Multi-target trajectory planning method and device based on redundant heterogeneous slag leveling robot

Abstract

The invention discloses a multi-target trajectory planning method and device based on a redundant heterogeneous slag leveling robot, and the method comprises the steps: carrying out the population initialization of a dynamic search window based on the guidance of an evaluation mechanism, and generating a certain number of initial paths for the tail end gripper of a mechanical arm of the redundant heterogeneous slag leveling robot as an initial population; based on the initial population, taking a global fitness function as a constraint condition, and adopting an NSGA-II multi-target genetic algorithm to plan a motion track of a redundant heterogeneous slag leveling robot, so that the redundant heterogeneous slag leveling robot rakes the coal slag according to the motion track; the global fitness function includes a path length fitness function, a path smoothness fitness function, and a speed smoothness fitness function. The method can effectively solve the problem of trajectory planning of the robot tail end gripper under complex working conditions.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robots, in particular to a multi-target trajectory planning method and device based on a redundant heterogeneous flat slag robot. BACKGROUND

[0002] Industrial coal furnaces are a kind of furnaces that use coal as fuel to produce heat energy, mainly applied in the steel and iron industries. The combustion of industrial coal furnaces requires continuous feeding, pushing and flat slagging operations by manual labor. However, the working environment in front of the coal furnace has potential hazards such as high temperature, dust and toxic gases. Workers who are in the high temperature zone for a long time and inhale coal dust for a long time are prone to suffer from digestive system or nervous system diseases and serious lung diseases such as pulmonary fibrosis. In order to reduce the health hazards to workers in front of the high temperature furnace, robots in front of the high temperature furnace have been studied at home and abroad. For example, by designing a furnace front operation focusing robot, workers are relieved from the harsh furnace front operation environment, or designing a stable and flexible mechanism to meet the movement and operation requirements of the coal bunker cleaning robot in a narrow space, providing scientific basis and help for the development of future coal bunker cleaning robots, and designing a variable wheel diameter coal mine robot, providing a new idea for the research of future special detection robots and the intelligentization of coal mines.

[0003] Path planning can be divided into global path planning and local path planning. At present, intelligent algorithms applied to path planning mainly include genetic algorithm, particle swarm optimization algorithm, ant colony algorithm, Q-learning algorithm, RRT (rapidly-exploring random tree) algorithm, etc. Different algorithms have advantages and disadvantages. The NSGA-II algorithm has the advantages of strong multi-objective optimization ability, high calculation efficiency and strong robustness, and is applied in various fields such as unmanned aerial vehicle path planning, automatic driving, mobile robot path planning and mechanical arm trajectory optimization.

[0004] Although the NSGA-II algorithm has shown significant advantages in mobile robot path planning, its application scenarios mainly face static environments with low constraint conditions and lack deep optimization of kinematic parameters. SUMMARY

[0005] In order to overcome the shortcomings of the prior art, the purpose of the embodiments of the present application is to provide a multi-target trajectory planning method and device based on a redundant heterogeneous flat slag robot, which can effectively solve the trajectory planning problem of the robot end gripper under complex working conditions.

[0006] To solve the above problems, the first aspect of the embodiments of the present application discloses a multi-target trajectory planning method based on a redundant heterogeneous flat slag robot, comprising:

[0007] The initial population of a certain number of initial paths for the end gripper of the redundant heterogeneous bulldozer robot arm is generated based on a dynamic search window population initialization guided by a judgment mechanism;

[0008] Based on the initial population, the motion trajectory of the redundant heterogeneous bulldozer robot is planned by using a NSGA-II multi-objective genetic algorithm with a global fitness function as a constraint condition, so that the coal slag is raked by the redundant heterogeneous bulldozer robot according to the motion trajectory.

[0009] The global fitness function includes a path length fitness function, a path smoothness fitness function, and a speed smoothness fitness function.

[0010] As a preferred embodiment, in the first aspect of the embodiment of the application, the initial population of a certain number of initial paths for the end gripper of the redundant heterogeneous bulldozer robot arm is generated based on a dynamic search window population initialization guided by a judgment mechanism, which includes:

[0011] S11, the path point of the end gripper corresponding to the starting point of the rake pushing path is taken as the starting point of the gripper path.

[0012] S12, the gripper path point corresponding to the current rake pushing path point is obtained, which is denoted as the current gripper path point.

[0013] S13, a circular search window with a radius R is made at the previous gripper path point, and a circular arc intersecting the current gripper path point in the circular search window is taken as the current gripper target path point.

[0014] S14, the current gripper target path point is evaluated by an evaluation function, the optimal path point is selected when the evaluation function is the minimum, and an initial path is finally generated by continuously iterating the search based on the optimal path point.

[0015] The evaluation function is:

[0016]

[0017] Wherein, f1 and f2 are respectively a path length fitness function and a path smoothness fitness function; f1=d(S i-1 ,S i )+d(S i-1 ',S i '), d(e,f) represents the distance from e to f, S i represents the i-th gripper target path point, i.e. the current gripper target path point, S irepresents the support point path point corresponding to the ith gripper target path point, i.e. the current support point path point, τ1 and τ2 are the path length fitness weight and the path smoothness fitness weight respectively, the values of the gripper radius fitness function f3, the rake rod fitness function f4 and the gripper acceleration fitness function f5 are as follows:

[0018]

[0019] wherein the longitudinal coordinate of the rake rod at the coal furnace opening Gripper radius a is the gripper moving acceleration value, a max is the set maximum acceleration value limiting the gripper movement; x zs and y zs are the horizontal coordinate value and the longitudinal coordinate value of the current gripper target path point, x pz and y pz are the horizontal coordinate value and the longitudinal coordinate value of the current rake path point, d m1 , r m , r2 and θ respectively represent the distance between the maximum working radius of the mechanical arm and the center of the coal furnace, the radius setting value related to the maximum working radius of the mechanical arm, the outer radius of the coal furnace and the furnace opening angle.

