Mechanical arm trajectory tracking control method based on discrete fast terminal sliding mode control

Abstract

The invention 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, establishing a discrete dynamic model of a mechanical arm system; secondly, based on the discrete dynamic model of the mechanical arm system, a discrete expansion state observer is designed, and lumped disturbance in the mechanical arm system is estimated; a discrete fast terminal sliding mode controller is designed, and the state of a mechanical arm system is kept on a sliding mode surface; a model prediction controller based on a sliding mode is designed, so that the mechanical arm system quickly reaches a sliding mode surface; and combining the discrete fast terminal sliding mode controller and the model prediction controller based on the sliding mode to construct a master controller. According to the method, the discrete time extended state observer is used for estimating the centralized uncertainty of the mechanical arm system, and the estimation performance is improved; a model prediction controller is utilized to drive a system state to a sliding mode manifold with an optimal motion trail, and high tracking precision and response speed are obtained under the condition that the input torque is smooth.

Description

Technical Field

[0001] The invention belongs to the technical field of artificial intelligence and relates to a robot arm trajectory tracking control method based on discrete fast terminal sliding mode control. Background Art

[0002] In recent years, as the most commonly used tool in the industrial field, robotic arms play a vital role in manufacturing, aviation, and healthcare. Since the working environment of robotic arms is complex and full of various uncertainties, load disturbances are inevitable. In recent years, researchers have proposed many control strategies to suppress load disturbances.

[0003] Sliding mode control (SMC) methods are applied to complex nonlinear systems due to their advantages such as fast response speed and sensitivity to parameter uncertainty and load disturbance. For example, the non-singular fast terminal sliding mode control method for manipulators handles unknown external disturbances by designing adaptive mechanisms and smooth hyperbolic tangent functions. However, it should be noted that the above research methods cannot eliminate the chattering phenomenon under large disturbances. To solve this problem, an observer-based sliding mode control method has been proposed for manipulator systems. In this control scheme, the disturbance is estimated by an estimator, the controller serves as the feedback controller of the manipulator, and the observer serves as the feedforward compensation part to compensate the disturbance in real time. However, in these works, the optimal performance of the input torque is ignored, which may lead to high costs while the energy of the manipulator 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 manipulator 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 combined method of SMC and MPC, MPSMC introduces SMC-induced jitter when dealing with disturbances, while the ability of SMPC to suppress uncertainty is still a problem.

[0005] Therefore, designing a fusion control strategy with higher robot trajectory tracking control accuracy, faster response speed and effective uncertainty suppression is still one of the key issues that need to be urgently solved in this field. Summary of the invention

[0006] The purpose of the present invention is to provide a robot arm trajectory tracking control method based on discrete fast terminal sliding mode control to address the technical problems existing in the above-mentioned prior art, which has higher robot arm trajectory tracking accuracy, faster response speed, effectively suppresses uncertainty, and improves estimation performance.

[0007] To achieve the above object, the present invention provides a manipulator trajectory tracking control method based on discrete fast terminal sliding mode control, which includes the following steps: S1. Establish a discrete dynamic model of the manipulator system; S2. Based on the discrete dynamic model of the manipulator system, design a discrete extended state observer to estimate the lumped disturbance in the manipulator system; S3. Design a discrete fast terminal sliding mode controller to keep the manipulator system state on the sliding mode surface: first establish the sliding mode surface according to the lumped disturbance, and then design a discrete fast terminal sliding mode controller according to the sliding mode surface; S4. Design a sliding mode-based model predictive controller to make the manipulator system quickly reach the sliding mode surface: first convert the sliding mode surface into a control input increment, then construct a recursive equation of the sliding mode surface, and construct an objective function of the sliding mode surface and the control input increment; obtain the model predictive controller by optimizing the objective function; S5. Combine the discrete fast terminal sliding mode controller and the sliding mode-based model predictive controller to construct a total controller.

[0008] In the above step S1, the discrete dynamic model of the manipulator system is expressed as: ; wherein, ; q ( k ) is the k manipulator joint angle at time ; is the k manipulator joint angular velocity at time is the system lumped disturbance; M ( q ) is a symmetric positive definite inertia matrix; is the friction torque vector; is the external disturbance torque vector; T is the system sampling period; is the Coriolis matrix; G ( q ) is the gravity torque vector; is the input matrix vector.

[0009] In the above step S2, the discrete extended state observer is expressed as: ; wherein, , and are the state estimates of the observer respectively; , , and is the error constant factor; , and are the observer gains; According to the discrete extended state observer, the lumped disturbance estimation in the robotic arm system is expressed as: .

[0010] In the above step S3, a sliding mode surface is established based on the lumped disturbance s ( k ), which is expressed as: ; where e 1 and e 2 are the tracking errors of the robotic arm angle and angular velocity respectively; c 1 and c 2 are the scaling factors, is the non - linear exponent, ; According to the above sliding mode surface, a discrete fast terminal sliding mode controller is designed, which is expressed as: ; where is the joint reference angular velocity.

