Continuous body robot position control method based on nonlinear disturbance observer

Abstract

The invention provides a continuum robot position control method based on a nonlinear disturbance observer. Comprising the following steps: step 1, designing a non-linear disturbance observer NDO to observe external disturbance; 2, designing a feedback controller to track the tail end position of the continuum robot; and step 3, subtracting the disturbance estimated by the nonlinear disturbance observer NDO from the output of the feedback controller as total control input, and inputting the total control input into the continuum robot system. The invention provides a control strategy based on a nonlinear disturbance observer for strong nonlinearity and coupling characteristics of a continuum robot. The control strategy meets the separation principle, and therefore feedback controller parameters and observer parameters can be independently designed according to the requirements of a user for the dynamic response performance and the anti-interference performance. A feedback controller parameter setting method based on a frequency domain index is further provided, and PD controller analysis design can be carried out according to the given frequency domain index.

Description

Technical Field

[0001] The invention relates to the field of continuum robot control, and in particular to a continuum robot position control method based on a nonlinear disturbance observer. Background Art

[0002] Continuum Robot is a soft robot that imitates biological structures (such as elephant trunks, octopus tentacles, snakes, etc.). It is characterized by a continuous and flexible structure that can bend and deform flexibly in three-dimensional space. Compared with traditional rigid robots, continuum robots have higher flexibility and adaptability, and are particularly suitable for operating tasks in narrow, complex or unstructured environments.

[0003] The position control accuracy of the continuum robot has a very important influence on the application of the continuum robot. However, the unmodeled dynamics in the continuum robot and the external disturbance will affect the control accuracy of the continuum robot. Therefore, it is necessary to design a disturbance-resistant controller for it. The integral link in the PID controller has an anti-disturbance effect, but it will deteriorate the dynamic effect of the system while improving the anti-disturbance. The sliding mode controller also has a certain anti-disturbance effect, but it will cause chattering. Compared with single-degree-of-freedom controllers such as PID controllers or sliding mode controllers, the two-degree-of-freedom controller uses one degree of freedom to achieve system tracking control and the other degree of freedom to estimate disturbances, which can achieve better dynamic control effects. ADRC is a typical two-degree-of-freedom controller. It regards the nonlinearity of the system and the external disturbances as total disturbances and uses an extended state observer to estimate the total disturbance. However, the continuum robot is a strongly nonlinear system. Using an extended state observer to estimate will increase the burden on the system and make its control effect worse.

[0004] Therefore, for the nonlinear system of the continuum robot, an available solution needs to be provided to improve the position control effect of the continuum robot. Summary of the invention

[0005] The problem to be solved by the present invention is to design a position control method of a continuum robot based on a nonlinear disturbance observer in view of the deficiencies in the prior art.

[0006] In a first aspect, the present invention provides a continuum robot position control method based on a nonlinear disturbance observer, comprising the following steps: Step 1, design a nonlinear disturbance observer NDO to observe external disturbances; Step 2, design a feedback controller to track the end position of the continuum robot; In step 3, the output of the feedback controller minus the disturbance estimated by the nonlinear disturbance observer (NDO) is used as the total control input and input into the continuum robot system.

[0007] Based on the above, the designed nonlinear disturbance observer NDO is: (1) In formula (1), is the gain matrix of the linear disturbance observer; is an external disturbance, controlled by the input and system output And its dynamic representation, namely: (2) Since the disturbance is unknown and generally changes slowly, ,Will Substituting formula (2) into formula (1), we get: (3) The error of the linear disturbance observer is defined as: (4) Then the error dynamics of the linear disturbance observer is: (5) Right now: (6) Add an auxiliary vector to the linear disturbance observer: (7) Requirements: (8) Select and is the following value to satisfy condition (8); (9) is the observer gain, which is a constant; Taking the derivative of the auxiliary vector (7) and substituting equations (3) and (8) into it, we obtain: (10) The expression of the nonlinear disturbance observer NDO is obtained as: (11) Based on the above, the designed feedback controller is: (12) is the equivalent control input, expressed as: (13) in, is the desired angle, is the actual angle of the continuum robot, and is the feedback controller parameter, which is a diagonal matrix.

