Self-adaptive trajectory tracking control method for pole-climbing detection robot
By constructing a dynamic model and adaptive controller for the pole-climbing robot, the problem of poor control accuracy of the pole-climbing robot was solved, achieving high-precision trajectory tracking in complex environments and improving the dynamic and steady-state performance of the pole-climbing robot.
Patent Information
- Application Number
- CN202511710857.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-20
- Publication Date
- 2026-02-13
AI Technical Summary
In the existing technology, the trajectory control method of pole climbing robot has failed to effectively solve the problem of poor control accuracy during the climbing process, especially when facing different trajectory lines, it is difficult to guarantee accurate control.
A dynamic model of a pole-climbing robot is constructed, an adaptive controller is designed, transient and steady-state performance requirements are transformed into computational constraints through preset performance functions, and error transformation technology is used to approximate the uncertainty using a radial basis function neural network. The control input is designed to achieve trajectory tracking.
Ensuring that the trajectory tracking error converges within a given performance boundary within a predefined time improves the dynamic and steady-state performance of the pole-climbing robot, enabling accurate trajectory tracking in complex environments.
Smart Images
Figure CN121523038A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of pole climbing robots, and particularly relates to a self-adaptive trajectory tracking control method for a pole climbing detection robot. BACKGROUND
[0002] In the aspect of pole climbing detection, the traditional manual detection method has problems such as low efficiency, high risk and many blind spots. With the rapid development of automatic control technology and computer technology, pole climbing detection robots have become the core equipment for pole climbing detection because they can work autonomously in complex and closed environments.
[0003] In the prior art, the trajectory control method for the pole climbing robot mainly focuses on solving the steady-state performance of the robot system, but does not consider the dynamic performance of the robot system. It is difficult to ensure accurate control of the pole climbing robot during the climbing process when facing different trajectory lines.
[0004] Therefore, there is an urgent need for a self-adaptive trajectory tracking control method for a pole climbing detection robot to solve the problem of poor control accuracy of the pole climbing robot during the climbing process. SUMMARY
[0005] The present application provides a self-adaptive trajectory tracking control method for a pole climbing detection robot to solve the problem of poor control accuracy of the pole climbing robot during the climbing process.
[0006] To achieve the above-mentioned purpose, the following technical solutions are adopted: A self-adaptive trajectory tracking control method for a pole climbing detection robot, comprising the following steps: First, taking the pole climbing robot as the object, a dynamic model of the pole climbing robot for climbing is constructed; Second, the control target is determined; Third, the transient and steady-state performance requirements are converted into calculation constraints by a preset performance function, the calculation constraints are converted into boundedness by an error conversion technology, and a self-adaptive controller is designed to obtain a control input for controlling the pole climbing robot.
[0007] To optimize the above technical solutions, the following specific measures are taken: Further, the pole climbing robot comprises a front sensor section and a rear driving section, the front sensor section and the rear driving section are connected through a positive hinge, the rear driving section is equipped with double-sided independent driving wheels, and the front sensor section is equipped with a driven support wheel.
[0008] Further, the first step comprises the following steps: The dynamic model of the pole climbing robot for climbing is constructed: , wherein, is the position vector, is the displacement of the climbing robot along the climbing centerline, is the angle of the rear drive joint in the cross section relative to the climbing centerline, is the rotation angle of the active hinge; is the velocity vector, is the linear velocity of the climbing robot along the climbing centerline, is the angular velocity of the climbing robot around the climbing centerline, is the angular velocity of the active hinge rotation; is the control input, is the equivalent axial force, is the equivalent rotational moment, is the active torque of the active hinge, and are the input torques of the left and right drive wheels of the climbing robot, respectively; is the inertia matrix, which is expressed as: where, and are the masses of the front sensor joint and the rear drive joint, respectively, and are the moments of inertia of the front sensor joint and the rear drive joint around the center of mass, respectively, is the length of the rear drive joint; is the Coriolis force matrix, which is expressed as: , is the potential force vector generated by the climbing pole wall contact potential energy, which is expressed as: where, is the equivalent stiffness of the climbing pole wall contact, is the inner radius of the climbing pole; is the damping matrix, which is expressed as: where, , and are the axial fluid damping coefficient, the rotational fluid damping coefficient, and the active hinge damping coefficient, respectively; is the potential force vector generated by the tube wall contact potential energy, which is expressed as: where, is the drive wheel radius, is the drive wheel track.
