Tracking Control Method and Device for Cable-Driven Snake-like Flexible Arm Based on Friction Compensation

Abstract

The present invention discloses a tracking control method and device for a cable-driven snake-like flexible arm based on friction compensation. The dynamic model of the snake-like flexible arm is fully considered, a snake-like flexible arm model containing friction is established for friction, its internal state is observed using a state observer, and an adaptive control law is designed to compensate for friction. The RBF neural network is used to solve the flexibility and uncertainty in the model, and an adaptive sliding mode controller is designed using an adaptive method to control the snake-like flexible joint. The control accuracy of the controller is verified through simulation. In practical applications, the snake-like flexible arm is widely used in some narrow spaces such as the wings of airplanes and has high flexibility. Therefore, there are high requirements for control accuracy. The adaptive controller designed in this invention can be applied to the control of the snake-like flexible arm.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot control, and particularly relates to a tracking control method and device for a cable-driven snake-like flexible arm based on friction compensation. Background Art

[0002] The cable-driven snake-like manipulator is a hyper-redundant manipulator designed based on the principle of bionics. It is composed of multiple rigid or flexible joints in series, and is also known as an elephant trunk robot, bionic octopus, bionic tentacle, etc. Such robots use a plurality of densely distributed motion joints to simulate biological continuous structures (such as snake bodies, elephant trunks, octopus tentacles, etc.), and at the same time use cable drive to simulate the driving effect of biological tendons. Since no power components such as motors are installed on the cable-driven snake-like manipulator, its structural weight and size can be greatly reduced, which helps to design and manufacture manipulators with slender structures. The cable-driven snake-like manipulator has a large number of joints and degrees of freedom, is flexible in movement, has a large working space, and can carry equipment to perform operation tasks in narrow and enclosed environments. Such robots have broad application prospects in many fields such as aerospace, nuclear industry, and medical devices.

[0003] Determination of the snake-like manipulator model: Since the cable can only bear tension and cannot bear pressure, the snake-like arm needs to maintain the mechanism pose with the "antagonistic" force between the cables. Therefore, a large number of redundant cables are required. As the number of degrees of freedom of the mechanism increases, the number of cables increases sharply, resulting in a sharp increase in the number of drives, an increase in the difficulty of cable layout and base design, and a sharp increase in equipment cost. To solve this problem, designers introduce passive degrees of freedom in the cable-driven snake-like arm to minimize the number of cables as much as possible. According to whether the cable-driven snake-like arm contains passive degrees of freedom, it can be divided into main / passive rigid snake-like arms, main / passive snake-like flexible arms, and fully active snake-like arms. Among them, the first two both contain passive degrees of freedom, and the movement between joints affects each other. Each degree of freedom of the fully active snake-like arm can be independently driven without affecting the movement of other joints.

[0004] Structure selection: The main / passive snake-like flexible arm has the following advantages:

[0005] (1) It can use easily bendable structures such as springs, rubbers, and cuts to design flexible joints, thereby reducing the diameter of the snake-like arm and making the arm structure simple and compact.

[0006] (2) The main / passive snake-like flexible arm has a large number of degrees of freedom, a large length-to-diameter ratio, strong variability, and good passive compliance.

[0007] There are still many problems in the control of cable-driven snake-like manipulators: due to the existence of flexible joints such as springs and rubbers, the difficulty of control increases. The cable-driven snake-like manipulator has a large number of degrees of freedom and driving numbers, which poses challenges to its control while ensuring the flexibility of the mechanism movement. At present, the dynamic model of the cable-driven snake-like manipulator is established after a large simplification of the actual mechanism, and the factors such as cable hole clearance and friction are insufficiently considered, resulting in a large error between the theoretical calculation value and the actual movement. At the same time, the control method of the cable-driven snake-like manipulator lacks compensation for model uncertainty interference, making the reliability of the mechanism low when performing actual tasks and unable to meet the industrial operation requirements at the present stage. By establishing a perfect dynamic model and designing a motion controller that can resist model uncertainty interference on this basis, it helps to improve the low motion control accuracy and poor reliability of the current cable-driven snake-like manipulator, and helps to improve its adaptability to the industrial environment. Based on the improvement of the model and control method, the cable-driven snake-like manipulator is expected to be widely used in actual production and life in the future, so as to improve social production efficiency and economic benefits.