[0008] Based on the above, the Lyapunov function of the observation error is constructed, and then it is differentiated to obtain the condition that makes the derivative always less than 0, which is the condition for the stability of the nonlinear disturbance observer; then the entire control input is substituted into the dynamic model of the continuum robot to obtain the characteristic equation of the closed-loop system, and the condition that makes the pole of the system characteristic equation located in the left half plane of the s-plane is determined, which is the condition for the stability of the entire closed-loop system.

[0009] In a second aspect, the present invention provides a continuum robot position control system based on a nonlinear disturbance observer, comprising: Nonlinear disturbance observer NDO, used to observe external disturbances of the continuum robot; A feedback controller for tracking the end position of the continuum robot; The disturbance estimated by the nonlinear disturbance observer (NDO) is subtracted from the output of the feedback controller to obtain the total control input, which is input into the continuum robot.

[0010] Based on the above, the nonlinear disturbance observer NDO is designed as: (1) In formula (1), is the gain matrix of the linear disturbance observer; is an external disturbance, controlled by the input and system output And its dynamic representation, namely: (2) Since the disturbance is unknown and generally changes slowly, ,Will Substituting formula (2) into formula (1), we get: (3) The error of the linear disturbance observer is defined as: (4) Then the error dynamics of the linear disturbance observer is: (5) Right now: (6) Add an auxiliary vector to the linear disturbance observer: (7) Requirements: (8) Select and is the following value to satisfy condition (8); (9) is the observer gain, which is a constant; Taking the derivative of the auxiliary vector (7) and substituting equations (3) and (8) into it, we obtain: (10) The expression of the nonlinear disturbance observer NDO is obtained as: (11) Based on the above, the feedback controller is designed as: (12) is the equivalent control input, expressed as: (13) in, is the desired angle, is the actual angle of the continuum robot, and is the feedback controller parameter, which is a diagonal matrix.

[0011] Based on the above, the Lyapunov function of the observation error is constructed, and then it is differentiated to obtain the condition that makes the derivative always less than 0, which is the condition for the stability of the nonlinear disturbance observer; then the entire control input is substituted into the dynamic model of the continuum robot to obtain the characteristic equation of the closed-loop system, and the condition that makes the pole of the system characteristic equation located in the left half plane of the s-plane is determined, which is the condition for the stability of the entire closed-loop system.

[0012] In a third aspect, the present invention provides a parameter setting method for setting the parameters of the continuum robot position control system based on the nonlinear disturbance observer, firstly setting the parameters of the feedback controller according to the requirements of the feedback controller and Then, the observer gain c of the nonlinear disturbance observer NDO is adjusted according to the anti-interference requirements; Tune the parameters of the feedback controller: The output of the feedback controller is dripped into the dynamic model of the continuum robot, and the transfer function of the forward channel is obtained as follows: (14) Use crossover frequency and phase margin Two frequency domain indicators are used to design the feedback controller parameters; Substituting into the open-loop transfer function (14) we get: (15) The crossover frequency and phase margin meet the following conditions: (16) (17) By solving the two conditions (16) and (17), we can obtain: (18) Given crossover frequency and phase margin , the parameters of the feedback controller can be obtained and ; Parameter tuning for nonlinear disturbance observer NDO: In the case where the requirements for anti-interference are high but the requirements for noise are not high, a larger observer gain c is selected, while in the case where the requirements for anti-interference are not high but the requirements for noise are high, a smaller observer gain c is selected; the value range of the observer gain c is 10 -5 ~10 -4 .

[0013] In a fourth aspect, the present invention provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the continuum robot position control method based on a nonlinear disturbance observer, or implements the steps of the parameter setting method.