[0009] Further, according to , the above dynamics model is converted into a state equation as follows: .
[0010] Further, the second step comprises the following steps: Confirming that the controller is in normal communication with each drive motor of the pole climbing robot, and confirming that the given reference trajectory information is known, including the reference trajectory and its differential is continuous and bounded.
[0011] Further, the third step comprises the following steps: Determining the tracking error : , wherein , and respectively represent the displacement deviation of the robot along the pole climbing center line, the angular deviation of the robot drive joint in the cross section relative to the pole climbing center line, and the rotation angle deviation of the active hinge.
[0012] Further, the following steps are also included: Setting an asymmetric global preset performance function for adapting to the pole climbing constraints, as follows: , wherein is a time-varying scaling function at time t, and its calculation formula is: , wherein is the steady-state error bound, is the preset convergence rate, is the preset convergence time; From the calculation formula of , at the initial moment , substituting the above asymmetric global preset performance function can obtain ; When , , satisfies ; wherein is a boundary parameter, and its expression is: , is the pole climbing physical constraint, which is set as: .
[0013] Further, the following steps are also included: According to the tracking error Design the normalization function as follows: , Differentiation yields: , The derivative is always positive; According to the normalization function, we can obtain , And there are , .
[0014] Furthermore, it also includes the following steps: Let the barrier function be as follows: , in, , For time-varying boundary functions, The boundary convergence rate; And there are: , ,Depend on achievable We can obtain: ; right Solving for the inverse function: when : , Further inverse derivation shows that... ; when : , Furthermore, through inverse solution, we can see that... ; Then we can obtain , ; right Differentiate:
[0015] Will Expand:
[0016] in, , The expression is:
[0017] in:
[0018] Combining the above formula, we can obtain: .
[0019] Furthermore, it also includes the following steps: Based on the state equation and the barrier function, the transformation error vector is defined as: wherein, is a virtual control law; Take Lyapunov function , the derivative of which can be obtained as: wherein, , , ; Design a virtual control law: wherein, is a positive definite gain matrix; Integrating the above formula can obtain: ; Take Lyapunov function , the derivative of which can be obtained as: , According to is a symmetric and positive definite matrix, is a skew-symmetric matrix, and can obtain: wherein, Substitute it into the above formula to obtain: ; According to the above uncertainty term, define the total uncertainty: , For the above uncertainty term, a radial basis function neural network RBFNN is used for approximation: , wherein, the input vector , is an ideal weight matrix, is an approximation error, satisfying , is an activation function, and a Gaussian function is used: wherein, is a center point, is a width parameter; Then, the control input is: , wherein, is the Moore-Penrose pseudo-inverse of , the control gain is a positive definite gain matrix, is a neural network weight upper bound estimate, ; Set a single-parameter adaptive law: wherein, is a design parameter.