[0020] S15, repeatedly performing steps S11-S14 to generate a preset number of initial paths as an initial population.

[0021] As a preferred embodiment, in the first aspect of the embodiment of the present application, the calculation method of the distance d m1 between the maximum working radius of the mechanical arm and the center of the coal furnace comprises:

[0022] Based on the torque constraint analysis of the linkage mechanism of the rake rod and the support point of the rake when the mechanical arm is under maximum stress, the constraint formula of the rake rod length L can be obtained through the stress analysis of the mechanical arm and the rake rod mass calculation formula:

[0023]

[0024] wherein G0 is the upper limit of the weight of the mechanical arm, p is the derivative of the proportion of the inner rod length of the rake rod, and J is the diameter of the rake rod;

[0025] The coordinates of the coal furnace boundary point A and the coal furnace opening lower boundary point B1 are (x a , y a ), (x b1 , y b1 ) respectively, and a functional relationship between the support point orbit radius d2 and the rod length L and p can be established, and then the constraint relationship between d m1 and the rod length L is obtained:

[0026]

[0027] wherein the angle β1 between the line connecting the coal furnace boundary point A and the lower boundary point B1 of the coal furnace opening and the abscissa:

[0028]

[0029] The coordinates of the furthest end C reached by the rake and the upper boundary point B2 of the coal furnace opening are respectively (x c ,y c ), (x b2 ,y b2 ), in order to ensure that the rake can reach the furthest end and the nearest end of the pushing area through any opening position, it is necessary to ensure that the gripper end of the rake is within the working range of the mechanical arm, and thus a constraint relationship between d m1 and the length L of the rod can be established:

[0030] d m1 ≥ L - x b2 -r m (8)

[0031]

[0032] d m1 ≥ L*cos(β3) - x c -r m (10)

[0033] wherein the angle β2 between the line connecting the furthest end C reached by the rake and the upper boundary point B2 of the coal furnace opening and the abscissa, and the angle β3 between the line connecting the furthest end C reached by the rake and the lower boundary point B1 of the coal furnace opening and the abscissa:

[0034]

[0035] The minimum value of the length L of the rod is obtained by minimizing the length L of the rod and the radius d2 of the support point track as the optimization objective, taking formula (5) and formula (6) as the equality constraint, searching for the minimum value of the objective by the NSGA-II algorithm, and obtaining the minimum value of the length L of the rod after optimization by MATLAB.

[0036] The minimum value of L is brought into formula (7)-(10) respectively, and the intersection is taken to obtain the upper and lower boundaries of d m1 , and the midpoint value of the upper and lower boundaries of d m1 is taken as the distance between the final maximum working radius of the mechanical arm and the center of the coal furnace.

[0037] As a preferred embodiment, in the first aspect of the embodiment of the present application, based on the initial population, a global fitness function is used as a constraint condition, and a NSGA-II multi-objective genetic algorithm is used to plan the motion trajectory of the redundant heterogeneous bulldozer robot, so that the coal residue is raked by the redundant heterogeneous bulldozer robot according to the motion trajectory, comprising:

[0038] Based on the initial population of the initial path of the gripper, the initial population of the corresponding support point path is determined;

[0039] Under the premise of meeting the path safety target constraint function, the NSGA-II multi-objective genetic algorithm is used to plan the motion trajectory of the redundant heterogeneous bulldozer robot, so that the path length adaptability function, the path smoothness fitness function, and the speed smoothness fitness function are all minimum values:

[0040]

[0041] Wherein, S zs is the gripper path, S zc is the support point path, and safetypath is the path safety target constraint function; F1, F2, and F3 are the path length adaptability function, the path smoothness fitness function, and the speed smoothness fitness function, respectively.

[0042] As a preferred embodiment, in the first aspect of the embodiment of the present application, the path safety target constraint function safetypath is:

[0043]

[0044] Wherein, the longitudinal coordinate of the rake rod at the opening of the coal furnace The gripper radius x zs and y zs are the horizontal coordinate value and the longitudinal coordinate value of the gripper path point, x pz and y pz are the horizontal coordinate value and the longitudinal coordinate value of the rake path point, d m1 , r m , r2, and θ represent the distance between the maximum working radius of the mechanical arm and the distance from the center of the coal furnace, the radius setting value related to the maximum working radius of the mechanical arm, the outer radius of the coal furnace, and the opening angle of the furnace.

[0045] As a preferred embodiment, in the first aspect of the embodiment of the present application, the path length adaptability function F1 is:

[0046] F1=F zs +F zc

[0047] Wherein, F zsFor the gripper path length:

[0048]

[0049] gripper path S zs ={S1,S2,...,S n}, where n represents the gripper path S zs The total number of nodes in S j Represents the gripper path S zs The j-th path point in the path, x zs (j) represents the gripper path S zs The x-coordinate and y-coordinate of the j-th path point in the equation. zs (j) represents the gripper path S zs The ordinate of the j-th path point in the path;

[0050] F zc Support point path length:

[0051]

[0052] Support point path S zc ={S1',S2',...,S n ′},S j 'Represents the path S of the support point zc The j-th path point in the path, x zc (j) represents the support point path S zc The x-coordinate and y-coordinate of the j-th path point in the equation. zc (j) represents the support point path S zc The ordinate of the j-th path point in the path;

[0053] The path smoothness fitness function F2 is:

[0054]

[0055] Where, γ j Represents the gripper path S zs The turning point at the j-th path point in the path, (S j+1 -S j )·(S j -S j-1 ) represents the vector dot product;

[0056] The speed smoothness fitness function F3 is:

[0057]

[0058] Among them, v zs (j) represents the gripper path S zs The velocity v at the j-th path point in the path. zc(j) represents the support point path S zc The velocity at the j-th path point in the path.

