Global fractional order nonsingular terminal sliding mode control method for snake-like robot

Abstract

The application discloses a global fractional non-singular terminal sliding mode control method for a snake robot, and comprises the following steps: based on a dynamic model of an N-joint snake robot, a tracking error dynamic model of the N-joint snake robot is reconstructed; a time delay estimator is designed to observe external disturbance of uncertain items of the N-joint snake robot system in real time; according to a global terminal sliding mode surface, a fractional order characteristic and a non-singular characteristic, a global fractional non-singular terminal sliding mode surface is constructed by using output error of the N-joint snake robot system; and based on the global fractional non-singular terminal sliding mode surface and the time delay estimator, a global fractional non-singular terminal sliding mode controller of the N-joint snake robot system based on time delay is designed by combining a power approaching rate, so that high-precision tracking control is realized.

Description

Technical Field

[0001] This invention relates to the technical field of electrical automation, and more particularly to a global fractional-order nonsingular terminal sliding mode control method for a snake robot. Background Technology

[0002] Bionic snake-like robots offer numerous advantages in power grids due to their line-finding capabilities, encompassing various aspects such as power grid operation and maintenance, fault detection and repair, and safety monitoring. They can automatically inspect transmission or distribution lines, checking for issues like breaks, corrosion, and loosening. Their flexible structure and multi-joint design allow them to adapt to various line shapes and terrain conditions, including plains, mountains, and forests. Equipped with high-resolution cameras and infrared sensors, the snake-like robot can monitor line parameters such as temperature, humidity, and voltage in real time, promptly detecting anomalies and providing crucial reference information for maintenance personnel, greatly facilitating line inspection work in challenging environments.

[0003] However, in practice, there are still shortcomings in the high-precision tracking control of biomimetic snake robots. Snake robots are highly nonlinear, strongly coupled, have inaccurate mathematical modeling, and are subject to interference in the actual environment, making it difficult for conventional control methods to achieve high-precision tracking control. Summary of the Invention

[0004] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0005] In view of the aforementioned existing problems, the present invention is proposed.

[0006] Therefore, this invention provides a global fractional-order non-singular terminal sliding mode control method for snake robots, which optimizes mathematical modeling and proposes a global fractional-order non-singular terminal sliding mode control method based on the power-law approach rate of time delay estimation technology.

[0007] To address the aforementioned technical problems, this invention provides the following technical solution: It includes: reconstructing the dynamic model of the tracking error of an N-joint snake robot based on its dynamic model; designing a time delay estimator to monitor external disturbances of uncertainties in the N-joint snake robot system in real time; constructing a global fractional-order non-singular terminal sliding surface based on the global terminal sliding surface, fractional-order characteristics, and non-singular characteristics, utilizing the output error of the N-joint snake robot system; and designing a global fractional-order non-singular terminal sliding surface controller for the N-joint snake robot system based on time delay, using the global fractional-order non-singular terminal sliding surface and the time delay estimator, combined with the power-law approach rate.

[0008] As a preferred embodiment of the global fractional-order nonsingular terminal sliding mode control method for a snake-like robot described in this invention, the method includes: reconstructing the tracking error dynamic model of the N-joint snake-like robot based on its dynamic model, including:

[0009]

[0010] Where, q φ =[φ1,…,φ N-1 ,φ N ,p x ,p y ] T ∈R (N+2)×1 φ i It is the i-th joint angle of the snake robot, (p x ,p y M(φ) ∈ R is the coordinate of the centroid of the snake robot; (N+2)×(N+2) It is the system's inertia matrix. It is the matrix of Coriolis force and centripetal force. G(φ)∈R (N+2)×2N and These are the matrices of gravity and friction, respectively. u is the joint input torque, u = [u1, ..., u] N-1 ,0,0,0] T ∈R (N+2)×1 .

[0011] The tracking error of an N-joint snake robot is defined as:

[0012]

[0013] in, It is the target trajectory of the N-joint snake robot; q φ e(t) is the actual trajectory of the N-joint snake robot; e(t)∈R (N +2)×1It is the tracking error of the N-joint snake robot.

