Inequality constraint control method for friction stir welding robots with complex curved surfaces

Abstract

This invention discloses an inequality constraint control method for friction stir welding robots operating on complex curved surfaces. The method includes: acquiring the angular displacement of the robot's drive motor and the input torque of the load driven by the drive motor; and controlling the drive motor based on the angular displacement and input torque using a pre-established inequality constraint control model. This method, utilizing the pre-established inequality constraint control model, controls the drive motor based on its angular displacement and input torque. It enables the control focus to be on trajectory tracking when the angular displacement moves away from the boundary, guiding the angular displacement away from the boundary and towards the desired trajectory. This method exhibits high stability and robustness.

Description

Technical Field

[0001] This invention relates to the field of robot system dynamics control, and in particular to an inequality constraint control method for a friction stir welding robot with complex curved surfaces. Background Technology

[0002] In the rapid development of industrial automation and intelligent manufacturing technologies, industrial robots, as core execution units, directly impact production line efficiency and product quality. Especially in cutting-edge fields such as semiconductor packaging and precision medical device manufacturing, unprecedented demands are placed on the control precision and dynamic response capabilities of robot drive motors (drive motors and harmonic reducers can form the robot's joint modules). The complexity of robot drive motors inherently makes them prone to uncertainties. As a multivariable, highly interconnected, time-varying nonlinear system, achieving precise and efficient trajectory tracking via drive motors is a significant challenge. Summary of the Invention

[0003] This invention aims to at least partially solve one of the technical problems in related technologies. To this end, one objective of this invention is to propose an inequality constraint control method for friction stir welding robots with complex curved surfaces. This method enables the control focus to be placed on trajectory tracking when the angular displacement moves away from the boundary, allowing the angular displacement to move away from the boundary and towards the desired trajectory. It has the advantages of high stability and strong robustness.

[0004] A second objective of this invention is to provide a computer-readable storage medium.

[0005] The third objective of this invention is to provide a controller.

[0006] To achieve the above objectives, a first aspect of the present invention proposes an inequality constraint control method for a friction stir welding robot with complex curved surfaces. The method includes: acquiring the angular displacement of the drive motor of the friction stir welding robot and the input torque of the load driven by the drive motor; and controlling the drive motor according to the angular displacement and the input torque using a pre-established inequality constraint control model. The inequality constraint control model is determined by a dynamic model of the mechanical system containing the drive motor with parameter uncertainties, a second-order constraint form of the servo constraints of the mechanical system containing the drive motor, and constraint forces of the mechanical system containing the drive motor under uncertainties. The dynamic model of the mechanical system containing the drive motor with parameter uncertainties is constructed based on the dynamic model of the drive motor under inequality constraints. The second-order constraint form of the servo constraints of the mechanical system containing the drive motor is constructed based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainties under sufficiently smooth conditions. The dynamic model of the drive motor under inequality constraints is obtained by limiting the displacement of the drive motor within a preset stroke range while converting the displacement of the drive motor from a bounded domain to an unbounded domain based on the dynamic model of the drive motor.

[0007] The inequality constraint control method for friction stir welding robots with complex curved surfaces according to embodiments of the present invention utilizes a pre-established inequality constraint control model to control the drive motor based on the angular displacement and input torque of the drive motor. This method enables the control focus to be placed on trajectory tracking when the angular displacement moves away from the boundary, allowing the angular displacement to move away from the boundary and towards the desired trajectory. It has the advantages of high stability and strong robustness.

