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

Abstract

The invention discloses a global fractional order nonsingular terminal sliding mode control method for a snakelike robot, and the method comprises the steps: reconstructing an N-joint snakelike robot tracking error dynamic model based on a dynamic model of an N-joint snakelike robot; designing a time delay estimator, and observing external disturbance of uncertain items of the N-joint snakelike robot system in real time; according to the global terminal sliding mode surface, the fractional order characteristics and the nonsingular characteristics, an N-joint snake-shaped robot system is used for outputting errors, and a global fractional order nonsingular terminal sliding mode surface is constructed; and designing a global fractional order nonsingular terminal sliding mode controller of the N-joint snake-shaped robot system based on time delay based on a global fractional order nonsingular terminal sliding mode surface and a time delay estimator in combination with a power reaching rate, and realizing high-precision tracking control.

Description

Technical Field

[0001] The invention relates to the technical field of electrical automation, and in particular to a global fractional-order non-singular terminal sliding mode control method for a snake-like robot. Background Art

[0002] The bionic snake-like robot has many advantages in the power grid with its line-finding ability, covering multiple aspects such as power grid operation and maintenance, fault detection and repair, and safety monitoring. It can automatically patrol along the transmission line or distribution line to check whether the line is broken, corroded, loose, etc. Its flexible structure and multi-joint design enable it to adapt to various line forms and terrain conditions, including plains, mountains, forests, etc. 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, detect abnormal conditions in a timely manner, and provide important reference information for operation and maintenance personnel, which greatly facilitates the line patrol work of operation and maintenance personnel in special environments.

[0003] However, in actual situations, there are still some shortcomings in the high-precision tracking control of bionic snake-like robots. The snake-like robots are highly nonlinear, strongly coupled, have inaccurate mathematical modeling, and there are interferences in the actual environment. These problems make it difficult for conventional control methods to achieve high-precision tracking control. Summary of the invention

[0004] The purpose of this section is to summarize some aspects of embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and the invention title of this application to avoid blurring the purpose of this section, the specification abstract and the invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

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

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

[0007] In order to solve the above technical problems, the present invention provides the following technical solutions: including, based on the dynamic model of the N-joint snake-like robot, reconstructing the tracking error dynamic model of the N-joint snake-like robot; designing a time delay estimator to observe the uncertain external disturbance of the N-joint snake-like robot system in real time; based on the global terminal sliding surface, fractional-order characteristics, and non-singular characteristics, using the output error of the N-joint snake-like robot system, constructing a global fractional-order non-singular terminal sliding surface; based on the global fractional-order non-singular terminal sliding surface and the time delay estimator, combined with the power approach rate, designing a global fractional-order non-singular terminal sliding mode controller based on time delay for the N-joint snake-like robot system.

[0008] As a preferred solution of the global fractional-order non-singular terminal sliding mode control method of a snake-like robot described in the present invention, wherein: based on the dynamic model of the N-joint snake-like robot, the tracking error dynamic model of the N-joint snake-like robot is reconstructed, including:

[0009]

[0010] Among them, q φ =[φ1,…,φ N-1 ,φ N ,p x ,p y ] T ∈R (N+2)×1 ,φ i is the i-th joint angle of the snake-like robot, (p x ,p y ) is the center of mass coordinate of the snake robot; M(φ)∈R (N+2)×(N+2) is the inertia matrix of the system, is the Coriolis force and centripetal force matrix G(φ)∈R (N+2)×2N and are the gravity and friction matrices, u is the joint input torque, u=[u1,…,u N-1 ,0,0,0] T ∈R (N+2)×1 .

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

[0012]

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

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

[0015]

[0016] in, is the second-order differential of e(t), yes The second-order differential of Yes φ The second-order differential of (t).

[0017] definition Matrix, the dynamic model of the N-joint snake-like robot is changed as follows:

[0018]

[0019] in, is the dimensionless parameter gain matrix,

[0020] Substitute the second-order differential of the tracking error to construct the tracking error dynamics model of the N-joint snake-like robot:

[0021]

[0022] As a preferred solution of the global fractional-order non-singular terminal sliding mode control method of a snake-like robot described in the present invention, a time delay estimator is designed, including:

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

[0024]

[0025] in, is the estimated value of F(t) based on the time delay estimator; Δt is the time delay interval. Only when the time delay interval is small enough can the accuracy of the estimation of uncertainties and disturbances be guaranteed.

