Trajectory tracking control method for robot arm based on discrete fast terminal sliding mode control

Abstract

The application belongs to the technical field of artificial intelligence, and discloses a mechanical arm trajectory tracking control method based on discrete fast terminal sliding mode control, which comprises the following steps: firstly, a discrete dynamic model of a mechanical arm system is established; then, based on the discrete dynamic model of the mechanical arm system, a discrete extended state observer is designed to estimate the lumped disturbance in the mechanical arm system; then, a discrete fast terminal sliding mode controller is designed to keep the mechanical arm system state on a sliding surface; and a model predictive controller based on the sliding mode is designed to make the mechanical arm system quickly reach the sliding surface; and the discrete fast terminal sliding mode controller and the model predictive controller based on the sliding mode are combined to construct a total controller. The application estimates the lumped uncertainty of the mechanical arm system by using the discrete time extended state observer, and improves the estimation performance; the model predictive controller is used to drive the system state to the sliding manifold with the optimal motion trajectory, and under the condition that the input torque is relatively smooth, higher tracking accuracy and response speed are obtained.

Description

Technical Field

[0001] This invention belongs to the field of artificial intelligence technology and relates to a robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control. Background Technology

[0002] In recent years, robotic arms have become one of the most commonly used tools in the industrial field, playing a vital role in manufacturing, aerospace, and healthcare. Due to the complex and uncertain working environment of robotic arms, load disturbances are unavoidable. In recent years, researchers have proposed many control strategies to suppress load disturbances.

[0003] Sliding mode control (SMC) methods are widely used in complex nonlinear systems due to their advantages such as fast response speed and sensitivity to parameter uncertainties and load disturbances. For example, the nonsingular fast terminal sliding mode control method for robotic arms handles unknown external disturbances by designing adaptive mechanisms and smooth hyperbolic tangent functions. However, it should be noted that under large disturbances, the above-mentioned methods cannot eliminate chattering. To address this issue, observer-based sliding mode control methods have been proposed for robotic arm systems. In this control scheme, the disturbance is estimated by an estimator, the controller acts as the feedback controller for the robotic arm, and the observer acts as the feedforward compensation part to compensate for the disturbance in real time. However, in these works, the optimal performance of the input torque is neglected, which may lead to high costs, while the energy of the robotic arm system is limited, especially in complex environments. Model predictive control (MPC) considering disturbances and constraints is one of the most widely used optimal control methods in robotic arm systems, but it still increases the complexity of controller design.

[0004] Compared with a single control strategy, the fusion control strategy of multiple control methods has higher trajectory tracking control accuracy and faster response speed. In the combination of SMC and MPC, MPSMC introduces chattering caused by SMC when dealing with disturbances, while the ability of SMPC to suppress uncertainty remains a problem.

[0005] Therefore, designing a fusion control strategy with higher accuracy in robotic arm trajectory tracking and control, faster response speed, and effective suppression of uncertainty remains one of the key issues that urgently need to be addressed in this field. Summary of the Invention

[0006] The purpose of this invention is to address the technical problems existing in the prior art by providing a robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control, which achieves higher trajectory tracking accuracy, faster response speed, and effective suppression of uncertainty, thereby improving estimation performance.

[0007] To achieve the above objectives, this invention provides a robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control, which includes the following steps:

[0008] S1, Establish the discrete dynamic model of the robotic arm system;

[0009] S2. Based on the discrete dynamic model of the robotic arm system, a discrete extended state observer is designed to estimate the lumped disturbances in the robotic arm system.

[0010] S3, Design a discrete fast terminal sliding mode controller to keep the state of the robotic arm system on the sliding surface: First, establish the sliding surface based on the lumped disturbance, and then design the discrete fast terminal sliding mode controller based on the sliding surface;

[0011] S4. Design a sliding mode-based model predictive controller to enable the robotic arm system to quickly reach the sliding surface: First, convert the sliding surface into control input increments, then construct the recursive equation of the sliding surface, and construct the objective functions of the sliding surface and control input increments; the model predictive controller is obtained by optimizing the objective functions.

[0012] S5 combines a discrete fast terminal sliding mode controller and a sliding mode-based model predictive controller to construct a master controller.

