Control Method of Underactuated Robot System

Abstract

The present invention discloses a control method for an underactuated robot system, which solves the technical problems in the prior art that external unknown disturbances have an adverse effect on the position control effect of the underactuated robot system and the convergence speed is slow. The control method includes the following steps: using an extended state observer to output the estimated values of joint positions, joint speeds and the estimated value of the lumped disturbance, and designing a disturbance compensation term from the estimated value of the lumped disturbance; designing a first sub-sliding mode surface corresponding to the driving joints in the first-layer fast terminal sliding mode surface, and outputting a first equivalent control law from the first sub-sliding mode surface; designing a second sub-sliding mode surface corresponding to the non-driving joints in the first-layer fast terminal sliding mode surface, and outputting a second equivalent control law from the second sub-sliding mode surface; designing a second-layer sliding mode surface, and outputting a switching control law from the second-layer sliding mode surface; designing a total control law according to the disturbance compensation term, the first equivalent control law, the second equivalent control law and the switching control law to control the underactuated robot system.

Description

Technical Field

[0001] The present invention relates to the technical field of underactuated robot system control, and more particularly, to a control method for an underactuated robot system. Background Art

[0002] An underactuated robot system is a special robot system in which the number of system control inputs is less than the degrees of freedom of the system, and has characteristics such as low energy consumption, light weight, and high efficiency. Underactuated robot systems are widely used in fields such as aviation, industry, agriculture, and medicine, greatly improving industrial production efficiency and people's quality of life. However, the dynamic characteristics of underactuated robot systems are highly complex, and the control methods of general fully actuated systems cannot be directly used. In addition, underactuated robots themselves are more susceptible to some uncertain factors, especially unknown external disturbances. These uncertainties need to be properly handled, otherwise they may damage the desired control performance, seriously affecting the control accuracy of the underactuated robot system, further leading to system instability and even system damage.

[0003] In order to effectively compensate for unknown external disturbances in underactuated robot systems, many domestic and foreign scholars have adopted sliding mode control to improve the control performance of underactuated robot systems and maintain system stability. As a typical and effective robust control method, sliding mode control has characteristics such as stability, reliability, and strong robustness.

[0004] However, for some underactuated robot systems, due to the inability to directly obtain the sliding mode surface parameters, the applicability of conventional single-layer sliding mode surfaces is not high. Although the hierarchical sliding mode control strategy can improve the control effect of underactuated robot systems to a certain extent when they are subjected to unknown external disturbances, there are still some limitations in the control accuracy and stability of existing hierarchical sliding mode control strategies. When dealing with unknown external disturbances, the convergence speed of the position error needs to be improved, and the inevitable chattering problem needs to be further solved. Summary of the Invention

[0005] The main object of the present invention is to provide a control method for an underactuated robot system to solve the technical problems in the prior art that unknown external disturbances have an adverse effect on the position control effect of the underactuated robot system and the slow convergence speed.

[0006] To achieve the above object, the present invention provides a control method for an underactuated robot system, and the technical solution is as follows:

[0007] A control method for an underactuated robot system, comprising the following steps:

[0008] An extended state observer is used to process the joint data of an underactuated robot system under unknown disturbances and output the estimated joint position, the estimated joint velocity, and the estimated lumped disturbance. The disturbance compensation term is designed based on the estimated lumped disturbance;

[0009] The first sub-sliding mode surface corresponding to the actuated joints in the first-layer fast terminal sliding mode surface is designed using the actuated joint position error between the estimated actuated joint position and the desired value and its first derivative, and the first equivalent control law is output from the first sub-sliding mode surface;

[0010] The second sub-sliding mode surface corresponding to the unactuated joints in the first-layer fast terminal sliding mode surface is designed using the unactuated joint position error between the estimated unactuated joint position and the desired value and its first derivative, and the second equivalent control law is output from the second sub-sliding mode surface;

