Track planning method for slag salvaging robot in high-temperature slag environment

Abstract

The application discloses a trajectory planning method for a slag salvaging robot in a high-temperature slag environment and belongs to the technical field of industrial robot trajectory planning and intelligent control. On the basis of establishing a kinematic model of the slag salvaging robot and a 3-5-3 polynomial interpolation trajectory, a bucket fluid resistance speed constraint model based on the physical characteristics of the slag is first introduced to ensure operation safety; secondly, an improved double-population particle swarm optimization algorithm is used for time optimization, the self-learning factor adjustable parameter k of the algorithm is associated with the servo cycle of the driving motor, and the speed constraint penalty value of kinematics is fed back to the time variable population from the joint position population. The application effectively solves the problems that the motor is overloaded due to the fact that the slag resistance is ignored in the prior art and the algorithm iteration and the hardware response are not matched, and can maximize the operation efficiency of the slag salvaging robot under the premise of ensuring safety and smooth control.

Description

Technical Field

[0001] This invention relates to the field of industrial robot trajectory planning and intelligent control technology, and in particular to a trajectory planning method for slag removal robots in high-temperature molten slag environments. Background Technology

[0002] In the metal smelting industry, slag removal operations are conducted in harsh environments with high temperatures and the presence of toxic and harmful gases. Traditional manual slag removal methods are inefficient and seriously endanger workers' health. Adopting slag removal robots to replace manual labor is an inevitable trend in the industry's development.

[0003] Existing trajectory planning methods for slag removal robots, such as the scheme disclosed in CN117031954A, can achieve time-optimal trajectory planning based on an improved particle swarm optimization algorithm. However, this scheme mainly considers the robot's kinematic constraints, namely the maximum joint speed limit. In actual slag removal, the bucket needs to be immersed in high-temperature, viscous molten slag for operation, and will be subject to significant nonlinear fluid resistance. If time-optimal planning is performed only based on the kinematic constraints under no-load conditions, it may cause the actual motor load to exceed the rated torque, triggering overcurrent alarms in the drive or even damaging the equipment. In addition, the existing particle swarm optimization algorithm does not fully consider the matching problem between the algorithm iteration step size and the robot's hardware servo response capability, which can easily cause overshoot or jitter in the physical execution of the theoretically optimal trajectory. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a trajectory planning method for slag removal robots in high-temperature molten slag environments. This method introduces fluid resistance constraints based on the physical properties of molten slag and constructs a dual-population particle swarm optimization algorithm associated with the hardware servo cycle. Under the premise of ensuring robot operational safety, it achieves truly time-optimal trajectory planning that conforms to actual physical conditions.

[0005] The technical solution of this invention is as follows: A trajectory planning method for a slag-retrieving robot in a high-temperature molten slag environment. The slag-retrieving robot includes at least six joints, corresponding to a base, a base drive motor, a boom, a forearm, a stick, and a bucket. The trajectory planning method includes: based on the slag-retrieving task, and using the constructed forward kinematics equations, inverse kinematics equations, and DH parameter table of the slag-retrieving robot, establishing a joint space interpolation function based on a 3-5-3 polynomial, and determining the trajectory path points, objective function, and constraints corresponding to the particle swarm optimization algorithm; wherein the constraints include joint kinematic constraints and bucket fluid resistance velocity constraints. The joint kinematic constraints are used to limit the maximum speed of each joint, and the bucket fluid resistance velocity constraints are based on the physics of molten slag. Features are established to limit the bucket's excessive speed during slag removal operations, which could overload the bottom drive motor. An improved dual-population particle swarm optimization algorithm is used to perform individual time-optimal trajectory planning for the six joints corresponding to the base, bottom drive motor, boom, forearm, stick, and bucket of the slag removal robot, resulting in time-optimal trajectory curves that satisfy all constraints. The dual-population particle swarm optimization algorithm establishes a two-layer nested optimization structure of joint position population and time variable population. The time variable population uses local and global self-learning factors for iterative optimization, and the joint position population feeds back the speed over-limit penalty value to the time variable population based on the iteration results of the time variable population to adjust the particle flight direction, thereby reducing the number of invalid iterations.

