Proportional intelligent control method and device of electric power inspection robot under slip disturbance

Abstract

This invention provides a proportional intelligent control method and device for a power line inspection robot under slip disturbance, relating to the field of control technology for intelligent power line inspection robots. The method includes: constructing a dynamic model containing slip disturbance by introducing slip parameters based on the kinematic principles of wheeled robots, wheel parameters, and longitudinal slip characteristics; discretizing the model to obtain a discretized dynamic model; determining the trajectory tracking control target (the actual position converges to the desired trajectory through iteration) and defining the desired inspection trajectory; designing a proportional iterative learning control algorithm to dynamically correct the control input; and verifying the convergence characteristics of the algorithm based on stability theory. This invention can ensure trajectory tracking accuracy under slip disturbance and improve control robustness.

Description

Technical Field

[0001] This invention relates to the field of control technology for intelligent power inspection robots, and in particular to a proportional intelligent control method and device for power inspection robots under slip disturbance. Background Technology

[0002] Intelligent inspection robots, with their superior mobility, are widely used in modern industry, especially in power grid inspection scenarios. Their core objective is to efficiently identify and address system hazards and faults, preventing major accidents such as power outages caused by equipment problems. Compared to manual inspections, intelligent power grid inspection robots can meet the daily inspection needs of the power grid, enabling all-weather intelligent and scheduled inspections, significantly improving the efficiency and safety of inspection work.

[0003] Currently, most mainstream intelligent power grid inspection robots are wheeled robots, and their accuracy in traveling along a predetermined trajectory is a key indicator for measuring the completion of inspection tasks. Early control solutions for wheeled robots primarily used Proportional-Integral-Derivative (PID) control. Through the coordinated adjustment of the proportional, integral, and derivative components, the tracking accuracy of the inspection trajectory and the stability of the robot itself can be guaranteed. This method has the advantages of simple structure and ease of engineering implementation, and performs stably in ideal inspection environments such as indoor spaces, laying a technological foundation for the development of power grid safety.

[0004] However, with the continuous expansion of power plant scale, the working environment of inspection robots is becoming increasingly complex, with frequent occurrences of slippery roads, muddy areas, and turning sections, leading to problems such as longitudinal slippage and even rollover accidents. Unfortunately, most existing research on wheeled robot control is based on the ideal assumption of "pure rolling with no slippage." This assumption requires that the ground hardness, friction coefficient, robot speed, and acceleration all be within ideal ranges, completely ignoring the unavoidable slippage disturbances in actual applications. This causes a significant decrease in the control performance of traditional PID control algorithms in slippage scenarios, making it difficult to meet actual inspection needs.

[0005] Specifically, existing wheeled robot inspection trajectory tracking and control technology has the following key shortcomings:

[0006] 1. Ideal assumptions are out of sync with the actual environment: Existing control strategies (such as velocity-based global asymptotic stability control strategy, virtual velocity control strategy, sliding mode control strategy, etc.) can achieve good trajectory tracking results in an ideal "pure rolling and slip-free" environment. However, in actual inspection scenarios, slippery, muddy, turning and other working conditions will inevitably cause slippage, resulting in a serious decrease in the accuracy of robot trajectory tracking, or even loss of control, and failure to complete the inspection task according to the predetermined trajectory.

[0007] 2. Dependence on accurate models and insufficient robustness: Existing control methods mostly rely on accurate dynamic models of robot systems. However, in practical applications, the dynamic behavior of robot systems is highly nonlinear and strongly coupled, and the model parameters change dynamically with the environment, making it difficult to achieve accurate modeling. This results in insufficient robustness of existing control methods in dynamic environments, making them unable to adapt to complex inspection conditions.

[0008] 3. Significant limitations of alternative solutions: For the slip disturbance problem, some studies have attempted to optimize it using methods such as adaptive control, fuzzy control, and neural networks. However, these solutions still have obvious shortcomings: adaptive control requires prior knowledge of the system structure and has poor adaptability to unknown or dynamically changing systems; fuzzy control is difficult to balance stability and robustness, and its control effect is easily affected by rule design; neural networks require a large amount of computing resources and training data, making them difficult to deploy efficiently on inspection robots with limited resources, thus limiting their practical application value.

[0009] Based on existing patented technologies, the related solutions have also failed to effectively overcome the aforementioned bottlenecks:

[0010] The patent with publication number CN116719320A proposes a trajectory tracking method for wheeled robots based on PID control. Although it clarifies the influence of PID parameters on trajectory tracking performance, it places stringent requirements on the robot structure and does not consider the influence of slippage disturbances. It is only suitable for ideal working environments such as indoors and cannot cope with the longitudinal slippage problem that is common in power inspection scenarios, making it difficult to guarantee the robot's driving accuracy along the inspection trajectory.