[0008] Furthermore, the inequality constraint control method for friction stir welding robots with complex curved surfaces proposed in the above embodiments of the present invention may also have the following additional technical features:

[0009] According to an embodiment of the present invention, the process of constructing the inequality constraint control model includes: based on the dynamic model of the drive motor, limiting the displacement of the drive motor within a preset stroke range, and simultaneously converting the displacement of the drive motor from a bounded domain to an unbounded domain to obtain a dynamic model of the drive motor under the inequality constraint; based on the dynamic model of the drive motor under the inequality constraint, constructing a dynamic model of the mechanical system containing the drive motor with parameter uncertainty, and constructing a second-order constraint form of the servo constraint of the mechanical system containing the drive motor under sufficiently smooth conditions based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainty, and constructing the constraint force of the mechanical system containing the drive motor under uncertainty based on the second-order constraint form of the servo constraint of the mechanical system containing the drive motor; based on the characteristics of the mechanical system containing the drive motor and the characteristics of the servo constraint, constructing the assumption requirements; based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainty, the second-order constraint form of the servo constraint of the mechanical system containing the drive motor, and the constraint force of the mechanical system containing the drive motor under uncertainty, decomposing the uncertain part in the dynamic model of the mechanical system containing the drive motor with parameter uncertainty, and establishing the inequality constraint control model according to the assumption requirements.

[0010] According to an embodiment of the present invention, the expression for the dynamic model of the drive motor under the inequality constraints is:

[0011]

[0012]

[0013]

[0014]

[0015] in, Indicates time, Indicates angular displacement The corresponding unconstrained state variables, express The derivative with respect to time corresponds to the angular velocity. Transformation form, express The second derivative with respect to time corresponds to angular acceleration. Transformation form, The functional form representing the inertia matrix of the mechanical system containing the drive motor after transformation. The functional form representing the Coriolis force and centrifugal force terms. The functional form representing gravity, friction, and transformation terms. This represents the input torque of the load. This represents the inertia matrix of the mechanical system containing the drive motor after transformation. This represents the inertia matrix of the drive motor. Represents Coriolis force and centrifugal force. This represents the nonlinear damping torque. This represents gravity, friction, and conversion terms. Represents nonlinear frictional torque. This represents the inertia of the drive motor. This indicates the upper limit of the angular displacement of the drive motor rotor. This represents the lower limit of the angular displacement of the drive motor rotor.

[0016] According to one embodiment of the present invention, the expression for the dynamic model of the mechanical system containing the drive motor with parameter uncertainties is as follows:

[0017]

[0018] in, Indicates time, This represents the angular displacement of the drive motor rotor. This represents the angular velocity of the drive motor rotor. This represents the angular acceleration of the drive motor rotor. This represents the uncertainty parameter of the mechanical system in which the drive motor is located. This represents the input torque of the load. This represents the inertia matrix of the mechanical system containing the drive motor after transformation. Represents Coriolis force and centrifugal force. Represents nonlinear frictional force. It represents gravity, friction, and conversion terms.

[0019] According to one embodiment of the present invention, the expression of the second-order constraint form of the servo constraint of the mechanical system in which the drive motor is located is as follows:

[0020]

[0021] in, Indicates the index of the drive motor. This represents the total number of degrees of freedom in the mechanical system containing the drive motor. This represents the angular displacement of the drive motor rotor. Indicates time, Represents the acceleration constraint transformation matrix The line, number Column elements, Indicates the first The angular acceleration of the rotor of the drive motor. Indicates the first The generalized coordinate components corresponding to each servo constraint.

[0022] According to one embodiment of the present invention, the expression for the constraint force of the mechanical system containing the drive motor under uncertain conditions is as follows:

[0023]

[0024] in, This represents the ideal constraint force required by the mechanical system containing the drive motor. Indicates angular displacement dependent on generalized coordinates and time The nominal inertia matrix of the mechanical system containing the drive motor after conversion. express The square root matrix, express The inverse matrix, Indicates angular displacement dependent on generalized coordinates and time The acceleration constraint transformation matrix, Indicates angular displacement dependent on generalized coordinates angular velocity and time State variables, Indicates angular displacement dependent on generalized coordinates angular velocity and time Coriolis force and centrifugal force, Indicates angular displacement dependent on generalized coordinates and time The inverse inertial matrix of the mechanical system containing the drive motor after transformation. Indicates angular displacement dependent on generalized coordinates and time The nominal gravity, friction, and conversion terms. Indicates angular displacement dependent on generalized coordinates and time The nominal nonlinear frictional force.