[0006] Optionally, in the technical solution of the present invention, the update rules for the local self-learning factor c1 and the global self-learning factor c2 in the time variable population are respectively: c1 = c1min + (c1max - c1min) × (1 - kg / G)^k, and c2 = c2min + (c2max - c2min) × (kg / G)^k, where c1max and c1min are the maximum and minimum values ​​of the local learning factors, c2max and c2min are the maximum and minimum values ​​of the global learning factors, kg is the current iteration number, G is the maximum iteration number, and k is an adjustable parameter related to the servo cycle Ts of the drive motor; the joint position population calculates the 3-5-3 polynomial coefficients corresponding to the joint space interpolation function and generates a trajectory based on the iteration results of the time variable population, and feeds back the velocity out-of-bounds penalty value to the time variable population to adjust the particle flight direction; the iteration results of the time variable population are obtained by iterative optimization using velocity-position updates that include local self-learning factors c1 and global self-learning factors c2; in the improved dual-population particle swarm optimization algorithm, the velocity out-of-bounds penalty value is a numerical index used to correct the particle search direction and eliminate infeasible solutions.

[0007] Through the above technical solution, the present invention can achieve the following technical effects:

[0008] 1. Enhanced safety: The technical solution of this invention ensures that the optimized shortest time trajectory is physically safe by establishing a bucket fluid resistance speed constraint based on the physical properties of molten slag, thus avoiding the risk of motor overload caused by ignoring molten slag resistance.

[0009] 2. Enhanced engineering practicality: By associating the algorithm parameter k with the servo period Ts, the algorithm convergence and hardware execution capability are optimized in a coordinated manner, effectively reducing overshoot and jitter during trajectory execution.

[0010] 3. Improved optimization efficiency: A two-layer nested optimization structure of joint position population and time variable population is adopted. The joint position population provides real-time kinematic constraint feedback on the iteration results of the time variable population, which can reduce a large number of invalid fitness calculations and accelerate the search process for feasible solutions that meet complex constraints. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the slag removal robot in an embodiment of the present invention;

[0012] Figure 2 This is a flowchart illustrating a trajectory planning method for a slag-removing robot in a high-temperature molten slag environment, as described in an embodiment of the present invention. Detailed Implementation

[0013] To facilitate those skilled in the art to understand the technical problems, technical solutions, and expected technical effects to be achieved by this application, the technical solutions of this application will be described in detail below with reference to specific embodiments.

[0014] like Figure 1 As shown, the slag removal robot in this embodiment of the invention is consistent with CN117031954A and includes: a base 1, a bottom drive motor 2, a bottom side baffle 3, a counterweight 4, a robotic arm drive motor 5, a boom 6, a boom hydraulic cylinder 7, a forearm hydraulic cylinder 8, a forearm 9, a stick 10, a stick hydraulic cylinder 11, a stick guide device 12, a bucket guide device 13, and a bucket 14. The base 1 is installed on the ground, the bottom drive motor 2 is installed on the base 1, the bottom side baffle 3 is installed on the base 1, the counterweight 4 is installed on the bottom side baffle 3, the robotic arm drive motor 5 is installed on the counterweight 4, the boom 6 is installed on the bottom side baffle 3, the lower end of the boom hydraulic cylinder 7 is connected to the base 1, and the upper end is connected to the middle of the boom 6. One end of the boom hydraulic cylinder 8 is connected to the boom 6, and the other end is connected to the boom 9. The boom 9 is mounted on the boom 6, the stick 10 is mounted on the boom 9, the upper part of the stick hydraulic cylinder 11 is mounted on the stick 10, and the lower part is mounted on the stick guide device 12. The upper part of the bucket guide device 13 is mounted on the stick 10, and the lower part is mounted on the bucket 14.

[0015] based on Figure 1 The slag-removing robot shown in this embodiment of the invention, and the trajectory planning method for the slag-removing robot in a high-temperature molten slag environment, include:

[0016] 101. Construct the forward kinematics equations, inverse kinematics equations, and DH parameter table of the slag removal robot.

[0017] Forward kinematic equations, inverse kinematic equations, and DH parameter tables are the mathematical foundation and core support for robot trajectory planning.

[0018] Denavit-Hartenberg (DH) parameter tables are a standardized modeling method for describing the relative positions and attitudes of adjacent links in a serial robot. Each joint is defined by four parameters: 1. Link length. :along Axis, from Move to 1. Distance; 2. Linkage torsion angle : around Axis, from Rotate to 3. Joint offset; :along Axis, from Move to 4. Joint angle : around Axis, from Rotate to The angle.

[0019] The DH parameter table of the slag removal robot establishes the linkage coordinate system relationship of a total of 6 joints from the base (1) to the bucket (14). The 6 joints are specifically the joints corresponding to the base, bottom drive motor, boom, forearm, stick and bucket respectively.

[0020] Forward kinematics equations: Forward kinematics is based on known joint variables (joint angles) (or displacement), to solve for the position and orientation of the robot's end effector (bucket) in Cartesian space. Mathematically expressed as: Each of them It is a 4×4 homogeneous transformation matrix derived from the DH parameters.

