A substation inspection robot adaptive trajectory tracking control parameter multi-objective optimization method based on NSGA-II

Abstract

The application is a kind of substation inspection robot adaptive trajectory tracking control parameter multi-objective optimization method based on NSGA-Ⅱ, first, the kinematics model of the robot and the path tracking error differential equation are established, second, based on NAGA-Ⅱ algorithm, a multi-objective optimization model in robot trajectory tracking is established, taking the size of tracking error and convergence time as optimization principle, the Pareto frontier of tracking curve with different curvatures is obtained; finally, according to the expected proportion of tracking error size and convergence time set by the substation, the Pareto frontier of the current tracking path is evaluated and analyzed by using the TOPSIS method, and the optimal solution required at present is obtained. The application considers the change of the space center occupied by the inspection robot, improves the tracking accuracy, and simultaneously reduces the size of tracking error and convergence time by using the multi-objective optimization method, which has important significance in improving the intelligence degree of substation inspection robot, increasing the work efficiency, expanding the application range and the like.

Description

Technical Field

[0001] This invention relates to an adaptive control parameter optimization method for a substation inspection robot, specifically a multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-Ⅱ, belonging to the field of service robot technology. Background Technology

[0002] Currently, China's power system has a large number of substations requiring regular inspections. These inspections are crucial for identifying equipment problems. However, the vast majority of these inspections are currently conducted manually, which is inefficient, of poor quality, prone to misjudgments, and can easily lead to economic losses for substations. With the rapid development of service robot technology and intelligent algorithms, wheeled robots are beginning to be used in substation inspections, replacing manual labor in certain tasks.

[0003] Substations contain a wide variety of equipment with irregular locations, including confined spaces and unstructured environments. Therefore, inspection robots need path-tracking capabilities within these confined spaces, enabling them to perform inspections along pre-defined paths within a limited area. On one hand, the optimal path in such confined spaces is often a curve with high curvature and short arcs. Current substation inspection robots require coordination with camera pan-tilt units, omnidirectional wheel rotation, and robotic arm joint movements, which affects the robot's overall center of mass and the spatial center it occupies. Consequently, the tracking performance of current methods deteriorates due to these factors. On the other hand, maintaining tracking accuracy in confined spaces requires significant time. Conversely, achieving optimal tracking accuracy in the shortest possible time compromises the overall accuracy. Therefore, robots cannot simultaneously optimize both tracking accuracy and time.

[0004] Therefore, if an adaptive control method that takes into account the changing center of the space occupied by the robot can be designed, and the tracking effect can be optimized in terms of accuracy and time by adjusting the parameters of the control method, then the substation inspection robot can achieve better tracking effect in actual inspection tasks, thereby better completing the inspection tasks. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II, so as to enable the substation inspection robot to complete trajectory tracking more accurately and quickly.

[0006] A multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II includes the following steps:

[0007] S1: Determine the characteristic parameters of the substation inspection robot, including: the robot wheel radius, the distance between the center of the space occupied by the robot and the center of the drive wheel axis, and calculate the robot's kinematic model accordingly.

[0008] S2: Calculate the path tracking error differential equation based on the content of S1.

[0009] S3: Based on the actual operating conditions of the substation, select the current road segment for geometric abstraction and calculate the instantaneous curvature of the curve to be tracked.

[0010] S4: Construct an adaptive control model that considers the distance between the center of the space occupied by the robot and the center of the drive wheel axis.

[0011] S5: Based on the NSGA-II genetic algorithm, establish a multi-objective optimization model for robot trajectory tracking. The algorithm input consists of three parameters of the adaptive controller. The optimization objectives are the magnitude of the tracking error and the convergence time. The requirement is that both the error magnitude and the convergence time should be minimized.

[0012] S6: Based on the NSGA-II algorithm, multi-objective optimization is performed to obtain the Pareto front under the instantaneous curvature of the curve to be tracked.

[0013] S7: The substation sets the expected ratio of tracking error magnitude to convergence time based on the actual situation, and uses the TOPSIS method to evaluate and analyze the Pareto front of the current tracking path. By combining the expected ratio, the optimal solution required at the current time is obtained, and the robot can complete the tracking according to the adaptive control parameters of the optimal solution.

[0014] In step S1, the geodetic coordinate system is denoted as... Let the robot's own coordinate system be denoted as . The center point of the robot drive wheel axis is The robot occupies a central space. The wheel radius is The distance between the center of the space occupied by the robot and the center of the drive wheel axis is , for and The included angle, the robot's linear velocity is angular velocity is The center of the space occupied by the robot The pose coordinates are ( , , ), center of drive wheel axis The pose coordinates are ( , , The robot's kinematic model is as follows:

[0015]

[0016] Given the desired pose coordinates of the mobile robot, ( , , ).

[0017] The tracking error is:

[0018] .