[0025] According to one embodiment of the present invention, the assumption requires at least the following:

[0026] (1) For any ,as well as , ,in, This represents the uncertainty parameter of the mechanical system in which the drive motor is located. express Take any constant, Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The converted inertia matrix of the mechanical system containing the drive motor;

[0027] (2) They exhibit consistency in terms of constraints, among which, Indicates angular displacement dependent on generalized coordinates angular velocity and time The acceleration constraint transformation matrix, express The derivative matrix, Indicates angular displacement dependent on generalized coordinates angular velocity and time Expected acceleration;

[0028] (3) For any given Acceleration constraint transformation matrix Full rank, reversible;

[0029] (4) Given the assumptions in (3), for a given positive definite weight matrix ,make:

[0030]

[0031] in, Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The weighted acceleration energy function used for optimized control. Indicates the definition symbol, Indicates angular displacement dependent on generalized coordinates and time The positive definite weighted matrix, express The transpose of the matrix, Indicates angular displacement dependent on generalized coordinates and time The acceleration constraint transformation matrix, Indicates angular displacement dependent on generalized coordinates and time The nominal inertia matrix of the mechanical system containing the drive motor after conversion. Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The feedback control gain matrix, Indicates angular displacement dependent on generalized coordinates and time The drive motor has an inertia matrix that does not exhibit uncertainty. Let the positive definite weight matrix have the following properties: This makes it possible for all All of them have:

[0032]

[0033] in, Represents the smallest number. Represents the smallest eigenvalue. Indicates the number of servo constraints. yes transpose, Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The weighted acceleration energy function used for optimized control. Uncertainty boundary parameters of inertial systems The estimated value, in the absence of uncertainty, .

[0034] According to an embodiment of the present invention, the inequality constraint control model for:

[0035]

[0036] in,

[0037]

[0038]

[0039]

[0040] in, ,

[0041]

[0042]

[0043] choose , so that:

[0044]

[0045] in, This represents the angular displacement of the drive motor rotor. This represents the angular velocity of the drive motor rotor. Indicates time, Represents the ideal constraint term. This represents the initial condition compensation term. This represents the uncertainty suppression term. This represents the ideal constraint force required by the mechanical system containing the drive motor. This represents the control gain coefficient. Indicates angular displacement dependent on generalized coordinates and time The nominal inertia matrix of the mechanical system containing the drive motor after conversion. express The transpose of the matrix, Indicates angular displacement dependent on generalized coordinates and time The acceleration constraint transformation matrix, Represents a positive definite weight matrix The reverse, Represents the error vector. Indicates angular displacement dependent on generalized coordinates angular velocity and time The weighted terms of the Lyapunov function, Indicates angular displacement dependent on generalized coordinates angular velocity and time The damping coefficient, Indicates angular displacement dependent on generalized coordinates angular velocity and time The uncertainty boundary parameters of the mechanical system in which the drive motor is located. Indicates angular displacement dependent on generalized coordinates and time Uncertainty boundary parameters of inertial systems The estimated value, Represents positive numbers. Indicates angular displacement dependent on generalized coordinates angular velocity and time The error vector, Indicates the reference trajectory term. This represents the acceleration constraint transformation matrix. The inertia matrix representing the absence of uncertainty in the drive motor. The uncertain part, The inertia matrix represents the inertia matrix of the drive motor, indicating that there is no uncertainty. Represents Coriolis force and centrifugal force. This represents gravity, friction, and conversion terms. Representing Coriolis force and centrifugal force The uncertain part, Representing gravity, friction, and conversion terms The uncertain part.

[0046] To achieve the above objectives, a second aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the inequality constraint control method for a friction stir welding robot with complex curved surfaces as described above.

[0047] To achieve the above objectives, a third aspect of the present invention provides a controller, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the inequality constraint control method for a friction stir welding robot with complex curved surfaces as described above.