[0011] The second-layer sliding mode surface is designed using the first-layer actuated fast terminal sliding mode surface and the first-layer unactuated fast terminal sliding mode surface, and the switching control law is output from the second-layer sliding mode surface;

[0012] The total control law is designed according to the disturbance compensation term, the first equivalent control law, the second equivalent control law, and the switching control law to control the underactuated robot system;

[0013] The model of the underactuated robot system is:

[0014]

[0015] where q is the joint position of the underactuated robot system, q = [q a q u T q a is the actuated joint, and q u is the unactuated joint; is the joint velocity, is the joint acceleration, M(q) is the symmetric positive definite inertia matrix of the underactuated robot system; is the combination term of the centrifugal force and the Coriolis force of the underactuated robot system; G(q) is the gravity term of the underactuated robot system; u is the control input; B is the input transformation matrix, B = [1 0] T ; τ d is the external disturbance received by the underactuated robot system, τ d = [d 1 d 2 T d 1 is the matching disturbance in the same channel as the control input, and d 2 is the non-matching disturbance in a different channel from the control input.

[0016] ​​It has been verified that the control method of the under-actuated robot system of the present invention uses a total control law composed of an interference compensation term, a first equivalent control law, a second equivalent control law, and a switching control law, enabling the under-actuated robot system to effectively cope with the occurrence of interference even in the presence of unknown external interference, achieving stable control from the initial position to the desired position, with the position error converging rapidly, maintaining good control accuracy, no obvious chattering in the control torque, and good stability.

[0017] The following further describes the present invention in conjunction with the accompanying drawings and specific embodiments. Some of the additional aspects and advantages of the present invention will be given in the following description, some will become apparent from the following description, or be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The drawings forming a part of the present invention are used to assist in understanding the present invention. The content provided in the drawings and the related descriptions in the present invention can be used to explain the present invention, but do not constitute an improper limitation to the present invention. In the drawings:

[0019] Figure 1 It is a schematic flowchart of an embodiment of the control method for the under-actuated robot system of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0020] The following clearly and completely describes the present invention in conjunction with the accompanying drawings. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it should be particularly noted that:

[0021] The technical solutions and technical features provided in each part including the following description in the present invention can be combined with each other without conflict.

[0022] In addition, the embodiments of the present invention involved in the following description are usually only a part of the embodiments of the present invention, rather than all the embodiments. Therefore, all other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0023] Regarding the terms and units in the present invention. The terms "comprising", "having" and any variations thereof in the specification, claims and relevant parts of the present invention are intended to cover non-exclusive inclusion.

[0024] Figure 1 It is a schematic flowchart of an embodiment of the control method for the under-actuated robot system of the present invention. In Figure 1 In, represents a signal comparator, whose function is to solve e 1 、e2 , and

[0025] As Figure 1 shown, an embodiment of the control method for an underactuated robot system includes the following steps:

[0026] (1) Use an extended state observer to process the joint data of the underactuated robot system when it is subject to unknown disturbances and output the estimated joint position, the estimated joint velocity, and the estimated lumped disturbance, and design a disturbance compensation term from the estimated lumped disturbance;

[0027] The model of the underactuated robot system is:

[0028] The extended state observer is:

[0029]

[0030] The disturbance compensation term is:

