A multi-target digging track planning method for a mining electric shovel based on a sinusoidal transition S-shaped curve

Abstract

A multi-objective digging trajectory planning method for mining electric shovels based on a sinusoidal transition S-curve belongs to the field of trajectory planning technology. First, the functional expressions of the geometric model of the working material pile, the forward kinematic model of the bucket tooth tip of the mining electric shovel, and the mapping function between the drive motor and the push rod are constructed respectively. Second, a driving force prediction model for the mining electric shovel digging process is established based on historical data, outputting the output forces of the push motor and the lifting motor. Third, the velocity and displacement expressions and optimization models of the sinusoidal transition S-curve applied to the drive motor are established. Finally, an optimization algorithm is used, with the objective function as the optimization objective and the constraint function as the optimization boundary, to optimize the variables and obtain a comprehensive optimal digging trajectory that achieves optimal operating efficiency, bucket loading capacity, and equipment energy consumption while meeting actual working conditions. This invention can enhance the comprehensive operating performance and operational stability of mining electric shovels under complex working material pile conditions.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of trajectory planning, and relates to a multi-target digging trajectory planning method for a mining shovel based on a sinusoidal transition S-shaped curve. BACKGROUND

[0002] With the development of intelligent mines, the intelligentization and unmannedization of mining shovels have become an important trend. Digging trajectory planning is one of the core technologies of the autonomous operation of a mining shovel, which affects the operation efficiency, shovel loading capacity, equipment energy consumption and running stability of the mining shovel. At present, researches are mostly concentrated on optimizing the parameters of a specific type of trajectory on a single performance indicator, which is difficult to simultaneously consider the collaborative optimization of the operation efficiency, shovel loading capacity and equipment energy consumption under complex and dynamic stockpile conditions.

[0003] Chinese invention patent 202411529073.X provides a mining shovel trajectory planning method based on a full-process asymmetric multi-segment S-shaped curve, which plans the operation of the motor by designing an asymmetric seven-segment S-shaped speed curve, and optimizes the lowest energy consumption per unit volume of digging as a single target. This method optimizes energy consumption to a certain extent, but the jerk model used has a step change at the phase switching point, which is discontinuous and restricts the further improvement of running stability. At the same time, the optimization target is single, and the operation time and shovel loading capacity are not included in the collaborative optimization framework, making it difficult to obtain a comprehensive optimal solution under varying conditions. In addition, the calculation of driving force relies on theoretical formulas, and the complex nonlinear relationship between digging driving force, stockpile shape and trajectory is not fully modeled, which limits the adaptability of the planning results in front of actual complex stockpiles.

[0004] Chinese invention patent 202410016797.8 provides a mining shovel digging trajectory planning method based on a radial basis function to construct an implicit surface, which uses a radial basis function to fit the point cloud scanned by a laser radar, uses a quintic polynomial to describe the digging trajectory, and optimizes the trajectory by taking the unit volume digging power consumption as the optimization target. This method enhances the ability to represent the geometry of the stockpile through surface fitting, but the calculation of digging resistance relies on empirical formulas, and the complex nonlinear relationship between the dynamically changing stockpile shape, digging depth and driving force is not fully modeled, so the physical reasonableness and adaptability of the planned trajectory are still limited when facing actual complex and dynamic stockpile conditions.

[0005] In summary, there is an urgent need to invent a new trajectory planning method, which can face the real working material pile working condition of dynamic change, realize the collaborative optimization of multiple targets of working efficiency, shovel loading capacity and equipment energy consumption under the premise of strictly meeting the motor driving force and mechanism kinematics constraint, and fundamentally improve the high-order kinematic stability of the excavation trajectory, thereby effectively enhancing the comprehensive working performance and running stability of the mining shovel in the complex mining environment. SUMMARY

[0006] In view of the problems existing in the prior art, the present application provides a mining shovel multi-objective excavation trajectory planning method based on a sinusoidal transition S-shaped curve, which transitions the acceleration process of the push motor and the lifting motor by a sinusoidal function, thereby realizing continuous change of the acceleration and jerk of the push motor and the lifting motor, and ultimately realizing high-order smooth motion of the excavation trajectory. At the same time, a multi-objective optimization model is constructed by taking the excavation time, the reciprocal of the excavation volume, and the total energy consumption divided by the excavation volume, thereby realizing comprehensive optimization of working efficiency, shovel loading capacity and equipment energy consumption under complex dynamic material piles. At the same time, a driving force prediction model of the mining shovel excavation process is established, so that the constraint of the optimization process on the driving force is more reasonable.

[0007] In order to achieve the above purpose, the technical scheme adopted by the present application is:

[0008] A mining shovel multi-objective excavation trajectory planning method based on a sinusoidal transition S-shaped curve, the mining shovel multi-objective excavation trajectory planning method comprising the following steps:

[0009] Step 1, constructing a function expression of the geometric model of the working material pile. Specifically:

[0010] The laser radar deployed on the mining shovel scans the working material pile, and after denoising and segmentation processing, the three-dimensional point cloud of the working material pile is obtained, and then a polynomial surface fitting reconstruction method is used on the three-dimensional point cloud of the working material pile to construct a geometric model of the working material pile for trajectory planning, as shown in formula (1):

[0011] (1)

[0012] Wherein, represents the horizontal coordinate of a point, represents the horizontal coordinate value of the point, represents the vertical coordinate value of the point; represents the vertical coordinate value of the point, represents the function expression of the geometric model of the working material pile.