[0014] Compared with the prior art, the present invention has the following significant advantages: Aiming at the strong nonlinearity and coupling characteristics of the continuum robot, the present invention proposes a control strategy based on a nonlinear disturbance observer, wherein the nonlinear disturbance observer is used to observe and compensate for the nonlinear dynamics and external disturbances in the system, and the feedback controller (proportional differential controller) is used to realize the tracking control of the system. The control strategy of the present invention satisfies the separability principle, so the feedback controller parameters and the observer parameters can be independently designed according to the user's requirements for dynamic response performance and anti-disturbance performance. And further proposed a feedback controller parameter tuning method based on frequency domain indicators, which can be used to perform analytical design of PD controllers based on given frequency domain indicators. By constructing the Lyapunov function, the asymptotic stability of NDO is strictly proved, and the stability of the closed-loop system is ensured by combining the pole configuration method. Finally, the superiority of the proposed control strategy compared with the classical PID control strategy is proved by simulation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a control block diagram of the method of the present invention.

[0016] Figure 2 It is the disturbance estimation corresponding to different c in Example 3 of the present invention.

[0017] Figure 3 This is a comparison chart of the control effects of Example 3 of the present invention and PID.

[0018] Figure 4 This is a control effect diagram of NDO and PID under a sinusoidal trajectory in Example 3 of the present invention.

[0019] Figure 5 The circular trajectory tracking control diagram in Example 3 of the present invention; (a) is the trajectory of the continuum robot in the task space.

[0020] (b) is the force on the three driving wires in Example 3 of the present invention.

[0021] (c) is the error between the reference trajectory and the simulation trajectory on the three coordinate axes of x, y, and z in Example 3 of the present invention. DETAILED DESCRIPTION

[0022] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0023] Example 1 This embodiment provides a continuum robot position control method based on a nonlinear disturbance observer, comprising the following steps: Step 1, design a nonlinear disturbance observer NDO to observe external disturbances; Step 2, design a feedback controller to track the end position of the continuum robot; In step 3, the output of the feedback controller minus the disturbance estimated by the nonlinear disturbance observer (NDO) is used as the total control input and input into the continuum robot system.

[0024] In the present invention, the dynamic model considering disturbance in the continuum robot is: Among them, M is the inertia matrix, C is the Coriolis force matrix, K is the elasticity matrix, and q is the output of the continuum robot.

[0025] Design of nonlinear disturbance observer NDO The designed nonlinear disturbance observer NDO is: (1) In formula (1), is the gain matrix of the linear disturbance observer; is an external disturbance, controlled by the input and system output And its dynamic representation, namely: (2) Since the disturbance is unknown and generally changes slowly, ,Will Substituting formula (2) into formula (1), we get: (3) The error of the linear disturbance observer is defined as: (4) Then the error dynamics of the linear disturbance observer is: (5) Right now: (6) Add an auxiliary vector to the linear disturbance observer: (7) Requirements: (8) Select and is the following value to satisfy condition (8); (9) is the observer gain, which is a constant; Taking the derivative of the auxiliary vector (7) and substituting equations (3) and (8) into it, we obtain: (10) The expression of the nonlinear disturbance observer NDO is obtained as: (11) By using This auxiliary variable can be used without using the output signal The disturbance is estimated by taking the second-order derivative of , which reduces the impact of noise on the estimated disturbance.

[0026] Designing a Feedback Controller The designed feedback controller is: (12) is the equivalent control input, expressed as: (13) in, is the desired angle, is the actual angle of the continuum robot, and is the feedback controller parameter, which is a diagonal matrix.

[0027] Designing control systems The feedback controller is used to track the end position of the continuum robot. The nonlinear disturbance observer NDO is used to eliminate the influence of external disturbances and model errors. The input of the continuum robot system is equal to the output of the feedback controller minus the disturbance estimated by the disturbance observer. Its expression is: (19) The control block diagram of the system can be obtained from the total control input of the continuum robot as follows: Figure 1 shown.