[0011] In the above step S4, in order to make the state of the robotic arm system quickly reach the sliding mode surface and save control resources at the same time, it is necessary to optimize the control input accordingly. The sliding mode surface is converted into the form of the control input increment , and then the recursive equation of the sliding mode surface is obtained by one - step recursion: ; where ; ; The objective functions of the sliding mode surface and the control input increment are constructed as follows: ; where is the sliding mode state at the N th moment, is the transpose of ; is the control input increment of the model predictive controller of the robotic arm system at the N th moment, is the transpose of ; is the weight factor of the control input increment; According to the above recursive equation and objective function, the model predictive controller is obtained by minimizing the objective function, which is expressed as follows: ; Among them, ; ; ; ; ; I represents the identity matrix; and are the minimum and maximum values of the control input increment, respectively.

[0012] In the above step S5, the total controller is expressed as: ; Among them, That is, the input matrix vector.

[0013] Compared with the prior art, the robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control provided by the present invention has the following beneficial effects: (1) The present 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. These two parts of the control laws are combined to obtain the final control law, realizing accurate tracking of the robotic arm trajectory and meeting the high-precision requirements of industrial robots (such as in the aviation field, medical field, etc.) for robot trajectory tracking control; (2) The discrete-time extended state observer (DTESO) proposed by the present invention is used to estimate the lumped uncertainty of the robotic arm system, improving the estimation performance.

[0014] (3) Based on the discrete-time extended state observer (DTESO), the present invention designs a DFTSMPOC strategy for the robotic arm system. The strategy derives a prediction equation based on the sliding mode function and ensures that the system quickly reaches the sliding mode manifold through the optimal control stage of the model predictive controller; and the present invention is optimized based on the sliding mode function, effectively combining the high robustness of the sliding mode control and the optimality of the model predictive controller.

[0015] (4) The discrete DFTSMPOC strategy proposed by the present invention uses the model predictive controller to drive the system state to the sliding mode manifold with the optimal motion trajectory. With the control input torque as the optimization function, high tracking accuracy and response speed can be obtained under the condition that the input torque is relatively smooth. Description of the Drawings

[0016] Figure 1Schematic diagram of the robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control provided in Embodiment 1 of the present invention; Figure 2 Schematic diagram of 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; Figure 3 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; Figure 4 Interference estimation simulation results based on discrete extended state observer. Detailed implementation manners

[0017] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be described in detail below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other implementation manners obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope protected by the present invention.

[0018] Embodiment 1 This embodiment provides a robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control, as Figure 1 and Figure 2 shown, which includes the following steps: S1. Establish a discrete dynamic model of the robotic arm system.

[0019] The dynamic model of the robotic arm system is expressed as follows: ; where are respectively the angle, angular velocity and angular acceleration of the joints of the robotic arm system, n represents the dimension; is a symmetric positive definite inertia matrix; is the Coriolis matrix; is the gravity torque vector; is the friction torque vector; is the external disturbance torque vector; is the input torque vector.

[0020] The above dynamic model is discretely processed by the forward Euler method and further expressed as the following discrete state space equation, that is, the discrete dynamic model of the robotic arm system: ; where ; q ( k ) is kThe joint angle of the robotic arm at a moment; ; is k the joint angular velocity of the robotic arm at a moment; is the lumped disturbance of the system; M ( q ) is a symmetric positive definite inertia matrix; is the frictional torque vector; is the external disturbance torque vector; T is the system sampling period; is the Coriolis matrix; G ( q ) is the gravity torque vector; is the input matrix vector.

[0021] S2. Based on the discrete dynamic model of the robotic arm system, a discrete extended state observer is designed to estimate the lumped disturbance in the robotic arm system.

[0022] In this step, according to the discrete dynamic model of the robotic arm system, using the estimation errors of the system states and , a discrete extended state observer (DTESO) is designed to estimate the lumped disturbance of the robotic arm system.

[0023] The discrete extended state observer is expressed as: ; where , and are the state estimates of the observer respectively; , , and are the error constant factors; , and are the observer gains; this discrete extended state observer not only considers the estimation error of the system state , but also introduces the estimation error of , improving the estimation performance.

[0024] According to the discrete extended state observer, the lumped disturbance estimation in the robotic arm system is expressed as: .

[0025] S3. Design a discrete fast terminal sliding mode controller to keep the robotic arm system state on the sliding mode surface: First, establish the sliding mode surface according to the lumped disturbance, and then design the discrete fast terminal sliding mode controller according to the sliding mode surface.

[0026] Specifically, a sliding mode surface is established based on lumped interference s ( k ), expressed as: ; Among them, e 1 and e 2 are respectively the tracking errors of the manipulator angle and angular velocity, which can be determined by the difference between the reference joint angle signal and the actual manipulator joint angle, that is , , , are respectively the joint reference angle and angular velocity; c 1 and c 2 are scaling factors, is a non-linear exponent, ; According to the above sliding mode surface, a discrete fast terminal sliding mode controller (DFTSMC) is designed, expressed as: ; Among them, is the joint reference angular velocity.