[0013] Step 2, establishing a forward kinematics model of the shovel teeth tip of the mining shovel. Specifically:

[0014] Based on the initial push rod elongation The angle between the initial push rod and the vertical direction By planning the speed of the push motor and displacement Increase motor speed and displacement This is mapped to the movement trajectory of the bucket teeth of a mining electric shovel in three-dimensional space. That is, the excavation trajectory. Let x, y, z represent the coordinates of the bucket teeth of a mining electric shovel in the x, y, and z directions, and their mapping relationship be expressed as follows:

[0015] (2)

[0016] in, The mapping function represents the kinematic model determined by the mechanical structure of the mining electric shovel.

[0017] Step 3: Establish the mapping function between the drive motor and the push rod. The drive motor includes a push motor and a lifting motor. The mapping function is shown in formula (3):

[0018] (3)

[0019] in, Indicates the extension of the push rod; and These represent the pushing speed and pushing acceleration along the axial direction of the push rod, respectively. , , The angle, angular velocity, and angular acceleration of the push rod relative to the vertical direction are respectively determined. This represents the mapping function between the drive motor and the push rod, determined by the mechanical structure of the mining electric shovel.

[0020] Step 4: Collect historical data. The collected historical data includes the functional expression of the geometric model of the historical material pile, the motion state of the historical push rod, the operating state of the historical push motor and lifting motor, the historical initial push rod elongation, and the initial push rod's angle relative to the vertical direction. Specifically:

[0021] The functional expression of the geometric model of the historical work stockpile is obtained by using the polynomial surface fitting and reconstruction method described in step 1, based on the three-dimensional point cloud of the historical work stockpile.

[0022] The motion state of the historical push rod is obtained by a linear displacement sensor and an inclinometer installed on the push rod. The motion state of the push rod includes the push rod elongation, the pushing speed and pushing acceleration along the push rod axis, and the angle, angular velocity and angular acceleration of the push rod relative to the vertical direction.

[0023] The historical operating status of the push motor and the lifting motor is obtained by encoders and torque sensors installed on the push motor and the lifting motor. The operating status includes the displacement, speed and output force of the push motor and the lifting motor.

[0024] The initial elongation of the push rod and the angle between the initial push rod and the vertical direction were obtained by a linear displacement sensor and an inclinometer installed on the push rod at the start of excavation.

[0025] Step 5: Based on the historical data collected in Step 4, establish a driving force prediction model for the mining electric shovel excavation process to output the output force of the push motor and the hoisting motor. The specific steps are as follows:

[0026] Step 5.1: Using the forward kinematic model of the bucket tooth tip of the mining electric shovel established in Step 2, process the historical operating status of the pusher motor and the hoisting motor, the historical initial pusher rod elongation, and the angle between the initial pusher rod and the vertical direction obtained in Step 4 to obtain the corresponding historical excavation trajectory.

[0027] Step 5.2: Based on the functional expression of the geometric model of the historical excavation stockpile obtained in Step 4 and the historical excavation trajectory obtained in Step 5.1, calculate the dynamic excavation depth during the historical excavation process. .

[0028] Steps 5.3 and 4, the historical data collected in step 4, the historical excavation trajectory obtained in step 5.1, and the dynamic excavation depth obtained in step 5.2 together constitute the training sample set. A neural network model is trained using this training sample set to establish a driving force prediction model for the mining electric shovel excavation process. The specific formula is as follows:

[0029] (4)

[0030] in, This indicates the output force of the push motor; This indicates an increase in the motor's output force; This represents a predictive model of the driving force during the excavation process of an electric shovel in mining.

[0031] Step 6: Establish the velocity and displacement expressions for the drive motor using a sinusoidal transition S-curve. By using a sinusoidal function to transition the drive motor's acceleration process, continuous variation in acceleration and jerk is achieved, improving the smoothness of the drive motor's operation. Given the maximum motor speed... and the seven-stage termination time ,in =1, 2, 3, 4, 5, 6, 7. By applying boundary constraints to the initial and final velocities, accelerations, and jerks of the motor at each stage, the jerk expression for the sinusoidal transition S-curve applied to the drive motor is obtained, as shown in formula (5):

[0032] (5)

[0033] in, Indicates in The acceleration of time; Indicates the first frequency coefficient; Indicates the second frequency coefficient; Indicates the third frequency coefficient; Indicates the fourth frequency coefficient; Indicates in time; Indicates the end time of the first stage; Indicates the end time of the second phase; Indicates the end time of the third stage; Indicates the end time of the fourth stage; Indicates the end time of the fifth stage; Indicates the end time of the sixth stage; Indicates the end time of the seventh stage; Represents pi; This represents half of the maximum acceleration value during the acceleration process. This represents half of the maximum acceleration during the deceleration process. and The expression is as follows:

[0034] (6)

[0035] (7)

[0036] in, , , , use express, =1,2,3,4 Represented as frequency coefficients, their specific mathematical expression is as follows:

[0037] (8)

[0038] The acceleration expression for the sinusoidal transition S-curve applied to the motor is obtained by integrating formula (5), as shown in formula (9):

[0039] (9)

[0040] in, Indicates in Acceleration at any moment.

[0041] The speed expression for the sinusoidal transition S-curve applied to the motor is obtained by integrating formula (9), as shown in formula (10):

[0042] (10)

[0043] in, Indicates in The speed of time; ~ use express, Indicates in The speed of time =1, 2, 3, 4, 5, 6.