[0019] In step S2, the tracking error differential equation is:

[0020] .

[0021] In step S3, according to the substation inspection robot specification, the minimum turning diameter should not exceed twice the length of the robot itself, and the range of curvature K is set as follows:

[0022]

[0023] The curvature k is calculated as follows:

[0024]

[0025] Considering the specific unstructured environment of the substation and the length of the robot itself, the arc length should be calculated within a certain range.

[0026] The adaptive control method in step S4 is as follows:

[0027]

[0028] in:

[0029]

[0030] The objective of the multi-objective optimization model for adaptive trajectory tracking control parameters in step S5 is:

[0031]

[0032] In step S6, the specific process of optimizing the optimization model using the NSGA-II algorithm is divided into the following 9 sub-processes:

[0033] S61: Calculate the instantaneous curvature of the curve to be tracked, determine the value range of the individual based on the value range of the adaptive control parameters, and then initialize the population;

[0034] S62: Perform non-dominated ranking of the population, and simultaneously calculate crowding, calculating the rank and crowding value for each individual.

[0035] S63: Set the maximum number of iterations for the algorithm. If the maximum number of iterations is exceeded, the iteration will stop.

[0036] S64: Compare the rank values ​​of all individuals. The individual with the lower rank value is the better individual. If two individuals have the same rank value, then compare their crowding degree. The individual with the higher crowding degree is the better individual.

[0037] S65: Perform crossover, mutation, and merging on the population to continuously update and obtain a new population;

[0038] S66: Repeat the calculation of the non-dominated ranking of the current population and calculate the crowding degree;

[0039] S67: Update the population, evaluate it using an elite strategy, and generate a new, better population through competition;

[0040] S68: Determine whether the set maximum number of iterations has been reached. If not, return to S64 and continue with steps S64-S68.

[0041] S69: The iteration ends, and the Pareto front of the currently executed arc length segment is obtained.

[0042] In step S7, the evaluation process of the TOPSIS method consists of the following three sub-processes:

[0043] S71: The substation determines the expected ratio of tracking error to tracking time based on the actual environment and operating conditions.

[0044] S72: Use the ratio of tracking error to expected tracking time as the evaluation weighting coefficient.

[0045] S73: Evaluate the Pareto front using the TOPSIS method to obtain the optimal solution under the current conditions.

[0046] Compared with existing structures, the present invention has the following advantages:

[0047] (1) This invention takes into account the changes in the center of space occupied by the robot during the inspection process, such as the movement of the robotic arm on the robot, the pitch adjustment of the gimbal on the robot, and the forward and backward turning of the universal follower wheel, and establishes a more accurate pose tracking control model. Compared with other tracking control models, the tracking accuracy of this invention is greater.

[0048] (2) In the case of the change of the center of the space occupied by the robot, the present invention uses an adaptive control method to enable the robot to estimate the change in the center and quickly correct the pose error during the process of the center changing, and ensure that the error converges to zero during the tracking process, so that the robot eventually tracks to the set path.

[0049] (3) The present invention uses the NSGA-II algorithm to optimize the adaptive control parameters, which can solve the problem that the tracking accuracy and time consumption in the path tracking of the substation inspection robot cannot be minimized at the same time, so that the robot can complete the tracking task with the maximum accuracy and the shortest time.

[0050] (4) The present invention uses the improved TOPSIS method to evaluate the Pareto front, which can fully consider the actual environment and working conditions of the substation, select the optimal solution in the solution set under the current conditions, so that the robot can perform path tracking according to the optimal adaptive control parameters under the current evaluation system, and achieve the best tracking effect. Attached Figure Description

[0051] Figure 1 A flowchart of a multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II;

[0052] Figure 2 A kinematic model for a substation inspection robot;

[0053] Figure 3 This is a diagram illustrating the overall architecture of a multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II.

[0054] Figure 4 Structure diagram of the simulation model for adaptive trajectory tracking control of a substation inspection robot;

[0055] Figure 5 A schematic diagram showing the magnitude of adaptive trajectory tracking control error and convergence time of a substation inspection robot.

[0056] Figure 6 This is a flowchart of multi-objective optimization of adaptive control parameters based on the NSGA-II algorithm;

[0057] Figure 7 Pareto front plot for robot tracking the current instantaneous curvature. Detailed Implementation

[0058] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0059] like Figure 1 As shown, a multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II includes the following steps:

[0060] S1: Determine the characteristic parameters of the substation inspection robot, including: robot wheel radius, distance between the center of the space occupied by the robot and the center of the drive wheel axis. Using these parameters, calculate the actual kinematic model of the robot during operation, ensuring that the desired operating model and the actual kinematic model are the same.

[0061] S2: Calculate the path tracking error differential equation based on the content of S1.

