Mechanical arm trajectory tracking control method for improving integral sliding mode control

Abstract

The invention provides a mechanical arm trajectory tracking control method for improving integral sliding mode control, which relates to the field of mechanical arm control and comprises the following steps: establishing a dynamic model of a mechanical arm system; the future state of the mechanical arm system is optimized and predicted through model prediction control; designing a sliding mode surface and improving the reaching law to obtain a self-adaptive improved integral sliding mode controller; analyzing the stability of the system, and determining a control law according to an analysis result; constructing a control model combining the improved integral sliding mode controller and the mechanical arm; trajectory tracking control of the mechanical arm is achieved by selecting system parameters, expected trajectory information and disturbance information. According to the method, model predictive control and integral sliding mode control are combined, so that the vibration phenomenon generated by the sliding mode control can be effectively inhibited, the uncertainty of the system can be supplemented, and the problems of insufficient tracking precision and the like caused by the uncertainty in the trajectory tracking process of the mechanical arm are solved.

Description

Technical Field

[0001] The invention relates to the technical field of robot arm control, and in particular to a robot arm trajectory tracking control method with improved integral sliding film control. Background Art

[0002] With the development of robotics technology, its application fields are constantly expanding, and it has been widely used in industrial manufacturing, medical health, aerospace, ocean or geological exploration. As the field of robotics technology expands, people's requirements for robot control are constantly increasing. The key to achieving complex robot movements lies in whether it can accurately run the preset joint trajectory, that is, the accuracy of the robot arm's trajectory. Therefore, in the current field of robot manufacturing, the robot arm trajectory tracking problem is one of the current research hotspots, which directly determines the accuracy and efficiency of the entire robot's movement.

[0003] At present, researchers have proposed a series of methods for the control of robotic arms, including PID control, fuzzy control, neural network control, etc. However, since the robotic arm is a complex system with nonlinearity, strong coupling, and uncertainty in the dynamic model, and there are multiple uncertain factors such as friction, noise, and external environment in the actual operation process, it is difficult to achieve fast and accurate trajectory tracking control. For example: the traditional PID control has poor effect on nonlinear systems, difficult parameter adjustment, and cannot handle the constraints in the complex system of the robotic arm; the rule calculation of fuzzy control is complex and the performance is greatly affected by the trajectory, which makes optimization difficult; although neural networks and iterative control have good tracking effects, they require a lot of training data and time. First, the demand for computing resources is high, and second, the amount of preliminary preparation work is large, and the decision-making process is not transparent, and it is impossible to achieve fast and accurate control. In summary, the current robotic arm trajectory tracking control method has problems such as large errors, inability to effectively handle constraints, low processing efficiency, high processing cost, and susceptibility to interference from external factors, which seriously restricts the application of robotic arms and even robots as a whole. Summary of the invention

[0004] In view of the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a robot arm trajectory tracking control method with improved integral synovial film control. The method combines model predictive control with integral synovial film control, which can effectively suppress the vibration phenomenon caused by synovial film control and supplement the uncertainty of the system, thereby solving the accuracy problem caused by uncertainty in the trajectory tracking process of the robot arm and realizing fast and accurate robot arm trajectory tracking.

[0005] The purpose of the present invention is achieved through the following technical solutions: A robot arm trajectory tracking control method with improved integral sliding film control, comprising: Step S1, establishing a dynamic model of the robotic arm system; Step S2, optimizing and predicting the future state of the robotic arm system through model predictive control; Step S3, designing the sliding film surface and improving the reaching law to obtain an adaptive improved integral sliding film controller; Step S4, analyzing the stability of the system and determining the control law according to the analysis results; Step S5, constructing a control model combining an improved integral sliding film controller and a robotic arm; Step S6: Realize robot arm trajectory tracking control by selecting system parameters, expected trajectory information, and disturbance information.