[0044] The displacement expression of the sinusoidal transition S-curve applied to the motor is obtained by integrating formula (10), as shown in formula (11):

[0045] (11)

[0046] in, Indicates in Displacement at any given moment; ~ use express, Indicates in Displacement at any moment =1, 2, 3, 4, 5, 6.

[0047] This yields the speed expression (Formula 10) and displacement expression (Formula 11) for the sinusoidal transition S-curve applied to the drive motor.

[0048] Step 7: Establish the optimization model, which includes optimization variables, objective function, and constraint functions. The specific steps are as follows:

[0049] Step 7.1: Apply the sinusoidal transition S-curve established in Step 6 to the speed and displacement expressions of the drive motor, respectively, and apply them to the push motor and the lifting motor to establish the optimization variables of the optimization model. The specific expressions are as follows:

[0050] (12)

[0051] in, Represents the optimization variable; This indicates the maximum speed of the push motor during the digging process of a mining electric shovel; This indicates the maximum speed of the lifting motor during the digging process of a mining electric shovel; Indicates the first of the push motor At the end of the phase, =1, 2, 3, 4, 5, 6, 7; Indicates the first step of lifting the motor At the end of the phase, =1, 2, 3, 4, 5, 6, 7.

[0052] Step 7.2, calculate the output force of the pushing and lifting motors, the specific steps are as follows:

[0053] Step 7.2.1, optimize the variables... , and , Substituting these values ​​into the speed and displacement expressions for the push motor and lifting motor calculated in step 6, respectively, yields the speed of the push motor. and displacement Increase the speed of the motor and displacement .

[0054] Step 7.2.2, take the current initial push rod elongation obtained in step 4. The angle between the initial push rod and the vertical direction The speed of the push motor obtained in step 7.2.1 Displacement Increase motor speed Displacement Substituting the mapping function of the kinematic model from step 2, we obtain the mining trajectory; , The speed of the push motor obtained in step 7.2.1 Displacement Increase motor speed Displacement Substituting the mapping function between the drive motor and the push rod from step 3, we obtain the motion state of the push rod.

[0055] Step 7.2.3: The dynamic excavation depth during the excavation process is obtained by using the calculation method in step 5.2, which combines the excavation trajectory obtained in step 7.2.2 and the geometric model of the working material pile obtained in step 1.

[0056] Step 7.2.4: Input the excavation trajectory and motion state of the push rod obtained in step 7.2.2, and the dynamic excavation depth obtained in step 7.2.3 into the driving force prediction model of the electric shovel excavation process in step 5.3 to obtain the output force of the push motor and the output force of the lifting motor.

[0057] Step 7.3: Obtain the excavation time by optimizing variables; calculate the excavation volume by using the function expression of the excavation trajectory obtained in Step 7.2.2 and the geometric model of the working material pile obtained in Step 1; and calculate the total excavation energy consumption by using the speed and displacement of the push motor and the lifting motor obtained in Step 7.2.1 and the output force of the push motor and the lifting motor obtained in Step 7.2.4.

[0058] Step 7.4: Establish the objective function of the optimization model, the specific expression of which is as follows:

[0059] (13)

[0060] in, This represents the objective function of the optimization model; , , Let represent the sub-objective function of the optimization model, where Indicates the time of excavation. This represents the reciprocal of the excavated volume. This represents the total energy consumption of excavation divided by the excavation volume; , , Represents the multi-objective weighting coefficients, where express The weighting coefficients, express The weighting coefficients, express The weighting coefficients.

[0061] Set appropriate multi-objective weighting coefficients according to the operating conditions.

[0062] Step 7.5: Establish the constraint functions for the optimization model. These constraint functions include time constraints, motor speed constraints, mechanism kinematic constraints, spatial height constraints, motor output force constraints, and load constraints. Specifically:

[0063] The time constraint is that the termination time of the 7th stage of the pushing motor in step 7.1 is equal to the termination time of the 7th stage of the lifting motor.

[0064] The motor speed constraint is as follows: the speed of the push motor and the speed of the lift motor obtained in step 7.2.1 must both be greater than or equal to zero and less than the maximum speed.

[0065] The kinematic constraints of the mechanism are as follows: Step 7.2.2 obtains the motion state of the push rod, wherein the extension of the push rod should be between the minimum stroke and the maximum stroke; the angle between the push rod and the vertical direction should be between the minimum and the maximum value.

[0066] The spatial height constraint is as follows: Step 7.2.2 obtains the excavation trajectory, and the coordinate value of the bucket tooth tip of the mining electric shovel corresponding to the excavation trajectory in the z direction is greater than 0.

[0067] The motor output force constraint is that the output force of the pushing and lifting motor calculated in step 7.2.4 is less than the maximum value.

[0068] The loading capacity constraint is that the excavation volume calculated in step 7.3 should be within the rated loading capacity of 0.95 buckets and 1.05 buckets.

[0069] Step 8: Using an optimization algorithm, the objective function defined in Step 7.4 is used as the optimization objective, and the constraint function defined in Step 7.5 is used as the optimization boundary to optimize the variables defined in Step 7.1. Once the convergence condition is met, the obtained optimal optimization variables are substituted into the methods of Steps 7.2.1 and 7.2.2 to obtain a comprehensive optimal digging trajectory that achieves optimal operating efficiency, bucket loading capacity, and equipment energy consumption while meeting actual working conditions. This optimal digging trajectory can achieve high-order smooth motion.