[0059] A second aspect of this invention discloses a multi-objective trajectory planning device based on a redundant heterogeneous slag leveling robot, comprising:

[0060] The generation unit is used for the initialization of the dynamic search window population guided by the evaluation mechanism, and generates a certain number of initial paths for the end gripper of the redundant heterogeneous slag leveling robot as the initial population.

[0061] The planning unit is used to plan the motion trajectory of the redundant heterogeneous slag leveling robot based on the initial population and with the global fitness function as a constraint, using the NSGA-II multi-objective genetic algorithm, so that the redundant heterogeneous slag leveling robot can level the coal slag according to the motion trajectory.

[0062] The global fitness function includes a path length fitness function, a path smoothness fitness function, and a speed smoothness fitness function.

[0063] A third aspect of the present invention discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. When the processor executes the computer program, it implements the steps of the multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot disclosed in the first aspect of the present invention.

[0064] The fourth aspect of this invention discloses a computer-readable storage medium storing a computer program, wherein the computer program causes a computer to perform the steps of the multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot disclosed in the first aspect of this invention.

[0065] The fifth aspect of this invention discloses a computer program product that, when run on a computer, causes the computer to execute the steps of the multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot disclosed in the first aspect of this invention.

[0066] The sixth aspect of this invention discloses an application publishing platform for publishing computer program products. When the computer program product is run on a computer, the computer executes the steps of the multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot disclosed in the first aspect of this invention.

[0067] Compared with the prior art, the beneficial effects of the embodiments of the present invention are as follows:

[0068] In view of the strong coupling multi-constraint requirements (path length, smoothness, safety and speed continuity need to be optimized synchronously) of the end effector trajectory planning of the redundant heterogeneous robot system of the high-temperature furnace, the multi-objective optimization trajectory planning algorithm (denoted as DWDF-NSGA-II algorithm) of dynamic window search and double fitness evaluation mechanism is used; the algorithm effectively solves the trajectory planning problem of the robot end gripper under complex working conditions by constructing a dynamic constraint processing model and a composite fitness function. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 is a flowchart of a multi-objective trajectory planning method based on a redundant heterogeneous flat slag robot provided by the embodiment of the present application;

[0070] Figure 2 is a structural schematic diagram of the overall station layout provided by the embodiment of the present application;

[0071] Figure 3 is a schematic diagram of the available gripper path point provided by the embodiment of the present application;

[0072] Figure 4 is a schematic diagram of the dynamic search window provided by the embodiment of the present application;

[0073] Figure 5 is a schematic diagram of the state of the end gripper under the greatest stress provided by the embodiment of the present application;

[0074] Figure 6 is a schematic diagram of the end gripper under the greatest stress provided by the embodiment of the present application;

[0075] Figure 7 is a schematic diagram of the farthest end and the nearest end of the pushing material provided by the embodiment of the present application;

[0076] Figure 8 is a schematic diagram of the regular pushing material path provided by the embodiment of the present application;

[0077] Figure 9 is a schematic diagram of the irregular pushing material path provided by the embodiment of the present application;

[0078] Figure 10 is a trajectory and speed curve planned by NSGA-II under the regular pushing material path provided by the embodiment of the present application;

[0079] Figure 11 is a trajectory and speed curve planned by NSGA-II under the irregular pushing material path provided by the embodiment of the present application;

[0080] Figure 12 is a trajectory and speed curve planned by DWDF-NSGA-II under the regular pushing material path provided by the embodiment of the present application;

[0081] Figure 13 is a trajectory and speed curve planned by the DWDF-NSGA-II under the irregular pushing path provided by the embodiment of the application;

[0082] Figure 14 is a structural schematic diagram of a multi-objective trajectory planning device based on a redundant heterogeneous flat slag robot. DETAILED DESCRIPTION

[0083] The specific embodiment is only an explanation of the embodiment of the application, and is not a limitation of the embodiment of the application, and those skilled in the art can make modifications to the embodiment without creative contribution according to the needs after reading the specification, but as long as the modifications are within the scope of the claims of the embodiment of the application, they are protected by the patent law.

[0084] The application is a multi-objective optimization trajectory planning algorithm (denoted as DWDF-NSGA-II algorithm) through dynamic window search and double fitness evaluation mechanism; the algorithm effectively solves the trajectory planning problem of the robot end gripper under complex working conditions by constructing a dynamic constraint processing model and a composite fitness function, which is described in detail below in combination with the drawings.

[0085] Embodiment one

[0086] Please refer to Figure 1 , Figure 1 is a flowchart of a multi-objective trajectory planning method based on a redundant heterogeneous flat slag robot according to an embodiment of the application. As shown in the figure, the multi-objective trajectory planning method based on the redundant heterogeneous flat slag robot comprises the following steps. Figure 1

[0087] S110, initialize the population based on the dynamic search window guided by the evaluation mechanism, and generate a certain number of initial paths for the end gripper of the redundant heterogeneous flat slag robot mechanical arm as an initial population.