[0006] Based on the further optimization of the above scheme, the specific method of establishing the dynamic model of the robotic arm system in step S1 is: Taking into account the influence of uncertain factors such as coupling, noise and external interference on the manipulator model, the dynamic equation of the U-link rigid manipulator is established using the Lagrange equation method:

[0007] Where: ,and Represent the joints of the robot arm 1、2、…、u The joint angles; ,and Represent the joints of the robot arm 1、2、…、u The joint angular velocity; ,and Represent the joints of the robot arm 1、2、…、u The joint angular acceleration of ,and Represent the joints of the robot arm 1、2、…、u The driving torque, i.e. represents the control torque vector; represents the inertial mass matrix of the system, Represents the Coriolis force and centrifugal force matrix, represents the joint gravity matrix ( ); Represents external unknown disturbance; ( and Respectively In a certain proportional relationship) represents the uncertain but bounded part of the system and satisfies:

[0008] assumed:

[0009] but:

[0010] Therefore, the dynamic model of the robotic arm system V for: .

[0011] Based on the further optimization of the above scheme, the specific method of optimizing and predicting the future state of the robotic arm system through model predictive control in step S2 is: First, establish the following second-order system:

[0012] Among them: state variables ; Output vector y=q ; represents the control vector; Then, in t At this moment, according to the current state x(t) , the backward prediction time step is h ,get:

[0013] In the formula, v MPC represents the control quantity of the model predictive controller; After that, we build the cost function J :

[0014] Where: represents the weight factor, They represent joint angle error and joint angular velocity error respectively; Finally, establish system state constraints and control input constraints:

[0015] According to the cost function J right y The model predictive controller is obtained by minimizing :

[0016] In the formula, k 1 、k 2 respectively represent the influence on the joint angle error and joint angular velocity, both of which are constants.

[0017] Based on the further optimization of the above scheme, the specific method of designing the sliding membrane surface and improving the reaching law in step S3 to obtain the adaptive improved integral sliding membrane device is: First, assuming that the desired angle is a quadratic differentiable function, the joint angle errors are defined as e , angular velocity error Angular acceleration error :

[0018] Where: They represent the desired angle, desired angular velocity, and desired angular acceleration of the joint respectively; After that, the adaptive integral terminal synovial function is established:

[0019]

[0020] Where: It represents the integral term coefficient, which determines the influence of the integral term on the synovial function; represents the exponential parameter; , It represents the sensitivity of the adjustment control to the error change rate, both of which are constants; m、n They work together to adjust the characteristics of the synovial function to adapt to the nonlinearity and uncertainty of the manipulator system and improve the robustness of the control. Both are constants; but Derivation :

[0021] make , get the equivalent control torque :

[0022] Then, considering eliminating the influence of total disturbance, an improved reaching law is established based on the exponential reaching law:

[0023] Where: s = s ISMC , represents the designed synovial surface; , indicating that when s As it increases, the approximate linear interval range decreases, and the hyperbolic tangent function exist s When it is smaller, it tends to be saturated; It represents the coefficient in the exponential convergence law and its influence on the convergence speed; k It represents the coefficient of the linear approach term, which determines the influence of the linear approach part on . Its value will affect the motion characteristics and chattering of the system on the sliding surface. N represents a constant parameter, whose value can affect the approach speed; Building a robust controller based on improved reaching law and adaptive techniques:

[0024] Finally, the total torque of the system under adaptive integral sliding film control is obtained:

[0025] but:

[0026] Where: v ISMC Represents the control variable of the sliding mode controller.

[0027] Based on further optimization of the above solution, the improved integral sliding film controller finally obtained in step S3 is: .

[0028] Based on the further optimization of the above scheme, the stability of the system is analyzed in step S4, and the specific method of determining the control law according to the analysis result is as follows: Building stability functions V(x) :

[0029] Where: M represents the Coriolis force and centrifugal force matrix; like , then the equilibrium point of the system x is asymptotically stable.

[0030] The following are the technical effects of the solution of the present invention: The present invention firstly utilizes model predictive control to achieve effective optimization of the prediction of future system states, thereby improving the accuracy and response speed of control; then, an adaptive integral sliding mode control model is obtained by combining the sliding surface and the improved convergence law, which effectively enhances the robustness of the system in the face of modeling errors and external disturbances, and ensures that the system state can converge stably. At the same time, based on sliding mode control, this control method reduces the complexity of engineering implementation by ensuring the stability of the system through a stability analysis method; finally, the improved controller can achieve higher trajectory tracking accuracy and better dynamic performance, allowing the robot to maintain excellent working performance in a changing environment, thereby completing fast, accurate, and effective robot trajectory tracking, which not only reduces the errors caused by external environmental interference during the tracking process, but also improves efficiency and reduces the amount of data, making it easier for this method to be applied to robot trajectory tracking control in different fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Flow chart of the robot arm trajectory tracking control method in an embodiment of the present invention.