[0013] In step S1 above, the discrete dynamic model of the robotic arm system is expressed as:

[0014] ;

[0015] in, ; q ( k )for k The joint angle of the robotic arm at any given moment; ; for k The angular velocity of the robotic arm joints at any given moment; For system lumped interference; M ( q ) is a symmetric positive definite inertial matrix; This is the friction torque vector; The external disturbance torque vector; T The system sampling period; It is a Coriolis matrix; G ( q ) is the gravitational torque vector; The input matrix is ​​a vector.

[0016] In step S2 above, the discrete extended state observer is represented as:

[0017] ;

[0018] in, , and These are the state estimates of the observers; , , and This is the error constant factor; , and It is the observer gain;

[0019] Based on the aforementioned discrete extended state observer, the lumped disturbance estimation in the robotic arm system Represented as:

[0020] .

[0021] In step S3 above, a sliding surface is established based on lumped disturbances. s ( k ), represented as:

[0022] ;

[0023] in, e 1 and e 2 represents the tracking errors of the robotic arm's angle and angular velocity, respectively; c 1 and c 2 is the scaling factor. It is a non-linear exponent. ;

[0024] Based on the above sliding surface, a discrete fast terminal sliding mode controller is designed, expressed as follows:

[0025] ;

[0026] in, This is the reference angular velocity for the joint.

[0027] In step S4 above, to quickly bring the robotic arm system to the sliding surface while conserving control resources, it is necessary to optimize the control input. This involves converting the sliding surface into incremental control inputs. The form is then used to obtain the recursive equation for the sliding surface in one step:

[0028] ;

[0029] in, ; ;

[0030] The objective function for constructing the sliding surface and controlling the input increment is as follows:

[0031] ;

[0032] in, for N The sliding mode state at a given moment. for Transpose of; for N The robot arm system model predicts the control input increment of the controller at each time step. for Transpose of; Weighting factors to control the input increment;

[0033] Based on the above recursive equation and objective function, the model predictive controller is obtained by minimizing the objective function, as follows:

[0034] ;

[0035] in, ; ; ; ; ; I Represents the identity matrix; , These are the minimum and maximum values ​​for controlling the input increment, respectively.

[0036] In step S5 above, the main controller is represented as:

[0037] ;

[0038] in, That is, the input matrix vector.

[0039] Compared with existing technologies, the robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control provided by this invention has the following advantages:

[0040] (1) This invention first proposes a new Discrete-Time Extended State Observer (DTESO), and then constructs a Discrete Fast Terminal Sliding Mode Controller (DFTSMC) and a Sliding Mode-Based Model Predictive Controller (MPC) based on the Discrete-Time Extended State Observer. The Discrete Fast Terminal Sliding Mode Controller is used as the equivalent control law, and the Sliding Mode-Based Model Predictive Controller is used as the switching control law. The two control laws are combined to obtain the final control law, which realizes accurate tracking of the robot arm trajectory and meets the high-precision requirements of robot trajectory tracking control for industrial robots (such as in the aerospace and medical fields).

[0041] (2) The Discrete Time Extended State Observer (DTESO) proposed in this invention is used to estimate the lumped uncertainty of the robotic arm system, thereby improving the estimation performance.

[0042] (3) Based on the Discrete-Time Extended State Observer (DTESO), the present invention designs the DFTSMOC strategy for the robotic arm system. This strategy derives the prediction equation based on the sliding mode function and ensures that the system quickly reaches the sliding manifold through the optimal control stage based on the model predictive controller. Furthermore, the present invention optimizes based on the sliding mode function, effectively combining the high robustness of sliding mode control and the optimality of the model predictive controller.

[0043] (4) The discrete DFTSMPC strategy proposed in this invention uses a model predictive controller to drive the system state to a sliding manifold with the optimal motion trajectory, and uses the control input torque as the optimization function. Under the condition that the input torque is relatively smooth, it can obtain higher tracking accuracy and response speed. Attached Figure Description

[0044] Figure 1 This is a schematic flowchart of the robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control provided in Embodiment 1 of the present invention;

[0045] Figure 2 This is a schematic diagram illustrating the principle of the robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control provided in Embodiment 1 of the present invention.

[0046] Figure 3 The above are the trajectory tracking simulation results of the robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control in Embodiment 1 of the present invention.

[0047] Figure 4 The simulation results are based on the disturbance estimation of the discrete extended state observer. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0049] Example 1

[0050] This embodiment provides a robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control, such as... Figure 1 and Figure 2 As shown, it includes the following steps:

[0051] S1. Establish a discrete dynamic model of the robotic arm system.