[0021] Inverse Kinematics: Inverse kinematics is the inverse problem of forward kinematics: given the target pose (position and attitude) of the end-cap bucket, solve for the corresponding joint variables. Inverse solutions often have multiple solutions, and the optimal solution must be selected by considering factors such as joint constraints and obstacle avoidance.

[0022] In the overall technical solution of time-optimal trajectory planning, forward kinematics, inverse kinematics, and the DH parameter table serve as a bridge connecting "joint space planning" and "task space requirements." Their functions run through all key aspects of trajectory planning, including: establishing trajectory path points, joint space interpolation, velocity and acceleration constraint checking, particle swarm fitness calculation, simulation verification, and trajectory output.

[0023] The purpose of establishing forward and inverse kinematic models and the DH parameter table is not to directly solve the time-optimal problem, but to construct a complete mathematical mapping from task description to joint execution. Forward and inverse kinematic models and the DH parameter table are prerequisites and computational foundations for trajectory planning. Only with an accurate kinematic model can subsequent polynomial interpolation, constraint checking, and optimization solutions have physical meaning and engineering feasibility.

[0024] 102. Based on the slag removal task, and using the constructed forward kinematics equations, inverse kinematics equations, and DH parameter table of the slag removal robot, establish a joint space interpolation function based on a 3-5-3 polynomial, and determine the trajectory path points, objective function, and constraints corresponding to the particle swarm optimization algorithm.

[0025] In non-ferrous metal or steel smelting processes, a layer of high-temperature molten slag, composed of metal oxides, slagging agents, and residual flux, floats on the surface of the smelting furnace or holding furnace. The task of slag removal operations is to control the end effector bucket of a slag removal robot to immerse itself in the molten slag layer and, with a specific posture and path, scoop the floating slag from the surface of the molten pool and transfer it to a slag bag. This operating environment has the following extreme characteristics: 1. High-temperature environment: The temperature of the molten slag is typically between 1000℃ and 1300℃, and the robot's end effector needs to operate continuously under high-temperature radiation; 2. High-viscosity fluid medium: The density of the molten slag can reach 2.5-4.0 g / cm³, and the dynamic viscosity changes significantly with temperature. When the bucket moves horizontally in the molten slag at a certain speed, it will experience significant fluid resistance; 3. Variable resistance conditions: The magnitude of the resistance is closely related to the immersion depth of the bucket, the surface area facing the flow, the movement speed, and the real-time temperature and density of the molten slag. The force conditions on the bucket change drastically at different stages: cutting into the slag layer, horizontal scraping, and lifting out the slag.

[0026] If the constraints of molten slag fluid resistance are not considered, and time-optimal trajectory planning is performed solely based on the no-load joint speed limit, the following serious consequences will occur: 1. Motor overload risk: When the bucket moves at high speed in the molten slag, the load torque formed by fluid resistance will be superimposed on the joint motor. If the planned speed is too high, the actual output torque of the motor may exceed the rated torque or even the peak torque, triggering the overcurrent protection of the driver or burning out the motor windings. 2. Increased trajectory tracking error: Since the resistance is approximately proportional to the square of the speed, the additional load during high-speed movement will exceed the adjustment capacity of the servo system, causing the actual trajectory to deviate significantly from the planned trajectory, which may result in the bucket colliding with the furnace wall or incomplete slag removal. 3. Increased mechanical fatigue: Frequent overload impacts will accelerate the wear of the reducer gears and connecting rod bearings, shortening the equipment life.

[0027] Therefore, it is necessary to establish a bucket fluid resistance speed constraint model reflecting the physical properties of molten slag during the trajectory planning stage, transforming the motor torque limit into a dynamic constraint on the bucket end speed. Through this model, the algorithm can proactively avoid any dangerous speed ranges that could cause motor overload while pursuing operational efficiency (shortest time), ensuring the robot's long-term, safe, and stable operation in harsh metallurgical environments.

[0028] To overcome the above-mentioned defects, in addition to the kinematic constraints of each joint, i.e. the maximum speed limit, the constraint conditions in the embodiments of the present invention also include a bucket fluid resistance speed constraint model established based on the physical properties of molten slag, which is used to limit the bucket from overloading the bottom drive motor and the robotic arm drive motor due to excessive speed during slag removal operations.

[0029] Optionally, the model for the bucket's fluid resistance velocity constraint is: Vmax' = f(T, ρ, θ), where T is the slag temperature field parameter, ρ is the slag density, and θ is the bucket attitude angle. Based on the Vmax' = f(T, ρ, θ) model, when the bucket is in the slag removal section, its maximum allowable speed Vmax' is limited by the fluid resistance constraint to prevent motor overload. When the bucket is below the slag surface, the dynamic maximum allowable speed Vmax' is obtained by looking up a table or calculating a function based on the real-time temperature T and density ρ, with the constraint V_slag ≤ Vmax', where V_slag is the bucket's operating speed in the slag.