[0014] The second-order derivative of the tracking error of the aforementioned N-joint snake robot is:

[0015]

[0016] in, It is the second differential of e(t). yes The second derivative, It is q φ The second derivative of (t).

[0017] definition The matrix is ​​used to modify the dynamic model of the N-joint snake robot as follows:

[0018]

[0019] in, It is a dimensionless parameter-tuning gain matrix.

[0020] Substituting the second derivative of the tracking error, we construct a dynamic model of the tracking error of an N-joint snake robot:

[0021]

[0022] As a preferred embodiment of the global fractional-order nonsingular terminal sliding mode control method for a snake-like robot described in this invention, the method includes: designing a time delay estimator, comprising,

[0023] The time delay estimator is defined as follows:

[0024]

[0025] in, F(t) is the estimate based on the time delay estimator; Δt is the time delay interval, and only when the time delay interval is small enough can the accuracy of the estimation of the uncertainty and disturbance terms be guaranteed.

[0026] As a preferred embodiment of the global fractional-order nonsingular terminal sliding mode control method for a snake-like robot described in this invention, the method includes: designing a global fractional-order nonsingular terminal sliding mode surface, comprising,

[0027] The global nonsingular fast terminal sliding surface is designed as follows:

[0028]

[0029]

[0030] Where ηe(t) is the tracking error proportional term of the N-joint snake robot, and η is the proportional term tuning gain; For fractional-order nonsingular terminal integrals; ΥD ε e(τ) is the fractional-order term, Υ is the fractional-order term tuning gain, and D ε Let ε be the fractional integral, and ε be the order of the fractional integral. For non-singular terms, ω, And σ are non-singular term tuning gains, which must satisfy: and σ is a positive odd number.

[0031] The first-order differential of the globally nonsingular fast terminal sliding surface is as follows:

[0032]

[0033] in, It is the first differential of s(t) with respect to time t. They are s1(t), s2(t), ..., s N (t),s N+1 (t),s N+2 (t) is the first differential of time t.

[0034] As a preferred embodiment of the global fractional-order nonsingular terminal sliding mode control method for a snake-like robot described in this invention, the designed power-order approaching law is as follows:

[0035] The power-law approach law is designed as follows:

[0036]

[0037] in, and It is the gain of the power-approach rate.

[0038] As a preferred embodiment of the global fractional-order nonsingular terminal sliding mode control method for a snake-like robot described in this invention, it further includes:

[0039] Based on a global fractional-order nonsingular terminal sliding surface and a time delay estimator, combined with a power-law approach rate, the time-delay-based global fractional-order nonsingular terminal sliding controller u(t) for an N-joint snake robot system is designed as follows:

[0040]

[0041] The beneficial effects of this invention are as follows: Based on the dynamic model of an N-joint snake robot, this invention optimizes and constructs a dynamic model for the tracking error of the N-joint snake robot, simplifying the actual mathematical model. Simultaneously, a time delay estimator is used to estimate uncertainties and disturbances, thereby compensating for them in the snake robot system. A novel sliding surface is constructed using a global terminal sliding surface, non-singular terms, and fractional-order terms, which eliminates arrival time, accelerates convergence speed during the sliding phase, ensures finite-time convergence, avoids singularities, and enhances robustness, achieving high-precision tracking control. Attached Figure Description

[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0043] Figure 1 This is a schematic diagram of the principle control framework of a global fractional-order nonsingular terminal sliding mode control method for a snake robot according to the present invention.

[0044] Figure 2 A comparison of the tracking performance of the global fractional nonsingular terminal sliding mode control (SMC) method and the traditional PID control method for a three-DOF snake robot with joint angle 1 under target trajectory 1 (aim1);

[0045] Figure 3 A comparison of the tracking performance of the global fractional nonsingular terminal sliding mode control (SMC) method and the traditional PID control method for a three-DOF snake robot with joint angle 2 as the target trajectory 2 (aim2).