[0026] As a preferred solution of the global fractional-order non-singular terminal sliding mode control method of a snake-like robot described in the present invention, wherein: a global fractional-order non-singular terminal sliding mode surface is designed, including:

[0027] The global non-singular fast terminal sliding surface is designed as:

[0028]

[0029]

[0030] Among them, ηe(t) is the tracking error proportional term of the N-joint snake-like robot, and η is the proportional term parameter adjustment gain; is the fractional-order non-singular terminal integral term; ΥD ε e(τ) is the fractional-order term, Υ is the parameter gain of the fractional-order term, D ε is the fractional integral, ε is the fractional integral order; is a non-singular term, ω, and σ are non-singular parameter adjustment gains, which must satisfy: and σ is a positive odd number.

[0031] The first-order differential of the global non-singular fast terminal sliding surface is as follows:

[0032]

[0033] in, is the first-order 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)The first-order differential with respect to time t.

[0034] As a preferred solution of the global fractional-order non-singular terminal sliding mode control method of a snake-like robot described in the present invention, the designed power approach rate is as follows:

[0035] The power approach rate is designed as follows:

[0036]

[0037] in, and is the tuning gain of the power approach rate,

[0038] As a preferred solution of the global fractional-order non-singular terminal sliding mode control method of a snake-like robot described in the present invention, it also includes:

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

[0040]

[0041] Beneficial effects of the present invention: Based on the dynamic model of the N-joint snake-like robot, the present invention optimizes and constructs the tracking error dynamic model of the N-joint snake-like robot, and simplifies the actual mathematical model. At the same time, the time delay estimator is used to estimate the uncertainty terms and disturbances so as to compensate them in the system snake-like robot system. The global terminal sliding surface, non-singular terms and fractional-order terms are used to construct a new sliding surface, which has the characteristics of eliminating the arrival time, accelerating the convergence speed of the sliding stage, ensuring finite time convergence, avoiding singular phenomena and enhancing robustness, and realizing high-precision tracking control. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0043] Figure 1 A schematic diagram of the principle control framework of a global fractional-order non-singular terminal sliding mode control method for a snake-like robot according to the present invention;

[0044] Figure 2 This is a comparison chart of the tracking effects of the global fractional-order non-singular terminal sliding mode control method (SMC) and the traditional PID control method (PID) for the joint angle 1 of the three-degree-of-freedom snake-like robot under the target trajectory 1 (aim1);

[0045] Figure 3 This is a comparison chart of the tracking effects of the global fractional-order non-singular terminal sliding mode control method (SMC) and the traditional PID control method (PID) for the joint angle 2 of the three-degree-of-freedom snake-like robot under the target trajectory 2 (aim2);

[0046] Figure 4 The present invention is a flowchart of a global fractional-order non-singular terminal sliding mode control method for a snake-like robot. DETAILED DESCRIPTION

[0047] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0048] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present 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 term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0050] The present invention is described in detail with reference to schematic diagrams. When describing the embodiments of the present invention, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of the present invention. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.

[0051] At the same time, in the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "upper, lower, inner and outer" are based on the directions or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as limiting the present invention. In addition, the terms "first, second or third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0052] In the present invention, unless otherwise clearly specified and limited, the terms "install, connect, connect" should be understood in a broad sense, for example: it can be a fixed connection, a detachable connection or an integral connection; it can also be a mechanical connection, an electrical connection or a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0053] Example 1

[0054] Reference Figure 1 , Figure 4, which is the first embodiment of the present invention, provides a global fractional-order non-singular terminal sliding mode control method for a snake-like robot. The method of the present invention is based on the dynamic model of the N-joint snake-like robot, and reconstructs the tracking error dynamic model of the N-joint snake-like robot; designs a time delay estimator to observe the uncertain external disturbance of the N-joint snake-like robot system in real time; based on the global terminal sliding surface, fractional-order characteristics, and non-singular characteristics, the output error of the N-joint snake-like robot system is used to construct a global fractional-order non-singular terminal sliding surface; based on the global fractional-order non-singular terminal sliding surface and the time delay estimator, combined with the power approach rate, a global fractional-order non-singular terminal sliding mode controller based on time delay for the N-joint snake-like robot system is designed.

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

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

[0057]

[0058] Among them, q φ =[φ1,…,φ N-1 ,φ N ,p x ,p y ] T ∈R (N+2)×1 ,φ i is the i-th joint angle of the snake-like robot, (p x ,p y ) is the center of mass coordinate of the snake robot; M(φ)∈R (N+2)×(N+2) is the inertia matrix of the system, is the Coriolis and centripetal force matrix, G(φ)∈R (N+2)×2N and are the gravity and friction matrices, u is the joint input torque, u=[u1,…,u N-1 ,0,0,0] T ∈R (N+2)×1 .