[0062] S3: Based on the actual operating conditions of the substation, select the current road segment for geometric abstraction and calculate the instantaneous curvature of the curve to be tracked.

[0063] S4: Construct an adaptive control model that considers the distance between the center of the space occupied by the robot and the center of the drive wheel axis.

[0064] S5: Based on the NSGA-II genetic algorithm, establish a multi-objective optimization model for robot trajectory tracking. The algorithm input consists of three parameters of the adaptive controller. The optimization objectives are the magnitude of the tracking error and the convergence time. The requirement is that both the error magnitude and the convergence time should be minimized.

[0065] S6: Based on the NSGA-II algorithm, multi-objective optimization is performed to obtain the Pareto front under the instantaneous curvature of the curve to be tracked.

[0066] S7: The substation sets the expected ratio of tracking error magnitude to convergence time based on the actual situation, and uses the TOPSIS method to evaluate and analyze the Pareto front of the current tracking path. By combining the expected ratio, the optimal solution required at the current time is obtained, and the robot can complete the tracking according to the adaptive control parameters of the optimal solution.

[0067] In step S1, the geodetic coordinate system is denoted as... Let the robot's own coordinate system be denoted as . The center point of the robot drive wheel axis is The robot occupies a central space. The wheel radius is The distance between the center of the space occupied by the robot and the center of the drive wheel axis is , for and The included angle, the robot's linear velocity is angular velocity is The center of the space occupied by the robot The pose coordinates are ( , , ), center of drive wheel axis The pose coordinates are ( , , The robot's kinematic model is as follows:

[0068] .

[0069] Given the desired pose coordinates of the mobile robot, ( , , The robot tracks its trajectory based on the desired pose coordinates and adjusts the rotation speed of its two wheels to achieve linear velocity control. and angular velocity The adjustments allow the robot to gradually track the desired trajectory.

[0070] The robot's path tracking error is divided into three parts: the first part is the error of the horizontal coordinate x; the second part is the error of the vertical coordinate y; and the third part is the error between the angle between the robot's central axis and the x-axis and the desired angle.

[0071] The tracking error is:

[0072] .

[0073] In step S2, after obtaining the first derivative of the robot tracking error, the differential equation of the path tracking error can be obtained using the above kinematic model. The transformation process is as follows:

[0074] .

[0075] In step S3, when the robot moves to a certain point, the robot needs to determine the target point position of the path to be tracked and calculate the curvature of the path to be tracked at that point based on the position.

[0076] According to the specifications for substation inspection robots, the minimum turning diameter should not exceed twice the length of the robot itself, and the range of values ​​for curvature K is set as follows:

[0077]

[0078] The curvature k is calculated as follows:

[0079]

[0080] Considering the specific unstructured environment of the substation and the length of the robot itself, the curvature should be calculated within a certain range.

[0081] In step S4, based on the obtained path tracking error differential equation, a controller is designed according to adaptive control theory. The specific adaptive control method is as follows:

[0082]

[0083] in:

[0084]

[0085] In some situations, substation inspection robots may experience movements such as the robotic arm's motion, the gimbal's pitch adjustment, and the omnidirectional steering of their servo wheels. These movements cause changes in the robot's overall spatial center, which, while not necessarily large, can still impact conventional adaptive control methods, leading to decreased tracking accuracy. This is particularly detrimental in unstructured substation environments, affecting the robot's inspection performance. The adaptive control method in this invention can adaptively adjust the distance *d* between the robot's overall spatial center and the axis of its drive wheels, thereby improving tracking accuracy.

[0086] The objective of the multi-objective optimization model for adaptive trajectory tracking control parameters in step S5 is:

[0087]

[0088] Where e and t represent the magnitude of the tracking error and the convergence time, respectively, the objective of multi-objective optimization is to minimize the values ​​of these two.

[0089] In step S6, the specific process of optimizing the optimization model using the NSGA-II algorithm is divided into the following 9 sub-processes:

[0090] S61: Calculate the instantaneous curvature of the curve to be tracked, determine the value range of the individual based on the value range of the adaptive control parameters, and then initialize the population;

[0091] S62: Perform non-dominated ranking of the population, and simultaneously calculate crowding, calculating the rank and crowding value for each individual.

[0092] S63: Set the maximum number of iterations for the algorithm. If the maximum number of iterations is exceeded, the iteration will stop.

[0093] S64: Compare the rank values ​​of all individuals. The individual with the lower rank value is the better individual. If two individuals have the same rank value, then compare their crowding degree. The individual with the higher crowding degree is the better individual.

[0094] S65: Perform crossover, mutation, and merging on the population to continuously update and obtain a new population;

[0095] S66: Repeat the calculation of the non-dominated ranking of the current population and calculate the crowding degree;

[0096] S67: Update the population, evaluate it using an elite strategy, and generate a new, better population through competition;

[0097] S68: Determine whether the set maximum number of iterations has been reached. If not, return to S44 and continue with steps S44-S48.

