A robot adaptive sliding mode control method and system
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANDONG UNIV
- Filing Date
- 2025-10-21
- Publication Date
- 2026-05-12
AI Technical Summary
Traditional sliding mode control methods suffer from poor dynamic performance and weak anti-interference capabilities in robotic arm motion control. This is mainly because the approach law design with static fixed parameters cannot adapt to the needs of the system state trajectory at different dynamic stages, resulting in slow convergence speed and severe chattering.
An adaptive sliding mode approach law is adopted. By constructing a control method that includes system state variables, position error and velocity error, and adaptive adjustment of gain term, the approach speed is dynamically adjusted according to the change of Euclidean distance between the equilibrium point and the current position, so as to achieve fast convergence and suppress chattering.
It significantly improves the speed at which the robotic arm approaches the sliding surface, addresses the issues of slow response, long convergence time, and large tracking error, and enhances control accuracy and anti-interference capabilities.
Smart Images
Figure CN121374562B_ABST
Abstract
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:
[0008] A mechanical arm adaptive sliding mode control method, comprising the following steps:
[0009] An adaptive sliding mode reaching law is constructed, which contains system state variables, a distance function based on position error and velocity error, and a gain term adaptively adjusted with the system convergence state, 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 greater than the set range, the distance function based on the position error and the velocity error dominates, changes exponentially, and the reaching speed to the sliding mode surface is greater than the set value, 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 variable dominates, and the reaching rate to the sliding mode surface is within the predetermined range.
[0010] As an optional implementation, the adaptive sliding mode reaching law is:
[0011]
[0012] wherein k1, k2, k3, k4 are all coefficients and are all greater than zero, E represents the Euclidean distance of the equilibrium point and the current position in the state space, and d is a normal number, is a saturation function.
[0013] As a further implementation, the saturation function is:
[0014]
[0015] wherein x is the input value of the sat() function.
[0016] 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 of the joint to move to the sliding surface.
[0017] As an optional implementation, the joint expression of the mechanical arm after introducing the adaptive sliding mode reaching law is:
[0018]
[0019] wherein, , , are the inertia matrix, the Coriolis matrix and the gravity vector of the mechanical arm, , , are the angle, the angular velocity and the angular acceleration of the joint of the mechanical arm, , , are the estimated value of the joint torque, the estimated value of the friction torque and the estimated value of the external disturbance torque.
[0020] As a further step, the estimated value of the frictional torque is obtained from the friction model.
[0021] As a further step, the estimate of the external disturbance torque is obtained using sensors.
[0022] Furthermore, the Coriolis matrix and the gravity vector of the robotic arm are obtained from the robotic arm parameters.
[0023] An adaptive sliding mode control system for a robotic arm is configured to: construct an adaptive sliding mode approach law, wherein the adaptive sliding mode approach law includes system state variables, a distance function based on position error and velocity error, and a gain term that adaptively adjusts with the system convergence state. When the difference between the Euclidean distance between the equilibrium point and the current position in the state space and a set value is greater than a set range, the distance function based on position error and velocity error dominates and changes exponentially, and the approach speed to the sliding 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 a set range, the system state variables dominate, and the approach rate to the sliding surface is within a predetermined range.
[0024] A robotic arm includes the aforementioned adaptive sliding mode control system or includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the aforementioned method.
[0025] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0026] This invention can significantly improve the speed of state approaching the sliding surface and effectively suppress control chattering. The joint position control algorithm based on the adaptive sliding surface approaching law provided by this invention can improve the problems of slow response, long convergence time, and large tracking error of traditional methods over a wide range.
[0027] This invention does not rely on acceleration signals or perform inverse dynamics solutions. At the same time, it filters the estimated torque, thereby improving the accuracy of torque estimation.
[0028] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description
[0029] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.
[0030] Figure 1 A schematic diagram of a function buffer in one embodiment;
[0031] Figure 2 This is a schematic diagram comparing the control accuracy of the method provided by the present invention and a conventional control method according to one embodiment;
[0032] Figure 3 This is a schematic diagram of the input curve of the control start-up algorithm to the motor in one embodiment, where (b) is an enlarged view of the starting segment of (a). Detailed Implementation
[0033] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0034] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, 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 invention pertains.
[0035] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0036] Where there is no conflict, the embodiments and features described in this application may be combined with each other.
[0037] Example 1
[0038] An adaptive sliding mode control method for a robotic arm is first introduced, as follows: The transmission principle of the flexible joint of the robotic arm is described below:
[0039]
[0040] in, , , Here are the inertia matrix, the Coriolis (centripetal) matrix, and the gravity vector of the robotic arm. , , These are the angles, angular velocities, and angular accelerations of the robotic arm joints. , , These are joint torque, friction torque, and external disturbance torque, respectively.
[0041] We make
[0042]
[0043] in , Let be the target angle and its first derivative, respectively. Interference can be further reduced by first-order filtering.
[0044] Commonly used sliding mode functions are shown below:
[0045]
[0046] in, It is a constant, determined empirically. , ;
[0047] The designed adaptive sliding mode reaching law is shown below:
[0048]
[0049] Here, E, as the Euclidean distance, is derived from the state space. and Absolutely, that is
[0050] ;
[0051] If the system does not converge, then and If E is larger, then Larger size, faster convergence speed ( , The term approaches , The power is also large); conversely, if it approaches the ,but Smaller size, slower convergence speed, less prone to overshoot ( , The term approaches 0. (Power is also small).