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

[0060]

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

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

[0063]

[0064] in, is the second-order differential of e(t), yes The second-order differential of Yes φ The second-order differential of (t).

[0065] definition Matrix, the dynamic model of the N-joint snake-like robot is changed as follows:

[0066]

[0067] in, is the dimensionless parameter gain matrix,

[0068] Substitute the second-order differential of the tracking error to construct the tracking error dynamics model of the N-joint snake-like robot:

[0069]

[0070] S2: Design a time delay estimator to observe the uncertain external disturbance of the N-joint snake robot system in real time. The following points need to be explained in this step:

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

[0072]

[0073] in, is the estimated value of F(t) based on the time delay estimator; Δt is the time delay interval. Only when the time delay interval is small enough can the accuracy of the estimation of uncertainties and disturbances be guaranteed.

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

[0075] The global non-singular fast terminal sliding surface is designed as:

[0076]

[0077] Among them, ηe(t) is the tracking error proportional term of the N-joint snake-like robot, and η is the proportional term parameter adjustment gain; is the fractional-order non-singular terminal integral term; ΥD ε e(τ) is the fractional-order term, Υ is the parameter gain of the fractional-order term, D ε is the fractional integral, ε is the fractional integral order; is a non-singular term, ω, and σ are non-singular parameter adjustment gains, which must satisfy: and σ is a positive odd number.

[0078] The first-order differential of the global non-singular fast terminal sliding surface is as follows:

[0079]

[0080] in, is the first-order 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)The first-order differential with respect to time t.

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

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

[0083]

[0084] Preferably, it is also necessary to explain that, compared with the prior art, this embodiment discloses a global fractional-order non-singular terminal sliding mode control method for a snake-like robot, which aims to replace the dynamic model of an actual N-joint snake-like robot with a tracking error dynamic model to simplify the mathematical model. The set of uncertainties and disturbance terms is compensated and fed back in real time using a time delay estimator. The design of the control method of the global fractional-order non-singular terminal sliding mode can achieve fast and high-precision tracking control, and there is no global convergence stagnation problem, ensuring the tracking effect.

[0085] Example 2

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

[0087] In order to verify and illustrate the technical effect adopted in this method, in this embodiment, a traditional PID control method is selected to be compared with the method of the present invention, and the test results are compared by scientific demonstration to verify the real effect of this method.

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

[0089] The vectors and inertia matrix used by 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 robot are φ=[φ1,φ2] T , u=[u1,u2] T The initial condition of the snake robot is φ(0)=[0,0] T rad,

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

[0092] The parameters of the global fractional-order non-singular terminal sliding mode controller of the present 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 comparison controller is a traditional PID controller: The comparison 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: Reference Figure 1 In the SIMULINK environment of MATLAB 2019a, a snake robot controlled object model is built according to the existing snake robot physical quantity parameters and mathematical models. The global fractional-order non-singular terminal sliding mode control method and the traditional PID control method are used to track and control the drivable joint 1 and drivable joint 2 under different target trajectories and obtain the test result data. Both methods will start the automated test equipment and use MATLB software programming to implement the simulation test of the comparison method. The simulation data is obtained according to the test results. Each method tests 4 groups of data, and each group of data is sampled for 15s. The target trajectory of each group of data input and the tracking trajectory of the output are calculated and compared to verify the feasibility of the proposed algorithm.

[0095] Reference Figure 2 The tracking effect comparison of the present invention's drivable joint angle 1 under the target trajectory 1 (aim1) on the global fractional-order non-singular terminal sliding mode control method (SMC) and the traditional PID control method (PID). Figure 3The present invention can drive the joint angle 2 under the target trajectory 2 (aim2) to compare the tracking effect of the global fractional order non-singular terminal sliding mode control method (SMC) and the traditional PID control method (PID). As can be seen from the figure, the global fractional order non-singular terminal sliding mode control method (SMC) and the traditional PID control method (PID) can track the target trajectory 1 (aim1) and the target trajectory 2 (aim2) as a whole. However, whether it is the target trajectory 1 (aim1) or the target trajectory 2 (aim2), the tracking effect of the global fractional order non-singular terminal sliding mode control method (SMC) is obviously better than the traditional PID control method (PID), mainly manifested in that the global fractional order non-singular terminal sliding mode control method (SMC) can quickly track the target trajectory 1 (aim1) and the target trajectory 2 (aim2) at the beginning, and the global fractional order non-singular terminal sliding mode control method (SMC) is better than the traditional PID control method (PID) in terms of control accuracy and stability. In summary, the local fractional-order non-singular terminal sliding mode control method (SMC) is superior to the traditional PID control method (PID) in all aspects.

