Control method for underactuated robotic system

Abstract

The application discloses a control method of an underactuated robot system, comprising the following steps: acquiring joint position and joint speed of the underactuated robot system under unknown disturbance; designing a finite-time disturbance observer of the unknown disturbance of the underactuated robot system according to the joint position and the joint speed, and then solving a disturbance compensation term according to the finite-time disturbance observer; designing a sliding mode surface of the unknown disturbance of the underactuated robot system according to the joint position and the joint speed, and then solving an equivalent control law and a smooth super-twisting switching control law according to the sliding mode surface; and designing a total control law according to the disturbance compensation term, the equivalent control law and the smooth super-twisting switching control law to control the underactuated robot system. The application enables the underactuated robot system to realize stable control from an initial position to a desired position under unknown external disturbance, and the position error converges rapidly, the control precision is high, and the control torque has no obvious chattering.

Description

Technical Field

[0001] This invention relates to the technical field of underactuated robot system control, and more specifically, to a control method for underactuated robot systems. Background Technology

[0002] Underactuated robot systems are a special type of robot system where the number of control inputs is less than the system's degrees of freedom. They are characterized by low energy consumption, light weight, and high efficiency. Underactuated robot systems are widely used in aerospace, industry, agriculture, and medicine, significantly improving industrial production efficiency and people's quality of life. However, the dynamic characteristics of underactuated robot systems are highly complex, making it impossible to directly use the control methods of general fully actuated systems. Furthermore, underactuated robots are more susceptible to uncertainties, especially unknown external disturbances. These uncertainties need to be properly handled; otherwise, they may impair the desired control performance, severely affecting the control accuracy of the underactuated robot system, further leading to system instability or even damage.

[0003] To effectively compensate for disturbances in underactuated robot systems, many scholars both domestically and internationally have adopted sliding mode control to improve the control performance of underactuated robot systems and maintain system stability. Sliding mode control, as a typical and effective robust control method, possesses characteristics such as stability, reliability, and strong robustness.

[0004] To improve system robustness, Chinese invention patent CN113311707A discloses a continuous sliding mode control method considering disturbances in bridge cranes. This method designs a continuous sliding mode controller for underactuated bridge crane systems, thereby improving system stability. However, this sliding mode control strategy cannot obtain accurate information about unknown disturbances, and it performs disturbance compensation under the assumption that the disturbance is bounded. Furthermore, the controller contains a sign function, which is prone to chattering problems, affecting system control performance. Summary of the Invention

[0005] The main objective of this invention is to provide a control method for underactuated robot systems, so as to solve the technical problem that unknown external interference has an adverse effect on the position control effect during the control process in the prior art, and to achieve stable control of underactuated robot systems.

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

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

[0008] To obtain the joint positions and velocities of an underactuated robot system under unknown disturbances;

[0009] Design a finite-time disturbance observer for the unknown disturbances experienced by the underactuated robot system based on the joint position and joint velocity, and then solve the disturbance compensation term based on the finite-time disturbance observer.

[0010] Based on the joint position and joint velocity, design the sliding surface of the underactuated robot system to deal with unknown disturbances, and then solve the equivalent control law and the smooth super-twist switching control law based on the sliding surface.

[0011] The overall control law is designed based on the disturbance compensation term, the equivalent control law, and the smooth super-twist switching control law to control the underactuated robot system.

[0012] Verification has shown that the control method of the underactuated robot system of the present invention, by employing an equivalent control law, a smooth super-twist switching control law, and a total control law composed of an interference compensation term, enables the underactuated robot system to effectively cope with the occurrence of interference even in the presence of unknown external interference, achieve stable control from the initial position to the desired position, rapidly converge the position error, maintain good control accuracy, and exhibit no significant chattering in the control torque.

[0013] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0014] The accompanying drawings, which form part of this invention, are used to aid in understanding the invention. The content provided in the drawings and their related descriptions can be used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0015] Figure 1 This is a flowchart illustrating an embodiment of the control method for an underactuated robot system according to the present invention. Detailed Implementation

[0016] The present invention will now be clearly and completely described in conjunction with the accompanying drawings. Those skilled 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:

[0017] The technical solutions and features provided in the various parts of this invention, including the following description, can be combined with each other without conflict.

[0018] Furthermore, the embodiments of the present invention described below are generally only some, not all, of the embodiments of the present invention. Therefore, all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0019] Regarding the terminology and units used in this invention: The terms "comprising," "having," and any variations thereof in the specification, claims, and related parts of this invention are intended to cover non-exclusive inclusion.