[0048] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0049] Figure 1 This is a flowchart of an inequality constraint control method for a friction stir welding robot with complex curved surfaces, according to an embodiment of the present invention.

[0050] Figure 2 This is a schematic diagram of a joint module of a friction stir welding robot according to an embodiment of the present invention;

[0051] Figure 3 This is a flowchart of constructing an inequality constraint control model according to an embodiment of the present invention;

[0052] Figure 4 This is a process for constructing an inequality constraint control model according to a specific embodiment of the present invention. Figure 1 ;

[0053] Figure 5 This is a comparison chart of simulation results of a sinusoidal signal under different algorithms according to the present invention;

[0054] Figure 6 This is a comparison chart of simulation results of a step signal under different algorithms according to the present invention;

[0055] Figure 7 This is a process for constructing an inequality constraint control model according to a specific embodiment of the present invention. Figure 2 ;

[0056] Figure 8 This is a structural block diagram of the controller according to an embodiment of the present invention. Detailed Implementation

[0057] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0058] It should be noted that, regarding the control problem of drive motors, researchers both domestically and internationally have successively developed various control methods and achieved certain results. These studies include proportional-integral-derivative (PID) control, H-∞ control, adaptive control, fuzzy control, sliding mode control, neural network control, and their combined application. Each of these control methods has its own characteristics and can effectively control different objects.

[0059] However, the problem of inequality constraints on drive motors arising from safety, physical limitations, and other requirements remains to be addressed. It should be noted that drive motor inequality constraints are at least one constraint, represented by inequality notation, present during the design, control, or optimization of the drive motor. These inequality constraints are used to ensure that the rotation angle of the joint is within a specific operating range, i.e., that the angular displacement of the joint is within well-defined boundaries.

[0060] To address the aforementioned technical problems, embodiments of the present invention provide an inequality constraint control method for a friction stir welding robot with complex curved surfaces. The inequality constraint control method for a friction stir welding robot with complex curved surfaces according to embodiments of the present invention will be described in detail below with reference to the accompanying drawings and specific implementation details.

[0061] Figure 1 This is a flowchart of an inequality constraint control method for a friction stir welding robot with complex curved surfaces, according to an embodiment of the present invention. Figure 1 As shown, the inequality constraint control method for friction stir welding robots with complex curved surfaces may include:

[0062] S101, collects the angular displacement of the drive motor of the friction stir welding robot and the input torque of the load driven by the drive motor;

[0063] S102, using a pre-established inequality constraint control model, the drive motor is controlled based on angular displacement and input torque. The inequality constraint control model is determined by the dynamic model of the mechanical system containing the drive motor with parameter uncertainties, the second-order constraint form of the servo constraints of the mechanical system containing the drive motor, and the constraint forces of the mechanical system containing the drive motor under uncertainties. The dynamic model of the mechanical system containing the drive motor with parameter uncertainties is constructed based on the dynamic model of the drive motor under inequality constraints. The second-order constraint form of the servo constraints of the mechanical system containing the drive motor is constructed based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainties under sufficiently smooth conditions. The dynamic model of the drive motor under inequality constraints is obtained by limiting the displacement of the drive motor within a preset stroke range while converting the displacement of the drive motor from a bounded domain to an unbounded domain, based on the dynamic model of the drive motor.

[0064] Specifically, when controlling the drive motor of the friction stir welding robot, the angular displacement of the drive motor can be collected. and the input torque of the load driven by the drive motor Using a pre-established inequality constraint control model, based on angular displacement... and input torque Control the drive motor.

[0065] It should be noted that the inequality constraint control model in this embodiment of the invention is determined by the dynamic model of the mechanical system containing the drive motor with parameter uncertainties, the second-order constraint form of the servo constraints of the mechanical system containing the drive motor, and the constraint forces of the mechanical system containing the drive motor under uncertainties. Therefore, when controlling the drive motor using the pre-established inequality constraint control model, the drive motor simultaneously satisfies the requirements of inequality constraints and accurate trajectory tracking under the influence of uncertainties. When the angular displacement is far from the boundary, the control focuses on trajectory tracking. When the angular displacement is close to the boundary, the focus of the control is to generate greater gain, so that the state moves away from the boundary and towards the desired trajectory.