[0028] When there is no external disturbance and model error, that is, when d=0, the dynamic model of the continuum robot can be obtained: (20) Substituting equation (7) and equation (20) into equation (10), we can obtain: (twenty one) Substituting formula (8) into formula (21), we can obtain: (twenty two) The derivative of formula (7) with respect to time t is: (twenty three) Comparing equation (22) and equation (23), we can get: (twenty four) Right now: (25) The initial state of is 0, so when there is no external disturbance and modeling error, It is always 0, which means that the disturbance observer does not work. Therefore, when there is no external disturbance and modeling error, adding the nonlinear disturbance observer NDO will not affect the tracking effect of the system.

[0029] Therefore, the parameters of the nonlinear disturbance observer NDO and the parameters of the feedback controller can be designed separately and independently. The feedback controller is designed according to the requirements of the tracking effect, and then the parameters of the nonlinear disturbance observer NDO are designed according to the requirements of the anti-interference effect.

[0030] Stability design The stability of the method of this embodiment includes the stability of the nonlinear disturbance observer and the stability of the entire closed-loop system.

[0031] Construct a Lyapunov function of the observation error (the error between the actual disturbance and the estimated value of NDO), and then differentiate it to obtain the condition that makes the derivative always less than 0, which is the condition for the stability of the nonlinear disturbance observer; then substitute the entire control input into the dynamic model of the continuum robot to obtain the characteristic equation of the closed-loop system, and determine the condition that makes the pole of the system characteristic equation located in the left half plane of the s-plane, which is the condition for the stability of the entire closed-loop system.

[0032] Stability of Nonlinear Disturbance Observer (NDO) The error of the nonlinear disturbance observer is defined as: (26) Then the derivative of the error is: (27) From the dynamic model of the continuum robot considering disturbances, we can get: (28) Substituting formula (28) into formula (10), we can obtain: (29) Substituting formula (29) into (27), we can obtain: (30) Construct a Lyapunov function: (31) Taking the derivative of the Lyapunov function, we get: (32) because ,and is a positive definite diagonal matrix, is also a positive definite diagonal matrix, so , so the derivative of the Lyapunov function (32) can be transformed into: (33) Therefore, as long as the gain coefficient c of the nonlinear disturbance observer is greater than 0, the derivative of the Lyapunov function satisfies , the nonlinear disturbance observer NDO is asymptotically stable.

[0033] The stability of the entire closed-loop system Substituting the total control input (12) into the dynamic model of the continuum robot, the closed-loop system is obtained as follows: (34) Substituting the equivalent control input (13) into equation (34) yields: (35) in, , , and is a diagonal matrix, and is a positive definite reversible matrix, so equation (35) can be transformed into: (36) Since the nonlinear disturbance observer is stable, is less than a column vector whose elements are constants, so If the diagonal matrix is ​​smaller than one element which is a constant, Equation (36) can be equivalent to two decoupled systems, where the characteristic equation of any closed-loop system is: (37) The solution of the closed-loop characteristic equation is: (38) when and satisfy >0 and >0, the solution of the closed-loop characteristic equation is in the left half plane of the s plane. So when the matrix and The closed-loop system is stable when the following conditions are met.

[0034] (39) Example 2 Based on the same inventive concept, the embodiment of the present application also provides a continuum robot position control system based on a nonlinear disturbance observer. The implementation scheme for solving the problem provided by the continuum robot position control system based on a nonlinear disturbance observer is similar to the implementation scheme recorded in the method of Example 1, so the specific limitations in one or more continuum robot position control systems based on a nonlinear disturbance observer provided below can refer to the limitations on the method in Example 1, and will not be repeated here.