[0052] The remaining terms are constants, which can be adjusted according to the equipment and will affect motion accuracy, response speed, etc.
[0053] in, , , , The term E represents the Euclidean distance between the equilibrium point and the current position in the state space, and d is a positive constant whose value is related to E. Saturation function. As shown below:
[0054]
[0055] When the sliding state is far from the desired trajectory, i.e. ,but The exponential growth rate becomes the dominant factor driving the trajectory towards the sliding surface. However, an exponential growth rate can sometimes have adverse effects. To mitigate these adverse effects, methods such as... Figure 1 The circular surface shown, which is d away from the origin, serves as a function "buffer".
[0056] Specifically as follows, when hour, , Dominated by the sliding surface, the function exhibits exponential changes and approaches the sliding surface relatively quickly. At this time No longer in a dominant position It is dominant, but due to the continuous decrease of E, it leads to Therefore, the approach rate is relatively slow at this point.
[0057] Now, we will analyze the expression for joint transmission. , It can be obtained from the parameters of the robotic arm. , The estimated values can be obtained from the corresponding friction models and sensors, respectively. , Therefore, the joint expression of the robotic arm can be represented as follows:
[0058]
[0059] Based on (3) and (4), we can obtain:
[0060]
[0061] Substituting (6) into (7) gives:
[0062] The motion error of the proposed method is compared with that of the traditional control method through simulation. Figure 2 As shown.
[0063] It can be seen that the proposed algorithm is more accurate in terms of precision. Subsequently, simulations were used to compare the two algorithms on the controller input, such as... Figure 3 As shown, the method provided in this embodiment has higher control precision and less fluctuation.
[0064] Example 2
[0065] An adaptive sliding mode control system for a robotic arm is configured to: construct an adaptive sliding mode approach law, wherein the adaptive sliding mode approach law includes system state variables, a distance function based on position error and velocity error, and a gain term that adaptively adjusts with the system convergence state. When the difference between the Euclidean distance between the equilibrium point and the current position in the state space and a set value is greater than a set range, the distance function based on position error and velocity error dominates and changes exponentially, and the approach speed to the sliding 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 a set range, the system state variables dominate, and the approach rate to the sliding surface is within a predetermined range.
[0066] Example 3
[0067] A robotic arm includes the aforementioned adaptive sliding mode control system or includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, complete the steps in the method provided in Embodiment 1.
[0068] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of one or more computer-usable storage media (including, but not limited to, disk storage, etc.) containing computer-usable program code. CD - ROM It takes the form of a computer program product implemented on (such as optical memory, etc.).
[0069] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0070] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxesFigure 1 The function specified in one or more boxes.
[0071] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0072] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art without creative effort within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. An adaptive sliding mode control method for a robotic arm, characterized in that, Includes the following steps: An adaptive sliding mode approach law is constructed, which includes system state variables, a distance function based on position and velocity errors, and a gain term that adaptively adjusts with the system's convergence state. 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 a set range, the distance function based on position and velocity errors dominates and changes exponentially, resulting in a speed of approaching the sliding surface 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 a set range, the system state variables dominate, and the speed of approaching the sliding surface is within a predetermined range.
2. The adaptive sliding mode control method for a robotic arm as described in claim 1, characterized in that, The adaptive sliding mode reaching law is: Where k1, k2, k3, and k4 are all coefficients, 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 positive constant. It is a saturation function.
3. The adaptive sliding mode control method for a robotic arm as described in claim 2, characterized in that, The saturation function is: Here, x is the input value of the sat() function.
4. The adaptive sliding mode control method for a robotic arm as described in claim 2, characterized in that, When the sliding state deviates from the desired trajectory, then The term becomes the dominant factor driving the state trajectory to move towards the sliding surface.
5. The adaptive sliding mode control method for a robotic arm as described in claim 1, characterized in that, it introduces... The joint expressions of the robotic arm after the adaptive sliding mode reaching law are as follows: in, , , These are the inertia matrix, the Coriolis matrix, and the gravity vector of the robotic arm, respectively. , , These are the angles, angular velocities, and angular accelerations of the robotic arm joints. , , These are the estimated values for joint torque, friction torque, and external disturbance torque, respectively.
6. The adaptive sliding mode control method for a robotic arm as described in claim 5, characterized in that, The estimated value of the frictional torque is obtained from the friction model.
7. The adaptive sliding mode control method for a robotic arm as described in claim 1, characterized in that, The estimated value of the external disturbance torque is obtained using sensors.
8. The adaptive sliding mode control method for a robotic arm as described in claim 1, characterized in that, The Coriolis matrix and the gravity vector of the robotic arm are obtained from the robotic arm parameters.
9. An adaptive sliding mode control system for a robotic arm, characterized in that, It is configured to: construct an adaptive sliding mode approach law, which includes system state variables, a distance function based on position error and velocity error, and a gain term that adaptively adjusts with the system convergence state. 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 position error and velocity error dominates and changes exponentially, and the approach speed to the sliding 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 dominate, and the approach rate to the sliding surface is within the predetermined range.
10. A robotic arm, characterized in that, The method may include the adaptive sliding mode control system for a robotic arm as described in claim 9, or include a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps of the method as described in any one of claims 1-8.