[0088] The redundant structure trajectory planning requires that the speed of the rake in the furnace be constant when pushing the material along the fixed route, and it is necessary to ensure that the trajectory of the end gripper of the mechanical arm is smooth and continuous, and the speed of the mechanical arm gripper and support point is stable, to prevent sudden changes from causing large joint torque and safety hazards.

[0089] Figure 2 Fig. 1 shows a structural schematic diagram of a redundant heterogeneous flat slag robot raking coal slag; please refer to Figure 2 ​As shown, the entire redundant heterogeneous robot system (e.g., using an IRB4600 industrial robot) consists of a robot body, a robotic arm 20, a circular slide rail 50, a rake (including a rake handle and a rake head) 30, and a rake handle support 40. The robot body moves around the circular slide rail 50 located outside the rake handle support 40. The rake handle support 40 is circular and is set around the periphery of the coal furnace to support the rake handle 30. One end of the rake handle passes through the rake handle support 40 and is fixedly connected to the rake head that extends into the opening of the coal furnace 10. The other end of the rake handle is connected to the end gripper of the robotic arm 20 so that the robotic arm 20 can drive the rake 30 to perform a rakeing operation on the coal slag.

[0090] Population initialization is fundamental to algorithm iteration, and its quality directly affects the convergence speed and the accuracy of the optimal solution. Traditional methods typically construct the initial population by randomly generating initial paths. However, randomly generated paths often contain a large number of invalid nodes and redundant paths, which not only significantly increases computational overhead and reduces algorithm efficiency but also easily leads the algorithm into local optima.

[0091] To address this problem, this invention proposes a dynamic search window population initialization method guided by an evaluation mechanism. This method generates path nodes within a fixed-size circular search window and uses a designed evaluation function to filter the nodes within the window. This significantly improves the quality of the initial population while maintaining population diversity, laying the foundation for efficient convergence of subsequent algorithms. The specific steps for obtaining the initial population are as follows:

[0092] A. Determine the path point of the robotic arm end gripper corresponding to the starting point of the rake pushing path (rake point), and use it as the starting point of the robotic arm end gripper path.

[0093] B. Obtain the available path points of the robotic arm end effector corresponding to a certain rake point, such as... Figure 3 As shown.

[0094] C. At the path point of the robotic arm's end effector gripper, create a circular search window with radius R. The arc segment where this search window intersects with the available robotic arm end effector path point corresponding to the current rake point is used as the available robotic arm end effector path point. The position of the search window will continuously change based on the generated path point of the robotic arm's end effector gripper. For example... Figure 4 As shown. Where R = V max V max This is the maximum speed value set to limit the movement of the robotic arm's end effector.

[0095] D、In order to obtain a higher quality initial path, the application evaluates the mechanical arm gripper path points in the dynamic search window by designing an evaluation function, filters the optimal path point at the minimum of the evaluation function, and iteratively searches on this basis to finally generate a high-quality initial path. The evaluation function is as follows:

[0096] The evaluation function is as follows:

[0097]

[0098] Wherein, f1 and f2 are path length fitness function and path smoothness fitness function respectively; f1=d(S i-1 ,S i )+d(S i-1 ',S i '), d(e,f) represents the distance from e point to f point, S i represents the i-th gripper target path point, i.e. the current gripper target path point, S i ' represents the support point path point corresponding to the i-th gripper target path point, i.e. the current support point path point, τ1 and τ2 are path length fitness weight and path smoothness fitness weight respectively, the values of gripper radius fitness function f3, rake fitness function f4 and gripper acceleration fitness function f5 are as follows:

[0099]

[0100] Wherein the longitudinal coordinate of the rake at the opening of the coal furnace Gripper radius a is the gripper moving acceleration value, a max is the set maximum acceleration value limiting the movement of the gripper; x zs and y zs are the horizontal coordinate value and the vertical coordinate value of the current gripper target path point, x pz and y pz are the horizontal coordinate value and the vertical coordinate value of the current rake path point, d m1 , r m , r2, θ respectively represent the distance between the maximum working radius of the mechanical arm and the center of the coal furnace, the radius setting value related to the maximum working radius of the mechanical arm, the outer radius of the coal furnace, and the opening angle of the furnace.

[0101] E, repeatedly performing steps A-D to generate a preset number of initial paths as an initial population.

[0102] Wherein, the distance between the maximum working radius of the mechanical arm and the center of the coal furnace is determined by constructing a mathematical model.

[0103] The system adopts a scheme of IRB4600 mechanical arm and circular slide rail cooperative configuration, and realizes accurate control of the rake rod by simulating the action of holding with hands. The end effector of the mechanical arm is fixed to the rear end of the rake rod, the front end of the rake rod passes through the guide hole of the support, and the front end of the rake rod can be moved up and down and left and right by controlling the movement of the mechanical arm, so as to complete the pushing operation. When the system needs to carry out large stroke feeding, the mechanical arm and the support can move cooperatively along the circular slide rail, so that the rake can be accurately positioned at any position and direction in space to meet the operation requirements of different areas in the furnace. After completing the pushing operation in the current area, the system exits the rake from the working area through the coordinated movement of the mechanical arm and the support, and moves to the next operation area along the slide rail, realizing continuous automatic pushing operation.

