Self-adaptive sliding mode control method and system for mechanical arm

Abstract

The invention belongs to the technical field of mechanical arm control, and provides a mechanical arm self-adaptive sliding mode control method and system, a self-adaptive sliding mode reaching law is constructed, and the self-adaptive sliding mode reaching law comprises a system state variable, a distance function based on a position error and a speed error and a gain item which is self-adaptively adjusted along with a system convergence state; when the difference between the Euclidean distance between the balance point and the current position in the state space and a set value is larger than a set range, the distance function based on the position error and the speed error is dominant and changes exponentially, and the approaching speed to the sliding mode surface is larger than the set value; when the difference value between the Euclidean distance between the balance point and the current position in the state space and the set value is within the set range, the system state variable is dominant, the sliding mode surface approaching rate is within the preset range, and the control precision is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mechanical arm control, and particularly relates to a mechanical arm adaptive sliding mode control method and system. BACKGROUND

[0002] The statements in this section merely provide background information related to the application and do not necessarily constitute prior art.

[0003] Mechanical arms have been widely used in many industries such as agriculture, industry and service. In actual tasks such as grabbing, carrying and stacking, the mechanical arm often faces the influence brought by the change of the effective load. Even if the load does not change, the strong nonlinearity of the mechanical arm itself, model uncertainty and unmodeled dynamics will cause the motion control precision to decrease. The introduction of the load will quickly change the inertia matrix and the gravity matrix, significantly affect the dynamic characteristics of the mechanical arm, and thus put higher requirements on high-precision trajectory tracking control.

[0004] Sliding mode controller is a typical method of sliding mode control by using sliding mode reaching law. In recent years, it has been widely studied due to its convenient design and advantages in calculation. The role of reaching law is to drive the system state trajectory to reach the designed sliding surface in a limited time. However, the traditional sliding mode reaching law may have a slow reaching speed when the system is close to or far from the sliding surface. In practical applications, this will lead to poor dynamic performance and decreased anti-interference ability of the system.

[0005] The traditional sliding mode reaching law method has inherent technical limitations. The fundamental problem lies in the design of the reaching law with static fixed parameters, which cannot adapt to the contradictory demands of the system state trajectory in different stages of the dynamic reaching process. Specifically, when the system state is far from the sliding surface, the fixed gain of the conservative design limits the reaching speed to ensure the feasibility of the control signal and suppress chattering, resulting in slow convergence and delayed dynamic response in the initial stage. When the state is close to the sliding surface, the fixed gain also limits the reaching speed to avoid high-frequency chattering caused by the discontinuous control law, which causes the system to lack the ability to reach the critical region and prolongs the convergence time. This mismatch between static design and dynamic demand not only degrades the overall dynamic performance of the system, but also seriously weakens the inherent strong robustness advantage of sliding mode control due to the insufficient disturbance suppression ability in the reaching stage, which becomes a key technical bottleneck restricting the development of sliding mode control in high-performance control applications. SUMMARY

[0006] To solve the above problems, the application provides a mechanical arm adaptive sliding mode control method and system, which does not need to rely on acceleration signals and does not need to solve inverse dynamics.

[0007] According to some embodiments, the application adopts the following technical solutions: A mechanical arm adaptive sliding mode control method, comprising the following steps: An adaptive sliding mode reaching law is constructed, the adaptive sliding mode reaching law comprises system state variables, a distance function based on position error and velocity error, and a gain term adaptively adjusted according to the convergence state of the system, and when the difference between the Euclidean distance between the equilibrium point and the current position in the state space and the set value is greater than the set range, the distance function based on the position error and the velocity error is dominant, and the reaching speed to the sliding mode surface is greater than the set value, when the difference between the Euclidean distance between the equilibrium point and the current position in the state space and the set value is within the set range, the system state variables are dominant, and the reaching rate to the sliding mode surface is within the predetermined range.

[0008] As an optional implementation, the adaptive sliding mode reaching law is:

[0009] Wherein, k1, k2, k3, k4 are all coefficients, and are all greater than zero, E represents the Euclidean distance between the equilibrium point and the current position in the state space, and d is a normal number, The saturation function is a saturation function.

[0010] As a further implementation, the saturation function is:

[0011] Wherein, x is the input value of the sat() function.

[0012] As an optional implementation, when the sliding state deviates from the desired trajectory, then The term becomes the dominant factor for driving the state trajectory to move to the sliding surface.

[0013] As an optional implementation, the joint expression of the mechanical arm after introducing the adaptive sliding mode reaching law is:

[0014] Wherein, , , The inertia matrix, the Coriolis matrix and the gravity vector of the mechanical arm, , , The angle, angular velocity and angular acceleration of the joint of the mechanical arm, , , The estimated value of the joint torque, the estimated value of the friction torque and the estimated value of the external disturbance torque.

[0015] Further, the estimated value of the friction torque is obtained by a friction model.

[0016] As further, the estimated value of the external disturbance torque is obtained by using sensors.