[0008] At present, a variety of control methods can be used for the motion control of cable-driven snake-like manipulators. Zhongning JIANG et al. used the time width modulation method (TWM) to make the cable length track the expected cable length. Tran, Zhenglong Sun et al. calculated the feedforward amount of the cable length based on the kinematic model. These methods do not introduce the pose feedback of the snake-like arm in the task space and essentially belong to open-loop motion control, unable to achieve motion compensation and with low control accuracy. Hesheng Wang et al. studied the visual servo control method of cable-driven snake-like manipulators. Jianzhong Tang et al. calculated the driving cable length using the kinematic model of the cable-driven hyper-redundant manipulator and achieved the end pose tracking of the mechanism through a cable length PID controller. Although the trajectory tracking function of the snake-like arm can be realized by controlling the cable length, the "antagonistic force" between the redundant cables is uncontrollable. In recent years, with the development of intelligent control technology, some intelligent algorithms have been used to design the control law of cable-driven snake-like arms. Goharimanesh et al. proposed a fuzzy reinforcement learning method for continuous robots based on the Cosserat rod model and used the Taguchi method and genetic algorithm to tune its control parameters. Guochen Niu et al. designed a fuzzy logic controller to achieve the joint angle control of the cable-driven continuous manipulator. However, intelligent control methods consume a large amount of computer resources and the control effect for complex mechanisms with variable parameters is not ideal at present. Due to the large number of degrees of freedom and driving numbers of the mechanism, the influence of unmodeled dynamics on the performance of the controller is large. Therefore, the motion controller of the cable-driven snake-like manipulator must have strong robustness while ensuring motion accuracy, which is a technical problem that needs to be solved urgently by those skilled in the art. Summary of the Invention

[0009] To solve the above technical problems, the present invention analyzes the model of the cable-driven flexible manipulator, establishes a dynamic model, and uses the adaptive neural network sliding mode control method to ensure the motion control accuracy and robustness of the mechanism.

[0010] To achieve the above object, the present invention provides a tracking control method for a cable-driven snake-like flexible arm based on friction compensation, including the following steps:

[0011] S1: Input the target point, set the initial state of the snake-like flexible arm, and give the desired position and velocity information;

[0012] S2: Establish a model of the snake-like flexible arm with friction;

[0013] S3: Design an overall adaptive controller according to the model of the snake-like flexible arm;

[0014] S4: Obtain the position and velocity information of the snake-like flexible arm through sensors and encoders, observe the internal state of the snake-like flexible arm model through a state observer, design an adaptive control law according to the internal state information, and design an adaptive RBF neural network for the uncertainty and flexibility of the snake-like flexible arm model;

[0015] S5: Control the motor speed of the snake-like flexible arm based on the adaptive control law to control the continuous and stable operation of the snake-like flexible arm;

[0016] S6: Judge whether the target point is reached. If the target point is reached, the snake-like flexible arm stops running. If the target point is not reached, repeat steps S4 - S6 until the target point is reached.

[0017] Further, S2 specifically includes:

[0018] S21: Consider a simple snake-like flexible arm system, and its dynamic equation is described as follows:

[0019]

[0020]

[0021] where, θ ∈ R n and q ∈ R n respectively represent the joint angles on the motor side and the link side, M(q) ∈ R n×n represents the inertia matrix, represents the Coriolis force and centrifugal force, G(q) ∈ R n represents the gravity, τ f represents the friction force, K represents the stiffness coefficient, J represents the torque of the motor, and τ represents the control input torque;

[0022] S22: Define the state variables The above model can be transformed into the following form:

[0023]

[0024] The LuGre friction model is selected to describe the friction force τ existing during the transmission from the motor side to the link side f , and the model is improved to enable it to adaptively observe the friction at the current moment. The LuGre friction model is as follows:

[0025]

[0026] where σ0, σ1, and σ2 are friction coefficients, is a function related to the speed, z is the average deformation of the bristles, and F c is the Coulomb friction force, and F s is the static friction force, is the switching speed;

[0027] Simplifying the above equation gives:

[0028] Dividing the internal state z into two parts z0 and z1, at this time τ f is re-expressed as:

[0029]

[0030] Furthermore, a state observer is designed to observe the two parts of the internal state respectively. The designed state observer is as follows:

[0031]

[0032]

[0033] where, is the estimated value of the state z, r is the sliding mode surface, where y and y d represent the actual trajectory and the desired trajectory respectively, e is the error, and k1 is a constant greater than 0.