[0030] Specifically, in the technical solution of this invention, the objective function is f(t)min = min ∑_{i=0}^{n} (t1 + t2 + t3), and the joint kinematic constraints are: V1 ≤ Vmax, V2 ≤ Vmax, V3 ≤ Vmax and V_slag ≤ Vmax', where V1, V2, and V3 are the polynomial velocities of each segment, V_slag is the operating speed of the bucket in the molten slag, Vmax is the maximum limit speed of the joint, and Vmax' is the maximum allowable speed under fluid resistance constraints.

[0031] Similarly, the interpolation formulas for the 3-5-3 polynomials are: x1(t) = j3 t1^3 + j2 t1^2 + j1 t1 + j0, x2(t) = e5 t2^5 + e4 t2^4 + e3 t2^3 + e2 t2^2 + e1 t2 + e0, x3(t) = f3 t3^3 + f2 t3^2 + f1 t3 + f0, where the coefficients of the unknown terms ji, ei, and fi are the polynomial coefficients of each segment, xi(t) is the trajectory of each joint, and ti is the running time of each segment.

[0032] It's easy to understand that, unlike general-purpose robotic arms which only consider the physical speed limit of the motor, the technical solution of this invention explicitly defines a "fitness function correction term based on molten slag fluid resistance and high-temperature constraints" as the bucket fluid resistance speed constraint condition for the slag-retrieving robot. This overcomes the nonlinear viscous resistance encountered by the bucket at the end of the slag-retrieving robot as it moves in molten slag, solving a technical problem specific to the application field of "slag retrieval." In contrast, existing solutions for general-purpose robotic arms focus on pure mathematical convergence speed, without teaching or inspiring how to transform the physical properties of molten slag into algorithmic constraints. Establishing a bucket fluid resistance speed constraint based on the physical properties of molten slag achieves a synergistic effect—the algorithm not only converges quickly but also better conforms to the actual physical process of slag retrieval, preventing motor overload or slag splashing caused by excessive speed of the bucket in the slag.

[0033] Specifically, in this embodiment of the invention, the interpolation formulas for the 3-5-3 polynomials are: x1(t) = j3 t1^3 + j2 t1^2 + j1 t1 + j0, x2(t) = e5 t2^5 + e4 t2^4 + e3 t2^3 + e2 t2^2 + e1 t2 + e0, x3(t) = f3 t3^3 + f2 t3^2 + f1 t3 + f0, where the unknown coefficients ji, ei, and fi are the polynomial coefficients of each segment, xi(t) is the trajectory of each joint, and ti is the running time of each segment.

[0034] 103. An improved dual-population particle swarm optimization algorithm is used to perform time-optimal trajectory planning for the trajectories of the six joints corresponding to the base, bottom drive motor, boom, forearm, stick, and bucket in the slag removal robot, so as to obtain the time-optimal trajectory curve that satisfies all constraints.

[0035] To facilitate understanding of the deep association introduced into the improved dual-population particle swarm optimization algorithm in this embodiment, the following is a brief introduction to the relationship between "trajectory path points, objective function, and constraints" in step 102 and "using the improved dual-population particle swarm optimization algorithm to perform time-optimal planning of the trajectory of each joint of the slag removal robot" in step 103:

[0036] Trajectory path points define the search space of the particle swarm optimization (PSO) algorithm. Inverse kinematics transforms the path points in the task space into a sequence of angle values ​​for each joint at key positions. Each particle in the PSO algorithm represents a set of candidate time segments. Given a set of time values, these fixed angle path points must be combined to uniquely determine the trajectory curve of the entire joint through 3-5-3 polynomial interpolation. Without the trajectory path points determined in step 102, the time variables searched by the particle algorithm cannot construct a complete motion trajectory, and the optimization will lose its physical meaning.

[0037] The objective function is the fitness evaluation criterion for the particle swarm optimization (PSO) algorithm. The optimization objective is explicitly to minimize the sum of the three interpolation times. In the improved PSO algorithm's fitness function calculation, for each particle satisfying the velocity constraint, this total time value is directly used as its fitness value. The PSO algorithm updates the individual optimal and global optimal positions by comparing the fitness values ​​of each particle. The objective function defined in step 102 above is the sole directional guide for the iterative evolution of the PSO algorithm; the algorithm approaches this objective by continuously trying shorter time combinations.