[0096] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A global fractional-order non-singular terminal sliding mode control method for a snake-like robot, characterized by: The following steps are included: S1. Based on the dynamic model of the N-joint snake-like robot, the tracking error dynamic model of the N-joint snake-like robot is reconstructed; S2, design a time delay estimator to observe the uncertain external disturbance of the N-joint snake robot system in real time; S3, based on the global terminal sliding surface, fractional-order characteristics, and non-singular characteristics, the global fractional-order non-singular terminal sliding surface is constructed using the output error of the N-joint snake-like robot system; S4. Based on the global fractional-order non-singular terminal sliding mode surface and time delay estimator, combined with the power approach rate, a global fractional-order non-singular terminal sliding mode controller based on time delay for the N-joint snake-like robot system is designed.

2. The global fractional-order non-singular terminal sliding mode control method for a snake-like robot according to claim 1, characterized in that: The dynamic model of the S1 N-joint snake-like robot is as follows, Among them, q φ =[φ1,…,φ N-1 ,φ N ,p x ,p y ] T ∈R (N+2)×1 ,φ i is the i-th joint angle of the snake-like robot, (p x ,p y ) is the center of mass coordinate of the snake robot; M(φ)∈R (N+2)×(N+2) is the inertia matrix of the system, is the Coriolis and centripetal force matrix, G(φ)∈R (N+2)×2N and are the gravity and friction matrices, u is the joint input torque, u=[u1,…,u N-1 ,0,0,0] T ∈R (N+2)×1 ; The tracking error of the N-joint snake robot is defined as: in, is the target trajectory of the N-joint snake-like robot; q φ (t) is the actual trajectory of the N-joint snake-like robot; e(t)∈R (N+2)×1 is the tracking error of the N-joint snake-like robot; The second-order differential of the tracking error of the N-joint snake-like robot is: in, is the second-order differential of e(t), yes The second-order differential of Yes φ The second-order differential of (t); definition Matrix, the dynamic model of the N-joint snake-like robot is changed as follows: in, is the dimensionless parameter gain matrix, Substitute the second-order differential of the tracking error to construct the tracking error dynamics model of the N-joint snake-like robot:

3. The global fractional-order non-singular terminal sliding mode control method for a snake-like robot according to claim 1 or 2, characterized in that: The time delay estimator of S2 is designed as follows, The time delay estimator is defined as follows: in, is the estimated value of F(t) based on the time delay estimator; Δt is the time delay interval. Only when the time delay interval is small enough can the accuracy of the estimation of uncertainties and disturbances be guaranteed.

4. The global fractional-order non-singular terminal sliding mode control method for a snake-like robot according to claim 1 or 2, characterized in that: The global fractional-order non-singular terminal sliding surface of S3 is designed as follows: The global non-singular fast terminal sliding surface is designed as: s(t)=[s1(t),s2(t),…,s N (t),s N+1 (t),s N+2 (t)] T (8), η=diag(η1,η2,…,η N ,or N+1 ,or N+2 ) γ=diag(Y1,Y2,…,Y N ,Y N+1 ,Y N+2 ) e(t)=[e1(t),e2(t),…,e N (t),e N+1 (t),e N+2 (t)] T e(0)=[e1(0),e2(0),…,e N (0),e N+1 (0),e N+2 (0)] T Among them, ηe(t) is the tracking error proportional term of the N-joint snake-like robot, and η is the proportional term parameter adjustment gain; is the fractional-order non-singular terminal integral term; ΥD ε e(τ) is the fractional-order term, Υ is the parameter gain of the fractional-order term, D ε is the fractional integral, ε is the fractional integral order; is a non-singular term, ω, and σ are non-singular parameter adjustment gains, which must satisfy: and σ is a positive odd number; The first-order differential of the global non-singular fast terminal sliding surface is as follows: in, is the first-order 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)The first-order differential with respect to time t.

5. A global fractional-order non-singular terminal sliding mode control method for a snake-like robot according to any one of claims 1 to 4, characterized in that: The power approach rate of S4 is designed as follows: The power approach rate is designed as follows: in, and is the tuning gain of the power approach rate, 6. A global fractional-order non-singular terminal sliding mode control method for a snake-like robot according to any one of claims 1 to 4, characterized in that: The S4 also includes, Based on the global fractional-order non-singular terminal sliding mode surface and time delay estimator, combined with the power approach rate, the global fractional-order non-singular terminal sliding mode controller u(t) based on time delay for the N-joint snake-like robot system is designed as:

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