[0011] Patent CN116166013A proposes a virtual reference trajectory tracking control method that combines interference observation and trajectory reconstruction. It estimates the slip disturbance using a tracking differentiator and superimposes it onto the original reference trajectory to achieve interference pre-compensation at the trajectory level. However, this method relies on real-time interference observation, and the controller gain needs to be manually adjusted, lacking self-learning capability. Furthermore, if the characteristics of the slip disturbance change over a long period, the parameters need to be readjusted, limiting its applicability in repetitive interference and long-term adaptive power line inspection scenarios.

[0012] In summary, existing intelligent power inspection robot control technologies cannot effectively compensate for the impact of longitudinal slippage disturbances, making it difficult to ensure the stability and trajectory tracking accuracy of the robot in complex dynamic environments. How to solve this problem has become a key technical bottleneck that urgently needs to be overcome in the field of intelligent power inspection. Summary of the Invention

[0013] To address this, embodiments of the present invention provide a proportional intelligent control method and device for power inspection robots under slip disturbance, which solves problems such as trajectory deviation and insufficient control robustness of wheeled robots caused by longitudinal slip in intelligent power inspection scenarios.

[0014] To address the aforementioned problems, embodiments of the present invention provide a proportional intelligent control method for a power inspection robot under slip disturbance, the method comprising:

[0015] Based on the kinematic principles of wheeled robots, and combining preset wheel parameters and longitudinal slip characteristics, a dynamic model of a wheeled robot with slip disturbance is constructed by introducing slip parameters that reflect the difference between the desired speed and the actual speed of the robot wheels.

[0016] Based on a preset sampling period, the dynamic model of the wheeled robot with slip disturbance is discretized to obtain a discretized dynamic model;

[0017] Based on the requirements of the power inspection task, the robot trajectory tracking control objective is determined, and the desired inspection trajectory that satisfies the control objective is defined. The control objective is to make the actual position of the robot converge to the desired inspection trajectory with the number of iterations.

[0018] Based on the discretized dynamics model and the desired inspection trajectory, a proportional iterative learning control algorithm is designed. This algorithm is used to dynamically correct the control input based on the robot trajectory tracking error.

[0019] Based on the preset stability theory, the inspection trajectory tracking performance of the proportional iterative learning control algorithm is analyzed to verify the convergence characteristics of the robot's actual position with the number of iterations, so as to ensure the trajectory tracking accuracy under slip disturbance.

[0020] Preferably, the construction of the dynamic model of the wheeled robot with slip disturbance specifically includes:

[0021] The slip parameter is defined as a function of time. The slip parameter is related to the actual speed and the desired speed of the robot's left and right wheels, and satisfies the following: when the slip parameter is 1, the robot is in a no-slip state; when the slip parameter is greater than 1, the robot's actual speed is less than the desired speed, and the larger the slip parameter is, the greater the degree of slip.

[0022] By combining the slip parameters, wheel spacing, and wheel radius, a mapping relationship between the robot's linear velocity, angular velocity, and control input is established, thereby constructing the dynamic model of the wheeled robot with slip disturbance.

[0023] Preferably, the dynamic model of the wheeled robot with slip disturbance is as follows:

[0024] ;

[0025] In the formula, for The time derivative of the pose at time t; The radius of the robot's wheels; These are the slip parameters; It is half the distance between the wheels; For robots in The heading angle at any given moment; and The speeds are for the left and right wheels.

[0026] Preferably, the discretization of the wheeled robot dynamics model with slip disturbance is specifically performed using a processing method based on preset numerical discretization rules, including Euler discretization rules.

[0027] The discretized dynamic model obtained after discretization represents the mapping relationship between robot state variables and control inputs in the form of system matrix and input matrix.

[0028] Preferably, the discretized dynamic model is:

[0029] ;

[0030] In the formula, , The robots are respectively in Time and Position at any given moment; is the step size coefficient, where For the radius of the robot's wheels, These are the slip parameters; Let be the system matrix, where Sampling time, Half the wheel track, For robots in The heading angle at any given moment; In order to be in The control input at any time, among which and The speeds are for the left and right wheels.

[0031] Preferably, the robot trajectory tracking control objective is:

[0032] ;

[0033] In the formula, For the first The actual position of the next iteration; For the desired inspection trajectory; When the number of iterations The limit as it approaches infinity;

[0034] The desired inspection trajectory is as follows:

[0035] ;

[0036] In the formula, for The expected inspection trajectory at any given time; This is the step size coefficient; For the system matrix; The desired control input.

[0037] Preferably, the control law of the proportional iterative learning control algorithm is:

[0038] ;

[0039] In the formula, , The first , The next iteration The actual control input at any given time; , All are gain matrices; For the first The next iteration Tracking error at any given moment; For the first The next iteration Tracking error at any given moment.