[0017] As further, the Coriolis matrix and the gravity vector of the robot arm are obtained by robot arm parameter identification.

[0018] A robot arm adaptive sliding mode control system is configured to: construct an adaptive sliding mode reaching law, the adaptive sliding mode reaching law including system state variables, a distance function based on position error and velocity error, and a gain term adaptively adjusted according to the convergence state of the system, and when the difference between the Euclidean distance between the equilibrium point and the current position in the state space and the set value is greater than the set range, the distance function based on the position error and the velocity error is dominant, and the reaching speed to the sliding mode surface changes exponentially and is greater than the set value, and when the difference between the Euclidean distance between the equilibrium point and the current position in the state space and the set value is within the set range, the system state variables are dominant, and the reaching rate to the sliding mode surface is within the predetermined range.

[0019] A robot arm includes the above-mentioned robot arm adaptive sliding mode control system or includes a memory and a processor and computer instructions stored on the memory and running on the processor, and when the computer instructions are run by the processor, the steps in the above-mentioned method are completed.

[0020] Compared with the prior art, the beneficial effects of the present application are: The present application can significantly improve the speed of state approaching the sliding mode surface and effectively suppress control chattering. Based on the joint position control algorithm of the adaptive sliding mode reaching law provided by the present application, the problems of slow response, long convergence time and large tracking error of the traditional method can be improved in a larger range.

[0021] The present application does not need to rely on acceleration signals and does not perform inverse dynamics solution, and at the same time, the estimated torque is filtered, improving the accuracy of torque estimation.

[0022] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the following preferred embodiments are described in detail below, and the accompanying drawings are used for explanation. BRIEF DESCRIPTION OF DRAWINGS

[0023] The drawings accompanying the specification of the present application form a part of the present application and are used to provide a further understanding of the present application, the illustrative embodiments of the present application and the description thereof serve to explain the present application and do not constitute an improper limitation of the present application.

[0024] Figure 1 is a function buffer diagram of an embodiment; Figure 2 is a control precision comparison diagram of the method provided by the present application and the traditional control method of an embodiment; Figure 3Fig. 1 is a schematic diagram of an input curve of a control start algorithm of an embodiment to a motor, in which (b) is an enlarged view of the start section of (a). DETAILED DESCRIPTION

[0025] The application will be further described below in connection with the drawings and embodiments.

[0026] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0027] It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0028] The embodiments in the application and the features in the embodiments can be combined with each other without conflict.

[0029] Embodiment one A mechanical arm adaptive sliding mode control method, first introduces the principle of flexible joint transmission of mechanical arm, as follows:

[0030] Among them, , , is the inertia matrix, the Coriolis (centripetal) matrix, the gravity vector of the mechanical arm, , , are the angle, angular velocity and angular acceleration of the joint of the mechanical arm, , , are the joint torque, friction torque and external disturbance torque respectively.

[0031] We let

[0032] Among them , are the target angle and its first order differential respectively, and can be further reduced by first order filtering to reduce interference.

[0033] The commonly used sliding mode function is as follows:

[0034] where, is a constant determined by experience, , ; The designed adaptive sliding mode reaching law is as follows:

[0035] Here E as the Euclidean distance is determined by the state space and is absolute, that is ; If the system does not converge, then and is large, that is, E is large, then is large, and the convergence speed is fast (the , term tends to , power is also large); on the contrary, if it approaches , then is small, and the convergence speed is slow, and it is not easy to occur overshoot (the , term tends to 0, power is also small).

[0036] The remaining terms are constants, which will affect the motion accuracy, response speed, etc. according to the adjustment of the device.

[0037] where, , , , , E term represents the Euclidean distance between the equilibrium point and the current position in the state space, d is a normal number, and its value is related to E. The saturation function is as follows:

[0038] When the sliding state is far away from the desired trajectory, that is , then term becomes the dominant factor to drive the state trajectory to move to the sliding surface. However, the exponential growth rate may sometimes cause adverse effects. In order to alleviate the adverse effects, a circular surface with a distance of d from the origin is used as the function "buffer zone" as shown in Figure 1

[0039] Specifically, when , , is dominant, at this time the function changes exponentially, and the approaching speed to the sliding surface is fast, when , at this time ​No longer dominant, is dominant, but due to the decreasing E , so the rate of approach is relatively flat.

[0040] Now, we analyze the joint transmission expression, , can be obtained by mechanical arm parameter identification, , The estimated value of the friction model and the sensor can be obtained respectively , , so the expression of the joint of the robot arm can be expressed as follows:

[0041] Based on (3), (4) can be obtained:

[0042] (6) into (7) is obtained: The simulation comparison of the proposed method and the traditional control method motion error is shown in Figure 2 .

[0043] It can be seen that the proposed algorithm is more accurate in accuracy, and then, by comparing the two algorithms through simulation, the controller input is shown in Figure 3 It can be seen that the control accuracy of the method provided by the embodiment is higher and the fluctuation is smaller.