[0032] Figure 2It is a schematic diagram of a robot arm trajectory tracking control method with improved integral sliding mode control in an embodiment of the present invention.

[0033] Figure 3 It is a schematic diagram of the position tracking curve of the joint without considering the uncertainty in the embodiment of the present invention; wherein, Figure 3 (a) is a schematic diagram of the position tracking curve of the first joint. Figure 3 (b) is a schematic diagram of the position tracking curve of the second joint.

[0034] Figure 4 Schematic diagram of the tracking error curve of the joint without considering the uncertainty in the embodiment of the present invention; wherein, Figure 4 (a) is a schematic diagram of the tracking error curve of the first joint. Figure 4 (b) is a schematic diagram of the tracking error curve of the second joint.

[0035] Figure 5 It is a schematic diagram of the position tracking curve of the joint in the case of considering the uncertainty in the embodiment of the present invention; wherein, Figure 5 (a) is a schematic diagram of the position tracking curve of the first joint. Figure 5 (b) is a schematic diagram of the position tracking curve of the second joint.

[0036] Figure 6 This is a schematic diagram of a tracking error curve of a joint considering uncertainties in an embodiment of the present invention; wherein: Figure 6 (a) is a schematic diagram of the tracking error curve of the first joint. Figure 6 (b) is a schematic diagram of the tracking error curve of the second joint.

[0037] Figure 7 Schematic diagram of the simplified structure of a two-degree-of-freedom robotic arm in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0039] Embodiment 1: A robot arm trajectory tracking control method based on improved integral sliding film control, referring to Figure 1 As shown, including: Step S1: Establish a dynamic model of the robotic arm system, specifically: Taking into account the influence of uncertain factors such as coupling, noise and external interference on the manipulator model, the dynamic equation of the U-link rigid manipulator is established using the Lagrange equation method:

[0040] Where: ,and Represent the joints of the robot arm 1、2、…、u The joint angles; ,and Represent the joints of the robot arm 1、2、…、u The joint angular velocity; ,and Represent the joints of the robot arm 1、2、…、u The joint angular acceleration of ,and Represent the joints of the robot arm 1、2、…、u The driving torque, i.e. represents the control torque vector; represents the inertial mass matrix of the system, Represents the Coriolis force and centrifugal force matrix, represents the joint gravity matrix ( ); Represents external unknown disturbance; ( and Respectively In a certain proportional relationship) represents the uncertain but bounded part of the system and satisfies:

[0041] assumed:

[0042] but:

[0043] Therefore, the dynamic model of the robotic arm system V for: .

[0044] Step S2: Optimize and predict the future state of the robotic arm system through model predictive control, specifically: First, establish the following second-order system:

[0045] Among them: state variables ; Output vector y=q ; represents the control vector; Then, in t At this moment, according to the current state x(t) , the backward prediction time step is h ,get:

[0046] In the formula, v MPC represents the control quantity of the model predictive controller; After that, we build the cost function J :

[0047] Where: represents the weight factor, They represent joint angle error and joint angular velocity error respectively; Finally, establish system state constraints and control input constraints:

[0048] According to the cost function J right y The model predictive controller is obtained by minimizing :

[0049] In the formula, k 1 、k 2 respectively represent the influence on the joint angle error and joint angular velocity, both of which are constants.

[0050] Step S3, design the sliding film surface and improve the reaching law to obtain an adaptive improved integral sliding film controller (such as Figure 2 ), specifically: First, assuming that the desired angle is a quadratic differentiable function, the joint angle errors are defined as e , angular velocity error Angular acceleration error :

[0051] Where: They represent the desired angle, desired angular velocity, and desired angular acceleration of the joint respectively; After that, the adaptive integral terminal synovial function is established:

[0052]

[0053] Where: It represents the integral term coefficient, which determines the influence of the integral term on the synovial function; represents the exponential parameter; , It represents the sensitivity of the adjustment control to the error change rate, both of which are constants; m、nThey work together to adjust the characteristics of the synovial function to adapt to the nonlinearity and uncertainty of the manipulator system and improve the robustness of the control. Both are constants; but Derivation :