[0070] Furthermore, the convergence condition is that the relative change in the objective function value between two adjacent iterations is less than a preset threshold. Preset threshold The range is 10 -6 .

[0071] Step 9: Output the optimal excavation trajectory.

[0072] The beneficial effects of this invention are as follows:

[0073] (1) The present invention trains a driving force prediction model for the mining electric shovel excavation process based on a training sample set, which makes the output force calculation of the push motor and the lifting motor closer to reality, and the planned optimal excavation trajectory has higher adaptability and reliability.

[0074] (2) The present invention establishes the velocity expression and displacement expression of the sinusoidal transition S-curve applied to the drive motor. By using the sinusoidal function to transition the acceleration process of the drive motor, the continuous change of the acceleration and jerk of the drive motor is realized, which improves the smoothness of the drive motor operation and thus realizes the high-order smooth motion of the excavation trajectory.

[0075] (3) By establishing an objective function that includes the excavation time, the reciprocal of the excavation volume, and the total excavation energy consumption divided by the excavation volume, and setting adjustable multi-objective weight coefficients, this invention achieves coordinated optimization of operating efficiency, bucket loading capacity and equipment energy consumption under the premise of meeting actual working conditions, generates a comprehensive optimal excavation trajectory, and enhances the comprehensive operating capability of mining electric shovels.

[0076] (4) In the process of optimizing variables, the present invention incorporates constraints on time, motor speed, mechanism kinematics, spatial height, motor output force, and load, which ensures the feasibility of the optimal excavation trajectory.

[0077] In summary, this invention improves the engineering adaptability and overall performance of the planned excavation trajectory through driving force prediction, high-order smoothing of motion trajectory, multi-objective collaborative optimization, and constraint protection. Attached Figure Description

[0078] Figure 1 This is a flowchart of the present invention.

[0079] Figure 2 This is a state diagram showing the application of the sinusoidal transition S-curve of the present invention to a drive motor. Figure 2 (a) in the figure represents the jerk state curve; Figure 2 (b) in the figure represents the acceleration state curve; Figure 2 (c) in the figure represents the velocity state curve; Figure 2 (d) in the figure represents the displacement state curve; Figure 2 middle Indicates jerk. Indicates acceleration. Indicates speed, Indicates displacement, horizontal axis The horizontal axis represents the time axis, with the unit being seconds. Indicates the end time of the seven stages. =1,2,3,4,5,6,7.

[0080] Figure 3 The optimal excavation trajectory is obtained through a specific implementation method. Detailed Implementation

[0081] The present invention will be further described below with reference to specific implementation examples.

[0082] like Figure 1 The diagram shown illustrates the principle of this invention. A detailed description of the invention will now be provided in conjunction with specific embodiments. This embodiment details the implementation process of the method of this invention on a WK55 1:7 scale experimental prototype.

[0083] A multi-objective digging trajectory planning method for mining electric shovels based on a sinusoidal transition S-curve includes the following steps:

[0084] Step 1: Construct the functional expression for the geometric model of the work stockpile. Specifically:

[0085] The laser radar deployed on the mining electric shovel is used to scan the working material pile. After noise reduction and segmentation, the three-dimensional point cloud of the working material pile is obtained. Then, the three-dimensional point cloud of the working material pile is reconstructed by polynomial surface fitting method to build a geometric model of the working material pile for trajectory planning, as shown in formula (1):

[0086] (1)

[0087] in, This represents the horizontal coordinate of a point. This represents the x-coordinate value of the point. This represents the ordinate value of the point; This represents the vertical coordinate value of the point. A function expression representing the geometric model of the work stockpile.

[0088] Step 2: Establish the forward kinematic model of the bucket teeth tip of the mining electric shovel. Specifically:

[0089] Based on the initial push rod elongation The angle between the initial push rod and the vertical direction By planning the speed of the push motor and displacement Increase motor speed and displacement This is mapped to the movement trajectory of the bucket teeth of a mining electric shovel in three-dimensional space. That is, the excavation trajectory. Let x, y, z represent the coordinates of the bucket teeth of a mining electric shovel in the x, y, and z directions, and their mapping relationship be expressed as follows:

[0090] (2)

[0091] in, The mapping function represents the kinematic model determined by the mechanical structure of the mining electric shovel.

[0092] Step 3: Establish the mapping function between the drive motor and the push rod. The drive motor includes a push motor and a lifting motor. The mapping function is shown in formula (3):

[0093] (3)

[0094] in, Indicates the extension of the push rod; and These represent the pushing speed and pushing acceleration along the axial direction of the push rod, respectively. , , The angle, angular velocity, and angular acceleration of the push rod relative to the vertical direction are respectively determined. This represents the mapping function between the drive motor and the push rod, determined by the mechanical structure of the mining electric shovel.

[0095] Step 4: Collect historical data. The collected historical data includes the functional expression of the geometric model of the historical material pile, the motion state of the historical push rod, the operating state of the historical push motor and lifting motor, the historical initial push rod elongation, and the initial push rod's angle relative to the vertical direction. Specifically:

[0096] The functional expression of the geometric model of the historical work stockpile is obtained by using the polynomial surface fitting and reconstruction method described in step 1, based on the three-dimensional point cloud of the historical work stockpile.

[0097] The motion state of the historical push rod is obtained by a linear displacement sensor and an inclinometer installed on the push rod. The motion state of the push rod includes the push rod elongation, the pushing speed and pushing acceleration along the push rod axis, and the angle, angular velocity and angular acceleration of the push rod relative to the vertical direction.