[0038] The constraints act as a filter in the solution space of the particle swarm optimization (PSO) algorithm. Joint velocities must not exceed the maximum speed limit. The PSO algorithm calculates the velocity curve by substituting each candidate time segment into an interpolation function. If any velocity segment exceeds the maximum speed limit, the particle is deemed infeasible and removed from the candidate population by assigning a maximum fitness value (a penalty mechanism). These constraints act as boundary guards within the algorithm, forcing the PSO algorithm to automatically avoid invalid time combinations that would cause motor overspeeding during the search for "shorter" solutions. This ensures that the final optimal solution is not only short in time but also physically feasible.

[0039] In the improved dual-swarm particle swarm optimization algorithm, this relationship is further refined into a two-layer nested coupling: the time variable population is responsible for searching candidate time segment combinations, and its search motivation comes from the objective function of step 102 (pursuing the minimum total time); the joint position population is responsible for real-time verification of whether the trajectory generated by the time population meets the constraints (velocity limit) of step 102. Once an out-of-bounds error is detected, the joint position population will feed back a penalty gradient to the time variable population to inhibit the time variable population from continuing to optimize in the dangerous region. This dual-swarm mechanism decouples the "objective" and "constraint" set in step 102, allowing the algorithm to satisfy slag fluid constraints (such as the newly added...) Under the premise of ), it can still efficiently approximate the time-optimal solution.

[0040] Specifically, the improved dual-population particle swarm algorithm in this embodiment includes: randomly generating N time variable particle swarms to form a time variable population in the optimization space of each joint, and generating M joint position particle swarms to form a joint position population, where M and N are both positive integers greater than or equal to 2.

[0041] The update rules for the local self-learning factor c1 and the global self-learning factor c2 in the time variable population are as follows:

[0042] c1 = c1min + (c1max - c1min) × (1 - kg / G)^k, and c2 = c2min + (c2max - c2min) × (kg / G)^k, where c1max and c1min are the maximum and minimum values ​​of the local learning factor, c2max and c2min are the maximum and minimum values ​​of the global learning factor, kg is the current iteration number, G is the maximum iteration number, and k is an adjustable parameter related to the servo cycle Ts of the drive motor;

[0043] The joint position population calculates the 3-5-3 polynomial coefficients corresponding to the joint space interpolation function based on the iteration results of the time variable population and generates the trajectory. The velocity over-limit penalty value is fed back to the time variable population to adjust the particle flight direction. The iteration results of the time variable population are obtained by iterative optimization of velocity-position updates containing local self-learning factor c1 and global self-learning factor c2.

[0044] In the improved dual-population particle swarm optimization algorithm, the velocity out-of-bounds penalty value is a numerical index used to correct the particle search direction and eliminate infeasible solutions.

[0045] Specifically, the adjustable parameter k satisfies the following relationship: k = floor(1 / (τ * Ts)), where τ is a preset proportional coefficient and Ts is the servo cycle of the bottom drive motor or the robotic arm drive motor, so that the gradient of the self-learning factor changes matches the acceleration and deceleration response bandwidth of the motor.

[0046] Unlike conventional technical solutions where parameter k is a preset constant, the technical solution of this application links parameter k in the self-learning factor to the servo cycle of the drive motor, turning it into a dynamic parameter. This makes the gradient of the self-learning factor change match the acceleration and deceleration bandwidth of the motor. In essence, it establishes a specific mapping relationship between the algorithm iteration parameters and the electrical characteristics of the physical hardware, which can effectively solve the engineering problem of "overshooting of the actual motor response due to the algorithm's too fast convergence".

[0047] Beneficial Effects: Based on the establishment of a kinematic model and a 3-5-3 polynomial interpolation trajectory for the slag-collecting robot, the technical solution of this application first introduces a bucket fluid resistance velocity constraint model based on the physical properties of molten slag to ensure operational safety. Secondly, an improved dual-population particle swarm optimization algorithm is used for time optimization. The self-learning factor of this algorithm, the adjustable parameter k, is related to the motor servo cycle, and the kinematic constraint penalty value is fed back to the time population through the position population. This invention effectively solves the problems of neglecting molten slag resistance leading to motor overload risk and the mismatch between algorithm iteration and hardware response in existing technologies. It can maximize the operational efficiency of the slag-collecting robot while ensuring safety and smooth control.

[0048] To facilitate understanding of the bucket fluid resistance velocity constraint model based on the physical properties of molten slag in this application embodiment, the specific expression and working principle of the bucket fluid resistance velocity constraint model designed for the slag-collecting robot bucket operating in high-temperature molten slag will be explained below. This model can be embedded as a constraint condition in the algorithm during the trajectory planning stage to avoid the risk of motor overload from the source.