[0104] Known system parameters: the inner circle radius r1 of the furnace is 1.625 m; the outer circle radius r2 is 3.25 m; the central angle of a single furnace space circle is α=π / 3; the opening angle of the furnace is θ=π / 6; the maximum working radius of the IRB4600 mechanical arm is 2.05 m, and when the mechanical arm works along the slide rail, it can work to the inner and outer sides of the circular slide rail, but since the rake rod is connected to the end of the mechanical arm, in order to avoid collision between the rake rod and the mechanical arm, and to enable the rake to completely cover the working area of the coal furnace, the mechanical arm is allowed to move 0.5 meters to the outer side of the circular track, and r m =2.55 m.

[0105] Pending system parameters: the length of the rake rod L is meters, the track radius d1 of the mechanical arm is meters, and the track radius d2 of the support point of the rake rod is meters, and the distance between the maximum working radius of the mechanical arm and the center of the coal furnace is d m1 .

[0106] As shown in Figure 5 , when the rake is located at this position, the mechanical arm reaches the maximum working radius and the gripper is subjected to the maximum force. The red dashed line is the farthest position that the mechanical arm can reach in the circular slide rail.

[0107] As shown in Figure 6 , it is the torque constraint analysis of the rake rod-support point linkage mechanism when the mechanical arm is subjected to the maximum force, and at this time, it is assumed that the upper limit of the weight of the mechanical arm is G0, the derivative of the proportion of the inner side rod length of the support point is p, and the diameter of the rake rod is J.

[0108] Through the force analysis of the mechanical arm and the rake rod mass calculation formula, the constraint formula of the length L of the rake rod can be obtained:

[0109]

[0110] Wherein, G0 is the upper limit of the weight of the mechanical arm, p is the derivative of the proportion of the inner side rod length of the rake rod, and J is the diameter of the rake rod.

[0111] The coordinates of the coal furnace boundary point A and the coal furnace opening lower boundary point B1 are (x a ,y a ), (x b1 ,y b1 ) respectively under the condition of known parameters, and a function relationship between the support point orbit radius d2 and the rod length L and p can be established, and then the constraint relationship between d m1 and the rod length L is obtained:

[0112]

[0113] The angle β1 between the line connecting the coal furnace boundary point A and the coal furnace opening lower boundary point B1 and the horizontal coordinate is:

[0114]

[0115] As shown in Figure 7 , the coordinates of the farthest end C reached by the rake, the nearest end C1 and the coal furnace opening upper boundary point B2 are (x c ,y c ), (x c1 ,y c1 ), (x b2 ,y b2 ) respectively, in order to ensure that the rake rod can reach the farthest end and the nearest end position of the pushing material working area through any opening position, it is necessary to ensure that the gripper end of the rake rod is within the working range of the mechanical arm, and thus the constraint relationship between d m1 and the rod length L can be established:

[0116] d m1 ≥L-x b2 -r m (4)

[0117]

[0118] d m1 ≥L*cos(β3)-x c -r m (6)

[0119] The angle β2 between the line connecting the farthest end C reached by the rake and the coal furnace opening upper boundary point B2 and the horizontal coordinate, and the angle β3 between the line connecting the farthest end C reached by the rake and the coal furnace opening lower boundary point B1 and the horizontal coordinate are:

[0120]

[0121] The optimization target aims to determine a multi-objective optimization function based on a specific mathematical structure and its constraint conditions to achieve the optimal configuration of the mathematical structure parameters. For the design optimization of the rake rod system, the following constraint conditions are mainly considered: during the pushing operation, the load bearing of the end effector of the mechanical arm should not exceed its limit threshold, and at the same time, it is necessary to ensure that the resistance torque under the action of coal residue resistance is within the allowable range. Based on the above constraints, an optimization function is established with the minimum length of the rake rod as the target. For the design optimization of the support point track, two key indicators need to be met: one is to ensure that the working area coverage of the rake is maximized, and the other is to ensure that the load bearing of the end effector of the mechanical arm does not exceed its limit value during the pushing operation. Therefore, the optimization of the support point track radius needs to achieve the minimum design under the premise of meeting the process constraints. By establishing a multi-objective optimization model, the relationship between system performance and structural compactness can be effectively balanced, and the optimization design of the overall system can be realized.

[0122] The present application takes the minimum length of the rod L and the support point track radius d2 as the optimization target, takes formula (1) and formula (2) as the equality constraint, searches for the minimum value of the target by using NSGA-II algorithm, and obtains the parameter variables after optimization by MATLAB, as shown in Table 1.

[0123] Table 1 Structure parameters obtained after optimization

[0124] [G0(N)] p J (mm) L (m) [d2] 40 5 30 4.8022 4.6970

[0125] The minimum value of L is brought into formulas (3), (4), (5) and (6) respectively, and the intersection is taken to obtain 5.3915≤d m1 ≤5.4359, in order to reserve a certain amount of redundancy, therefore, d m1 is taken as the midpoint value of the upper and lower boundaries 5.4137m.

[0126] S120, based on the initial population, a global fitness function is used as a constraint condition, and an NSGA-II multi-objective genetic algorithm is used to plan the motion trajectory of the redundant heterogeneous flat slag robot, so that the coal slag is raked by the redundant heterogeneous flat slag robot according to the motion trajectory; the global fitness function includes a path length adaptability function, a path smoothness fitness function, and a speed smoothness fitness function.

[0127] In the rake rod-support point track linkage mechanism trajectory planning of the present application, the designed fitness function not only needs to accurately reflect the smoothness of the movement of the mechanical arm gripper, but also needs to comprehensively consider the limitation of the coal furnace opening and the maximum working range of the mechanical arm. In order to achieve the goal of linkage structure trajectory planning, the design process of the fitness function is as follows.