[0098] The historical operating status of the push motor and the lifting motor is obtained by encoders and torque sensors installed on the push motor and the lifting motor. The operating status includes the displacement, speed and output force of the push motor and the lifting motor.

[0099] The initial elongation of the push rod and the angle between the initial push rod and the vertical direction were obtained by a linear displacement sensor and an inclinometer installed on the push rod at the start of excavation.

[0100] Step 5: Based on the historical data collected in Step 4, establish a driving force prediction model for the mining electric shovel excavation process to output the output force of the push motor and the hoisting motor. The specific steps are as follows:

[0101] Step 5.1: Using the forward kinematic model of the bucket tooth tip of the mining electric shovel established in Step 2, process the historical operating status of the pusher motor and the hoisting motor, the historical initial pusher rod elongation, and the angle between the initial pusher rod and the vertical direction obtained in Step 4 to obtain the corresponding historical excavation trajectory.

[0102] Step 5.2: Based on the functional expression of the geometric model of the historical excavation stockpile obtained in Step 4 and the historical excavation trajectory obtained in Step 5.1, calculate the dynamic excavation depth during the historical excavation process. .

[0103] Steps 5.3 and 4, the historical data collected in step 4, the historical excavation trajectory obtained in step 5.1, and the dynamic excavation depth obtained in step 5.2 together constitute the training sample set. A neural network model is trained using this training sample set to establish a driving force prediction model for the mining electric shovel excavation process. The specific formula is as follows:

[0104] (4)

[0105] in, This indicates the output force of the push motor; This indicates an increase in the motor's output force; This represents a predictive model of the driving force during the excavation process of an electric shovel in mining.

[0106] Step 6: Establish the velocity and displacement expressions for the sinusoidal transition S-curve applied to the drive motor. For example... Figure 2 As shown, the acceleration process of the drive motor is transitioned through a sinusoidal function, thereby achieving continuous variation in the drive motor's acceleration and jerk, improving the smoothness of the drive motor's operation. Given the maximum speed of the motor... and the seven-stage termination time ,in =1, 2, 3, 4, 5, 6, 7. By applying boundary constraints to the initial and final velocities, accelerations, and jerks of the motor at each stage, the jerk expression for the sinusoidal transition S-curve applied to the drive motor is obtained, as shown in formula (5):

[0107] (5)

[0108] in, Indicates in The acceleration of time; Indicates the first frequency coefficient; Indicates the second frequency coefficient; Indicates the third frequency coefficient; Indicates the fourth frequency coefficient; Indicates in time; Indicates the end time of the first stage; Indicates the end time of the second phase; Indicates the end time of the third stage; Indicates the end time of the fourth stage; Indicates the end time of the fifth stage; Indicates the end time of the sixth stage; Indicates the end time of the seventh stage; Represents pi; This represents half of the maximum acceleration value during the acceleration process. This represents half of the maximum acceleration during the deceleration process. and The expression is as follows:

[0109] (6)

[0110] (7)

[0111] in, , , , use express, =1,2,3,4 Represented as frequency coefficients, their specific mathematical expression is as follows:

[0112] (8)

[0113] The acceleration expression for the sinusoidal transition S-curve applied to the motor is obtained by integrating formula (5), as shown in formula (9):

[0114] (9)

[0115] in, Indicates in Acceleration at any moment.

[0116] The speed expression for the sinusoidal transition S-curve applied to the motor is obtained by integrating formula (9), as shown in formula (10):

[0117] (10)

[0118] in, Indicates in The speed of time; ~ use express, Indicates in The speed of time =1, 2, 3, 4, 5, 6.

[0119] The displacement expression of the sinusoidal transition S-curve applied to the motor is obtained by integrating formula (10), as shown in formula (11):

[0120] (11)

[0121] in, Indicates in Displacement at any given moment; ~ use express, Indicates in Displacement at any moment =1, 2, 3, 4, 5, 6.

[0122] This yields the speed expression (Formula 10) and displacement expression (Formula 11) for the sinusoidal transition S-curve applied to the drive motor.

[0123] Step 7: Establish the optimization model, which includes optimization variables, objective function, and constraint functions. The specific steps are as follows:

[0124] Step 7.1: Apply the sinusoidal transition S-curve established in Step 6 to the speed and displacement expressions of the drive motor, respectively, and apply them to the push motor and the lifting motor to establish the optimization variables of the optimization model. The specific expressions are as follows:

[0125] (12)

[0126] in, Represents the optimization variable; This indicates the maximum speed of the push motor during the digging process of a mining electric shovel; This indicates the maximum speed of the lifting motor during the digging process of a mining electric shovel; Indicates the first of the push motor At the end of the phase, =1, 2, 3, 4, 5, 6, 7; Indicates the first step of lifting the motor At the end of the phase, =1, 2, 3, 4, 5, 6, 7.

[0127] Step 7.2, calculate the output force of the pushing and lifting motors, the specific steps are as follows:

[0128] Step 7.2.1, optimize the variables... , and , Substituting these values ​​into the speed and displacement expressions for the push motor and lifting motor calculated in step 6, respectively, yields the speed of the push motor. and displacement Increase the speed of the motor and displacement .

[0129] Step 7.2.2, take the current initial push rod elongation obtained in step 4. The angle between the initial push rod and the vertical direction The speed of the push motor obtained in step 7.2.1 Displacement Increase motor speed Displacement Substituting the mapping function of the kinematic model from step 2, we obtain the mining trajectory; , The speed of the push motor obtained in step 7.2.1 Displacement Increase motor speed Displacement Substituting the mapping function between the drive motor and the push rod from step 3, we obtain the motion state of the push rod.