[0040] Preferably, the gain matrix satisfy:

[0041] ;

[0042] In the formula, It is the identity matrix; This is the step size coefficient; For the system matrix; Norm operators; Let be the convergence rate constant, and satisfy . ;

[0043] The system matrix For actual location The Lipschitz condition must be satisfied, i.e., there exists a constant. Make ,in , All are system matrices. and The robot was in any position during the first and second tracking processes, respectively. The actual location at any given moment.

[0044] This invention also provides a proportional intelligent control device for a power inspection robot under slip disturbance. This device is used to implement the aforementioned proportional intelligent control method for a power inspection robot under slip disturbance, specifically including:

[0045] The model building module is used to construct a dynamic model of a wheeled robot with slip disturbances based on the kinematic principles of wheeled robots, combined with preset wheel parameters and longitudinal slip characteristics, by introducing slip parameters that reflect the difference between the expected speed and the actual speed of the robot wheels.

[0046] The discretization module is used to discretize the dynamic model of the wheeled robot with slip disturbance based on a preset sampling period to obtain a discretized dynamic model.

[0047] The trajectory definition module is used to determine the robot trajectory tracking control target according to the power inspection task requirements, and define the expected inspection trajectory that satisfies the control target. The control target is to make the robot's actual position converge to the expected inspection trajectory with the number of iterations.

[0048] The control algorithm design module is used to design a proportional iterative learning control algorithm based on the discretized dynamics model and the desired inspection trajectory. The proportional iterative learning control algorithm is used to dynamically correct the control input based on the robot trajectory tracking error.

[0049] The performance analysis module is used to analyze the inspection trajectory tracking performance of the proportional iterative learning control algorithm based on a preset stability theory, and to verify the convergence characteristics of the robot's actual position with the number of iterations, so as to ensure the trajectory tracking accuracy under slip disturbances.

[0050] This invention also provides a power inspection robot, including the proportional intelligent control device for the power inspection robot under slip disturbance described above.

[0051] As can be seen from the above technical solutions, this invention application has the following beneficial effects:

[0052] (1) Existing technologies are mostly based on the ideal scenario of "pure rolling without slippage" to design control strategies, completely ignoring longitudinal slippage under working conditions such as wetness and mud in power line inspection, resulting in a sharp drop in trajectory tracking accuracy. This invention introduces slippage parameters and combines the kinematic principles of wheeled robots with wheel parameters to construct a dynamic model with slippage disturbance. This model quantifies slippage disturbance and integrates it into the robot's motion equations, making the model highly consistent with the complex actual environment of power line inspection, and fundamentally solving the technical pain point of the disconnect between ideal assumptions and reality.

[0053] (2) Existing control methods rely on the precise nonlinear and strongly coupled dynamic model of the robot system, and have poor adaptability to dynamic parameter changes. The proportional iterative learning control algorithm designed in this invention has a control law that dynamically corrects the control input based only on the tracking error of the previous iteration and the error of the current iteration, without needing to know the precise dynamic parameters of the system; at the same time, it uses the constraint gain matrix satisfy and using the system matrix The Lipschitz property ensures stable control even in scenarios with time-varying slip parameters and dynamically changing environments. This property significantly improves the robot's robustness to complex power line inspection conditions, preventing loss of control due to inaccurate models.

[0054] (3) This invention defines the control objective as the actual position converging to the desired trajectory when the number of iterations approaches infinity, and verifies the convergence through Lyapunov stability theory: as the number of iterations increases, both the input error and the position error tend to 0. Simulation results further confirm that: under fixed slip, the tracking error approaches 0 after 1500 iterations; under time-varying slip, high-precision fitting of the actual trajectory and the desired trajectory can be achieved after 1000 iterations; while traditional PID control, under the same slip scenario, suffers from severe trajectory deviation and the error cannot converge. This iterative convergence characteristic perfectly solves the core problem of trajectory deviation caused by slip disturbance, meeting the stringent requirements of power line inspection for trajectory accuracy.

[0055] (4) Compared with alternatives such as fuzzy control and neural networks, the P-ILC algorithm of this invention has a simple structure (containing only a gain matrix and an error term) and does not require complex computing units; the discretization model adopts the Euler discretization rule, the sampling period is easy to implement, and it can be adapted to the limited hardware resources of power inspection robots. At the same time, the algorithm is effective for different sliding scenarios such as fixed sliding and time-varying sliding, and does not require manual parameter tuning, which greatly reduces the difficulty and cost of engineering deployment. It can be widely used in various wheeled power inspection robots and solves the problem of limited practicality of alternative solutions. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Referring to the drawings will make the features and advantages of the present invention clearer. The drawings are illustrative and should not be construed as limiting the present invention in any way. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0057] Figure 1 A flowchart of a proportional intelligent control method for a power inspection robot under slip disturbance provided by the present invention;