[0020] Figure 1 This is a flowchart illustrating an embodiment of the control method for an underactuated robot system according to the present invention.

[0021] like Figure 1 As shown, an embodiment of the control method for an underactuated robot system includes the following steps:

[0022] (1) Obtain the joint positions and joint velocities of the underactuated robot system when subjected to unknown disturbances;

[0023] in, For the joint positions of an underactuated robot system, For joint velocity, Represents a real matrix. This represents the total number of joints in an underactuated robot system. Indicates the number of drive joints. This represents the number of non-driven joints. To drive the joint, It is a non-driven joint.

[0024] (2) Design a finite-time disturbance observer for the unknown disturbances experienced by the underactuated robot system based on the joint position and joint velocity, and then solve the disturbance compensation term based on the finite-time disturbance observer.

[0025] The expression for the finite-time disturbance observer is:

[0026] ;

[0027] ;

[0028] ;

[0029] The expression for the interference compensation term is:

[0030] ;

[0031] in, This is an estimate of the unknown interference. , , For the gain of the finite-time disturbance observer, all are positive definite diagonal matrices; exponent It is a constant and satisfies ; For auxiliary variables of finite-time disturbance observers; For the state variables of a finite-time disturbance observer, for The first derivative; Let be the positive definite inertia matrix of the underactuated robot system, and let its inverse matrix be . ; Represents the input transformation matrix; For control input; The Coriolis force and centrifugal force represent the underactuated robot system; Gravity represents the underactuated robot system; This is an interference compensation item; It is a positive definite diagonal constant matrix; and It is a function matrix related to joint position, whose dimensions correspond to the number of driven joints and the number of non-driven joints, respectively. Specifically, it can be represented as: ; It is a constant matrix; To estimate the disturbance value for the dimension corresponding to the driving joint. The disturbance estimate corresponding to the dimension of the non-driven joint can be specifically expressed as: .

[0032] (3) Design the sliding surface of the underactuated robot system to deal with unknown disturbances based on the joint position and joint velocity, and then solve the equivalent control law and the smooth super-twist switching control law based on the sliding surface;

[0033] The expression for the sliding surface is:

[0034]

[0035] The expression for the equivalent control law is:

[0036] ;

[0037] The expression for the smooth super-twisted switching control law is:

[0038] ;

[0039] Where S is the sliding surface; , and All are positive definite diagonal constant matrices; It is a constant matrix; To drive joint position error, Its first derivative; This refers to the position error of the non-driven joint. Its first derivative; To drive the desired joint position, The expected value of the non-driven joint position is given by... , Transpose of the matrix This represents the expected value of the joint position. To drive the desired joint velocity, The expected value of the non-driven joint velocity is given by... , Transpose of the matrix This represents the expected value of the joint velocity. This is an equivalent control law; and The matrix represents a function related to joint position and velocity, with its dimensions corresponding to the number of driven joints and the number of non-driven joints, respectively. Specifically, it can be represented as follows: ; Let be the positive definite inertia matrix of the underactuated robot system, and let its inverse matrix be . ; Represents the input transformation matrix; The Coriolis force and centrifugal force represent the underactuated robot system; Gravity represents the underactuated robot system; The desired acceleration value for driving the joint. This represents the expected acceleration value of the non-driven joint; For smooth, super-twisted switching control law; For the hyper-distorted variable, its derivative ;index It is a constant and satisfies ; and All are constant gains greater than zero.

[0040] (4) Design the overall control law based on the disturbance compensation term, the equivalent control law and the smooth super-twist switching control law to control the underactuated robot system;

[0041] The expression for the overall control law is:

[0042] ;

[0043] in, This is the overall control law; This is an equivalent control law; For smooth, super-twisted switching control law; This is an interference compensation item.

[0044] The overall control law of this invention This can be named the sliding mode control law for a finite-time disturbance observer, and it consists of three parts. The first part is the equivalent control law. The first part is used to realize the desired error dynamics; the second part is the smooth super-twisted switching control law. This is used to increase the smoothness of joint movements and suppress torque chattering in sliding mode control; the third part is the external disturbance compensation item. This is used to counteract unknown disturbances in underactuated robot systems; among them, a smooth super-twisted switching control law... and equivalent control law The smooth, super-twisted sliding mode control law u ss u ss = + As can be seen, when there are unknown external disturbances, this invention can achieve stable control from the initial position to the desired position by comprehensively controlling the underactuated robot system through equivalent control law, smooth super-twist switching control law and disturbance compensation term. The position error can converge quickly, maintain good control accuracy, and the control torque has no obvious chattering.