[0035] In an exemplary embodiment, a continuum robot position control system based on a nonlinear disturbance observer is provided, comprising: A continuum robot position control system based on a nonlinear disturbance observer, comprising: Nonlinear disturbance observer NDO, used to observe external disturbances of the continuum robot; A feedback controller for tracking the end position of the continuum robot; The disturbance estimated by the nonlinear disturbance observer (NDO) is subtracted from the output of the feedback controller to obtain the total control input, which is input into the continuum robot.

[0036] Example 3 This embodiment provides a parameter setting method, which is used for parameter setting of the continuum robot position control system based on the nonlinear disturbance observer described in Embodiment 2.

[0037] The parameter tuning idea of ​​this embodiment is: first, the parameters of the feedback controller are tuned according to the requirements of the feedback controller. and Then, the observer gain c of the nonlinear disturbance observer NDO is adjusted according to the anti-interference requirements; Tune the parameters of the feedback controller: The output of the feedback controller is dripped into the dynamic model of the continuum robot, and the transfer function of the forward channel is obtained as follows: (14) Use crossover frequency and phase margin Two frequency domain indicators are used to design the feedback controller parameters; Substituting into the open-loop transfer function (14) we get: (15) The crossover frequency and phase margin meet the following conditions: (16) (17) By solving the two conditions (16) and (17), we can obtain: (18) Given crossover frequency and phase margin , the parameters of the feedback controller can be obtained and ; Parameter tuning for nonlinear disturbance observer NDO: The parameter that needs to be adjusted in the nonlinear disturbance observer NDO is the coefficient c. The size of c affects the speed of the observer to estimate the disturbance and the size of the noise in the estimated disturbance. Different c corresponds to the disturbance estimation value and like Figure 2 shown.

[0038] Depend on Figure 2 It can be seen that as the parameter c increases, the estimated value can track the disturbance value d faster, but The noise in the image will also be more obvious, so it is necessary to select a suitable parameter c in different application scenarios.

[0039] Specifically, qualitative tuning is performed based on the anti-interference effect and the sensitivity to noise. The larger the parameter c is, the better the anti-interference effect is, but the more sensitive it is to noise, the greater the noise carried in the NDO estimation value is; the smaller the parameter c is, the worse the anti-interference effect is, but the less sensitive it is to noise, the smaller the noise carried in the NDO estimation value is. Therefore, when the requirements for anti-interference are high but the requirements for noise are not high, a larger observer gain c is selected, and when the requirements for anti-interference are not high but the requirements for noise are high, a smaller observer gain c is selected; the value range of the observer gain c is 10 -5 ~10 -4 .

[0040] Effect verification In order to verify the positioning control effect of the continuum robot position control system based on nonlinear disturbance observer obtained by parameter tuning, it is compared with the classic controller PID. In order to ensure the fairness of the comparison, the two control systems have the same rise time. The control effect of the continuum robot position control system (hereinafter replaced by NDO) and PID provided by the present invention is shown in the figure. Figure 3 As shown in Figure 2, NDO can achieve better disturbance suppression without overshoot, and NDO can reach the desired stable state faster.

[0041] Sinusoidal trajectory tracking control In order to verify the trajectory tracking effect, the continuum robot is made to perform periodic sinusoidal motion in the plane, that is, to ensure that the rotation angle of the continuum robot The continuum robot is made to bend along a preset trajectory, where the angular frequency of the motion is =0.15rad / s, the maximum amplitude of the bending angle is =0.8 / =45.86 , the minimum amplitude is =0.2 / =12.14 , the control effect of NDO and PID is as follows Figure 4 shown.

[0042] Depend on Figure 4 It can be seen that the control effects of the two controllers are almost the same. The root mean square error (RMSE) between the simulation trajectory and the reference trajectory of the two control methods can be calculated. NDO =0.2474, RMSE PID =0.2477. That is, in the tracking of the sinusoidal trajectory, the root mean square error of NDO is slightly smaller than that of PID, and the control effect is slightly better than that of PID.