[0027] S4, design a sliding mode-based model predictive controller to make the manipulator system quickly reach the sliding mode surface: First, convert the sliding mode surface into a control input increment, then construct a recursive equation of the sliding mode surface, and construct an objective function of the sliding mode surface and the control input increment; obtain the model predictive controller by optimizing the objective function.

[0028] In order to make the manipulator system state quickly reach the sliding mode surface and save control resources at the same time, it is necessary to optimize the control input accordingly. Convert the sliding mode surface into a control input increment form, and then recursively obtain the recursive equation of the sliding mode surface in one step: ; Among them, ; ; Construct an objective function of the sliding mode surface and the control input increment, as follows: ; Among them, is the N th moment of the sliding mode state, is the transpose of ; is the N th moment of the control input increment of the manipulator system model predictive controller, is the transpose of ; is the weight factor of the control input increment.

[0029] Based on the above recursive equation and objective function, a model predictive controller (MPC) is obtained by minimizing the objective function, which is expressed as follows: ; where, ; ; ; ; ; I represents the identity matrix; , are the minimum and maximum values of the control input increment, respectively.

[0030] In S5, a total controller is constructed by combining the discrete fast terminal sliding mode controller and the sliding mode-based model predictive controller.

[0031] The total controller is expressed as: ; where, i.e., the input matrix vector.

[0032] For the above discrete extended state observer, the Lyapunov function is constructed as: ; where, , , , .

[0033] Through stability analysis, for a robotic arm system with load disturbances and uncertainties, when using the above discrete extended state observer, if there exists a positive definite matrix and a positive number such that the following equation holds: ; where, , , . Then the estimation error of the discrete extended state observer is bounded.

[0034] Therefore, through the stability analysis of the above discrete extended state observer by the Lyapunov second method, the sliding mode surface function is 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 provided by the present invention based on discrete fast terminal sliding mode control.

[0035] Based on the above robotic arm trajectory tracking control method based on discrete fast terminal sliding mode control, a simulation experiment is carried out. The robotic arm has two joints, and the lumped disturbance is loaded on joint 1. The simulation settings are as follows: , , , , , , , , , , , , , , , .

[0036] Determine the input matrix vector according to the above steps S1 - S5, and the simulation results of the output of the robotic arm system and the desired trajectory are as Figure 3 shown, and the simulation results of the lumped disturbance estimated based on the discrete extended state observer and the applied disturbance are as Figure 4 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 well estimate the lumped total disturbance, improve the estimation performance; and obtain high tracking accuracy and response speed.

[0037] The above is only the preferred embodiment of the present invention. It should be noted that the above - mentioned preferred embodiment should not be regarded as a limitation of the present invention. The protection scope of the present invention should be subject to the scope defined by the claims. For those of ordinary skill in the art of this technology, without departing from the spirit and scope of the present invention, several improvements and refinements can still be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A robot arm trajectory tracking control method based on discrete fast terminal sliding mode control, characterized in that: The following steps are involved: S1, establish a discrete dynamic model of the robotic arm system; S2, based on the discrete dynamic model of the manipulator system, a discrete extended state observer is designed to estimate the lumped disturbance in the manipulator system; S3, design a discrete fast terminal sliding mode controller to keep the state of the robot system on the sliding surface: first, establish the sliding surface according to the lumped disturbance, and then design a discrete fast terminal sliding mode controller according to the sliding surface; S4, design a model predictive controller based on sliding mode to enable the robot 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 increment; obtain the model predictive controller by optimizing the objective function; S5, the discrete fast terminal sliding mode controller and the sliding mode-based model predictive controller are combined to construct the overall controller.

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

3. The robot arm trajectory tracking control method based on discrete fast terminal sliding mode control according to claim 2 is characterized in that: In step S2, the discrete extended state observer is expressed as: ； in, , and are the state estimates of the observer respectively; , , and is the error constant factor; , and is the observer gain; According to the discrete extended state observer, the lumped disturbance estimation in the manipulator system It is expressed as: 。 4. The robot arm trajectory tracking control method based on discrete fast terminal sliding mode control according to claim 3 is characterized in that: In step S3, a sliding surface is established based on the lumped interference s ( k ), expressed as: ； in, e 1 and e 2 are the robot arm angle and angular velocity tracking errors respectively; c 1 and c 2 is the scaling factor, is the nonlinear index, ; According to the above sliding surface, a discrete fast terminal sliding mode controller is designed, which is expressed as: ； in, is the reference angular velocity of the joint.

5. The robot arm trajectory tracking control method based on discrete fast terminal sliding mode control according to claim 1 is characterized in that: In step S4, the sliding surface is converted into a control input increment The recursive equation of the sliding surface is obtained by one step recursion: ； in, ; ; The objective function of constructing the sliding surface and the control input increment is as follows: ； in, for N The sliding mode state at the moment, for The transpose of for N The control input increment of the robot system model predictive controller at the moment, for The transpose of is the weight factor for controlling the input increment; According to the above recursive equation and objective function, the model predictive controller is obtained by minimizing the objective function, which is expressed as follows: ； in, ; ; ; ; ; I represents the identity matrix; , are the minimum and maximum values ​​of the control input increment respectively.

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

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