[0031] where q is the joint position of the underactuated robot system, q = [q a q u T , q a is the driving joint, q u is the non - driving joint; is the joint velocity, is the joint acceleration, M(q) is the symmetric positive - definite inertia matrix of the underactuated robot system; is the combination term of the centrifugal force and the Coriolis force of the underactuated robot system; G(q) is the gravity term of the underactuated robot system; u is the control input; B is the input transformation matrix, B = [1 0] T ; τ d is the external disturbance received by the underactuated robot system, τ d = [d 1 d 2 T , d 1 is the matching disturbance in the same channel as the control input, d 2 is the non - matching disturbance in a different channel from the control input; is the estimated joint position, is its first - order derivative; is the estimated joint velocity, is its first - order derivative; D is the lumped disturbance, D = [D 1 D 2 T = M -1 (q)τ​​​d , D 1 is the lumped disturbance component of the driving joint, D 2 is the lumped disturbance component of the non - driving joint, M(q) -1 is the inverse matrix of M(q); is the estimated value of the lumped disturbance, is the first - order derivative of; is the estimated value of D 1 ; is the estimated value of D 2 ; E 1 is the estimated error of the joint position; β 1 , β 2 , β 3 are the constant gains of the extended state observer; λ 1 , λ 2 are the constant exponents of the extended state observer; y is the joint position state output; u d is the disturbance compensation term; is the coefficient of the second - layer sliding mode surface; is a non - linear function containing the estimated value of the joint position. Specifically, it can be expressed as is the inverse matrix of the symmetric positive - definite inertia matrix containing the estimated value of the joint position.

[0032] (2) Design the first sub - sliding mode surface corresponding to the driving joint in the first - layer fast terminal sliding mode surface by using the driving joint position error between the estimated value and the expected value of the driving joint and its first - order derivative, and output the first equivalent control law from the first sub - sliding mode surface; design the second sub - sliding mode surface corresponding to the non - driving joint in the first - layer fast terminal sliding mode surface by using the non - driving joint position error between the estimated value and the expected value of the non - driving joint and its first - order derivative, and output the second equivalent control law from the second sub - sliding mode surface;

[0033] The first sub - sliding mode surface is:

[0034] The second sub - sliding mode surface is:

[0035] The first equivalent control law is:

[0036] The second equivalent control law is:

[0037] where, S 1 is the first sub - sliding mode surface; u eq1 is the first equivalent control law, obtained by differentiating S 1 and setting it equal to 0; S 2 is the second sub - sliding mode surface; u eq2 is the second equivalent control law, obtained by differentiating S2 Derivation and setting it equal to 0 gives: e 1 is the driving joint position error, is the estimated value of the driving joint position, q ad is the expected value of the driving joint position, is e 1 the first derivative of; e 2 is the non - driving joint position error, is the estimated value of the non - driving joint position, q ud is the expected value of the non - driving joint position, is e 2 the first derivative of; q d =[q ad q ud T is the expected value of the joint position, is the estimated value of the joint position; γ 1 、γ 2 、φ 1 、φ 2 are all the coefficients of the first - layer fast terminal sliding mode surface; p 1 、p 2 、q 1 、q 2 are all the positive odd - numbered coefficients corresponding to the first - layer fast terminal sliding mode surface, and satisfy is the estimated value of the joint velocity; is a non - linear function containing the estimated value of the joint position and the estimated value of the joint velocity. Specifically, it can be expressed as is the inverse matrix of the symmetric positive - definite inertia matrix containing the estimated value of the joint position, is the combined term of the centrifugal force and the Coriolis force containing the estimated value of the joint position and the estimated value of the joint velocity, is the gravity term containing the estimated value of the joint position; is the expected value of the acceleration of the driving joint; is the expected value of the acceleration of the non - driving joint.

[0038] (3) Design the second - layer sliding mode surface using the first - layer driving fast terminal sliding mode surface and the first - layer non - driving fast terminal sliding mode surface, and output the switching control law from the second - layer sliding mode surface;

[0039] The second - layer sliding mode surface is:

[0040] The switching control law is:

[0041] where S is the second - layer sliding mode surface; u sw is the switching control law; k, η are both control gains; is the estimated value of η,​ is the adaptive law, the first derivative of sign() is the sign function; ε is the constant gain of the adaptive law.

[0042] (4) Design the total control law according to the disturbance compensation term, the first equivalent control law, the second equivalent control law, and the switching control law to control the underactuated robot system;

[0043] The total control law is: u = u eq1 + u eq2 + u sw + u d .