[0034] Furthermore, the specific steps for designing an adaptive RBF neural network for the uncertainties and flexibility of the snake-like flexible arm model include:

[0035] Express the uncertainties and flexible terms of the snake-like flexible arm model itself as the following function:

[0036]

[0037] RBF is a three-layer neural network, including an input layer, a hidden layer and an output layer; the transformation from the input space to the hidden space is non-linear, while the transformation from the hidden space to the output space is linear. For an unknown continuous non-linear function f(x), in the compact set Ω ∈ R, it is approximated as:

[0038] f(x) = Θ T Φ(x) + Λε

[0039] where x ∈ Ω is the input vector, Θ ∈ R l is the ideal weight vector, l is the number of nodes, ε is the approximation error, Φ(x) = [Φ1(x),..., Φ l (x)] T ∈ R l is the Gaussian function, satisfying:

[0040]

[0041] ζ i = [ζ i1 , ζ i2 ,..., ζ il T is the center of the Gaussian function, ν i is the width of the Gaussian function;

[0042] Define the RBF neural network to approximate the uncertain quantity f(x).

[0043] Furthermore, the goal of the adaptive controller is to make the tracking error e and the sliding mode surface r tend to zero. The designed adaptive controller is as follows:

[0044]

[0045] where all α, and are positive definite and diagonal matrices, is the estimate of Θ T , α is the gain to be designed, and are the estimates of the unknown parameters of the LuGre friction model.

[0046] Furthermore, the adaptive control law is designed as follows:

[0047]

[0048]

[0049]

[0050] ​​

[0051] wherein λ0, λ1, λ2, λ3, A, B, C, and D are all constants and are positive definite;

[0052]

[0053]

[0054]

[0055] Y(x) = diag(φ1(x),..., φ n (x)).

[0056] wherein x 21 , x 22 ,..., x 2n , φ1(x),..., φ n (x) All column vectors or elements in the diagonal matrix are elements in the original matrices σ, x2, σ0, σ1, z1, Φ(x), which are the estimated values of z0 and z1 respectively, and is the error value between the actual value and the estimated value.

[0057] Furthermore, the adaptive law is obtained by designing a Lyapunov function and proving that the derivative of the Lyapunov function is less than 0. The expression of the Lyapunov function is as follows:

[0058]

[0059] In addition, to achieve the above object, the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the tracking control method of the cable-driven snake-like flexible arm based on friction compensation are implemented.

[0060] In addition, to achieve the above object, the present invention also provides a storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the tracking control method of the cable-driven snake-like flexible arm based on friction compensation are implemented.

[0061] The beneficial effects brought by the technical solution provided by the present invention are as follows:

[0062] The present invention fully considers the dynamic model of the snake-shaped flexible arm, establishes an improved LuGre friction model for friction, observes its internal state using a state observer, and designs an adaptive control law to compensate for friction; uses an RBF neural network to solve the flexibility and uncertainty in the model, and designs an adaptive sliding mode controller using an adaptive method to control the snake-shaped flexible joint, and verifies the control accuracy of the controller through simulation. In practical applications, the snake-shaped flexible arm is widely used in some narrow spaces such as the wings of airplanes, with high flexibility, so there are high requirements for control accuracy. The adaptive controller designed in this invention can be well applied to the control of the snake-shaped flexible arm. Description of the Drawings

[0063] Figure 1 It is a flowchart of a tracking control method for a cable-driven snake-shaped flexible arm based on friction compensation in an embodiment of the present invention;

[0064] Figure 2 It is a schematic diagram of the trajectory tracking of the first joint angle of the snake-shaped flexible arm in an embodiment of the present invention;

[0065] Figure 3 It is a schematic diagram of the trajectory tracking of the second joint angle of the snake-shaped flexible arm in an embodiment of the present invention;

[0066] Figure 4 It is a schematic diagram of the trajectory tracking error of the two joint angles of the snake-shaped flexible arm in an embodiment of the present invention;

[0067] Figure 5 It is a schematic diagram of the control input torque of the two joint angles of the snake-shaped flexible arm in an embodiment of the present invention

[0068] Figure 6 It is a schematic diagram of an electronic device in an embodiment of the present invention. Detailed Embodiments

[0069] The realization, functional characteristics and advantages of the object of the present invention will be further described in conjunction with the embodiments with reference to the drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0070] Refer to Figure 1 , an embodiment of the present invention provides a tracking control method for a cable-driven snake-shaped flexible arm based on friction compensation, which mainly includes the following steps:

[0071] S1: Input the target point, set the initial state of the snake-shaped flexible arm, and give the desired position and speed information;

[0072] S2: Establish a model of the snake-shaped flexible arm with friction;

[0073] S3: Design an overall adaptive controller according to the model of the snake-shaped flexible arm;

[0074] S4: Obtain the position and speed information of the snake-shaped flexible arm through sensors and encoders, observe the internal state of the snake-shaped flexible arm model through a state observer, design an adaptive control law based on the internal state information, and design an adaptive RBF neural network for the uncertainty and flexibility of the snake-shaped flexible arm model;

[0075] S5: Control the motor speed of the snake-shaped flexible arm based on the adaptive control law to control the continuous and stable operation of the snake-shaped flexible arm;

[0076] S6: Determine whether the target point has been reached. If the target point has been reached, the snake-shaped flexible arm stops operating. If the target point has not been reached, repeat steps S4 - S6 until the target point is reached.

[0077] Based on but not limited to the above method, step S2 specifically includes:

[0078] S21: Consider a simple snake-shaped flexible arm system, and its dynamic equation is described as follows:

[0079]

[0080]

[0081] where, θ ∈ R n and q ∈ R n respectively represent the joint angles on the motor side and the link side, M(q) ∈ R n×n represents the inertia matrix, represents the Coriolis force and centrifugal force, G(q) ∈ R n represents the gravity, τ f represents the friction force, K represents the stiffness coefficient, J represents the torque of the motor, and τ represents the control input torque;

[0082] S22: Define the state variable q = x1, The above model can be transformed into the following form:

[0083]

[0084] Select the LuGre friction model to describe the friction force τ existing during the transmission from the motor side to the link side f , and improve the model so that it can adaptively observe the friction at the current moment. The LuGre friction model is as follows:

[0085]

[0086] where, σ0, σ1, σ2 are friction coefficients, is a function related to the speed, z is the average deformation of the bristles, F cis the Coulomb friction force, F s is the static friction force, is the switching speed;

[0087] Simplifying the above equation gives:

[0088] Divide the internal state z into two parts z0 and z1, and at this time τ f is re-expressed as:

[0089]

[0090] Then, design state observers to observe the two parts of the internal state respectively. The designed state observers are as follows:

[0091]

[0092]

[0093] Among them, is the estimated value of the state z, r is the sliding mode surface, where y and y d represent the actual trajectory and the desired trajectory respectively, e is the error, and k1 is a constant greater than 0.

[0094] Based on but not limited to the above method, in step S4, the specific steps for designing the adaptive RBF neural network for the uncertainty and flexibility of the snake-like flexible arm model include:

[0095] Express the uncertainty of the snake-like flexible arm model itself and the terms containing flexibility as the following function:

[0096]

[0097] RBF is a three-layer neural network, including an input layer, a hidden layer, and an output layer; the transformation from the input space to the hidden space is non-linear, while the transformation from the hidden space to the output space is linear. For an unknown continuous non-linear function f(x), in the compact set Ω∈R, it is approximated as:

[0098] f(x) = Θ T Φ(x) + Λε

[0099] where x∈Ω is the input vector, Θ∈R l is the ideal weight vector, l is the number of nodes, ε is the approximation error, Φ(x) = [Φ1(x),..., Φ l (x)] T ∈R l is the Gaussian function, satisfying:

[0100]

[0101] ζ i = [ζ i1 , ζ i2 ,..., ζ il T is the center of the Gaussian function, and ν i is the width of the Gaussian function;

[0102] Define an RBF neural network to approximate the uncertain quantity f(x).

[0103] It should be understood that the goal of the adaptive controller is to make the tracking error e and the sliding mode surface r tend to zero. The designed adaptive controller is as follows:

[0104]

[0105] where all α, and are positive definite and diagonal matrices, is the estimate of Θ T , α is the gain to be designed, and are the estimates of the unknown parameters of the LuGre friction model.

[0106] Furthermore, the adaptation law corresponding to the adaptive controller is obtained by designing a Lyapunov function and proving the conditions for the asymptotic stability of the Lyapunov function (a and b are both positive constants), and the expression of the Lyapunov function is as follows:

[0107] Taking the derivative of the above equation gives:

[0108] From the asymptotic stability conditions (a and b are both positive constants), the designed adaptive control law is as follows:

[0109]

[0110]

[0111]

[0112]

[0113] where λ0, λ1, λ2, λ3, A, B, C, D are all constants and positive definite;

[0114]

[0115] ​

[0116]

[0117] Y(x) = diag(φ1(x),..., φ n (x)).