[0045] The following uses Lyapunov alternative functions to demonstrate the stability of the underactuated robot system when using this invention.

[0046] The Lyapunov candidate functions selected are:

[0047] ;

[0048] Differentiating it, we get:

[0049] ;

[0050] Substituting the designed overall control law, we can obtain:

[0051] ;

[0052] Considering that the observer estimation error converges to zero in a finite time, we can assume that... ,in Since it is a constant, we have

[0053]

[0054] Therefore, it can be seen that the overall control law used in this invention can make the sliding surface Converging to 0 ensures the stability of the underactuated robot system.

[0055] The foregoing has described the relevant content of the present invention. Those skilled in the art will be able to implement the present invention based on these descriptions. All other embodiments obtained by those skilled in the art based on the above description of the present invention without inventive effort should fall within the scope of protection of the present invention.

Claims

1. A control method for an underactuated robot system, including the following steps: To obtain the joint positions and velocities of an underactuated robot system under unknown disturbances; Design a finite-time disturbance observer for the unknown disturbances experienced by the underactuated robot system based on the joint position and joint velocity, and then solve the disturbance compensation term based on the finite-time disturbance observer. Based on the joint position and joint velocity, design the sliding surface of the underactuated robot system to deal with unknown disturbances, and then solve the equivalent control law and the smooth super-twist switching control law based on the sliding surface. The overall control law is designed based on the disturbance compensation term, the equivalent control law, and the smooth super-twist switching control law to control the underactuated robot system. in, For the joint positions of an underactuated robot system, For joint velocity, Represents a real matrix. This represents the total number of joints in an underactuated robot system. Indicates the number of drive joints. This represents the number of non-driven joints. To drive the joint, It is a non-driven joint; The expression for the smooth super-twisted switching control law is: ; in, For smooth, super-twisted switching control law; It is a positive definite diagonal constant matrix; It is a constant matrix; and It is a function matrix related to joint position, and its dimensions correspond to the number of driven joints and the number of non-driven joints, respectively. ; Let be the positive definite inertia matrix of the underactuated robot system, and let its inverse matrix be . ; S represents the input transformation matrix; S is the sliding surface. For the hyper-distorted variable, its derivative ;index It is a constant and satisfies ; and All are constant gains greater than zero.

2. The control method for an underactuated robot system as described in claim 1, characterized in that: The expression for the finite-time disturbance observer is: ； in, This is an estimate of the unknown interference. , , For the gain of the finite-time disturbance observer, all are positive definite diagonal matrices; For finite-time disturbance observers, auxiliary variables; exponent It is a constant and satisfies .

3. The control method for an underactuated robot system as described in claim 2, characterized in that: ； ； in, For the state variables of a finite-time disturbance observer, for The first derivative; For control input; The Coriolis force and centrifugal force represent the underactuated robot system; Gravity represents the force of an underactuated robot system.

4. The control method for an underactuated robot system as described in claim 3, characterized in that: The expression for the interference compensation term is: ； in, This is an interference compensation item; This is an estimate of the interference value corresponding to the dimension of the driving joint. This is the interference estimate for the dimension corresponding to the non-driven joint. .

5. The control method for an underactuated robot system as described in claim 1, characterized in that: The expression for the sliding surface is: ； in, and All are positive definite diagonal constant matrices; To drive joint position error, Its first derivative; This refers to the position error of the non-driven joint. Its first derivative; To drive the desired joint position, The expected value of the non-driven joint position is given by... , Transpose of the matrix This represents the expected value of the joint position. To drive the desired joint velocity, The expected value of the non-driven joint velocity is given by... , Transpose of the matrix This represents the expected value of the joint velocity.

6. The control method for an underactuated robot system as described in claim 5, characterized in that: The expression for the equivalent control law is: ； in, This is an equivalent control law; and It is a function matrix related to joint position and velocity, and its matrix dimensions correspond to the number of driven joints and the number of non-driven joints, respectively. ; The Coriolis force and centrifugal force represent the underactuated robot system; Gravity represents the underactuated robot system; The desired acceleration value for driving the joint. This represents the expected acceleration value of the non-driven joint.

7. The control method for an underactuated robot system as described in claim 1, characterized in that: The expression for the overall control law is: ； in, This is the overall control law; This is an equivalent control law; This is an interference compensation item.

Images