[0058] Figure 2 In this invention The trajectory tracking effect of a wheeled robot that iterates 300 times per second;

[0059] Figure 3 In this invention A diagram showing the trajectory tracking effect of a wheeled robot that iterates 500 times per second;

[0060] Figure 4 In this invention The trajectory tracking effect of a wheeled robot that iterates 1000 times per second;

[0061] Figure 5 In this invention Tracking error graph of a wheeled robot with 1000 iterations per hour;

[0062] Figure 6 In this invention A diagram showing the trajectory tracking effect of a wheeled robot that iterates 1500 times per second;

[0063] Figure 7 In this invention The trajectory tracking effect of a wheeled robot that iterates 300 times per second;

[0064] Figure 8 In this invention A diagram showing the trajectory tracking effect of a wheeled robot that iterates 500 times per second;

[0065] Figure 9 In this invention The trajectory tracking effect of a wheeled robot that iterates 1000 times per second;

[0066] Figure 10 In this invention Tracking error graph of a wheeled robot with 1000 iterations per hour;

[0067] Figure 11 In this invention A diagram showing the trajectory tracking effect of a wheeled robot controlled by PID.

[0068] Figure 12 In this invention Tracking error diagram of a wheeled robot controlled by PID control;

[0069] Figure 13 This invention provides a block diagram of a proportional intelligent control device for a power inspection robot under slip disturbance. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] Example 1: To address issues such as trajectory deviation and insufficient control robustness caused by longitudinal slippage in wheeled robots during intelligent power line inspection scenarios, such as... Figure 1 As shown, this invention proposes a proportional intelligent control method for a power inspection robot under slip disturbance, the method comprising:

[0072] S1: Based on the kinematic principles of wheeled robots, combined with preset wheel parameters and longitudinal slip characteristics, a dynamic model of a wheeled robot with slip disturbance is constructed by introducing slip parameters that reflect the difference between the desired speed and the actual speed of the robot wheels.

[0073] S2: Based on the preset sampling period, the dynamic model of the wheeled robot with slip disturbance is discretized to obtain the discretized dynamic model;

[0074] S3: Based on the requirements of the power inspection task, determine the robot trajectory tracking control target and define the expected inspection trajectory that satisfies the control target. The control target is to make the robot's actual position converge to the expected inspection trajectory with the number of iterations.

[0075] S4: Based on the discretized dynamics model and the desired inspection trajectory, a proportional iterative learning control algorithm is designed. The proportional iterative learning control algorithm is used to dynamically correct the control input based on the robot trajectory tracking error.

[0076] S5: Based on the preset stability theory, the inspection trajectory tracking performance of the proportional iterative learning control algorithm is analyzed to verify the convergence characteristics of the robot's actual position with the number of iterations, so as to ensure the trajectory tracking accuracy under slip disturbance.

[0077] As can be seen from the above technical solution, this invention proposes a proportional intelligent control method for a power inspection robot under slip disturbance. Based on the kinematics principle of wheeled robots, preset wheel parameters, and longitudinal slip characteristics, slip parameters reflecting the difference between the expected and actual wheel speeds are introduced to construct a dynamic model with slip disturbance, breaking through the ideal assumption of "pure rolling without slip" and making the model fit the actual inspection slip scenario. Based on the preset sampling period, the dynamic model with slip disturbance is discretized to obtain a discretized dynamic model, transforming the continuous model into a discrete form suitable for engineering deployment. According to the requirements of the power inspection task, the robot trajectory tracking control target (making the actual position converge to the desired trajectory with the number of iterations) is determined and the desired inspection trajectory is defined, clarifying the control direction and providing a target basis for subsequent algorithm design. Based on the discretized dynamic model and the desired inspection trajectory, a proportional iterative learning control algorithm is designed. This algorithm can dynamically correct the control input based on the trajectory tracking error, reduce the dependence on the accurate model, and improve the robustness of the dynamic environment. The inspection trajectory tracking performance of the proportional iterative learning control algorithm is analyzed based on the preset stability theory, and the convergence characteristics of the actual position with the number of iterations are verified to ensure the trajectory tracking accuracy under slip disturbance.

[0078] In step S1, based on the kinematic principles of wheeled robots and combined with preset wheel parameters and longitudinal slip characteristics, a dynamic model of a wheeled robot with slip disturbance is constructed by introducing slip parameters that reflect the difference between the desired speed and the actual speed of the robot wheels.

[0079] Specifically, we first establish a kinematic model for a two-wheeled robot, specifically for wheeled robots:

[0080] (1)

[0081] In the formula, for The time derivative of the pose at time t corresponds to the robot's instantaneous velocity, where, Let be the linear velocity of the robot along the X-axis in the Cartesian coordinate system. Let be the linear velocity of the robot along the Y-axis in the Cartesian coordinate system. Let ω be the robot's angular velocity. For robots in The heading angle at any given moment; This represents the linear velocity of the robot. Let be the angular velocity of the robot, and satisfy the following relationship: .