[0046] Figure 4 This is a flowchart of a global fractional-order nonsingular terminal sliding mode control method for a snake robot according to the present invention. Detailed Implementation

[0047] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0048] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0049] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0050] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0051] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0052] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0053] Example 1

[0054] Reference Figure 1 , Figure 4This first embodiment of the invention provides a global fractional-order non-singular terminal sliding mode control method for a snake-like robot. The method is based on the dynamic model of an N-joint snake-like robot, reconstructing the dynamic model of the tracking error; designing a time delay estimator to observe external disturbances to the uncertainties of the N-joint snake-like robot system in real time; constructing a global fractional-order non-singular terminal sliding surface based on the global terminal sliding surface, fractional-order characteristics, and non-singular characteristics, utilizing the output error of the N-joint snake-like robot system; and designing a time-delay-based global fractional-order non-singular terminal sliding mode controller for the N-joint snake-like robot system based on the global fractional-order non-singular terminal sliding surface and the time delay estimator, combined with the power-law approach rate.

[0055] S1: Based on the dynamic model of the N-joint snake robot, reconstruct the dynamic model of the tracking error of the N-joint snake robot. The following points need to be noted in this step:

[0056] The dynamic model of the N-joint snake robot is as follows.

[0057]

[0058] Where, q φ =[φ1,…,φ N-1 ,φ N ,p x ,p y ] T ∈R (N+2)×1 φ i It is the i-th joint angle of the snake robot, (p x ,p y M(φ) ∈ R is the coordinate of the centroid of the snake robot; (N+2)×(N+2) It is the system's inertia matrix. It is the matrix of Coriolis force and centripetal force. G(φ)∈R (N+2)×2N and These are the matrices of gravity and friction, respectively. u is the joint input torque, u = [u1, ..., u] N-1 ,0,0,0] T ∈R (N+2)×1 .

[0059] The tracking error of an N-joint snake robot is defined as:

[0060]

[0061] in, It is the target trajectory of the N-joint snake robot; q φ e(t) is the actual trajectory of the N-joint snake robot; e(t)∈R(N +2)×1 It is the tracking error of the N-joint snake robot.

[0062] The second-order derivative of the tracking error of the aforementioned N-joint snake robot is:

[0063]

[0064] in, It is the second differential of e(t). yes The second derivative, It is q φ The second derivative of (t).

[0065] definition The matrix is ​​used to modify the dynamic model of the N-joint snake robot as follows:

[0066]

[0067] in, It is a dimensionless parameter-tuning gain matrix.

[0068] Substituting the second derivative of the tracking error, we construct a dynamic model of the tracking error of an N-joint snake robot:

[0069]

[0070] S2: Design a time delay estimator to monitor external disturbances to the uncertainty term of the N-joint snake robot system in real time. This step requires explanation of:

[0071] The time delay estimator is defined as follows:

[0072]

[0073] in, F(t) is the estimate based on the time delay estimator; Δt is the time delay interval, and only when the time delay interval is small enough can the accuracy of the estimation of the uncertainty and disturbance terms be guaranteed.

[0074] S3: Based on the global terminal sliding surface, fractional-order characteristics, and non-singular characteristics, and utilizing the output error of the N-joint snake robot system, construct a global fractional-order non-singular terminal sliding surface. The following points need to be noted in this step:

[0075] The global nonsingular fast terminal sliding surface is designed as follows:

[0076] ;

[0077] Where ηe(t) is the tracking error proportional term of the N-joint snake robot, and η is the proportional term tuning gain; For fractional-order nonsingular terminal integrals; ΥD ε e(τ) is the fractional-order term, Υ is the fractional-order term tuning gain, and D ε Let ε be the fractional integral, and ε be the order of the fractional integral. For non-singular terms, ω, And σ are non-singular term tuning gains, which must satisfy: and σ is a positive odd number.

[0078] The first-order differential of the globally nonsingular fast terminal sliding surface is as follows:

[0079] ;

[0080] in, It is the first differential of s(t) with respect to time t. They are s1(t), s2(t), ..., s N (t),s N+1 (t),s N+2 (t) is the first differential of time t.