[0020] The beneficial effects of the present application are: The pole climbing robot is taken as an object to construct a pole climbing dynamics model; control targets are determined to ensure that the trajectory tracking error of the pole climbing robot converges within a predefined time under any initial condition and is always constrained within a given performance boundary; transient and steady state performance requirements are converted into calculation constraints by a preset performance function, and the calculation constraints are converted into boundedness by error conversion technology. While meeting the requirements of the asymmetric dynamics characteristics of the pole climbing robot, the trajectory tracking error is ensured to converge within a preset time and range, and the dynamic and steady state performance of the pole climbing robot control system is improved. BRIEF DESCRIPTION OF DRAWINGS
[0021] Figure 1 A flowchart of a pole climbing detection robot adaptive trajectory tracking control method proposed by the present application is shown in the figure; Figure 2 A pole climbing robot structure diagram of a pole climbing detection robot adaptive trajectory tracking control method proposed by the present application is shown in the figure; Figure 3 A simulation diagram of a pole climbing detection robot adaptive trajectory tracking control method proposed by the present application is shown in the figure Figure 1 ; Figure 4 A simulation diagram of a pole climbing detection robot adaptive trajectory tracking control method proposed by the present application is shown in the figure Figure 2 ; Figure 5 A simulation diagram of a pole climbing detection robot adaptive trajectory tracking control method proposed by the present application is shown in the figure Figure 3 ; Figure 6 A simulation diagram of a pole climbing detection robot adaptive trajectory tracking control method proposed by the present application is shown in the figure Figure 4 ; Figure 7 A simulation diagram of a pole climbing detection robot adaptive trajectory tracking control method proposed by the present application is shown in the figure Figure 5 ; Figure 8 A simulation diagram of a pole climbing detection robot adaptive trajectory tracking control method proposed by the present application is shown in the figure Figure 6 ; Figure 9 A simulation diagram of a pole climbing detection robot adaptive trajectory tracking control method proposed by the present application is shown in the figure Figure 7 ; Figure 10 A simulation diagram of a pole climbing detection robot adaptive trajectory tracking control method proposed by the present application is shown in the figure Figure 8 ; Figure 11 A simulation diagram of a pole climbing detection robot adaptive trajectory tracking control method proposed by the present application is shown in the figure Figure 9; Figure 12 A simulation schematic of a self-adaptive trajectory tracking control method of a pole climbing detection robot proposed in the present application Figure 10 Figure 13 A simulation schematic of a self-adaptive trajectory tracking control method of a pole climbing detection robot proposed in the present application Figure 10 One; Figure 14 A simulation schematic of a computer readable storage medium applying a self-adaptive trajectory tracking control method of a pole climbing detection robot proposed in the present application. DETAILED DESCRIPTION
[0022] In order to facilitate the understanding of the present application, the present application will be described in more detail below in conjunction with the drawings and specific embodiments. The preferred embodiments of the present application are shown in the drawings. However, the present application can be implemented in many different forms and is not limited to the embodiments described in the specification. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present application more thorough and comprehensive.
[0023] It should be noted that, unless otherwise defined, all technical and scientific terms used in the specification have the same meaning as commonly understood by those skilled in the art to which the present application belongs. The terms used in the specification of the present application are only for the purpose of describing the specific embodiments and are not intended to limit the present application. The term "and / or" used in the specification includes any and all combinations of one or more related listed items.
[0024] As shown in the accompanying Figure 1 A self-adaptive trajectory tracking control method of a pole climbing detection robot, comprising the following steps: First, taking the pole climbing robot as the object, a dynamic model of the pole climbing robot for climbing is constructed; Second, the control target is determined to ensure that the trajectory tracking error of the pole climbing robot converges within a predefined time under given initial conditions and is constrained within a given performance boundary; Third, the transient and steady-state performance requirements are converted into computational constraints by a pre-set performance function, the computational constraints are converted into boundedness by error conversion technology, and an adaptive controller is designed to obtain control input for controlling the position and speed of the pole climbing robot.
[0025] As shown in the accompanying Figure 2 In the above embodiment, the pole climbing robot includes a front sensor section and a rear driving section, the front sensor section and the rear driving section are connected through a driven hinge, the rear driving section is equipped with double-sided independent driving wheels, and the front sensor section is equipped with a driven support wheel. In use, it is driven to move along the pole by the driving wheels.