[0118] Where x 21 , x 22 , …, x 2n , φ1(x),..., φ n (x) all column vectors or elements in the diagonal matrix are elements in the original matrices σ, x2, σ0, σ1, z1, Φ(x), which are the estimated values of z0 and z1 respectively, and is the error value between the actual value and the estimated value.

[0119] Experimental simulation verification:

[0120] To verify the high-precision control effect of the controller designed in the present invention, in the simulation, two flexible joints were used, and the stiffness of the flexible joint was 0.05 Nm / rad. The motor speed was obtained from the derivative of the measured motor position. The goal of this experiment was to verify the tracking ability of the designed controller. In this experiment, the masses of the links m1 = m2 = 1.5 kg. The lengths of the links were l1 = l2 = 0.3 m. The Coulomb friction force F c = 0.2 N. The static friction force F s = 50 N. Let the trajectory to be tracked be sin(t). The initial values of the robot were x1 = [2, 1], x2 = [1, 1]. The model of the snake-like flexible arm was

[0121]

[0122]

[0123] The simulation results are as Figures 2 - 5 shown. In Figure 2 and Figure 3 , the reference trajectories and actual trajectories of the two snake-like flexible joint angles are shown respectively. It can be seen that the actual trajectories of the two snake-like flexible joint angles are basically consistent with the desired trajectories, indicating good tracking performance. Figure 4 shows the position errors of the two snake-like flexible joint angles. From Figures 2 - 4 , it can be seen that the errors quickly converge to a small set, which shows that the control scheme has good performance. Figure 5 shows the control inputs of the two snake-like flexible joint angles. According to the defined reference trajectories, the control inputs of the two snake-like flexible joints are within a reasonable range.

[0124] As can be seen from the above analysis, even in the presence of uncertain dynamics, external disturbances, and unknown friction, the control scheme proposed by the present invention can still achieve good performance.

[0125] As Figure 6 shown, a schematic diagram of the physical structure of an electronic device is illustrated. The electronic device may include: a processor 610, a communications interface 620, a memory 630, and a communication bus 640. Among them, the processor 610, the communications interface 620, and the memory 630 complete communication with each other through the communication bus 640. The processor 610 may call the logical instructions in the memory 630 to execute the steps of the above tracking control method, specifically including: S1: input a target point, set the initial state of the snake-like flexible arm, and give the desired position and speed information; S2: establish a snake-like flexible arm model containing friction; S3: design an overall adaptive controller according to the snake-like flexible arm model; S4: obtain the position and speed information of the snake-like flexible arm through sensors and encoders, observe the internal state of the snake-like flexible arm model through a state observer, design an adaptive control law according to the internal state information, and design an adaptive RBF neural network for the uncertainty and flexibility of the snake-like flexible arm model; S5: control the motor speed of the snake-like flexible arm based on the adaptive control law to control the continuous and stable operation of the snake-like flexible arm; S6: determine whether the target point is reached. If the target point is reached, the snake-like flexible arm stops operating. If the target point is not reached, repeat steps S4 - S6 until the target point is reached.

[0126] In addition, when the logical instructions in the above-mentioned memory 630 can be implemented in the form of software functional units and sold or used as an independent product, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this 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 to enable a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. And the aforementioned storage medium includes: USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs, etc., all kinds of media that can store program codes.

[0127] On the other hand, an embodiment of the present invention further provides a storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned tracking control method are implemented, specifically including: S1: Input a target point, set the initial state of the snake-shaped flexible arm, and give the desired position and speed information; S2: Establish a snake-shaped flexible arm model containing friction; S3: Design an overall adaptive controller according to the snake-shaped flexible arm model; S4: Obtain the position and speed information of the snake-shaped flexible arm through sensors and encoders, observe the internal state of the snake-shaped flexible arm model through a state observer, design an adaptive control law according to the internal state information, and design an adaptive RBF neural network for the uncertainty and flexibility of the snake-shaped flexible arm model; S5: Control the motor speed of the snake-shaped flexible arm based on the adaptive control law to control the continuous and stable operation of the snake-shaped flexible arm; S6: Determine whether the target point is reached. If the target point is reached, the snake-shaped flexible arm stops running. If the target point is not reached, repeat steps S4 - S6 until the target point is reached.