[0044] The total control law u of the present invention can be named the adaptive hierarchical fast terminal sliding mode control law, which consists of three parts. The first part is the first equivalent control law u eq1 and the second equivalent control law u eq2 , which are used to realize the desired error dynamics; the second part is the switching control law u sw , which contains the adaptive law to adjust the control gain η and play a role in suppressing chattering in sliding mode control; the third part is the disturbance compensation term u d , which is used to cancel the unknown disturbance in the underactuated robot system. It can be seen that when there is an unknown external disturbance, the present invention comprehensively controls the underactuated robot system through the disturbance compensation term, the first equivalent control law, the second equivalent control law, and the switching control law, can achieve stable control from the initial position to the desired position, the position error can quickly converge, maintain good control accuracy, the control torque has no obvious chattering, and the stability is good.

[0045] The following uses the Lyapunov candidate function to prove the stability of the underactuated robot system when the present invention is used.

[0046] Select the Lyapunov candidate function as: where

[0047] Find the first derivative of the Lyapunov candidate function V 1 as:

[0048]

[0049] Substitute the total control law designed by the present invention to obtain:

[0050]

[0051] Considering that the estimation error of the extended state observer can converge to 0 within a finite time, there is:

[0052]

[0053] Taking the derivative of both sides gives:

[0054] Furthermore, we obtain: where, represents the limit value when t → ∞.

[0055] According to Barbalat's lemma, we can get Therefore, the second - layer sliding surface S is asymptotically stable.

[0056] From we can obtain:

[0057] Since thus:

[0058] Therefore, according to Barbalat's lemma, we can get and That is, the first sub - sliding surface S 1 and the second sub - sliding surface S 2 are also asymptotically stable.

[0059] From this, it can be seen that the under - actuated robot system of the present invention can make the first sub - sliding surface S 1 、the second sub - sliding surface S 2 、the second - layer sliding surface S tend to 0, ensuring the stability of the under - actuated robot system.

[0060] The above has described the relevant content of the present invention. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Based on the above content of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Claims

1. Control method for an underactuated robot system, characterized in that: It includes the following steps: An extended state observer is used to process the joint data of the underactuated robot system when it is subject to unknown disturbances and output the estimated joint position, estimated joint velocity, and estimated lumped disturbance. The disturbance compensation term is designed based on the estimated lumped disturbance; The first sub-sliding mode surface corresponding to the actuated joints in the first-layer fast terminal sliding mode surface is designed using the actuated joint position error between the estimated value and the expected value of the actuated joints and its first derivative, and the first equivalent control law is output from the first sub-sliding mode surface; The second sub-sliding mode surface corresponding to the unactuated joints in the first-layer fast terminal sliding mode surface is designed using the unactuated joint position error between the estimated value and the expected value of the unactuated joints and its first derivative, and the second equivalent control law is output from the second sub-sliding mode surface; The second-layer sliding mode surface is designed using the first-layer actuated fast terminal sliding mode surface and the first-layer unactuated fast terminal sliding mode surface, and the switching control law is output from the second-layer sliding mode surface; The total control law is designed based on the disturbance compensation term, the first equivalent control law, the second equivalent control law, and the switching control law to control the underactuated robot system; The model of the underactuated robot system is: where q is the joint position of the under-actuated robot system, q = [q a q u T , q a is the actuated joint, and q u is the un-actuated joint; is the joint velocity, is the joint acceleration, M(q) is the symmetric positive definite inertia matrix of the under-actuated robot system; is the combined term of the centrifugal force and the Coriolis force of the under-actuated robot system; G(q) is the gravity term of the under-actuated robot system;​ u is the control input; B is the input conversion matrix, B = [10] T ; τ d is the external disturbance suffered by the underactuated robot system, τ d = [d 1 d 2 T , d 1 is the matching disturbance in the same channel as the control input, d 2 is the non-matching disturbance in a different channel from the control input.​ 2. The control method for an underactuated robot system according to claim 1, characterized in that: The extended state observer is: wherein, is the estimated value of the joint position, is its first derivative; is the estimated value of the joint velocity, is its first derivative; D is the lumped disturbance, D = [D 1 D 2 T = M -1 (q)τ d , D 1 is the lumped disturbance component of the driving joint, D 2 is the lumped disturbance component of the non - driving joint, M(q) -1 is the inverse matrix of M(q); is the estimated value of the lumped disturbance, is 's first derivative; E 1 is the estimated error of the joint position; β 1 , β 2 , β 3 are the constant gains of the extended state observer; λ 1 , λ 2 are the constant exponents of the extended state observer; y is the joint position state output.​ 3. The control method for an underactuated robot system according to claim 2, characterized in that: The disturbance compensation term is: where, u d is the interference compensation term; is the coefficient of the second layer sliding mode surface; is a non - linear function containing the estimated value of the joint position. Specifically, it can be expressed as is the inverse matrix of the symmetric positive definite inertia matrix containing the estimated value of the joint position; is the estimated value of D 1 ; is the estimated value of D 2 .