[0082] Adding longitudinal slip on this basis still has... Because the lateral direction is unaffected at this point. To describe the longitudinal slip in detail, parameters are introduced. , ,two The value corresponds to the speed of the left and right wheels. For the desired speed, This refers to the actual speed. According to the law of conservation of energy, given the slippage loss, the desired speed must be greater than the actual speed. It can intuitively demonstrate the degree of sliding of the wheeled robot. This corresponds to the no-slip state. The larger the value, the greater the actual speed loss and the more severe the vehicle slippage. Next, we will specifically analyze the kinematic model of a wheeled robot exhibiting longitudinal slippage, first defining the slippage parameters. It's about time. function The speeds of the left and right wheels are , Then the relationship between linear velocity, angular velocity and the velocities of the left and right wheels can be obtained as follows:

[0083] (2)

[0084] Then, by combining the no-slip model, we can obtain the kinematic model of the wheeled robot dynamics model with slip disturbances:

[0085] (3)

[0086] In the formula, for The time derivative of the pose at time t; The radius of the robot's wheels; These are the slip parameters; It is half the distance between the wheels; For robots in The heading angle at any given moment; and The speeds are for the left and right wheels.

[0087] In step S2, the dynamic model of the wheeled robot with slip disturbance is discretized based on a preset sampling period. Specifically, a processing method based on preset numerical discretization rules is adopted, including Euler discretization rules. The discretized dynamic model obtained after discretization represents the mapping relationship between robot state variables and control inputs in the form of system matrix and input matrix.

[0088] Specifically, define the sampling time. Using Euler's method, we can obtain:

[0089] (4)

[0090] After simplification, we get:

[0091] (5)

[0092] In the formula, , The robots are respectively in Time and Position at any given moment; This is the step size coefficient; Let be the system matrix, where Sampling time, Half the wheel track; In order to be in Time-based control input.

[0093] In step S3, based on the requirements of the power inspection task, the robot trajectory tracking control target is determined, and the desired inspection trajectory that satisfies the control target is defined. The control target is to make the robot's actual position converge to the desired inspection trajectory with the number of iterations.

[0094] Specifically, for the trajectory tracking problem of robot systems, the most important task is to achieve a high-precision fit between the final inspection trajectory and the desired inspection trajectory, thus mitigating the impact of slippage on the system. The robot inspection process is a repetitive motion process. To gradually improve the trajectory tracking accuracy during repeated runs, in step S3, the number of iterations is defined. Combining step S2, we can derive the robot's first... The trajectory is as follows:

[0095] (6)

[0096] In the formula, For the first The actual position of the next iteration; When the number of iterations The limit when it approaches infinity.

[0097] make To determine the desired inspection trajectory, the ultimate goal of this system is to find a suitable... So that under given time conditions, the final The control objective is: Therefore, it is assumed that there exists a desired input control. Able to achieve a given desired inspection trajectory have:

[0098] (7)

[0099] in, for The expected inspection trajectory at any given time; This is the system matrix.

[0100] In step S4, based on the discretized dynamic model and the desired inspection trajectory, a proportional-iterative learning control algorithm is designed. The proportional-iterative learning control (P-ILC) algorithm is used to dynamically correct the control input based on the robot trajectory tracking error.

[0101] Specifically, the control law of the proportional iterative learning control algorithm is:

[0102] (8)

[0103] In the formula, , The first , The next iteration The actual control input at any given time; , These are all gain matrices, and they are all bounded, each no greater than [value missing]. , ; For the first The next iteration Tracking error at any given moment; For the first The next iteration Tracking error at any given moment. Corresponding to the To address the tracking error during the next inspection, the ILC algorithm employed by this robot system can utilize only the tracking error from the previous inspection and the current tracking error. In other words, it relies solely on the robot's actual position information and desired position information without requiring the robot model to modify the control input itself, ultimately achieving high-precision tracking of the inspection trajectory.

[0104] In step S5, based on Lyapunov stability theory, the inspection trajectory tracking performance of the proportional iterative learning control algorithm is analyzed to verify the convergence characteristics of the robot's actual position with the number of iterations, so as to ensure the trajectory tracking accuracy under slip disturbance.

[0105] Specifically, firstly, we define the first The input error of the next iteration is Combining the control law designed in step S4 (7), we can obtain:

[0106] (9)

[0107] Among them, let , According to equations (6) and (7) in step S3, we get:

[0108] (10)

[0109] Combining equations (9) and (10) above, we can obtain:

[0110] (11)

[0111] Therefore, taking the norms of equations (11) and (10) respectively, we can obtain:

[0112] (12)

[0113] (13)

[0114] ( Since these are bounded parameters, complete slippage and loss of control are avoided. Therefore, we have At the same time, input Boundedness is a prerequisite for system controllability, therefore... Furthermore, the robot's operation is a non-abrupt, continuous process; therefore, the parameters... right The Lipschitz condition must be satisfied, i.e., there exists a constant. Make In this invention, the control gain is designed to satisfy the following conditions to ensure the safety and reliability of the inspection process: ,in It is the identity matrix; This is the step size coefficient; For the system matrix; Norm operators; Let be the convergence rate constant, and satisfy . .