[0043] Circular trajectory tracking control In order to verify the coordination effect of the three drive wires during the movement of the continuum robot, the continuum robot is rotated in space at a fixed bending angle, that is, it performs circular motion in space. The bending angle of the continuum robot is kept at =0.6 / =36.42 , so that its rotation angle is according to Trajectory motion, where k = 0.05rad / s = 3.035 / s. The trajectory of the continuum robot in the task space is as follows Figure 5 As shown in (a) in Figure 2, the forces on the three drive wires are Figure 5 As shown in (b) in the figure, the errors between the reference trajectory and the simulation trajectory on the x, y, and z axes are as follows: Figure 5 As shown in (c) in .

[0044] Depend on Figure 5 From (b) in the figure, we can see that according to the rotation angle The three drive wires work alternately, and only two wires work at the same time, that is, the tension on the three drive wires can be well coordinated, so that the continuum robot makes a circular trajectory in space. Figure 5 From (c) in the figure, we can see that on the x and y axes, the NDO method can quickly reduce the error, but the NDO method cannot keep the error on the x axis to 0. On the z axis, the NDO method always has a certain error, but this error is much smaller than the initial error on the x and y axes.

[0045] The root mean square error of NDO and PID in the three directions of x, y, and z, as well as the total root mean square error As shown in Table 1. The root mean square error of the NDO method in the x and y coordinates is smaller than that of PID, but the root mean square error in the z direction is larger than that of PID. Calculating the total root mean square error shows that the root mean square error of NDO is smaller, so compared with PID, NDO can achieve better circular trajectory tracking.

[0046] Table 1 Root mean square error under circular trajectory

[0047] Example 4 Each module in the above system can be implemented in whole or in part by software, hardware, or a combination thereof. Each module can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in a computer device in the form of software, so that the processor can call and execute operations corresponding to each module above.

[0048] In an exemplary embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the continuum robot position control method based on the nonlinear disturbance observer as described in Example 1 are implemented, or the steps of the parameter setting method as described in Example 2 are implemented.

[0049] In an exemplary embodiment, a computer program product is provided, comprising a computer program / instruction, characterized in that when the computer program / instruction is executed by a processor, the steps of the continuum robot position control method based on the nonlinear disturbance observer as described in Example 1 are implemented, or the steps of the parameter setting method as described in Example 2 are implemented.

[0050] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

[0051] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0052] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A continuum robot position control method based on nonlinear disturbance observer, characterized in that: The steps include: Step 1, design a nonlinear disturbance observer NDO to observe external disturbances; Step 2, design a feedback controller to track the end position of the continuum robot; Step 3: The output of the feedback controller minus the disturbance estimated by the nonlinear disturbance observer (NDO) is used as the total control input and input into the continuum robot system.

2. The position control method of a continuum robot based on a nonlinear disturbance observer according to claim 1, characterized in that: The designed nonlinear disturbance observer NDO is: （1） In formula (1), is the gain matrix of the linear disturbance observer; is an external disturbance, controlled by the input and system output And its dynamic representation, namely: （2） Since the disturbance is unknown and generally changes slowly, ,Will Substituting formula (2) into formula (1), we get: （3） The error of the linear disturbance observer is defined as: （4） Then the error dynamics of the linear disturbance observer is: （5） Right now: （6） Add an auxiliary vector to the linear disturbance observer: （7） Requirements: （8） Select and is the following value to satisfy condition (8); （9） is the observer gain, which is a constant; Taking the derivative of the auxiliary vector (7) and substituting equations (3) and (8) into it, we obtain: （10） The expression of the nonlinear disturbance observer NDO is obtained as: （11）。 3. The position control method of a continuum robot based on a nonlinear disturbance observer according to claim 2, characterized in that: The designed feedback controller is: （12） is the equivalent control input, expressed as: （13） in, is the desired angle, is the actual angle of the continuum robot, and is the feedback controller parameter, which is a diagonal matrix.