[0049] I. Specific Expression of the Bucket Fluid Resistance Velocity Constraint Model

[0050] Assuming that the total fluid resistance experienced by the bucket while moving in molten slag is primarily dominated by pressure differential resistance, it approximately conforms to the classical fluid resistance equation. To prevent the motor drive torque from exceeding the rated safety threshold, the following constraint model is defined:

[0051] ,

[0052] The parameters in the above formula are defined as follows:

[0053] symbol meaning unit illustrate Maximum permissible linear velocity of the bucket in molten slag m / s Constraint output values ​​are used to limit the speed of the bucket end effector. The conventional maximum linear velocity determined by the mechanical structure or motor speed m / s It is calculated from the reduction ratio, the rated speed of the motor, and the connecting rod length, and is a known constant. The rated torque (safety threshold) of the joint motor that drives the bucket movement. N·m Consulting the motor specifications, it is generally agreed that 80% of the rated torque is taken as the safety threshold. Transmission mechanism efficiency Dimensionless Considering the friction coefficients of the reducer and connecting rod, we take 0.85-0.95. Resistance coefficient related to slag temperature Dimensionless This was determined through experimental calibration or fluid simulation; higher temperatures generally result in better fluidity. smaller Slag density related to slag temperature kg / m³ Metallurgical physical property parameter table: density decreases slightly with increasing temperature. The projected area of ​​the bucket in the direction of velocity against the airflow m² Based on the current attitude angle of the bucket Real-time computing Equivalent arm from the center of fluid resistance to the joint rotation axis m The distance from the geometric center of the bucket to the axis of the drive joint changes with the attitude.

[0054] II. Model Working Principle: How to Prevent Motor Overload

[0055] The bucket fluid resistance velocity constraint model achieves the technical goal of "preventing motor overload" by placing the slag fluid dynamics constraint in the trajectory planning stage beforehand, rather than passively protecting it afterward. Its core logic chain is as follows:

[0056] 1. Establish the physical mapping relationship of "velocity-resistance-torque":

[0057] When the bucket is at speed At density When moving through the molten slag, the fluid resistance it experiences It can be estimated as follows: This resistance acts on the bucket, generating a load torque on the drive joint. for: To ensure the safe operation of the motor, the following must be met: .

[0058] 2. Inverse solution of the safe velocity boundary:

[0059] Applying the above inequality to velocity By solving the problem, we obtain the theoretical upper limit speed of the bucket moving in the molten slag: Considering transmission efficiency The actual maximum permissible speed is expressed as: Ultimately Mechanical hard speed limiter The smaller one is used as the constraint value .

[0060] 3. Mechanism for preventing motor overload in the algorithm:

[0061] The calculation process for the velocity constraint check step in trajectory planning is as follows:

[0062] Determine the work phase: Identify whether the current position of the excavator bucket is in the "immersion in molten slag" work phase;

[0063] If it is not a work segment: the constraint condition only uses the maximum speed of the conventional joint. ;

[0064] If it is a work segment: First, obtain the molten slag temperature in real time. and bucket attitude angle ,calculate , , , Secondly, substitute the values ​​into the above formula to calculate. Secondly, the time variable generated by the particle swarm optimization algorithm... The bucket speed obtained by substituting the interpolation function and taking its derivative and In comparison, finally, if If the trajectory scheme represented by the particle is deemed infeasible, an extremely high fitness penalty value is assigned, forcing the particle swarm to search in a direction with slower speed but relatively better total time.

[0065] From the working principle of preventing motor overload in the above bucket fluid resistance velocity constraint model, we can see that it has the following technical effects: 1. Active prevention: The torque limit of the motor is transformed into a speed limit in trajectory planning, so that when the final generated trajectory is physically executed, no matter how the slag state changes, the load torque of the motor will never exceed the rated value, fundamentally eliminating overload alarms or drive burnout. 2. Adaptive operating conditions: In the model... and The introduction of this allows the constraint boundary to be dynamically adjusted according to changes in the molten slag temperature. For example, freshly produced high-temperature molten slag has good fluidity (…). (Small), allowing for a naturally increased speed, balancing efficiency and safety. 3. Attitude sensitivity: through... and The influence of bucket posture on resistance and lever arm is taken into account, resulting in more precise constraints and avoiding efficiency losses caused by excessive speed limits for safety reasons.

[0066] In the improved dual-population particle swarm optimization algorithm, the velocity out-of-bounds penalty is a numerical metric used to correct the particle search direction and eliminate infeasible solutions. Its core meaning is: when the algorithm generates a set of candidate time variables ( Substituting the values ​​into the trajectory interpolation function causes the joint motion speed to exceed the preset maximum allowable value. or under slag constraint When the algorithm applies a large, positively correlated penalty to the candidate solution, it will be naturally eliminated in the fitness comparison, thereby forcing the entire particle swarm to converge toward the feasible region that satisfies the velocity constraint.