[0115] Therefore, Substituting the above conditions into equations (12) and (13), we can obtain: (14)

[0116] (15)

[0117] definition Assuming the initial state of tracking satisfies Substituting into equation (15), we get:

[0118] (16)

[0119] Substituting equation (16) into equation (14), we get:

[0120] (17)

[0121] Furthermore, define Then equation (17) can be expressed as:

[0122] (18)

[0123] Multiply both sides of equation (18) by Then we can obtain:

[0124] (19)

[0125] set up The norm-based inequality is:

[0126] (20)

[0127] The formula can be simplified to:

[0128] (twenty one)

[0129] in, .

[0130] Equation (21) can be further simplified to:

[0131] (twenty two)

[0132] when When large enough, Taking the limit of equation (22) at this point, we get:

[0133] (twenty three)

[0134] Similarly, take equation (16) The norm can be obtained as follows:

[0135] (twenty four)

[0136] Finally, combining equation (23), taking the limit of equation (24) yields:

[0137] (25)

[0138] The above process illustrates the actual position of the robot system under given gain conditions. As the number of task executions The increase in the slip parameter gradually converges to the desired reference trajectory. This demonstrates that even in the presence of slip, the ILC algorithm designed in this invention can still guarantee the reliability of robot inspection, and the slip parameter... The change in the specific value does not affect the final result.

[0139] To further illustrate the advantages of the method of the present invention, a simulation experiment was designed and conducted. The specific steps of the simulation experiment are as follows.

[0140] S1: Establish a dynamic model of the wheeled robot with slip disturbance:

[0141] (26)

[0142] Wheel spacing is The wheel radius is Let the introduced slip parameters be... The corresponding slip parameter under time-varying conditions is set as follows: .

[0143] S2: Discretize the dynamic model from step S1:

[0144] The simplified discrete kinematic model is as follows:

[0145] (27)

[0146] in, , It is a system matrix. It is the control input of the system, sampling time. The initial robot position is selected as .

[0147] S3: Determine the robot control objectives and define the desired inspection trajectory. :

[0148] Desired inspection trajectory set .in, , , .

[0149] S4: Design a model-free proportional iterative learning control algorithm:

[0150] (28)

[0151] Set the gain matrix as follows , , Corresponding to the The state error of the next iteration.

[0152] S5: Analyze the performance of inspection trajectory tracking.

[0153] First, define the... The input error of each iteration is have:

[0154] (29)

[0155] Among them, let , have:

[0156] (30)

[0157] Combining equations (29) and (30) above, we can obtain:

[0158] (31)

[0159] Therefore, taking the norms of equations (31) and (30) respectively, we can obtain:

[0160] (32)

[0161] (33)

[0162] Among them, let , , , .Will Substituting the above conditions into equations (32) and (33), we can obtain:

[0163] (34)

[0164] (35)

[0165] definition Tracking the initial state satisfies Substituting into equation (35), we get:

[0166] (36)

[0167] Substituting equation (36) into equation (34), we get:

[0168] (37)

[0169] definition Then equation (37) can be expressed as:

[0170] (38)

[0171] Multiply both sides of equation (38) by Then we can obtain:

[0172] (39)

[0173] set up The norm-based inequality is:

[0174] (40)

[0175] The formula can be simplified to:

[0176] (41)

[0177] in .

[0178] Equation (41) can be further simplified:

[0179] (42)

[0180] when When large enough, Taking the limit of equation (42) at this point, we get:

[0181] (43)

[0182] Similarly, take equation (36) The norm can be obtained as follows:

[0183] (44)

[0184] Finally, combining equation (43), taking the limit of equation (44) yields:

[0185] (45)

[0186] The above process illustrates the actual position of the wheeled inspection robot system under given gain conditions. As the number of task executions The increase gradually converges to the expected reference trajectory.

[0187] The following simulations using MATLAB are used to verify the performance of the method of the present invention under fixed slip disturbance and time-varying slip disturbance scenarios, and to compare it with the PID control method.

[0188] Figures 2 to 6 The graph shows the trajectory tracking performance and tracking error variation of a wheeled robot under fixed sliding parameters. It can be observed that the tracking error of the inspection trajectory gradually decreases as the number of task executions increases. After 500 task executions, the robot's actual trajectory is quite close to the expected inspection trajectory, and the tracking error decreases relatively quickly with the increase in the number of task executions (i.e., the number of iterations). Achieving a high-precision fit between the actual and expected trajectories requires even more iterations. This indicates that the presence of slippage affects the performance of the actual system, making the original task more complex.