[0130] Step 7.2.3: The dynamic excavation depth during the excavation process is obtained by using the calculation method in step 5.2, which combines the excavation trajectory obtained in step 7.2.2 and the geometric model of the working material pile obtained in step 1.

[0131] Step 7.2.4: Input the excavation trajectory and motion state of the push rod obtained in step 7.2.2, and the dynamic excavation depth obtained in step 7.2.3 into the driving force prediction model of the electric shovel excavation process in step 5.3 to obtain the output force of the push motor and the output force of the lifting motor.

[0132] Step 7.3: Obtain the excavation time by optimizing variables; calculate the excavation volume by using the function expression of the excavation trajectory obtained in Step 7.2.2 and the geometric model of the working material pile obtained in Step 1; and calculate the total excavation energy consumption by using the speed and displacement of the push motor and the lifting motor obtained in Step 7.2.1 and the output force of the push motor and the lifting motor obtained in Step 7.2.4.

[0133] Step 7.4: Establish the objective function of the optimization model, the specific expression of which is as follows:

[0134] (13)

[0135] in, This represents the objective function of the optimization model; , , Let represent the sub-objective function of the optimization model, where Indicates the time of excavation. This represents the reciprocal of the excavated volume. This represents the total energy consumption of excavation divided by the excavation volume; , , Represents the multi-objective weighting coefficients, where express The weighting coefficients, express The weighting coefficients, express The weighting coefficients.

[0136] Based on the operating conditions, appropriate multi-objective weighting coefficients are set. In this implementation case, the multi-objective weighting coefficients are set to [value missing]. , , .

[0137] Step 7.5: Establish the constraint functions for the optimization model. These constraint functions include time constraints, motor speed constraints, mechanism kinematic constraints, spatial height constraints, motor output force constraints, and load constraints. Specifically:

[0138] The time constraint is that the termination time of the 7th stage of the pushing motor in step 7.1 is equal to the termination time of the 7th stage of the lifting motor.

[0139] The motor speed constraint is as follows: the speed of the push motor and the speed of the lift motor obtained in step 7.2.1 must both be greater than or equal to zero and less than the maximum speed.

[0140] The kinematic constraints of the mechanism are as follows: Step 7.2.2 obtains the motion state of the push rod, wherein the extension of the push rod should be between the minimum stroke and the maximum stroke; the angle between the push rod and the vertical direction should be between the minimum and the maximum value.

[0141] The spatial height constraint is as follows: Step 7.2.2 obtains the excavation trajectory, and the coordinate value of the bucket tooth tip of the mining electric shovel corresponding to the excavation trajectory in the z direction is greater than 0.

[0142] The motor output force constraint is that the output force of the pushing and lifting motor calculated in step 7.2.4 is less than the maximum value.

[0143] The loading capacity constraint is that the excavation volume calculated in step 7.3 should be within the rated loading capacity of 0.95 buckets and 1.05 buckets.

[0144] Step 8: Using an optimization algorithm, the objective function defined in Step 7.4 is used as the optimization objective, and the constraint function defined in Step 7.5 is used as the optimization boundary to optimize the variables defined in Step 7.1. When the convergence condition is met, the obtained optimal optimization variables are substituted into the methods of Steps 7.2.1 and 7.2.2 to obtain a comprehensive optimal digging trajectory that achieves optimal work efficiency, bucket loading capacity, and equipment energy consumption while meeting actual working conditions. This optimal digging trajectory can achieve high-order smooth motion. In this implementation case, the convergence condition is that the relative change in the objective function value between two adjacent iterations is less than a preset threshold. , 10 -6 .

[0145] Step 9, output the optimal excavation trajectory, such as Figure 3 As shown, Figure 3 In the diagram, X(m), Y(m), and Z(m) represent the x, y, and z axes, respectively, in meters. The blue dots represent the 3D point cloud of the working material pile, and the red trajectory represents the optimal excavation trajectory for this case.

[0146] The above embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A multi-objective excavation trajectory planning method for mining electric shovels based on a sinusoidal transition S-curve, characterized in that, The multi-objective digging trajectory planning method for mining electric shovels includes the following steps: Step 1: Construct the functional expression for the geometric model of the work stockpile; Step 2: Establish a forward kinematic model of the bucket teeth of the mining electric shovel; Step 3: Establish a mapping function between the drive motor and the push rod, wherein the drive motor includes a push motor and a lifting motor; Step 4: Collect historical data, which includes the function expression of the geometric model of the historical work stockpile, the motion state of the historical push rod, the operating state of the historical push motor and lifting motor, the historical initial push rod elongation and the angle between the initial push rod and the vertical direction. Step 5: Based on the historical data collected in Step 4, establish a driving force prediction model for the mining electric shovel excavation process, which is used to output the output force of the push motor and the lifting motor. Step 6: Establish the velocity and displacement expressions for the sinusoidal transition S-curve applied to the drive motor; achieve continuous change of drive motor acceleration and jerk by using a sinusoidal function to transition the drive motor acceleration process; and specify the maximum speed of the motor. and the seven-stage termination time ,in =1, 2, 3, 4, 5, 6, 7. By applying boundary constraints to the initial and final velocities, accelerations, and jerks of the motor at each stage, the jerk expression for the sinusoidal transition S-curve applied to the drive motor is obtained. Step 7: Establish an optimization model, which includes optimization variables, objective function, and constraint functions; Step 8: Using an optimization algorithm, the objective function is used as the optimization objective and the constraint function is used as the optimization boundary to find the optimization variables. When the convergence condition is met, a comprehensive optimal digging trajectory that meets the actual working conditions and achieves the optimal working efficiency, bucket loading capacity and equipment energy consumption is obtained, thus realizing high-order smooth motion. Step 9: Output the optimal excavation trajectory.