[0067] To facilitate understanding of the technical solution of this invention, the following is a detailed explanation of the calculation method, mechanism of action, and dual-population cooperation of the speed violation penalty value:

[0068] I. Calculation method of speed over-limit penalty value

[0069] In the fitness evaluation phase of the particle swarm optimization algorithm, a penalty value is typically appended to the original objective function in the form of a penalty function. Its general mathematical form is: ,

[0070] Or collect more severe death penalty punishments: .

[0071] In the above formula: The original objective function (total time); For the first The maximum velocity of the segment polynomial trajectory (obtained by differentiating the polynomial and taking the extreme value). The upper limit of joint velocity (including general kinematic constraints and slag fluid resistance constraints); For a preset large number that is much larger than the normal total time (e.g.) ), which is the speed over-limit penalty value; This is the penalty coefficient (if a linear penalty is used).

[0072] II. Mechanism of Speed ​​Exceedance Penalty Value

[0073] 1. Transforming a constrained problem into an unconstrained problem: The Particle Swarm Optimization (PSO) algorithm is originally designed for unconstrained continuous optimization. By introducing a penalty value, the problem is transformed into an unconstrained problem, ensuring that the speed does not exceed a certain limit. "This hard constraint is softened (or hardened) into the fitness function, so that the algorithm can handle the constraint without modifying the core velocity-position update formula."

[0074] 2. Guiding the particle swarm to avoid infeasible regions: In the early stages of iteration, particles may be randomly scattered in time combination regions that lead to velocity overflow (e.g., (If the fitness is too small, it will cause a sudden increase in acceleration and velocity in the first stage). After these particles are given extremely poor fitness, they will be naturally ignored when updating the individual optimal (pbest) and the global optimal (gbest). Thus, gbest will always point to a feasible solution that at least satisfies the velocity constraint, and other particles will gradually be pulled away from the out-of-bounds region as they fly towards gbest.

[0075] 3. Maintaining population diversity and avoiding local optima: Directly deleting out-of-bounds particles without penalty could lead to a decrease in population size and loss of diversity. By imposing a large number penalty, these particles are retained, allowing them to participate in position updates, but not in leadership competition. These particles may cross the feasible region boundary during flight, serving as boundary explorers.

[0076] III. Synergistic Effects in Two-Population Structures

[0077] In the improved double-population nested structure, the feedback loop for the velocity out-of-bounds penalty value is more refined:

[0078] Population type Role The role of speed exceeding the limit penalty value Time-variable population search The penalty value received from the location population is directly used for fitness evaluation to determine the quality of particles. Joint position population Verify whether the trajectory meets the velocity constraints. Calculate and report the velocity violation penalty value. The position population performs kinematic solving on the trajectory generated by the current time population. If a velocity violation is found, the degree of violation is calculated and a penalty value is generated, which is then passed to the time population.

[0079] The speed over-limit penalty value is a crucial bridge connecting the "mathematical optimization objective" and the "physical execution constraints." It transforms the abstract motor speed limit into a numerical signal that the algorithm can understand, ensuring that the "shortest time trajectory" searched by the particle swarm optimization algorithm is safe, smooth, and feasible under real motor drive. After introducing the molten slag fluid resistance constraint, this penalty value further covers the dynamic speed boundary in high-temperature viscous fluid environments, thereby eliminating the risk of motor overload from the root of the algorithm.

[0080] The various embodiments of this application have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or improvement of the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A trajectory planning method for a slag-retrieving robot in a high-temperature molten slag environment, wherein the slag-retrieving robot comprises at least six joints, corresponding to a base, a bottom drive motor, a boom, a forearm, a stick, and a bucket; characterized in that, The trajectory planning method includes: Based on the slag removal task, and using the constructed forward kinematics equations, inverse kinematics equations, and DH parameter table of the slag removal robot, a joint space interpolation function based on a 3-5-3 polynomial is established to determine the trajectory path points, objective function, and constraints corresponding to the particle swarm optimization algorithm. The constraints include joint kinematic constraints and bucket fluid resistance velocity constraints. The joint kinematic constraints are used to limit the maximum speed of each joint. The bucket fluid resistance velocity constraints are established based on the physical properties of molten slag and are used to limit the bucket from moving too fast during slag removal operations, which could cause the bottom drive motor to overload. An improved dual-population particle swarm optimization algorithm is used to perform time-optimal trajectory planning for the trajectories of the six joints corresponding to the base, bottom drive motor, boom, forearm, stick, and bucket in the slag removal robot, resulting in time-optimal trajectory curves that satisfy all constraints. The dual-population particle swarm optimization algorithm establishes a two-layer nested optimization structure of joint position population and time variable population. The time variable population uses local and global self-learning factors for iterative optimization. The joint position population feeds back the velocity over-limit penalty value to the time variable population based on the iteration results of the time variable population to adjust the particle flight direction, thereby reducing the number of invalid iterations.