[0128] Firstly, the length of the robot end moving path is directly related to the energy consumption efficiency of the robot, so the path length is taken as one of the optimization targets. The path Szs ={S1,S2,...,S} n}, where n represents the gripper path S zs The total number of nodes in S j Represents the gripper path S zs The j-th path point in the path, x zs (j) represents the gripper path S zs The x-coordinate and y-coordinate of the j-th path point in the equation. zs (j) represents the gripper path S zs The ordinate of the j-th path point in the matrix. The path length F of the robotic arm's end effector. zs The expression is:

[0129]

[0130] Similarly, consider the support point path S zc ={S1′,S2′,...,S n Since the support point moves on a circular track, the path length F of the support point is... zc Represented by arc length:

[0131]

[0132] Among them, S j ′ represents the support point path S zc The j-th path point in the path, x zc (j) represents the support point path S zc The x-coordinate and y-coordinate of the j-th path point in the equation. zc (j) represents the support point path S zc The ordinate of the j-th path point.

[0133] From the path expression of the movement of the robotic arm's end effector gripper and support point, the fitness function of the total path length can be obtained:

[0134] F1 = F zs +F zc

[0135] Secondly, the smoother the path of the robotic arm's end effector, the less jitter and energy consumption there will be; therefore, path smoothness is considered as one of the optimization objectives. Since the support point moves on a predetermined track, only the path smoothness of the robotic arm's end effector needs to be considered. In this invention, path smoothness is defined by the average turning angle of the path, as shown in the following expression:

[0136]

[0137] Where, γ j Represents the gripper path S zs The turning point at the j-th path point in the path, (Sj+1 -S j )·(S j -S j-1 ) represents the vector dot product.

[0138] Speed ​​smoothness is a crucial indicator for ensuring safe operation. To prevent large joint torques and safety hazards caused by sudden speed changes during movement, it is necessary to ensure smooth speed between the robotic arm's gripper and support point. In this invention, speed smoothness is measured by the average rate of change of speed at the robotic arm's end effector and support point during operation, as shown in the following expression:

[0139]

[0140] Among them, v zs (j) represents the gripper path S zs The velocity v at the j-th path point in the path. zc (j) represents the support point path S zc The velocity at the j-th path point in the path.

[0141] The path safety objective requires ensuring that, during the process of the robotic arm pushing the rake to level the slag, the rake cannot exceed the limit of the coal furnace opening, and the gripper coordinates cannot exceed the maximum working range of the robotic arm. The corresponding constraint function is:

[0142]

[0143] Among them, the ordinate of the rake at the coal furnace opening. grip radius x zs and y zs x represents the x-coordinate and y-coordinate of the gripper path point. pz and y pz d represents the x and y coordinates of the rake path points. m1 r m r2 and θ represent the distance from the maximum working radius of the robotic arm to the center of the coal furnace, the radius setting related to the maximum working radius of the robotic arm, the outer radius of the coal furnace, and the furnace opening angle, respectively.

[0144] The trajectory planning model for the robotic arm's end effector gripper and support point is as follows:

[0145]

[0146] The specific steps include:

[0147] Based on the initial population of the initial path of the gripper, determine the initial population of the corresponding support point path.

[0148] The NSGA-Ⅱ multi-objective genetic algorithm is used to plan the motion trajectory of the redundant heterogeneous flat slag robot based on the above-mentioned mechanical arm end gripper and support point trajectory planning model.

[0149] In the coal furnace operation scene, first, the rake needs to be planned in the coal furnace working area. In order to effectively avoid the impact problem caused by the acceleration mutation, the S-shaped acceleration and deceleration strategy is integrated into the traditional circular arc interpolation and straight line interpolation method, so that the rake can smoothly transition in the starting and braking stages, and the soft start and stop are realized. In order to verify the effectiveness of the redundant structure trajectory planning algorithm, the present application designs two experimental schemes of regular and irregular material pushing paths. Based on the fusion of S-shaped acceleration and deceleration control strategy, the circular arc interpolation algorithm and the straight line interpolation algorithm are used to plan the trajectory of the above two material pushing paths, and the specific path planning results are as shown in Figures 8-9

[0150] Figure 8 9 Based on the regular and irregular material pushing paths planned respectively, the present application uses the proposed algorithm to plan the redundant structure trajectory of the high-temperature furnace redundant heterogeneous robot system. In order to verify the effectiveness of the proposed algorithm, the traditional NSGA-Ⅱ algorithm is used for comparison experiment.

[0151] The population size of all algorithms is set to N=100, the crossover and mutation probabilities are 0.7 and 0.3 respectively, and the maximum iteration number is 200. In order to reduce the influence of random factors in performance analysis, the running environment is AMD Ryzen75800X 8-core processor, the memory is 16GB, the software running environment is Windows11 system, and the running software is MATLAB 2022a.

[0152] Table 2 shows the comparison of multi-objective fitness values of optimal population individuals under two algorithms (NSGA-Ⅱ algorithm and DWDF-NSGA-II algorithm). From the experimental results in Table 2, compared with the NSGA-Ⅱ algorithm, the DWDF-NSGA-II algorithm proposed in the present application shows significant advantages in planning the redundant structure trajectory based on the two material pushing paths: the obtained redundant structure trajectory has shorter path length, higher path smoothness and better speed continuity.

[0153] Table 2 Comparison of multi-objective fitness values of optimal population individuals under two algorithms

[0154]

[0155] Figure 10 Figures 7 and 8 respectively show the trajectory and speed curve planned by NSGA-II under the regular material pushing path and the irregular material pushing path, Figure 11 Figure 12 Figure 13 ​​​​​Trajectories and velocity curves of the DWDF-NSGA-II planned under the regular pushing path and the irregular pushing path are shown respectively.

