a li Acceleration, j, representing the ith trajectory of the ith joint li The jerk of the ith track of the ith joint is shown.
The kinematic constraint conditions are the speeds, accelerations and jerks of the starting point, the intermediate path point and the target point of the motion trajectory, and the speeds, accelerations and jerks remain continuous. The constraint is 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
wherein t is [ t ] 1 ,t 2 ,…,t m ]，v max Is the maximum speed during the running process of the joint, and v is taken here max ＝100°/s，a max Is the maximum acceleration during the running process of the joint, and a is taken here max ＝100°/s 2 ，j max Is the maximum jerk during the joint operation, where j is taken max ＝400°/s 3 。
Defining a penalty function by using an outlier penalty function method as follows:
wherein S is pun The initial value of (2) 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 At the time S pun Gradually increasing.
The fitness function of the snake optimization algorithm is taken as:
setting the penalty term coefficient in the fitness function as k pun A time coefficient of k t The energy coefficient is k mj A smoothness coefficient of k j Respectively assigned as k pun ＝400,k t ＝56,k mj ＝0.2,k j ＝1050。
Performing multi-objective optimization on the continuous casting ladle mechanical arm track by adopting a snake optimization algorithm, and performing iterative calculation to obtain an optimal male position X best,ma And an optimal female position X best,fe Comparing fitness of individuals in the population, and taking the individual position with the minimum fitness as the optimal individual position X food Judging whether the maximum iteration number is reachedIf the maximum iteration number is not reached, the iteration number q=q+1 returns to the step (3), the main cycle is repeated, the food quantity Q and the temperature Temp are calculated iteratively, the next generation of individual position is updated, and the fitness is calculated; after the maximum iteration times are reached, obtaining an fitness function change curve, a track running total time change curve, a mechanical arm energy mean change curve and a mechanical arm impact mean change curve of a snake optimization algorithm, wherein the fitness function change curve, the track running total time change curve, the mechanical arm energy mean change curve and the mechanical arm impact mean change curve are respectively shown as figures 3-6; and updating time information in the B spline curve to obtain the position, speed, acceleration and jerk curves of all joints of the optimized continuous casting ladle mechanical arm, as shown in figures 7-12. And finally, the optimized continuous casting bale mechanical arm track shortens the total time by 6.6%, reduces the energy mean value by 43.4%, and reduces the impact mean value by 1.3%.
The technical solutions of the present application may be appropriately combined to form other embodiments that can be understood by those skilled in the art, and all equivalent changes made according to the patent claims are the scope of the claims of the present application.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present application, and not for limiting the same; although the application has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the application.
Claims (6)
1. A continuous casting ladle mechanical arm track multi-target optimization method based on a snake optimization algorithm is characterized by comprising the following steps:
step 1, constructing a working space of a continuous casting ladle mechanical arm according to the actual process basic task of the continuous casting ladle mechanical arm and combining with the actual continuous casting site, and determining the positions of a starting point, an environmental obstacle and a target point of a mechanical arm path;
step 2, planning a path of the continuous casting ladle mechanical arm by utilizing an RRT algorithm with obstacle avoidance, and obtaining the shortest path from a starting point to a target point of the continuous casting ladle mechanical arm;
step 3, smoothing the shortest path of the obtained continuous casting ladle mechanical arm by adopting a cubic B spline function, and adding initial time information into a path point sequence to plan the track of the mechanical arm;
step 4, taking the speed, the acceleration and the jerk of each joint of the mechanical arm as constraints, and carrying out multi-objective optimization on the running time, the energy and the impact of the track of the mechanical arm based on a snake optimization algorithm to obtain an fitness function, the total track running time, the mechanical arm energy average value and the mechanical arm impact average value of the snake optimization algorithm; and updating time information of the control points in the B spline function to obtain the position, speed, acceleration and jerk curves of all joints of the optimized continuous casting ladle mechanical arm.
2. The continuous casting ladle manipulator track multi-objective optimization method based on the snake optimization algorithm as claimed in claim 1, wherein the method is characterized in that: in the step 1, the basic process tasks of the continuous casting ladle mechanical arm are as follows: after a starting point, an environmental obstacle and a target point are actually set according to process requirements and sites, the continuous casting ladle mechanical arm firstly takes the process object from the starting point, bypasses the environmental obstacle and then places the process object to the target point.
3. The continuous casting ladle manipulator track multi-objective optimization method based on the snake optimization algorithm as claimed in claim 1, wherein the method is characterized in that: in the step 2, in the RRT algorithm, screening the next node of the current node by detecting an obstacle, reselecting a father node and the next path, and optimizing the target direction of the path to obtain the shortest path of the mechanical arm; in the path planning of the continuous casting ladle mechanical arm, the mechanical arm joint is equivalent to a cylinder enveloping object, the obstacle is equivalent to a spherical enveloping object, whether the cylinder and the sphere intersect or not is judged, the zone bit is set to 0 when no collision occurs, the zone bit is set to 1 when collision occurs, and if no collision occurs, the node is reserved.