2. The method for multi-objective excavation trajectory planning of a mining electric shovel based on a sinusoidal transition S-curve as described in claim 1, characterized in that, Step 1 specifically involves: The laser radar deployed on the mining electric shovel is used to scan the working material pile. After noise reduction and segmentation, the three-dimensional point cloud of the working material pile is obtained. The three-dimensional point cloud of the working material pile is reconstructed by polynomial surface fitting method to build the geometric model of the working material pile for trajectory planning, as shown in formula (1): (1) in, This represents the horizontal coordinate of a point. This represents the x-coordinate value of the point. This represents the ordinate value of the point; This represents the vertical coordinate value of the point. A function expression representing the geometric model of the work stockpile.

3. The method for multi-objective excavation trajectory planning of a mining electric shovel based on a sinusoidal transition S-curve as described in claim 2, characterized in that, Step 2 specifically involves: Based on the initial push rod elongation The angle between the initial push rod and the vertical direction By planning the speed of the push motor and displacement Increase motor speed and displacement This is mapped to the movement trajectory of the bucket teeth of a mining electric shovel in three-dimensional space. That is, the excavation trajectory. Let x, y, z represent the coordinates of the bucket teeth of a mining electric shovel in the x, y, and z directions, and their mapping relationship be expressed as follows: (2) in, The mapping function represents the kinematic model determined by the mechanical structure of the mining electric shovel.

4. The method for multi-objective excavation trajectory planning of a mining electric shovel based on a sinusoidal transition S-curve as described in claim 3, characterized in that, In step 3, the mapping function is as shown in formula (3): (3) in, Indicates the extension of the push rod; and These represent the pushing speed and pushing acceleration along the axial direction of the push rod, respectively. , , The angle, angular velocity, and angular acceleration of the push rod relative to the vertical direction are respectively determined. This represents the mapping function between the drive motor and the push rod, determined by the mechanical structure of the mining electric shovel.

5. The method for multi-objective excavation trajectory planning of a mining electric shovel based on a sinusoidal transition S-curve according to claim 4, characterized in that, In step 4: The functional expression of the geometric model of the historical work stockpile is obtained by using the polynomial surface fitting and reconstruction method described in step 1, based on the three-dimensional point cloud of the historical work stockpile. The motion state of the historical push rod is obtained by a linear displacement sensor and an inclinometer installed on the push rod. The motion state of the push rod includes the push rod elongation, the pushing speed and pushing acceleration along the push rod axis, and the angle, angular velocity and angular acceleration of the push rod relative to the vertical direction. The historical operating status of the push motor and the lifting motor is obtained by encoders and torque sensors installed on the push motor and the lifting motor. The operating status includes the displacement, speed and output force of the push motor and the lifting motor. The initial elongation of the push rod and the angle between the initial push rod and the vertical direction were obtained by a linear displacement sensor and an inclinometer installed on the push rod at the start of excavation.

6. The method for multi-objective excavation trajectory planning of a mining electric shovel based on a sinusoidal transition S-curve according to claim 5, characterized in that, Step 5 specifically involves: Step 5.1: Using the forward kinematic model of the bucket tooth tip of the mining electric shovel established in Step 2, process the historical operating status of the push motor and the hoisting motor, the historical initial push rod elongation and the angle between the initial push rod and the vertical direction obtained in Step 4 to obtain the corresponding historical excavation trajectory. Step 5.2: Based on the functional expression of the geometric model of the historical excavation stockpile obtained in Step 4 and the historical excavation trajectory obtained in Step 5.1, calculate the dynamic excavation depth during the historical excavation process. ; Steps 5.3 and 4, the historical data collected in step 4, the historical excavation trajectory obtained in step 5.1, and the dynamic excavation depth obtained in step 5.2 together constitute the training sample set. A neural network model is trained using this training sample set to establish a driving force prediction model for the mining electric shovel excavation process. The specific formula is as follows: (4) in, This indicates the output force of the push motor; This indicates an increase in the motor's output force; This represents a predictive model of the driving force during the excavation process of an electric shovel in mining.

7. The method for multi-objective excavation trajectory planning of a mining electric shovel based on a sinusoidal transition S-curve according to claim 6, characterized in that, In step 6, the sinusoidal transition S-curve is applied to the acceleration expression of the drive motor, as shown in formula (5): (5) in, Indicates in The acceleration of time; Indicates the first frequency coefficient; Indicates the second frequency coefficient; Indicates the third frequency coefficient; Indicates the fourth frequency coefficient; Indicates in time; Indicates the end time of the first stage; Indicates the end time of the second phase; Indicates the end time of the third stage; Indicates the end time of the fourth stage; Indicates the end time of the fifth stage; Indicates the end time of the sixth stage; Indicates the end time of the seventh stage; Represents pi; This represents half of the maximum acceleration value during the acceleration process. This represents half of the maximum acceleration value during the deceleration process; Integrating equation (5), we obtain the acceleration expression for the sinusoidal transition S-curve applied to the motor, as shown in equation (9): (9) in, Indicates in Acceleration at any moment; The speed expression for the sinusoidal transition S-curve applied to the motor is obtained by integrating formula (9), as shown in formula (10): (10) in, Indicates in The speed of time; ~ use express, Indicates in The speed of time =1, 2, 3, 4, 5, 6; The displacement expression of the sinusoidal transition S-curve applied to the motor is obtained by integrating formula (10), as shown in formula (11): (11) in, Indicates in Displacement at any given moment; ~ use express, Indicates in Displacement at any moment =1, 2, 3, 4, 5, 6; This leads to the velocity and displacement expressions for the sinusoidal transition S-curve applied to drive motors.