[0189] Figures 7 to 10 The graph shows the tracking performance and tracking error variation of a wheeled robot under time-varying slip parameters. It can be observed that: when As the slip parameter increases, from 2 to 4.5, its result is similar to that of a fixed slip parameter. Compared to the previous method, with the same number of iterations, the actual trajectory deviates more from the expected inspection trajectory, i.e., the error is larger. However, with a sufficient number of iterations, the tracking error can be reduced to a smaller range. This indicates that, regardless of whether it is fixed longitudinal slip or time-varying longitudinal slip, in wheeled robot systems with longitudinal slip, the P-ILC algorithm proposed in this invention has the ability to adapt the slip amplitude and the frequency of change, which can effectively compensate for the impact of slip on the inspection trajectory tracking performance, thereby enabling the robot to track the inspection trajectory with high precision.

[0190] Figure 11 and Figure 12 The performance comparison between the proposed method and the PID control method is presented. The system model and initial parameters remain unchanged; only the iterative control algorithm is replaced with PID control, with P=1.2, I=0.05, and D=0.01. The final results show that under this slip condition, even with the enhanced PID control algorithm, PID control struggles to achieve good results, deviating significantly from the actual performance. The effect of optimizing the PID control algorithm itself becomes very weak. In this case, using the ILC algorithm to increase the number of iterations is a better approach.

[0191] Example 2: Figure 13 As shown, this invention provides a proportional intelligent control device for a power inspection robot under slip disturbance. This device is used to implement the proportional intelligent control method for a power inspection robot under slip disturbance described in Embodiment 1 above, specifically including:

[0192] The model building module 100 is used to construct a dynamic model of a wheeled robot with slip disturbance based on the kinematic principles of a wheeled robot, combined with preset wheel parameters and longitudinal slip characteristics, by introducing slip parameters that reflect the difference between the expected speed and the actual speed of the robot wheel.

[0193] Discretization module 200 is used to discretize the dynamic model of a wheeled robot with slip disturbance based on a preset sampling period to obtain a discretized dynamic model;

[0194] The trajectory definition module 300 is used to determine the robot trajectory tracking control target according to the power inspection task requirements, and to define the expected inspection trajectory that satisfies the control target. The control target is to make the robot's actual position converge to the expected inspection trajectory with the number of iterations.

[0195] The control algorithm design module 400 is used to design a proportional iterative learning control algorithm based on the discretized dynamics model and the desired inspection trajectory. The proportional iterative learning control algorithm is used to dynamically correct the control input based on the robot trajectory tracking error.

[0196] The performance analysis module 500 is used to analyze the inspection trajectory tracking performance of the proportional iterative learning control algorithm based on the preset stability theory, and to verify the convergence characteristics of the robot's actual position with the number of iterations, so as to ensure the trajectory tracking accuracy under slip disturbance.

[0197] This embodiment provides a proportional intelligent control device for a power inspection robot under slip disturbance, used to implement the aforementioned proportional intelligent control method for a power inspection robot under slip disturbance. Therefore, the specific implementation of the proportional intelligent control device for a power inspection robot under slip disturbance can be found in the previous section on the embodiment of the proportional intelligent control method for a power inspection robot under slip disturbance. For example, the model building module 100, discretization module 200, trajectory definition module 300, control algorithm design module 400, and performance analysis module 500 are respectively used to implement steps S1, S2, S3, S4, and S5 in the aforementioned proportional intelligent control method for a power inspection robot under slip disturbance. Therefore, its specific implementation can be referred to the descriptions of the corresponding embodiments. To avoid redundancy, further details are omitted here.

[0198] Example 3: This embodiment of the invention provides a power inspection robot, including the proportional intelligent control device for the power inspection robot under sliding disturbance described in Example 2 above. The specific implementation method can be referred to the description of the corresponding embodiments. To avoid redundancy, it will not be repeated here.