[0054] make , get the equivalent control torque :

[0055] Then, considering eliminating the influence of total disturbance, an improved reaching law is established based on the exponential reaching law:

[0056] Where: s = s ISMC , represents the designed synovial surface; , indicating that when s As it increases, the approximate linear interval range decreases, and the hyperbolic tangent function exist s When it is smaller, it tends to be saturated; It represents the coefficient in the exponential convergence law and its influence on the convergence speed; k It represents the coefficient of the linear approach term, which determines the influence of the linear approach part on . Its value will affect the motion characteristics and chattering of the system on the sliding surface. N represents a constant parameter, whose value can affect the approach speed; Building a robust controller based on improved reaching law and adaptive techniques:

[0057] Finally, the total torque of the system under adaptive integral sliding film control is obtained:

[0058] but:

[0059] Where: v ISMC Represents the control variable of the sliding mode controller.

[0060] The improved integral sliding film controller finally obtained is: .

[0061] Step S4: Analyze the stability of the system and determine the control law according to the analysis results. The specific method is as follows: Building stability functions V(x) :

[0062] Where: M represents the Coriolis force and centrifugal force matrix; like , then the equilibrium point of the system x is asymptotically stable.

[0063] Step S5, constructing a control model combining an improved integral sliding film controller and a robotic arm; Step S6: Realize robot arm trajectory tracking control by selecting system parameters, expected trajectory information, and disturbance information: An improved controller composed of sliding surface, improved reaching law, adaptive integral sliding mode control and model predictive control is constructed to perform trajectory tracking control on the controlled object robot arm. The desired trajectory information and disturbance information are input, and the robot arm is enabled through the improved integral sliding film control method, so that the robot arm can accurately track the input signal and achieve smooth operation of the desired trajectory.

[0064] Embodiment 2: As a preferred embodiment of the present invention, based on the scheme of embodiment 1, in step S5, a control model combining an improved integral synovial controller and a robotic arm is constructed based on a two-degree-of-freedom robotic arm system model, and a simulation experiment is performed; the two-degree-of-freedom robotic arm system is referred to Figure 7 As shown: Among them, m 1 、m 2 represents the mass of the first connecting rod and the second connecting rod respectively, l 1 、l 2 respectively represent the length of the first connecting rod and the second connecting rod, q 1 、q 2 represents the joint angles of the first link and the second link respectively, and g represents the weight acceleration. The expressions of the parameters of the dynamic equation of the robot arm are:

[0065] in:

[0066]

[0067]

[0068] set up: m 1 =1kg,m 2 =1kg, l 1 =1m，l 2 =0.8m, b 1 =0.5m, b 2 =0.4m, g=9.8N / kg ; At the same time, set the system controller parameters, specifically: , , , , , , , , , , , ; Set the initial angle of the system , initial angular velocity They are:

[0069] Tracking the expected trajectory for:

[0070] The robot arm trajectory tracking is performed without considering the uncertainty and with considering the uncertainty: A. Do not consider uncertainties: External interference d for: N·m ; The simulation results are shown in the figure below. Without considering the uncertainties, this embodiment and the model predictive control method (i.e., MPC) alone can both achieve good trajectory tracking effects. However, the method in this embodiment takes less time for position tracking and velocity tracking, and can reach the desired trajectory faster; while the traditional model predictive control method takes some time to track, and the tracking error is large. From the simulation results, it can be seen that the maximum tracking error of the first joint under the model predictive control method is 0.49998 rad, and the maximum tracking error of the second joint is 0.24789 rad; while the maximum tracking error of the first joint of the method used in this embodiment is 0.0006485 rad, and the maximum tracking error of the second joint is 0.000001003 rad, and the tracking error is significantly lower than that of the model predictive control method.

[0071] B. Consider uncertainties: External interference d for:

[0072] Set all parameters to have percentages. H The uncertainty (in this example, H=20% ),but:

[0073] The simulation results are shown in the figure below. Under the premise of uncertainty, the model predictive control method (MPC) cannot track the trajectory, but the method in this embodiment can still track it well; it can be clearly seen from the figure that although the model predictive control method eventually tracks the speed curve, it has been in a vibrating state before 4s, while the method in this embodiment is affected by the initial value and has only a small amount of fluctuation before 0.5s, but the tracking has been in a stable state after 0.5s.