8. The method for multi-objective excavation trajectory planning of a mining electric shovel based on a sinusoidal transition S-curve according to claim 7, characterized in that, In formula (5) of step 6, and The expression is as follows: (6) (7) in, , , , use express, =1,2,3,4 Represented as frequency coefficients, their specific form is as follows: (8)。 9. A method for multi-objective excavation trajectory planning of a mining electric shovel based on a sinusoidal transition S-curve, as described in claim 8, is characterized in that... Step 7 specifically involves: Step 7.1: Apply the sinusoidal transition S-curve established in Step 6 to the speed and displacement expressions of the drive motor, respectively, and apply them to the push motor and the lifting motor to establish the optimization variables of the optimization model. The specific expressions are as follows: (12) in, Represents the optimization variable; This indicates the maximum speed of the push motor during the digging process of a mining electric shovel; This indicates the maximum speed of the lifting motor during the digging process of a mining electric shovel; Indicates the first of the push motor At the end of the phase, =1, 2, 3, 4, 5, 6, 7; Indicates the first step of lifting the motor At the end of the phase, =1, 2, 3, 4, 5, 6, 7; Step 7.2, calculate the output force of the pushing and lifting motors, the specific steps are as follows: Step 7.2.1, select the optimization variables... , and , Substituting these values ​​into the speed and displacement expressions for the push motor and lifting motor calculated in step 6, respectively, yields the speed of the push motor. and displacement Increase the speed of the motor and displacement ; Step 7.2.2, take the current initial push rod elongation obtained in step 4. The angle between the initial push rod and the vertical direction The speed of the push motor obtained in step 7.2.1 Displacement Increase motor speed Displacement Substituting the mapping function of the kinematic model from step 2, we obtain the mining trajectory; , The speed of the push motor obtained in step 7.2.1 Displacement Increase motor speed Displacement Substitute the mapping function between the drive motor and the push rod in step 3 to obtain the motion state of the push rod; Step 7.2.3: The dynamic excavation depth during the excavation process is obtained by using the calculation method in step 5.2, based on the functional expression of the excavation trajectory obtained in step 7.2.2 and the geometric model of the working material pile obtained in step 1. Step 7.2.4: Input the excavation trajectory and motion state of the push rod obtained in step 7.2.2, and the dynamic excavation depth obtained in step 7.2.3 into the driving force prediction model of the electric shovel excavation process in step 5.3 to obtain the output force of the push motor and the output force of the lifting motor. Step 7.3: Obtain the excavation time by optimizing variables; calculate the excavation volume by using the function expression of the excavation trajectory obtained in Step 7.2.2 and the geometric model of the working material pile obtained in Step 1; and calculate the total excavation energy consumption by using the speed and displacement of the push motor and the lifting motor obtained in Step 7.2.1 and the output force of the push motor and the lifting motor obtained in Step 7.2.

4. Step 7.4: Establish the objective function of the optimization model, the specific expression of which is as follows: (13) in, This represents the objective function of the optimization model; , , Let represent the sub-objective function of the optimization model, where Indicates the time of excavation. This represents the reciprocal of the excavated volume. This represents the total energy consumption of excavation divided by the excavation volume; , , Represents the multi-objective weighting coefficients, where express The weighting coefficients, express The weighting coefficients, express Weighting coefficients; Step 7.5: Establish the constraint functions for the optimization model. These constraint functions include time constraints, motor speed constraints, mechanism kinematic constraints, spatial height constraints, motor output force constraints, and load constraints. Specifically: The time constraint is that the termination time of the 7th stage of the pushing motor in step 7.1 is equal to the termination time of the 7th stage of the lifting motor. The motor speed constraint is as follows: the speed of the pushing motor and the speed of the lifting motor obtained in step 7.2.1 must both be greater than or equal to zero and less than the maximum speed; The kinematic constraints of the mechanism are as follows: Step 7.2.2 obtains the motion state of the push rod, wherein the extension of the push rod should be between the minimum stroke and the maximum stroke; the angle between the push rod and the vertical direction should be between the minimum and the maximum value. The spatial height constraint: Step 7.2.2 obtains the excavation trajectory, and the coordinate value of the bucket tooth tip of the mining electric shovel corresponding to the excavation trajectory in the z direction is greater than 0; The motor output force constraint is as follows: the output force of the pushing and lifting motors calculated in step 7.2.4 is less than the maximum value; The loading capacity constraint is that the excavation volume calculated in step 7.3 should be within the rated loading capacity of 0.95 buckets and 1.05 buckets.

10. A method for multi-objective excavation trajectory planning of a mining electric shovel based on a sinusoidal transition S-curve, as described in claim 9, is characterized in that... In step 8, the convergence condition is that the relative change in the objective function value between two adjacent iterations is less than a preset threshold. .

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