[0199] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0200] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0201] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0202] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A proportional intelligent control method for a power inspection robot under slip disturbance, characterized in that, include: Based on the kinematic principles of wheeled robots, and combining preset wheel parameters and longitudinal slip characteristics, a dynamic model of a wheeled robot with slip disturbance is constructed by introducing slip parameters that reflect the difference between the desired and actual speeds of the robot wheels. The dynamic model of the wheeled robot with slip disturbance is as follows: ； In the formula, for The time derivative of the pose at time t; The radius of the robot's wheels; These are the slip parameters; It is half the distance between the wheels; For robots in The heading angle at any given moment; and The speeds of the left and right wheels; Based on a preset sampling period, the dynamic model of the wheeled robot with slip disturbance is discretized to obtain a discretized dynamic model; Based on the requirements of the power line inspection task, a robot trajectory tracking control objective is determined, and a desired inspection trajectory that satisfies the control objective is defined. The control objective is to make the robot's actual position converge to the desired inspection trajectory with the number of iterations. The robot trajectory tracking control objective is as follows: ； In the formula, For the first The actual position of the next iteration; For the desired inspection trajectory; When the number of iterations The limit as it approaches infinity; The desired inspection trajectory is as follows: ； In the formula, for The expected inspection trajectory at any given time; This is the step size coefficient; For the system matrix; For the desired control input; Based on the discretized dynamics model and the desired inspection trajectory, a proportional iterative learning control algorithm is designed. This algorithm is used to dynamically correct the control input based on the robot trajectory tracking error. The control law of the proportional iterative learning control algorithm is as follows: ； In the formula, , The first , The next iteration The actual control input at any given time; , All are gain matrices; For the first The next iteration Tracking error at any given moment; For the first The next iteration Tracking error at any given moment; Based on the preset stability theory, the inspection trajectory tracking performance of the proportional iterative learning control algorithm is analyzed to verify the convergence characteristics of the robot's actual position with the number of iterations, so as to ensure the trajectory tracking accuracy under slip disturbance.

2. The proportional intelligent control method for a power inspection robot under slip disturbance according to claim 1, characterized in that, The construction of the dynamic model of the wheeled robot with slip disturbance specifically includes: The slip parameter is defined as a function of time. The slip parameter is related to the actual speed and the desired speed of the robot's left and right wheels, and satisfies the following: when the slip parameter is 1, the robot is in a no-slip state; when the slip parameter is greater than 1, the robot's actual speed is less than the desired speed, and the larger the slip parameter is, the greater the degree of slip. By combining the slip parameters, wheel spacing, and wheel radius, a mapping relationship between the robot's linear velocity, angular velocity, and control input is established, thereby constructing the dynamic model of the wheeled robot with slip disturbance.

3. The proportional intelligent control method for a power inspection robot under slip disturbance according to claim 1, characterized in that, The discretization of the dynamic model of the wheeled robot with slip disturbance is specifically performed using a processing method based on preset numerical discretization rules, including Euler discretization rules. The discretized dynamic model obtained after discretization represents the mapping relationship between robot state variables and control inputs in the form of system matrix and input matrix.

4. The proportional intelligent control method for a power inspection robot under slip disturbance according to claim 1 or 3, characterized in that, The discretized dynamic model is as follows: ； In the formula, , The robots are respectively in Time and Position at any given moment; is the step size coefficient, where For the radius of the robot's wheels, These are the slip parameters; Let be the system matrix, where Sampling time, Half the wheel track, For robots in The heading angle at any given moment; In order to be in The control input at any time, among which and The speeds are for the left and right wheels.

5. The proportional intelligent control method for a power inspection robot under slip disturbance according to claim 4, characterized in that, The gain matrix satisfy: ； In the formula, It is the identity matrix; This is the step size coefficient; For the system matrix; Norm operators; Let be the convergence rate constant, and satisfy . ; The system matrix For actual location The Lipschitz condition must be satisfied, i.e., there exists a constant. Make ,in , All are system matrices. and The robot was in any position during the first and second tracking processes, respectively. The actual location at any given moment.

6. A proportional intelligent control device for a power inspection robot under slip disturbance, characterized in that, The device is used to implement the proportional intelligent control method for the power inspection robot under slip disturbance as described in any one of claims 1 to 5, specifically including: The model building module is used to construct a dynamic model of a wheeled robot with slip disturbances based on the kinematic principles of wheeled robots, combined with preset wheel parameters and longitudinal slip characteristics, by introducing slip parameters that reflect the difference between the expected speed and the actual speed of the robot wheels. The discretization module is used to discretize the dynamic model of the wheeled robot with slip disturbance based on a preset sampling period to obtain a discretized dynamic model. The trajectory definition module is used to determine the robot trajectory tracking control target according to the power inspection task requirements, and define the expected inspection trajectory that satisfies the control target. The control target is to make the robot's actual position converge to the expected inspection trajectory with the number of iterations. The control algorithm design module is used to design a proportional iterative learning control algorithm based on the discretized dynamics model and the desired inspection trajectory. The proportional iterative learning control algorithm is used to dynamically correct the control input based on the robot trajectory tracking error. The performance analysis module is used to analyze the inspection trajectory tracking performance of the proportional iterative learning control algorithm based on a preset stability theory, and to verify the convergence characteristics of the robot's actual position with the number of iterations, so as to ensure the trajectory tracking accuracy under slip disturbances.

7. A power line inspection robot, characterized in that, The device includes the proportional intelligent control device for the power inspection robot under slip disturbance as described in claim 6.

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