[0098] S69: The iteration ends, and the Pareto front of the currently executed arc length segment is obtained.

[0099] In step S7, the evaluation process of the TOPSIS method consists of the following three sub-processes:

[0100] S71: The substation determines the expected ratio of tracking error to tracking time based on the actual environment and operating conditions;

[0101] S72: Use the ratio of tracking error to expected tracking time as the evaluation weighting coefficient;

[0102] S73: Evaluate the Pareto front using the TOPSIS method to obtain the optimal solution under the current conditions.

[0103] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II, characterized in that, It includes the following steps: S1: Determine the characteristic parameters of the substation inspection robot, including: robot wheel radius, distance between the center of the space occupied by the robot and the center of the drive wheel axis, and calculate the robot kinematic model accordingly; S2: Calculate the path tracking error differential equation based on the content of S1; S3: Based on the actual working conditions of the substation, select the current road segment for geometric abstraction and calculate the instantaneous curvature of the curve to be tracked. S4: Construct an adaptive control model that considers the distance between the center of the space occupied by the robot and the center of the drive wheel axis; S5: Based on the NSGA-II genetic algorithm, establish a multi-objective optimization model for robot trajectory tracking; the input of the algorithm is the three parameters of the adaptive controller; the optimization objectives are the magnitude of the tracking error and the convergence time; the error magnitude and convergence time should be minimized. S6: Based on the NSGA-II algorithm, multi-objective optimization is completed to obtain the Pareto front under the instantaneous curvature of the curve to be tracked; S7: The substation sets the expected ratio of tracking error magnitude to convergence time based on the actual situation, uses the TOPSIS method to evaluate and analyze the Pareto front of the current tracking path, and obtains the optimal solution required at the current time by combining the expected ratio. The robot can then complete the tracking according to the adaptive control parameters of the optimal solution. Step S6, the specific process of optimizing the optimization model using the NSGA-II algorithm, is divided into the following 9 sub-processes: S61: Set the curvature of the currently executed arc segment, determine the value range of the individual based on the value range of the adaptive control parameters, and then initialize the population; S62: Perform non-dominated ranking of the population, and simultaneously calculate crowding, calculating the rank and crowding value for each individual. S63: Set the maximum number of iterations for the algorithm. If the maximum number of iterations is exceeded, the iteration will stop. S64: Compare the rank values ​​of all individuals. The individual with the lower rank value is the better individual. If two individuals have the same rank value, then compare their crowding degree. The individual with the higher crowding degree is the better individual. S65: Perform crossover, mutation, and merging on the population to continuously update and obtain a new population; S66: Repeat the calculation of the non-dominated ranking of the current population and calculate the crowding degree; S67: Update the population, evaluate it using an elite strategy, and generate a new, better population through competition; S68: Determine whether the set maximum number of iterations has been reached. If not, return to S64 and continue with steps S64-S68. S69: The iteration ends, and the Pareto front of the currently executed arc length segment is obtained.

2. The multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II according to claim 1, characterized in that: In step S1, the geodetic coordinate system is denoted as... Let the robot's own coordinate system be denoted as . The center point of the robot drive wheel axis is The robot occupies the central space. The wheel radius is The distance between the center of the space occupied by the robot and the center of the drive wheel axis is , for and The included angle, the robot's linear velocity is angular velocity is The center of space occupied by the robot The pose coordinates are ( , , ), center of drive wheel axis The pose coordinates are ( , , The robot's kinematic model is as follows: Given the desired pose coordinates of the mobile robot, ( , , ); The tracking error is: 。 3. The multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II as described in claim 2, characterized in that: In step S2, the tracking error differential equation is: 。 4. The multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II according to claim 1, characterized in that: In step S3, according to the substation inspection robot specification, the minimum turning diameter should not exceed twice the length of the robot itself, and the range of curvature K is set as follows: The curvature k is calculated as follows: Considering the specific unstructured environment of the substation and the length of the robot itself, the arc length should be calculated within a certain range.

5. The multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II according to claim 3, characterized in that: The adaptive control method in step S4 is as follows: in: 。 6. The multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II according to claim 1, characterized in that: The objective of the multi-objective optimization model for adaptive trajectory tracking control parameters in step S5 is: 。 7. The multi-objective optimization method for adaptive trajectory tracking control parameters of a substation inspection robot based on NSGA-II according to claim 1, characterized in that: In step S7, the evaluation process of the TOPSIS method consists of the following three sub-processes: S71: The substation determines the expected ratio of tracking error to tracking time based on the actual environment and operating conditions; S72: Use the ratio of tracking error to expected tracking time as the evaluation weighting coefficient; S73: Evaluate the Pareto front using the TOPSIS method to obtain the optimal solution under the current conditions.

Images