2. The trajectory planning method according to claim 1, characterized in that, The model for the bucket fluid resistance velocity constraint is: Vmax' = f(T, ρ, θ), where T is the slag temperature field parameter, ρ is the slag density, and θ is the bucket attitude angle. Based on the Vmax' = f(T, ρ, θ) model, when the bucket is in the slag removal operation section, its maximum allowable speed Vmax' is limited by the fluid resistance constraint to prevent motor overload.

3. The trajectory planning method according to claim 2, characterized in that, To avoid the motor drive torque exceeding the rated safety threshold, the Vmax' = f(T, ρ, θ) model is defined as follows: ;in This is the maximum permissible linear velocity of the bucket in the molten slag. The conventional maximum linear velocity is determined by the mechanical structure or motor speed. The rated torque, or safety threshold, of the articulated motor that drives the bucket movement. For the efficiency of the transmission mechanism. The drag coefficient is related to the temperature of the molten slag. The density of the molten slag is related to its temperature. Let be the projected area of ​​the bucket facing the airflow in the velocity direction. It is the equivalent force arm from the center of fluid resistance to the joint rotation axis.

4. The trajectory planning method according to claim 1, 2, or 3, characterized in that, The improved dual-population particle swarm optimization algorithm specifically includes: Within the optimization space of each joint, N time variable particle swarms are randomly generated to form a time variable population, and M joint position particle swarms are generated to form a joint position population, where M and N are both positive integers greater than or equal to 2. The update rules for the local self-learning factor c1 and the global self-learning factor c2 in the time variable population are as follows: c1 = c1min + (c1max - c1min) × (1 - kg / G)^k, and c2 = c2min + (c2max - c2min) × (kg / G)^k, where c1max and c1min are the maximum and minimum values ​​of the local learning factor, c2max and c2min are the maximum and minimum values ​​of the global learning factor, kg is the current iteration number, G is the maximum iteration number, and k is an adjustable parameter related to the servo cycle Ts of the drive motor; The joint position population calculates the 3-5-3 polynomial coefficients corresponding to the joint space interpolation function based on the iteration results of the time variable population and generates a trajectory. The velocity over-limit penalty value is fed back to the time variable population to adjust the particle flight direction. The iteration results of the time variable population are obtained by iterative optimization using velocity-position updates that include local self-learning factors c1 and global self-learning factors c2. In the improved dual-population particle swarm optimization algorithm, the velocity out-of-bounds penalty value is a numerical index used to correct the particle search direction and eliminate infeasible solutions.

5. The trajectory planning method according to claim 4, characterized in that, The adjustable parameter k satisfies the following relationship: k = floor(1 / (τ * Ts)), where τ is a preset proportional coefficient and Ts is the servo cycle of the bottom drive motor or the robotic arm drive motor, so that the gradient of the self-learning factor changes matches the acceleration and deceleration response bandwidth of the motor.

6. The trajectory planning method according to claim 4 or 5, characterized in that, The speed over-limit penalty value The function expression is: or .

7. The trajectory planning method according to claim 1, characterized in that, The objective function is: f(t)min = min∑_{i=0}^{n} (t1 + t2 + t3), and the joint kinematic constraints are: V1 ≤ Vmax, V2 ≤ Vmax, V3 ≤ Vmax and V_slag ≤ Vmax', where V1, V2, and V3 are the polynomial velocities of each segment, V_slag is the operating speed of the bucket in the molten slag, Vmax is the maximum limit speed of the joint, and Vmax' is the maximum allowable speed under fluid resistance constraints.

8. The trajectory planning method according to claim 1 or 7, characterized in that, The interpolation formulas for the 3-5-3 polynomials are: x1(t) = j3 t1^3 + j2 t1^2 + j1 t1 + j0, x2(t) = e5 t2^5 + e4 t2^4 + e3 t2^3 + e2 t2^2 + e1 t2 + e0, x3(t) = f3 t3^3 + f2 t3^2 + f1 t3 + f0, where the coefficients of the unknown terms ji, ei, and fi are the polynomial coefficients of each segment, xi(t) is the trajectory of each joint, and ti is the running time of each segment.

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