[0044] Embodiment two An adaptive sliding mode control system of a robot arm is configured to: construct an adaptive sliding mode approach law, the adaptive sliding mode approach law contains system state variables, a distance function based on position error and velocity error, and a gain term that is adaptively adjusted with the system convergence state, and when the difference between the Euclidean distance of the balance point and the current position in the state space and the set value is greater than the set range, the distance function based on the position error and the velocity error is dominant, changes exponentially, and the approach speed to the sliding mode surface is greater than the set value, when the difference between the Euclidean distance of the balance point and the current position in the state space and the set value is within the set range, the system state variable is dominant, and the approach rate to the sliding mode surface is within the predetermined range.

[0045] Embodiment three A robot arm includes the above-mentioned adaptive sliding mode control system of a robot arm or includes a memory and a processor and computer instructions stored on the memory and running on the processor, when the computer instructions are run by the processor, the steps in the method provided by embodiment one are completed.

[0046] Those skilled in the art will appreciate that embodiments of the present application can be readily used as software, hardware, or a combination of software and hardware. In a software embodiment, the methods can be tangibly embodied in a machine-readable storage medium having stored thereon instructions that can be used to program a computer to perform any of the methods. The software implementation can be initialized by loading and executing a set of instructions arranged to perform one of the methods into the computer's memory. Alternatively, hard-wired circuitry can be used in place of, or in combination with, software instructions. Thus, the CD - ROM

[0047] The present application is described in reference to the drawings, which are as follows. Figure 1 Figure 1

[0048] Figure 1 Figure 1

[0049] Figure 1 Figure 1

[0050] The foregoing is considered as illustrative only of the principles of the application. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the application to the exact construction and practice described. Accordingly, all such variations are intended to be included within the scope of present application as defined in the following claims.​​​​​​​​​

Claims

1. A robot adaptive sliding mode control method, characterized in that, The method comprises the following steps: The adaptive sliding mode reaching law comprises system state variables, a distance function based on position error and velocity error, and a gain term adaptively adjusted according to a convergence state of the system, and when a difference between a Euclidean distance of the equilibrium point and the current position in a state space and a set value is greater than a set range, the distance function based on the position error and the velocity error is dominant, exponentially changes, and a reaching speed to a sliding mode surface is greater than the set value, and when the difference between the Euclidean distance of the equilibrium point and the current position in the state space and the set value is within the set range, the system state variables are dominant, and a reaching rate to the sliding mode surface is within a predetermined range.

2. The adaptive sliding mode control method for a robot arm according to claim 1, wherein, The adaptive sliding mode reaching law is: wherein k1, k2, k3, k4 are coefficients, and are all greater than zero, E represents the Euclidean distance between the equilibrium point and the current position in the state space, d is a normal number, is a saturation function.

3. The adaptive sliding mode control method of a robot arm according to claim 2, characterized in that, The saturation function is: wherein x is an input value of the sat() function.

4. The adaptive sliding mode control method of a robot arm according to claim 2, characterized in that, When the sliding state is far from the desired trajectory, then The term becomes the dominant factor in moving the driving state trajectory towards the sliding surface.

5. The adaptive sliding mode control method of a robot arm according to claim 1, characterized in that A joint expression of the robot arm after the adaptive sliding mode reaching law is: wherein, , , are the inertia matrix, the Coriolis matrix and the gravity vector of the robot arm, respectively, , , are the angles, the angular velocities and the angular accelerations of the joints of the robot arm, respectively, , , are the estimated values of the joint torques, the friction torques and the estimated values of the external disturbance torques, respectively.

6. The adaptive sliding mode control method of a robot arm according to claim 5, characterized in that, An estimated value of the friction torque is obtained from a friction model.

7. The adaptive sliding mode control method of a robot arm according to claim 1, characterized in that, An estimated value of the external disturbance torque is obtained by using a sensor.

8. The adaptive sliding mode control method of a robot arm according to claim 1, characterized in that, The Coriolis matrix and the gravity vector of the robot arm are obtained by parameter identification of the robot arm.

9. A robotic arm adaptive sliding mode control system, characterized in that, The adaptive sliding mode reaching law comprises system state variables, a distance function based on position error and velocity error, and a gain term adaptively adjusted according to a convergence state of the system, and when a difference between a Euclidean distance of the equilibrium point and the current position in a state space and a set value is greater than a set range, the distance function based on the position error and the velocity error is dominant, exponentially changes, and a reaching speed to a sliding mode surface is greater than the set value, and when the difference between the Euclidean distance of the equilibrium point and the current position in the state space and the set value is within the set range, the system state variables are dominant, and a reaching rate to the sliding mode surface is within a predetermined range.

10. A robot arm, characterized in that, The adaptive sliding mode control system of the robot arm or the computer program product comprises a memory and a processor, and computer instructions stored in the memory and run on the processor, and when the computer instructions are run by the processor, steps in the method of any one of claims 1-8 are completed.

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