[0026] In the above embodiment, the first step includes the following steps: A dynamic model of the pole climbing robot is constructed: , where, is the position vector, is the displacement of the pole climbing robot along the pole centerline, usually the displacement of the center of mass of the driving segment, is the angle of the rear driving segment of the pole climbing robot relative to the pole centerline in the cross section, is the rotation angle of the active hinge; is the velocity vector, is the linear velocity of the pole climbing robot along the pole centerline, is the angular velocity of the pole climbing robot around the pole centerline, is the angular velocity of the rotation of the active hinge; is the control input, is the equivalent axial force, is the equivalent rotational torque, is the active torque of the active hinge, and are the input torques of the left and right driving wheels of the pole climbing robot, respectively; is the inertia matrix, whose expression is: , where, and are the masses of the front sensor segment and the rear driving segment, respectively, and are the moments of inertia around the center of mass of the front sensor segment and the rear driving segment, respectively, is the length of the rear driving segment; is the Coriolis force matrix, whose expression is: , is the potential force vector generated by the pole wall contact potential energy, whose expression is: , where, is the equivalent stiffness of the pole wall contact, is the inner radius of the pole; is the damping matrix, whose expression is: , where, , and are the axial, rotational and active joint damping coefficients, respectively; is the potential force vector generated by the tube wall contact potential energy, which is expressed as: , where, is the driving wheel radius, is the driving wheel track.
[0027] In the above embodiment, according to , , the above dynamics model is converted into a state equation as follows: .
[0028] In the above embodiment, the second step includes the following steps: Confirm that the controller is in normal communication with each drive motor of the robot, and that the motor can obtain the controller signal without delay, and confirm that the given reference trajectory information is known, including the reference trajectory and its differential is continuous and bounded.
[0029] This control target design ensures that the pole climbing robot can quickly and accurately track the reference trajectory in a complex pole climbing environment, while meeting the preset performance requirements, and is robust to initial state and system uncertainty.
[0030] In the above embodiment, the third step includes the following steps: Determine the tracking error : , where, , and represent the displacement deviation of the robot along the pole center line, the angle deviation of the robot drive joint in the cross section relative to the pole center line, and the rotation angle deviation of the active joint, respectively.
[0031] In the above embodiment, the following steps are further included: When the pole climbing robot moves, its radial displacement can only deviate unilaterally under the constraint of the tube wall, while the axial and rotational degrees of freedom can deviate bilaterally. The boundary function of traditional preset performance control cannot handle unilateral constraints; at the same time, traditional preset performance control requires initial error within the boundary, which is not suitable for large pose deviation at the entrance of the pole.
[0032] Therefore, an asymmetric global preset performance function is designed to adapt to the pole climbing constraint, as follows: , wherein, is a time-varying scaling function at time t, and its calculation formula is: , wherein, is a steady-state error boundary, is a preset convergence rate, is a preset convergence time.
[0033] For the problem that the initial value of the traditional preset performance function needs to be greater than the initial error , through the calculation formula of , at the initial time , substituting the above asymmetric global preset performance function can obtain , that is, the initial boundary tends to infinity, which is used to contain any initial error; In addition, for the task requirement that the error enters the steady-state boundary within a fixed time , the piecewise function of the calculation formula of is used; when , , select to satisfy , so as to strictly ensure switching to the steady-state boundary at time; wherein, is a boundary parameter, and its expression is: , is a physical constraint of climbing a pole, including an axial pipe diameter allowance and a maximum deflection angle, which is further set as: , that is: .
[0034] Through the above calculation formula, for the radial error , since the pipe wall constraint can prevent excessive deviation, the asymmetric global preset performance function uses to set a relatively loose boundary; for the angle error, uses to set a relatively strict boundary to achieve accurate attitude control.
[0035] In the above embodiment, the following steps are further included: In the third step S3, for the characteristics of the pole climbing robot, in order to ensure that the designed controller is not affected by the initial condition, a normalization function is designed according to the tracking error , as follows: , further derivation can be obtained: , This derivative is always positive, ensuring strict monotonicity; According to the normalization function, we have , , and , This normalization function realizes the compression mapping of the tracking error from to while ensuring continuity and differentiability at zero.
[0036] In the above embodiment, the following steps are further included: On the basis of the normalization function, the barrier function is set as follows: , where , is a time-varying boundary function, is the boundary convergence rate; And we have: , This is because: From we have , so we have: ; Solve the inverse function of : When : , Further inverse derivation shows that ; Similarly, when : , Further, through the inverse solution, we have ; Then we have , that is: , .