4. The control method for an underactuated robot system according to claim 2, characterized in that: The first-layer fast terminal sliding mode surface is: Among them, S 1 is the first sub-sliding mode surface; S 2 is the second sub-sliding mode surface; e 1 is the driving joint position error, is the estimated value of the driving joint position, q ad is the expected value of the driving joint position, is the first derivative of e 1 ; e 2 is the non-driving joint position error, is the estimated value of the non-driving joint position, q ud is the expected value of the non-driving joint position, is the first derivative of e 2 ; q d = [q ad q ud T is the expected value of the joint position, is the estimated value of the joint position; γ 1 , γ 2 , φ 1 , φ 2 are all the coefficients of the first-layer fast terminal sliding mode surface; p 1 , p 2 , q 1 , q 2 are all the positive odd coefficients corresponding to the first-layer fast terminal sliding mode surface, and satisfy ​ 5. The control method for an underactuated robot system according to claim 4, characterized in that: The first equivalent control law and the second equivalent control law are: where, u eq1 is the first equivalent control law, obtained by differentiating S 1 and setting it equal to 0; u eq2 is the second equivalent control law, obtained by differentiating S 2 and setting it equal to 0; is the estimated value of the joint velocity; is a nonlinear function containing the estimated value of the joint position and the estimated value of the joint velocity. Specifically, it can be expressed as B is the inverse matrix of the symmetric positive definite inertia matrix containing the estimated value of the joint position, is the combined term of the centrifugal force and the Coriolis force containing the estimated value of the joint position and the estimated value of the joint velocity, is the gravity term containing the estimated value of the joint position; is a nonlinear function containing the estimated value of the joint position. Specifically, it can be expressed as is the expected value of the acceleration of the driving joint; is the expected value of the acceleration of the non - driving joint.

6. The control method for an underactuated robot system according to claim 4, characterized in that: The second-layer sliding mode surface is: Among them, S is the second-layer sliding mode surface; is the second-layer sliding mode surface coefficient.

7. The control method for an underactuated robot system according to claim 6, characterized in that: The switching control law is: where, u sw is the switching control law; is a non - linear function containing the estimated value of joint position. Specifically, it can be expressed as the inverse matrix of the symmetric positive definite inertia matrix containing the estimated value of joint position; k and η are both control gains, is the estimated value of η, is the adaptive law, is the first - order derivative of, sign() is the sign function; ε is the constant gain of the adaptive law; u eq1 is the first equivalent control law, obtained by differentiating S 1 and setting it equal to 0; u eq2 is the second equivalent control law, obtained by differentiating S 2 and setting it equal to 0.

8. The control method for an underactuated robot system according to claim 1, characterized in that: The total control law is: u = u eq1 + u eq2 + u sw + u d ; Among them, \(u\) is the total control law; \(u\) eq1 is the first equivalent control law; \(u\) eq2 is the second equivalent control law; \(u\) sw is the switching control law; \(u\) d is the disturbance compensation term.

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