[0156] The obtained trajectory and velocity curve show that the path of the mechanical arm gripper planned by the traditional algorithm changes sharply, and mutations occur at many places, lacking the required smooth transition, and the overall smoothness is difficult to meet the requirements, and the continuity and stability of the motion cannot be guaranteed. Figures 10-13 The velocity curve corresponding to the mechanical arm gripper path has a large amplitude mutation, further increasing the difficulty of motion control. The motion trajectory of the mechanical arm end gripper obtained by the improved algorithm is smoother than that of the traditional algorithm. From the velocity change graph, although there is continuous and continuous micro-fluctuation in the velocity-time image, the fluctuation amplitude is in the millimeter level, which is within the tolerance range allowed by the current process. And this algorithm effectively reduces the speed mutation degree of the mechanical arm gripper when working at the opening of the coal furnace, thereby greatly avoiding the occurrence of large joint torque caused by speed mutation, and ensuring the stable operation of the mechanical arm in complex working conditions.

[0157] Embodiment two

[0158] Please refer to Figure 14 , Figure 14 is a structural schematic diagram of a multi-target trajectory planning device based on a redundant heterogeneous flat slag robot disclosed by the embodiment of the present application. As Figure 14 shown, the multi-target trajectory planning device based on the redundant heterogeneous flat slag robot can include:

[0159] The generating unit 210 is configured to initialize a dynamic search window population based on a judgment mechanism, and generate a certain number of initial paths for the end gripper of the redundant heterogeneous flat slag robot as an initial population.

[0160] The planning unit 220 is configured to plan the motion trajectory of the redundant heterogeneous flat slag robot based on the initial population and using the NSGA-II multi-objective genetic algorithm with the global fitness function as a constraint condition, so that the coal slag is raked by the redundant heterogeneous flat slag robot according to the motion trajectory.

[0161] The global fitness function includes a path length adaptability function, a path smoothness fitness function, and a velocity smoothness fitness function.

[0162] The above describes in detail a multi-target trajectory planning method and device based on a redundant heterogeneous flat-slag robot according to the present application. The principle and implementation manner of the present application are described by applying specific examples in the embodiments of the present application. The above description of the embodiments is only used to help understand the method of the present application and its core idea. Meanwhile, for those skilled in the art, the specific implementation manner and application range will be changed according to the idea of the present application. In conclusion, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot, characterized in that, It includes: The dynamic search window population initialization guided by the evaluation mechanism generates a certain number of initial paths for the end gripper of the redundant heterogeneous slag leveling robot as the initial population. Based on the initial population, with the global fitness function as a constraint, the NSGA-II multi-objective genetic algorithm is used to plan the motion trajectory of the redundant heterogeneous slag leveling robot, so that the redundant heterogeneous slag leveling robot can level the coal slag according to the motion trajectory. The global fitness function includes a path length fitness function, a path smoothness fitness function, and a speed smoothness fitness function.

2. The multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot according to claim 1, characterized in that, The initial population of the dynamic search window, guided by an evaluation mechanism, generates a certain number of initial paths for the end effector of the redundant heterogeneous slag leveling robot arm as the initial population, including: S11. Take the path point of the robotic arm end gripper corresponding to the starting point of the rake pushing path as the starting point of the gripper path. S12. Obtain the gripper path point corresponding to the current rake pushing path point, and record it as the current gripper path point; S13. Create a circular search window with radius R at the previous gripper path point, and take the arc segment where the circular search window intersects with the current gripper path point as the current gripper target path point. S14. The current target path point of the gripper is evaluated by the evaluation function. When the evaluation function is minimized, the optimal path point is selected. Based on this, the search is continuously iterated to generate an initial path. The evaluation function is: Where f1 and f2 are the path length fitness function and the path smoothness fitness function, respectively; f1 = d(S i-1 ,S i )+d(S i-1 ′,S i ′), d(e,f) represents the distance from point e to point f, and S i S represents the target path point of the i-th gripper, i.e., the current target path point of the gripper. i ' represents the support point path point corresponding to the i-th gripper target path point, i.e., the current support point path point. τ1 and τ2 are the path length fitness weight and path smoothness fitness weight, respectively. The values ​​of the gripper radius fitness function f3, the rake arm fitness function f4, and the gripper acceleration fitness function f5 are shown below: The ordinate of the rake at the coal stove opening grip radius 'a' represents the acceleration value of the gripper's movement. max The maximum acceleration value set to limit the movement of the gripper; x zs and y zs Let x be the x and y coordinates of the current target path point of the gripper. pz and y pz d represents the x-coordinate and y-coordinate of the current rake path point. m1 r m r2 and θ represent the distance from the maximum working radius of the robotic arm to the center of the coal furnace, the radius setting related to the maximum working radius of the robotic arm, the outer radius of the coal furnace, and the furnace opening angle, respectively. S15. Repeat steps S11-S14 to generate a preset number of initial paths as the initial population.