[0052] The dynamic model of the robotic arm system is represented as follows:

[0053] ;

[0054] in, These are the angles, angular velocities, and angular accelerations of the joints in the robotic arm system. n Indicates dimension; It is a symmetric positive definite inertial matrix; It is a Coriolis matrix; It is the gravitational torque vector; This is the friction torque vector; The external disturbance torque vector; This is the input torque vector.

[0055] Discretizing the above dynamic model using the forward Euler method, it can be further expressed as the following discrete state-space equation, which is also the discrete dynamic model of the robotic arm system:

[0056] ;

[0057] in, ; q ( k )for k The joint angle of the robotic arm at any given moment; ; for k The angular velocity of the robotic arm joints at any given moment; For system lumped interference; M ( q ) is a symmetric positive definite inertial matrix; This is the friction torque vector; The external disturbance torque vector; T The system sampling period; It is a Coriolis matrix; G ( q ) is the gravitational torque vector; The input matrix is ​​a vector.

[0058] S2. Based on the discrete dynamic model of the robotic arm system, a discrete extended state observer is designed to estimate the lumped disturbances in the robotic arm system.

[0059] This step, based on the discrete dynamic model of the robotic arm system, uses the system state... and To estimate the estimation error, a Discrete Extended State Observer (DTESO) was designed to estimate the lumped disturbance of the robotic arm system.

[0060] The discrete extended state observer is represented as:

[0061] ;

[0062] in, , and These are the state estimates of the observers; , , and This is the error constant factor; , and It is the observer gain; this discrete extended state observer not only considers the system state The estimation error was also introduced. This reduces estimation error and improves estimation performance.

[0063] Based on the aforementioned discrete extended state observer, the lumped disturbance estimation in the robotic arm system Represented as:

[0064] .

[0065] S3. Design a discrete fast terminal sliding mode controller to keep the state of the robotic arm system on the sliding surface: First, establish the sliding surface based on the lumped disturbance, and then design the discrete fast terminal sliding mode controller based on the sliding surface.

[0066] Specifically, a sliding surface is established based on lumped disturbances. s ( k ), represented as:

[0067] ;

[0068] in, e 1 and e 2 represents the tracking errors of the robotic arm's angle and angular velocity, respectively. These errors can be determined by the difference between the reference joint angle signal and the actual robotic arm joint angle. , , , These are the joint reference angle and angular velocity, respectively. c 1 and c 2 is the scaling factor. It is a non-linear exponent. ;

[0069] Based on the above sliding surface, a Discrete Fast Terminal Sliding Mode Controller (DFTSMC) is designed, represented as follows:

[0070] ;

[0071] in, This is the reference angular velocity for the joint.

[0072] S4. Design a sliding mode-based model predictive controller to enable the robotic arm system to quickly reach the sliding surface: First, convert the sliding surface into control input increments, then construct the recursive equation of the sliding surface, and construct the objective function of the sliding surface and the control input increments; the model predictive controller is obtained by optimizing the objective function.

[0073] To enable the robotic arm system to quickly reach the sliding surface while conserving control resources, it is necessary to optimize the control input. This involves converting the sliding surface into incremental control inputs. The form is then used to obtain the recursive equation for the sliding surface in one step:

[0074] ;

[0075] in, ; ;

[0076] The objective function for constructing the sliding surface and controlling the input increment is as follows:

[0077] ;

[0078] in, for N The sliding mode state at a given moment. for Transpose of; for N The robot arm system model predicts the control input increment of the controller at each time step. for Transpose of; Weighting factors are used to control the input increment.

[0079] Based on the above recursive equation and objective function, the Model Predictive Controller (MPC) is obtained by minimizing the objective function, as follows:

[0080] ;

[0081] in, ; ; ; ; ; I Represents the identity matrix; , These are the minimum and maximum values ​​for controlling the input increment, respectively.

[0082] S5 combines a discrete fast terminal sliding mode controller and a sliding mode-based model predictive controller to construct a master controller.

[0083] The main controller is represented as:

[0084] ;

[0085] in, That is, the input matrix vector.

[0086] For the discrete extended state observer described above, the Lyapunov function is constructed as follows:

[0087] ;

[0088] in, , , , .

[0089] Through stability analysis, for a robotic arm system with load disturbances and uncertainties, using the aforementioned discrete extended state observer, if a positive definite matrix exists... and a positive number This makes the following equation true:

[0090] ;

[0091] in, , , Therefore, the estimation error of this discrete extended state observer is bounded.