4. The position control method of a continuum robot based on a nonlinear disturbance observer according to claim 3, characterized in that: Construct a Lyapunov function of the observation error, and then differentiate it to obtain the condition that makes the derivative always less than 0, which is the condition for the stability of the nonlinear disturbance observer; then substitute the entire control input into the dynamic model of the continuum robot to obtain the characteristic equation of the closed-loop system, and determine the condition that makes the pole of the system characteristic equation located in the left half plane of the s-plane, which is the condition for the stability of the entire closed-loop system.

5. A continuum robot position control system based on a nonlinear disturbance observer, characterized in that: include: Nonlinear disturbance observer NDO, used to observe external disturbances of the continuum robot; A feedback controller for tracking the end position of the continuum robot; The disturbance estimated by the nonlinear disturbance observer (NDO) is subtracted from the output of the feedback controller to obtain the total control input, which is input into the continuum robot.

6. The continuum robot position control system based on nonlinear disturbance observer according to claim 5, characterized in that: The nonlinear disturbance observer NDO is designed as: （1） In formula (1), is the gain matrix of the linear disturbance observer; is an external disturbance, controlled by the input and system output And its dynamic representation, namely: （2） Since the disturbance is unknown and generally changes slowly, ,Will Substituting formula (2) into formula (1), we get: （3） The error of the linear disturbance observer is defined as: （4） Then the error dynamics of the linear disturbance observer is: （5） Right now: （6） Add an auxiliary vector to the linear disturbance observer: （7） Requirements: （8） Select and is the following value to satisfy condition (8); （9） is the observer gain, which is a constant; Taking the derivative of the auxiliary vector (7) and substituting equations (3) and (8) into it, we obtain: （10） The expression of the nonlinear disturbance observer NDO is obtained as: （11）。 7. The continuum robot position control system based on nonlinear disturbance observer according to claim 6, characterized in that: The feedback controller is designed as: （12） is the equivalent control input, expressed as: （13） in, is the desired angle, is the actual angle of the continuum robot, and is the feedback controller parameter, which is a diagonal matrix.

8. The continuum robot position control system based on nonlinear disturbance observer according to claim 7, characterized in that: Construct a Lyapunov function of the observation error, and then differentiate it to obtain the condition that makes the derivative always less than 0, which is the condition for the stability of the nonlinear disturbance observer; then substitute the entire control input into the dynamic model of the continuum robot to obtain the characteristic equation of the closed-loop system, and determine the condition that makes the pole of the system characteristic equation located in the left half plane of the s-plane, which is the condition for the stability of the entire closed-loop system.

9. A parameter setting method for setting parameters of the continuum robot position control system based on nonlinear disturbance observer according to claim 8, characterized in that: First, adjust the parameters of the feedback controller according to the requirements of the feedback controller and Then, the observer gain c of the nonlinear disturbance observer NDO is adjusted according to the anti-interference requirements; Tune the parameters of the feedback controller: The output of the feedback controller is dripped into the dynamic model of the continuum robot, and the transfer function of the forward channel is obtained as follows: （14） Use crossover frequency and phase margin Two frequency domain indicators are used to design the feedback controller parameters; Substituting into the open-loop transfer function (14) we get: （15） The crossover frequency and phase margin meet the following conditions: （16） （17） By solving the two conditions (16) and (17), we can obtain: （18） Given crossover frequency and phase margin , the parameters of the feedback controller can be obtained and ; Parameter tuning for nonlinear disturbance observer NDO: In the case where the requirements for anti-interference are high but the requirements for noise are not high, a larger observer gain c is selected, while in the case where the requirements for anti-interference are not high but the requirements for noise are high, a smaller observer gain c is selected; the value range of the observer gain c is 10 -5 ~10 -4 .

10. A computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the continuum robot position control method based on a nonlinear disturbance observer as described in any one of claims 1 to 4, or implements the steps of the parameter setting method as described in claim 9.

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