[0037] By designing the above normalization function and barrier function, the problem of ensuring that the tracking error is constrained within the preset performance region is transformed into , a boundedness problem; In order to facilitate subsequent controller design, we take the derivative of :
[0038] Expand :
[0039] wherein, , the expression is:
[0040] wherein:
[0041] Combining the above formula can be obtained: .
[0042] In the above embodiment, the following steps are also included: Based on the state equation and the barrier function, the conversion error vector is defined as:
[0043] wherein, is a virtual control law; Take Lyapunov function , and its derivative can be obtained:
[0044] wherein, , , ; Design a virtual control law:
[0045] wherein, is a positive definite gain matrix; Integrating the above formula can be obtained:
[0046] Take Lyapunov function , and its derivative can be obtained:
[0047] According to is a symmetric and positive definite matrix, is a skew-symmetric matrix, and can be obtained:
[0048] wherein, , and substituting it into the above formula can be obtained:
[0049] In the controller design process, there are many uncertainties caused by the system, mainly including: due to the contact stiffness Unknown and the measurement error of the pipe radius Uncertainty; multiple damping coefficients due to wear, aging, etc. Uncertainty; due to load mass variation, error in moment of inertia calculation Uncertainty; due to inaccurate coupling coefficients Uncertainty. According to the above uncertainty terms, define the total uncertainty:
[0050] For the above uncertainty terms, a radial basis function neural network RBFNN is used for approximation:
[0051] where the input vector , is the ideal weight matrix, is the approximation error, satisfying , is the activation function, using Gaussian function:
[0052] where is the center point, is the width parameter; Then, the control input is:
[0053] where is the Moore-Penrose pseudo-inverse of , the control gain is a positive definite gain matrix, is the upper bound estimation of neural network weights, ; Set the single parameter adaptive law:
[0054] where is the design parameter.
[0055] The above control input is used to control the pole climbing robot.
[0056] The pole climbing robot is taken as an object to build a climbing dynamics model; control targets are determined to ensure that the trajectory tracking error of the pole climbing robot converges within a predefined time under any initial condition and is always constrained within a given performance boundary; a preset performance function is used to convert transient and steady state performance requirements into calculation constraints, and an error conversion technique is used to convert the calculation constraints into boundedness. While meeting the requirements of the asymmetric dynamics characteristics of the pole climbing robot, the trajectory tracking error is ensured to converge within a preset time and range, and the dynamic and steady state performance of the pole climbing robot control system is improved.
[0057] The present application also performs simulation verification based on the above scheme, including: the position signal is set as a linear ramp from 0 to 0.5 meters; and the is set as a general sine signal and a cosine signal. The initial state of the pole climbing robot is set as .
[0058] The simulation results are as follows, and the trajectory tracking curves in the attached Figure 3 to the attached Figure 5 show that the present application can achieve high-precision trajectory tracking in a short time under the condition that the initial state and the trajectory tracking instruction signal are different, indicating that it can achieve global stable tracking under a random initial state.
[0059] In order to further analyze the dynamic performance of the present application, the speed tracking curves are given as shown in the attached Figure 6 to the attached Figure 8 . It can be seen from the speed tracking curves in the attached Figures 6-8 that due to the influence of the initial state, the system will produce overshoot in the initial stage, which is caused by the large input in the initial stage, but the three states of the system all achieve stable tracking of the derivative of the instruction signal within 2 seconds, verifying that the designed controller has good steady state performance, and its dynamic performance also meets the system requirements. At the same time, the wheel driving torque and the hinge torque are given as shown in the attached Figure 9 and the attached Figure 10 .
[0060] It can be seen from the tracking error and performance boundary curves in the attached Figure 11 to the attached Figure 13 that the tracking errors of the axial position, the rotation angle and the hinge angle of the system are all within the set performance boundary, reaching the preset performance expectation, and the initial value and the convergence degree of the performance boundary are within a reasonable range, finally converging to the vicinity of zero boundary, verifying the correctness of the preset performance theoretical analysis and design under the condition that the designed controller is reasonable.