[0092] Therefore, the stability analysis of the discrete extended state observer is performed using Lyapunov's second method, and the sliding surface function is... The results are convergent, and the tracking errors of the robotic arm joint angles and angular velocities are bounded. This demonstrates the effectiveness of the robotic arm trajectory tracking control method based on discrete fast end-effector sliding mode control provided by this invention.

[0093] A simulation experiment was conducted based on the above-mentioned robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control. The robotic arm contains two joints, and the lumped disturbance is applied to joint 1. The simulation settings are as follows: , , , , , , , , , , , , , , , .

[0094] Following steps S1-S5 above to determine the input matrix vector, the resulting simulation results of the robotic arm system output and the desired trajectory are as follows: Figure 3 As shown, the simulation results of lumped disturbance and applied disturbance estimated based on the discrete extended state observer are as follows: Figure 4 As shown. From Figure 3 and Figure 4 It can be seen that the robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control provided by the present invention can effectively estimate the total concentrated disturbance, improve the estimation performance, and achieve high tracking accuracy and response speed.

[0095] The above are merely preferred embodiments of the present invention. It should be noted that the above preferred embodiments should not be considered as limitations on the present invention, and the scope of protection of the present invention should be determined by the scope defined in the claims. For those skilled in the art, several improvements and modifications can be made without departing from the spirit and scope of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control, characterized in that, Includes the following steps: S1, Establish the discrete dynamic model of the robotic arm system; S2. Based on the discrete dynamic model of the robotic arm system, a discrete extended state observer is designed to estimate the lumped disturbances in the robotic arm system. S3, Design a discrete fast terminal sliding mode controller to keep the state of the robotic arm system on the sliding surface: First, establish the sliding surface based on the lumped disturbance, and then design the discrete fast terminal sliding mode controller based on the sliding surface; S4. Design a sliding mode-based model predictive controller to enable the robotic arm system to quickly reach the sliding surface: First, convert the sliding surface into control input increments, then construct the recursive equation of the sliding surface, and construct the objective functions of the sliding surface and control input increments; the model predictive controller is obtained by optimizing the objective functions. S5 combines a discrete fast terminal sliding mode controller and a sliding mode-based model predictive controller to construct a master controller.

2. The robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control according to claim 1, characterized in that, In step S1, the discrete dynamic model of the robotic arm system is represented as follows: ； in, ; q ( k )for k The joint angle of the robotic arm at any given moment; ; for k The angular velocity of the robotic arm joints at any given moment; For system lumped interference; M ( q ) is a symmetric positive definite inertial matrix; This is the friction torque vector; The external disturbance torque vector; T The system sampling period; It is a Coriolis matrix; G ( q ) is the gravitational torque vector; The input matrix is ​​a vector.

3. The robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control according to claim 2, characterized in that, In step S2, the discrete extended state observer is represented as: ； in, , and These are the state estimates of the observers; , , and This is the error constant factor; , and It is the observer gain; Based on the aforementioned discrete extended state observer, the lumped disturbance estimation in the robotic arm system Represented as: 。 4. The robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control according to claim 3, characterized in that, In step S3, a sliding surface is established based on the lumped disturbance. s ( k ), represented as: ； in, e 1 and e 2 represents the tracking errors of the robotic arm's angle and angular velocity, respectively; c 1 and c 2 is the scaling factor. It is a non-linear exponent. ; Based on the above sliding surface, a discrete fast terminal sliding mode controller is designed, expressed as follows: ； in, This is the reference angular velocity for the joint.

5. The robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control according to claim 1, characterized in that, In step S4, the sliding surface is converted into control input increments. The form is then used to obtain the recursive equation for the sliding surface in one step: ； in, ; ; The objective function for constructing the sliding surface and controlling the input increment is as follows: ； in, for N The sliding mode state at a given moment. for transpose; for N The robot arm system model predicts the control input increment of the controller at each time step. for transpose; Weighting factors to control the input increment; Based on the above recursive equation and objective function, the model predictive controller is obtained by minimizing the objective function, as follows: ； in, ; ; ; ; ; I Represents the identity matrix; , These are the minimum and maximum values ​​for controlling the input increment, respectively.

6. The robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control according to claim 1, characterized in that, In step S5, the main controller is represented as: ； in, That is, the input matrix vector.

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