[0081] S4: Based on the global fractional-order non-singular terminal sliding surface and time delay estimator, combined with the power-law approach rate, design a time-delay-based global fractional-order non-singular terminal sliding mode controller for an N-joint snake robot system. The following points need to be noted in this step:

[0082] The global fractional-order nonsingular terminal sliding mode controller based on time delay is designed as follows:

[0083]

[0084] Preferably, this embodiment also discloses a global fractional-order non-singular terminal sliding mode control method for a snake robot, compared with the prior art. This method aims to replace the actual dynamic model of the N-joint snake robot with a tracking error dynamic model, thereby simplifying the mathematical model. The set of uncertainties and disturbances is compensated and fed back in real time using a time delay estimator. The global fractional-order non-singular terminal sliding mode control method design enables fast and high-precision tracking control, and avoids global convergence stagnation problems, ensuring tracking performance.

[0085] Example 2

[0086] Reference Figures 2-3 This is another embodiment of the present invention, which differs from the first embodiment in that it provides a test verification of a global fractional-order nonsingular terminal sliding mode control method for a snake robot, including:

[0087] To verify the effectiveness of the technology used in this method, this embodiment compares the traditional PID control method with the method of this invention. The experimental results are compared using scientific methods to verify the actual effectiveness of this method.

[0088] The physical parameters of the three-degree-of-freedom snake robot are as follows: the snake robot has N = 4 joints, the mass of a single joint is m = 0.25 kg and the mass of each joint is uniformly distributed, the joint length is l = 0.08 m, and the ground friction force is c. t =1,c n =10, J=0.0064kg×m 2 .

[0089] The vector and inertia matrices used in the three-degree-of-freedom snake robot system are: M θ =JI N +ml 2 S θ VS θ +ml 2 C θ VC θ V = A T (ZZ T ) -1 A; W = ml 2 S θ VC θ -ml 2 C θ VS θ ;

[0090] The input and output vectors of the snake-like robot are φ = [φ1, φ2], respectively. T , u = [u1, u2] T The initial conditions for the snake-like robot are φ(0) = [0,0]. T rad,

[0091] The target trajectory of joint angle 1 is: The target trajectory of joint angle 2 is: φ ref2 =sin(πt).

[0092] The parameters of the global fractional-order nonsingular terminal sliding mode controller of this invention are: Δt=0.005, η=diag(17.5,20,15,13.5,10), Y=diag(25,10.5,27,20,20), ε=1.5, σ = 5,

[0093] The controller used in comparison is a traditional PID controller: The controller parameter is k. tp =diag(3.5,2.95,0,0,0), k ti =diag(10.25,8.35,0,0,0), k td =diag(0.02.0.015,0,0,0).

[0094] Test environment: Refer to Figure 1 In the MATLAB 2019a SIMULINK environment, a controlled object model of the snake robot was built based on the existing physical parameters and mathematical model of the snake robot. The driven joints 1 and 2 were tracked and controlled under different target trajectories using both global fractional nonsingular terminal sliding mode control and traditional PID control methods, and test results were obtained. Both methods were simulated and tested using automated testing equipment and MATLAB software. Simulation data was obtained based on the experimental results. Four sets of data were tested for each method, with each set sampled for 15 seconds. The input target trajectory and output tracking trajectory for each set of data were calculated and compared to verify the feasibility of the proposed algorithm.

[0095] Reference Figure 2 This invention compares the tracking performance of a global fractional-order non-singular terminal sliding mode control (SMC) method and a traditional PID control method under a target trajectory (aim1) with a drive joint angle 1. (Refer to...) Figure 3This paper compares the tracking performance of the global fractional-order non-singular terminal sliding mode control (SMC) method and the traditional PID control method under the target trajectory 2 (aim2) according to the present invention. As shown in the figure, both the global fractional-order non-singular terminal sliding mode control (SMC) method and the traditional PID control method can track both target trajectory 1 (aim1) and target trajectory 2 (aim2) overall. However, for both target trajectory 1 (aim1) and target trajectory 2 (aim2), the tracking performance of the global fractional-order non-singular terminal sliding mode control (SMC) method is significantly better than that of the traditional PID control method. This is mainly because the global fractional-order non-singular terminal sliding mode control (SMC) method can quickly track both target trajectory 1 (aim1) and target trajectory 2 (aim2) from the beginning. Furthermore, the global fractional-order non-singular terminal sliding mode control (SMC) method is superior to the traditional PID control method in terms of control accuracy and stability. In summary, the fractional-order nonsingular terminal sliding mode control (SMC) method is superior to the traditional PID control method in all aspects.