Claims

1. A robot arm trajectory tracking control method with improved integral synovial control, characterized in that: include: Step S1, establishing a dynamic model of the robotic arm system; Step S2, optimizing and predicting the future state of the robotic arm system through model predictive control; Step S3, designing a sliding film surface and improving the reaching law to obtain an adaptive improved integral sliding film controller; Step S4, analyzing the stability of the system and determining the control law according to the analysis results; Step S5, constructing a control model combining an improved integral sliding film controller and a robotic arm; Step S6: Realize robot arm trajectory tracking control by selecting system parameters, expected trajectory information, and disturbance information.

2. The robot arm trajectory tracking control method of improved integral synovial control according to claim 1 is characterized in that: The specific method for establishing the dynamic model of the robotic arm system in step S1 is: The Lagrange equation method is used to establish the dynamic equation of the u-link rigid manipulator: Where: ,and Represent the joints of the robot arm 1、2、…、u The joint angles; ,and Represent the joints of the robot arm 1、2、…、u The joint angular velocity; ,and Represent the joints of the robot arm 1、2、…、u The joint angular acceleration of ,and Represent the joints of the robot arm 1、2、…、u The driving torque; represents the inertial mass matrix of the system, Represents the Coriolis force and centrifugal force matrix, represents the joint gravity matrix; Represents external unknown disturbance; satisfy: assumed: but: Therefore, the dynamic model of the robotic arm system V for: 。 3. The robot arm trajectory tracking control method of improved integral synovial control according to claim 1 or 2, characterized in that: The specific method for optimizing and predicting the future state of the robotic arm system by model predictive control in step S2 is: First, establish the following second-order system: Among them: state variables ; Output vector y=q ; represents the control vector; Then, in t At this moment, according to the current state x(t) , the backward prediction time step is h ,get: In the formula, v MPC represents the control quantity of the model predictive controller; After that, we build the cost function J : Where: represents the weight factor, They represent joint angle error and joint angular velocity error respectively; Finally, establish system state constraints and control input constraints: According to the cost function J right y The model predictive controller is obtained by minimizing : In the formula, k 1 、k 2 respectively represent the impact on joint angle error and joint angular velocity.

4. The robot arm trajectory tracking control method of improved integral synovial control according to claim 1 or 3, characterized in that: The specific method of designing the sliding membrane surface and improving the reaching law in step S3 to obtain the adaptive improved integral sliding membrane device is: First, assuming that the desired angle is a quadratic differentiable function, the joint angle errors are defined as e , angular velocity error Angular acceleration error : Where: They represent the desired angle, desired angular velocity, and desired angular acceleration of the joint respectively; After that, the adaptive integral terminal synovial function is established: Where: It represents the integral term coefficient, which determines the influence of the integral term on the synovial function; represents the exponential parameter; , Indicates the sensitivity of the adjustment control to the rate of change of the error; m、n They work together to adjust the characteristics of the synovial function to adapt to the nonlinearity and uncertainty of the manipulator system and improve the robustness of the control; but Derivation : make , get the equivalent control torque : Then, considering eliminating the influence of total disturbance, an improved reaching law is established based on the exponential reaching law: Where: s = s ISMC , represents the designed synovial surface; , indicating that when s As it increases, the approximate linear interval range decreases, and the hyperbolic tangent function exist s When it is small, it tends to be saturated; It represents the coefficient in the exponential convergence law and its influence on the convergence speed; k represents the coefficient of the linear approximation term; N represents a constant parameter; Building a robust controller based on improved reaching law and adaptive techniques: Finally, the total torque of the system under adaptive integral sliding film control is obtained: but: Where: v ISMC Represents the control variable of the sliding mode controller.

5. The robot arm trajectory tracking control method of improved integral synovial control according to claim 4 is characterized in that: The improved integral sliding film controller finally obtained in step S3 is: 。 6. The robot arm trajectory tracking control method of improved integral synovial control according to claim 5, characterized in that: In step S4, the stability of the system is analyzed, and the specific method of determining the control law according to the analysis result is as follows: Building stability functions V(x) : Where: M represents the Coriolis force and centrifugal force matrix; like , then the equilibrium point of the system x is asymptotically stable.

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