4. Continuous casting ladle based on snake optimization algorithm as claimed in claim 1The multi-target optimization method for the track of the mechanical arm is characterized by comprising the following steps of: in step 3, on the basis that the m path point sequences of the continuous casting ladle mechanical arm are obtained by the RRT algorithm, smoothing the path by using a 5-time B spline curve, and adding time information into the path point sequences, so that the path planning problem is converted into a track planning problem; the B spline function isWherein d i (i=0, 1,) N; n=m+3) is the control point coordinates, N i,k (i=0, 1,., n) is the basis function of a k-th order B-spline curve, k being taken as 5.
5. The continuous casting ladle manipulator track multi-objective optimization method based on the snake optimization algorithm as claimed in claim 1, wherein the method is characterized in that: in step 4, the adopted snake optimization algorithm is firstly initialized when algorithm parameters are set, the population number is determined to be N, and the threshold value of the food quantity Q is set to be Q 0 Setting the threshold of the temperature Temp as Temp 0 The individuals X in the population represent the time solutions corresponding to the path points of the B spline function; secondly, grouping all individuals, and equally dividing the individuals into males and females; then iteratively calculating the food quantity Q and the temperature Temp when Q<Q 0 When the search phase is entered, the snake searches for food only around it, searches for food by selecting any random location and updating their location relative to it, iteratively calculates the optimal male location X i,ma And an optimal female position X i,fe The method comprises the steps of carrying out a first treatment on the surface of the When Q is>Q 0 ,Temp>Temp 0 At the same time, the feeding mode is entered into the development stage, and in the case of food being available but at a high temperature, the snake is only concentrated on eating the available food, and at this time, the position X of the male or female individual is calculated iteratively i,j The method comprises the steps of carrying out a first treatment on the surface of the When Q is>Q 0 ,Temp<Temp 0 When the development stage is started, the mating mode is entered, the mating process is divided into a combat mode or a mating mode, in which each male fights against the best female, each female tries to select the best male, and at this time, the iterative calculation of X is performed i,ma And X i,fe In mating modeThe mating between each pair is related to the availability of the quantity of food, and the worst male position X is calculated worst,ma And the worst female position X worst,fe And iteratively calculate X i,ma And X i,fe 。
The optimization targets adopting the snake optimization algorithm are respectively set as the time S from the initial point to the target point 1 Energy S 2 Impact S 3 The definition is as follows:
wherein m represents the track point number, which is obtained by RRT algorithm, i represents the ith track point, t i (i=1, 2, …, m) represents the i-th trace point corresponding time, Δt i Represents the time taken for the ith track segment, a li Acceleration, j, representing the ith trajectory of the ith joint li The jerk of the ith track of the ith joint is represented, m=6, and the mechanical arm is six degrees of freedom;
the kinematic constraint conditions are the speeds, accelerations and jerks of the starting point, the middle path point and the target point of the motion track, and the speeds, accelerations and jerks remain continuous, and the definition constraint conditions are as follows:
|v li (t)|＝|P'(t)|<v max
|a li (t)|＝|P”(t)|<a max
|j li (t)|＝|P (3) (t)|＜j max
wherein t is [ t ] 1 ,t 2 ,…,t m ]，v max Is during the operation of the jointMaximum speed, a max Is the maximum acceleration during the running process of the joint, j max Is the maximum jerk in the running process of the joint;
defining a penalty function by using an outlier penalty function method as follows:
wherein S is pun The initial value of (2) 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 At the time S pun Gradually increasing;
the fitness function of the snake optimization algorithm is taken as:
setting the penalty term coefficient in the fitness function as k pun A time coefficient of k t The energy coefficient is k mj A smoothness coefficient of k j Respectively assigned as k pun ＝400,k t ＝56,k mj ＝0.2,k j ＝1050；
Performing multi-objective optimization on the continuous casting ladle mechanical arm track by adopting a snake optimization algorithm, and performing iterative calculation to obtain an optimal male position X best,ma And an optimal female position X best,fe Comparing fitness of individuals in the population, and taking the individual position with the minimum fitness as the optimal individual position X food Judging whether the maximum iteration times are reached, if the maximum iteration times are not reached, adding 1 to the iteration times, returning to a main loop, iteratively calculating the food quantity Q and the temperature Temp, updating the next generation of individual positions and calculating the fitness; after the maximum iteration times are reached, obtaining an fitness function, a track running total time, a mechanical arm energy mean value and a mechanical arm impact mean value of a snake optimizing algorithm; updating time information of control points in the B spline function to obtain the position, speed, acceleration and joint of the optimized continuous casting ladle mechanical armJerk curve.
6. The continuous casting ladle manipulator track multi-objective optimization method based on the snake optimization algorithm as claimed in claim 5, wherein the method is characterized in that: in the snake optimization algorithm, the threshold value of the food quantity Q is Q 0 =0.25, threshold of temperature Temp is Temp 0 ＝0.6。
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| CN117340890A (en) * | 2023-11-22 | 2024-01-05 | 北京交通大学 | Robot motion trail control method |
| CN117885115A (en) * | 2024-03-07 | 2024-04-16 | 中建三局集团有限公司 | Track optimization method and device for multiple optimization targets of welding robot |
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| CN117340890A (en) * | 2023-11-22 | 2024-01-05 | 北京交通大学 | Robot motion trail control method |
| CN117885115A (en) * | 2024-03-07 | 2024-04-16 | 中建三局集团有限公司 | Track optimization method and device for multiple optimization targets of welding robot |
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