[0061] Therefore, this application discloses an adaptive trajectory tracking control method for a pole-climbing detection robot. This method takes the pole-climbing robot as the object, constructs a climbing dynamic model, determines the control objective, and ensures that the trajectory tracking error of the pole-climbing robot converges within a predefined time under any initial conditions and is always constrained within a given performance boundary. Transient and steady-state performance requirements are transformed into computational constraints through a preset performance function, and these computational constraints are transformed into boundedness using error transformation technology. While satisfying the robot's asymmetric dynamic characteristics, this method ensures that the trajectory tracking error converges within a preset time and range, improving the dynamic and steady-state performance of the robot control system.
[0062] Based on the inventive concept of the above embodiments, this application also provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, performs the steps of the method described in any of the above embodiments. The following is in conjunction with the appendix... Figure 14 This describes the execution process of the above embodiments on a computer-readable storage medium.
[0063] like Figure 14 As shown, it illustrates the computer-readable storage medium of this application. If the aforementioned synchronization method is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions / computer programs to cause an Internet of Things device (which may be a personal computer, server, or network terminal, etc.) or processor to execute all or part of the steps of the methods of various embodiments of this application. The aforementioned storage medium includes various media such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks, as well as electronic terminals such as computers, mobile phones, laptops, tablets, cameras, and dedicated devices that have the aforementioned storage media.
[0064] The execution process of program data in a computer-readable storage medium can be described with reference to the above-described method embodiments of this application, and will not be repeated here.
[0065] The above merely provides the embodiments of the present application and does not limit the patent scope of the present application, and any equivalent structural transformation or direct or indirect application in other related technical fields by using the contents of the present application specification and drawings are also included in the patent protection scope of the present application. In the embodiments disclosed in the present application, the computer storage medium can be a tangible medium which can contain or store programs for use by or in connection with an instruction execution system, device or apparatus. The computer storage medium can include but is not limited to electronic, magnetic, optical, electromagnetic, infrared or semiconductor system, device or apparatus, or any suitable combination of the above. More specific examples of the computer storage medium can include one or more wire-based electrical connections, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device or any suitable combination of the above.
Claims
1. An adaptive trajectory tracking control method for a pole-climbing inspection robot, characterized in that, Includes the following steps: The first step is to construct a dynamic model of the pole-climbing robot for climbing. The second step is to determine the control objectives; The third step involves converting transient and steady-state performance requirements into computational constraints using a preset performance function, transforming these constraints into boundedness using error transformation techniques, and then designing an adaptive controller to obtain control inputs. These control inputs are used to control the pole-climbing robot.
2. The adaptive trajectory tracking control method for a pole-climbing detection robot according to claim 1, characterized in that: The pole-climbing robot consists of a front sensor section and a rear drive section, which are connected by an active hinge. The rear drive section is equipped with dual independent drive wheels, and the front sensor section is equipped with driven support wheels.
3. The adaptive trajectory tracking control method for a pole-climbing detection robot according to claim 2, characterized in that, The first step includes the following steps: Construct a dynamic model for the pole-climbing robot to climb: ， in, For position vectors, This represents the displacement of the pole-climbing robot along the centerline of the pole. This refers to the angle of the rear drive section of the pole-climbing robot relative to the centerline of the pole within its cross-section. For the angle of the active hinge; For velocity vector, Let be the linear velocity of the pole-climbing robot along the center line of the pole. Let ω be the angular velocity of the pole-climbing robot around the center line of the pole. The angular velocity of the active hinge rotation; To control the input, For equivalent axial force, For equivalent rotational torque, The active torque of the active hinge. and The input torques are respectively for the left and right drive wheels of the pole-climbing robot; The inertia matrix is expressed as follows: ,in, and These are the masses of the front sensor section and the rear drive section, respectively. and These are the moments of inertia about the center of mass of the front sensor segment and the rear drive segment, respectively. The length of the rear drive section; The Coriolis force matrix is expressed as follows: , Let be the potential energy vector generated by the contact potential energy with the pole wall during climbing, and its expression is: ,in, This represents the equivalent stiffness of the contact between the climbing pole and the wall. Let be the inner radius of the climbing pole; The damping matrix is expressed as follows: ,in, , and These are the axial fluid damping coefficient, the rotational fluid damping coefficient, and the active hinge damping coefficient, respectively. Let be the potential energy vector generated by the contact potential energy of the pipe wall, and its expression is: ,in, The radius of the drive wheel, The track width of the drive wheels.