[0128] It should be noted that in this article, the terms "including", "comprising" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such a process, method, article or system. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, method, article or system including that element.

[0129] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments. In the several device unit claims listing several devices, several of these devices may be embodied by the same hardware item. The use of the words first, second, and third, etc. does not indicate any order and these words can be interpreted as identifiers.

[0130] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent structure or equivalent process transformation made by using the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present invention.

Claims

1. A tracking control method for a cable-driven snake-like flexible arm based on friction compensation, characterized in that It includes the following steps: S1: Input the target point, set the initial state of the snake-like flexible arm, and give the desired position and velocity information; S2: Establish a snake-like flexible arm model with friction; S3: Design an overall adaptive controller according to the snake-like flexible arm model; S4: Obtain the position and velocity information of the snake-like flexible arm through sensors and encoders, observe the internal state of the snake-like flexible arm model through a state observer, design an adaptive control law according to the internal state information, and design an adaptive RBF neural network for the uncertainty and flexibility of the snake-like flexible arm model; S5: Control the motor speed of the snake-like flexible arm based on the adaptive control law to control the continuous and stable operation of the snake-like flexible arm; S6: Judge whether the target point is reached. If the target point is reached, the snake-like flexible arm stops running. If the target point is not reached, repeat steps S4 - S6 until the target point is reached; Among them, S2 specifically includes: S21: Consider a simple snake-like flexible arm system, and its dynamic equation is described as follows: wherein, and represent the joint angles on the motor side and the link side respectively, represents the inertia matrix, represents the Coriolis force and the centrifugal force, represents the gravity, represents the frictional force, represents the stiffness coefficient, represents the torque of the motor, represents the control input torque; S22: Define a state variable , the above model can be transformed into the following form: The LuGre friction model is selected to describe the friction existing during the transmission from the motor side to the link side , and the model is improved to enable it to adaptively observe the friction at the current moment. The LuGre friction model is as follows: wherein, is the friction coefficient, is a function related to the speed, is the average deformation of the bristles, is the Coulomb friction force, is the static friction force, is the switching speed; Simplifying the above equation gives: Divide the internal state into two parts and At this time is re-expressed as: ； In step S3, the goal of the adaptive controller is to make the tracking error and the sliding mode surface tend to zero. The designed adaptive controller is as follows: All of which 、 、 and are all positive definite and diagonal matrices, is 's estimate, is the gain to be designed, 、 and are estimates of the unknown parameters of the LuGre friction model; In step S4, design state observers to observe the two parts of the internal state respectively. The designed state observers are as follows: wherein, is the estimated value of the state , is the sliding mode surface ( ), where and respectively represent the actual trajectory and the desired trajectory is the error is a constant and greater than 0; In step S4, the specific steps of designing an adaptive RBF neural network for the uncertainty and flexibility of the snake-like flexible arm model include: Express the uncertainty of the snake-like flexible arm model itself and the terms containing flexibility as the following function: RBF is a three-layer neural network, including an input layer, a hidden layer and an output layer; the transformation from the input space to the hidden space is non-linear, while the transformation from the hidden space to the output space is linear. For an unknown continuous non-linear function , on the compact set , it can be approximated as: Among them is the input vector, is the ideal weight vector, is the number of nodes, is the approximation error, is the Gaussian function, satisfying: is the center of the Gaussian function, is the width of the Gaussian function; Define the RBF neural network to approximate the uncertainties ; In step S4, the adaptive control law is designed as follows: wherein are all constants and positive definite; Among them , , , , , , All elements in the column vectors or diagonal matrices are elements in the original matrix , estimated value of is the error value between the actual value and the estimated value.

2. According to the tracking control method of the cable-driven snake-like flexible arm based on friction compensation described in claim 1, the adaptive control law is obtained by designing a Lyapunov function and proving that the derivative of the Lyapunov function is less than 0. The expression of the Lyapunov function is as follows: 。 3. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the tracking control method of the cable-driven snake-like flexible arm based on friction compensation described in any one of claims 1 and 2.

4. A storage medium, on which a computer program is stored, characterized in that, When the computer program is executed by the processor, it implements the steps of the tracking control method of the cable-driven snake-like flexible arm based on friction compensation described in any one of claims 1 and 2.

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