[0096] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A global fractional-order nonsingular terminal sliding mode control method for a snake-like robot, characterized in that: Includes the following steps, S1, based on The dynamic model of the articulated snake robot was reconstructed. Dynamic model of tracking error in articulated snake robot; S2, Design a time delay estimator, for Real-time observation of external disturbances to uncertainties in articulated snake robot systems; S3. Based on the global terminal sliding surface, fractional-order characteristics, and non-singular characteristics, utilize... The output error of the articulated snake robot system is used to construct a global fractional-order nonsingular terminal sliding surface. S4. Based on the global fractional-order non-singular terminal sliding surface and time delay estimator, combined with the power-law approach rate, design... The articulated snake robot system is based on a time-delayed global fractional-order nonsingular terminal sliding mode controller; The time delay estimator for S2 is designed as follows. The time delay estimator is defined as follows: ； in, yes Estimated values ​​based on a time delay estimator; The time delay interval is such that only when the time delay interval is sufficiently small can the accuracy of the estimation of uncertainties and disturbances be guaranteed. It is a dimensionless parameter-tuning gain matrix. ; The power-law approximation law of S4 is designed as follows: The power-law approach law is designed as follows: ； in, and It is the gain of the power-approach rate. , , ; The S4 also includes, Based on a global fractional-order nonsingular terminal sliding surface and a time delay estimator, combined with a power-law approach rate... Jointed snake robot system based on time-delay global fractional-order nonsingular terminal sliding mode controller Designed as follows: ； in, For fractional-order term parameter tuning gain, For fractional integrals, The order of the fractional integral; , and For non-singular term parameter tuning gain, the following must be satisfied: and , It is a positive odd number.

2. The global fractional-order nonsingular terminal sliding mode control method for a snake-like robot according to claim 1, characterized in that, The dynamic model of the N-joint snake robot of S1 is as follows. ； in, , It is the first snake-like robot One joint angle, ( () represents the coordinates of the centroid of the snake-like robot; It is the system's inertia matrix. ; It is the matrix of Coriolis force and centripetal force. ; These are the matrices of gravity and friction, respectively. , ;u is the joint input torque, ; The tracking error of an N-joint snake robot is defined as: ； in, It is as described The target trajectory of the articulated snake robot; It is as described The actual trajectory of the articulated snake robot; It is as described Tracking error of articulated snake robots; The above Second-order derivative of tracking error for articulated snake robots: ； in, yes The second derivative, yes The second derivative, yes The second derivative; definition Matrix, The dynamic model of the articulated snake robot is modified as follows: ； in, It is a dimensionless parameter-tuning gain matrix. , ; Substituting the second derivative of the tracking error, we construct... Dynamic model of tracking error of articulated snake robot: 。 3. The global fractional-order nonsingular terminal sliding mode control method for a snake-like robot according to claim 1, characterized in that, The design of the global fractional nonsingular terminal sliding surface of S3 is as follows. The global nonsingular fast terminal sliding surface is designed as follows: in, for The tracking error ratio term of the articulated snake robot. Adjust the gain for the proportional term; For fractional-order non-singular terminal integrals; For fractional terms, For fractional-order term parameter tuning gain, For fractional integrals, The order of the fractional integral; For non-singular terms, , and For non-singular term parameter tuning gain, the following must be satisfied: and , It is a positive odd number; The first-order differential of the globally nonsingular fast terminal sliding surface is as follows: ； in, yes Regarding time The first-order differential, They are Regarding time The first differential.

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