4. The adaptive trajectory tracking control method for a pole-climbing detection robot according to claim 3, characterized in that: according to , The above dynamic model can be transformed into state equations as follows: 。 5. The adaptive trajectory tracking control method for a pole-climbing detection robot according to claim 4, characterized in that, The second step includes the following steps: Confirm that the controller and each drive motor of the pole-climbing robot are communicating normally, and confirm that the given reference trajectory information is known, including the reference trajectory itself. and its differential Continuous and bounded.
6. The adaptive trajectory tracking control method for a pole-climbing detection robot according to claim 5, characterized in that, The third step includes the following steps: Determine tracking error : ， in, , and These represent the displacement deviation of the robot along the centerline of the climbing pole, the angular deviation of the robot's drive joint relative to the centerline of the climbing pole within its cross-section, and the rotational deviation of the active hinge, respectively.
7. The adaptive trajectory tracking control method for a pole-climbing detection robot according to claim 6, characterized in that, It also includes the following steps: Suppose the asymmetric global preset performance function used to adapt to pole climbing constraints, as follows: ， in, Let be the time-varying scaling function at time t, and its calculation formula is: ， in, For steady-state error bound, To preset the convergence rate, Preset convergence time; pass From the calculation formula, we can see that at the initial time Substituting the above asymmetric global preset performance function, we can obtain ; when hour, , satisfy ; in, For boundary parameters, their expression is: ， As a physical constraint for pole climbing, it is set as follows: 。 8. The adaptive trajectory tracking control method for a pole-climbing detection robot according to claim 7, characterized in that, It also includes the following steps: Based on tracking error Design the normalization function as follows: ， Further differentiation yields: ， The derivative is always positive; According to the normalization function, we can obtain , And there are , .
9. The adaptive trajectory tracking control method for a pole-climbing detection robot according to claim 8, characterized in that, It also includes the following steps: Let the barrier function be as follows: , in, , For time-varying boundary functions, The boundary convergence rate; And there are: , ,Depend on achievable We can obtain: ; right Solving for the inverse function: when : , Further inverse derivation shows that... ; when : , Furthermore, through inverse solution, we can see that... ; Then we can obtain , ; right Differentiate: Will Expand: in, , The expression is: in: Combining the above formula, we can obtain: .
10. The adaptive trajectory tracking control method for a pole-climbing detection robot according to claim 9, characterized in that, It also includes the following steps: Based on the state equation and the barrier function, the transformation error vector is defined as: ,in, For virtual control laws; Get Lyapunov function Differentiating it, we get: ,in, , , ; Designing virtual control laws: ,in, It is a positive definite gain matrix; Combining the above formulas, we can obtain: ； Get Lyapunov function Differentiating it, we get: , according to It is a symmetric and positive definite matrix. Since it is a skew-symmetric matrix, we can obtain: ,in, Substituting it into the above formula, we get: ； Based on the above uncertainties, the total uncertainty is defined as follows: , To address the aforementioned uncertainties, a radial basis function neural network (RBFNN) is used for approximation. , Wherein, input vector , For the ideal weight matrix, To approximate the error, satisfy , The activation function is a Gaussian function. ,in, With the center point, For width parameters; Therefore, the control input is: ， in, for Moore-Penrose pseudoinverse, controlling gain It is a positive definite gain matrix. For estimating the upper bound of neural network weights, Set a single-parameter adaptive law: ,in, These are design parameters.