3. The multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot according to claim 2, characterized in that, The distance d from the center of the coal furnace to the maximum working radius of the robotic arm. m1 The calculation methods include: Based on the torque constraint analysis of the linkage mechanism between the rake rod and the support point when the robotic arm is under maximum force, the constraint formula for the rake rod length L can be obtained by analyzing the force on the robotic arm and calculating the mass of the rake rod: Where G0 is the upper limit of the robotic arm's weighing capacity, p is the derivative of the proportion of the inner length of the rake rod, and J is the diameter of the rake rod. The coordinates of the coal furnace boundary point A and the lower boundary point B1 of the coal furnace opening are obtained as follows: (x...) a ,y a ), (x b1 ,y b1 Simultaneously, a functional relationship can be established between the support point track radius d2, the rod length L, and p, thereby obtaining d m1 The constraint relationship between the rod and the rod length L: The angle β1 between the line connecting the boundary point A of the coal furnace and the lower boundary point B1 of the coal furnace opening and the x-coordinate is: Let the coordinates of the furthest point C reached by the rake leveling the ash and the upper boundary point B2 of the coal furnace opening be (x, y ... c ,y c ), (x b2 ,y b2 To ensure that the rake can reach the farthest and nearth ends of the material pushing area through any opening, it is necessary to ensure that the gripper end of the rake is within the working range of the robotic arm. Therefore, d can be established. m1 The constraint relationship between the rod and the rod length L: d m1 ≥L-x b2 -r m (8) d m1 ≥L*cos(β3)-x c -r m (10) Among them, the angle β2 between the line connecting the farthest point C reached by the rake leveling and the upper boundary point B2 of the coal furnace opening and the horizontal coordinate, and the angle β3 between the line connecting the farthest point C reached by the rake leveling and the lower boundary point B1 of the coal furnace opening and the horizontal coordinate: With the optimization objective of minimizing the rod length L and the track radius d2 of the support point, and with Equations (5) and (6) as equality constraints, the minimum value of the objective is searched using the NSGA-II algorithm, and the minimum value of the rod length L is obtained after optimization by MATLAB. Substituting the minimum value of L into formulas (7)-(10) and taking the intersection, we can obtain d. m1 The upper and lower boundaries, take d m1 The midpoint value of the upper and lower boundaries is used as the distance from the center of the coal furnace to the maximum working radius of the robotic arm.

4. The multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot according to claim 1, characterized in that, Based on the initial population, and with the global fitness function as a constraint, the NSGA-II multi-objective genetic algorithm is used to plan the motion trajectory of the redundant heterogeneous slag leveling robot, so that the redundant heterogeneous slag leveling robot can level the coal slag according to the motion trajectory, including: Based on the initial population of the initial path of the gripper, determine the initial population of the corresponding support point path. Under the premise of satisfying the path safety objective constraint function, the NSGA-II multi-objective genetic algorithm is used to plan the motion trajectory of the redundant heterogeneous slag leveling robot, so that the path length fitness function, path smoothness fitness function, and velocity smoothness fitness function are all minimized: Among them, S zs For the gripper path, S zc For the support point path, safetypath is the path safety objective constraint function; F1, F2, and F3 are the path length fitness function, the path smoothness fitness function, and the speed smoothness fitness function, respectively.

5. The multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot according to claim 4, characterized in that, The path safety objective constraint function, safetypath, is: Among them, the ordinate of the rake at the coal furnace opening. grip radius x zs and y zs x represents the x-coordinate and y-coordinate of the gripper path point. pz and y pz d represents the x and y coordinates of the rake path points. m1 r m r2 and θ represent the distance from the maximum working radius of the robotic arm to the center of the coal furnace, the radius setting related to the maximum working radius of the robotic arm, the outer radius of the coal furnace, and the furnace opening angle, respectively.

6. The multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot according to claim 4, characterized in that, The path length fitness function F1 is: F1=F zs +F zc Among them, F zs For the gripper path length: gripper path S zs ={S1,S2,...,S n }, where n represents the gripper path S zs The total number of nodes in S j Represents the gripper path S zs The j-th path point in the path, x zs (j) represents the gripper path S zs The x-coordinate and y-coordinate of the j-th path point in the equation. zs (j) represents the gripper path S zs The ordinate of the j-th path point in the path; F zc Support point path length: Support point path S zc ={S1′,S2′,...,S n ′},S j 'Represents the path S of the support point zc The j-th path point in the path, x zc (j) represents the support point path S zc The x-coordinate and y-coordinate of the j-th path point in the equation. zc (j) represents the support point path S zc The ordinate of the j-th path point in the path; The path smoothness fitness function F2 is: Where, γ j Represents the gripper path S zs The turning point at the j-th path point in the path, (S j+1 -S j )·(S j -S j-1 ) represents the vector dot product; The speed smoothness fitness function F3 is: Among them, v zs (j) represents the gripper path S zs The velocity v at the j-th path point in the path. zc (j) represents the support point path S zc The velocity at the j-th path point in the path.

7. A multi-objective trajectory planning device based on a redundant heterogeneous slag leveling robot, characterized in that, It includes: The generation unit is used for the initialization of the dynamic search window population guided by the evaluation mechanism, and generates a certain number of initial paths for the end gripper of the redundant heterogeneous slag leveling robot as the initial population. The planning unit is used to plan the motion trajectory of the redundant heterogeneous slag leveling robot based on the initial population and with the global fitness function as a constraint, using the NSGA-II multi-objective genetic algorithm, so that the redundant heterogeneous slag leveling robot can level the slag according to the motion trajectory. The global fitness function includes a path length fitness function, a path smoothness fitness function, and a speed smoothness fitness function.

8. An electronic device, characterized in that, The system includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor. When the processor executes the computer program, it implements the steps of the multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, It stores a computer program, wherein the computer program causes the computer to perform the steps of the multi-objective trajectory planning method based on a redundant heterogeneous slag leveling robot as described in any one of claims 1-6.

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