[0066] The inequality constraint control method for friction stir welding robots with complex curved surfaces in this invention utilizes a pre-established inequality constraint control model to control the drive motor based on the angular displacement and input torque of the drive motor. This method enables the control focus to be placed on trajectory tracking when the angular displacement moves away from the boundary, allowing the angular displacement to move away from the boundary and towards the desired trajectory. It has the advantages of high stability and strong robustness.

[0067] The drive motor in this embodiment of the invention can be a permanent magnet synchronous motor (PMSM). For example, a permanent magnet synchronous motor and a harmonic reducer can form the joint module of a friction stir welding robot, see [link to relevant documentation]. Figure 2 The joint modules of the friction stir welding robot are controlled by controlling the drive motors, such as permanent magnet synchronous motors. It should be noted that the friction stir welding robot has multiple joint modules, i.e., multiple drive motors.

[0068] In one embodiment of the present invention, such as Figure 3 As shown, the process of constructing an inequality constraint control model may include:

[0069] S201, based on the dynamic model of the drive motor, restricts the displacement of the drive motor within a preset stroke range, and transforms the displacement of the drive motor from a bounded domain to an unbounded domain, thus obtaining the dynamic model of the drive motor under inequality constraints.

[0070] Specifically, based on the dynamic model of the drive motor, the displacement of the drive motor is restricted within a preset stroke range, and the displacement of the drive motor is transformed from a bounded domain to an unbounded domain, resulting in a dynamic model of the drive motor under inequality constraints. It should be noted that the constructed dynamic model of the drive motor under inequality constraints is the foundation for constructing the dynamic model of the drive motor containing parameter uncertainties.

[0071] S202. Based on the dynamic model of the drive motor under inequality constraints, construct a dynamic model of the mechanical system containing the drive motor with parameter uncertainties. Based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainties, construct the second-order constraint form of the servo constraint of the mechanical system containing the drive motor under fully smooth conditions. Based on the second-order constraint form of the servo constraint of the mechanical system containing the drive motor, construct the constraint force of the mechanical system containing the drive motor under uncertain conditions.

[0072] Specifically, based on the dynamic model of the drive motor under inequality constraints, a dynamic model of the mechanical system containing the drive motor with parameter uncertainties is constructed. Based on this dynamic model, a second-order constraint form of the servo constraints for the mechanical system with parameter uncertainties is constructed under sufficiently smooth conditions. Finally, the constraint forces of the mechanical system under uncertainties are constructed based on this second-order constraint form.

[0073] S203, based on the characteristics of the mechanical system where the drive motor is located and the servo constraint characteristics, constructs the assumption requirements.

[0074] Specifically, certain assumptions and requirements are put forward regarding the characteristics of the mechanical system and the servo constraint characteristics of the drive motor.

[0075] S204. Based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainty, the second-order constraint form of the servo constraint of the mechanical system containing the drive motor, and the constraint force of the mechanical system containing the drive motor under uncertainty, the uncertainty part in the dynamic model of the mechanical system containing the drive motor with parameter uncertainty is decomposed, and an inequality constraint control model is established according to the assumption requirements.

[0076] Specifically, the constructed dynamic model of the mechanical system containing the drive motor with parameter uncertainties forms the basis for establishing the inequality constraint control model. The inequality constraint control model established in this embodiment of the invention can achieve robust constraint tracking control oriented towards uncertainty. Analyzing and effectively decomposing the uncertain parameters in the dynamic model of the mechanical system containing the drive motor with parameter uncertainties is the benchmark for model-based inequality constraint control design to handle uncertainties.

[0077] In one embodiment of the present invention, based on the dynamic model of the drive motor, the displacement of the drive motor is limited to the stroke range, resulting in a joint dynamic model under inequality constraints:

[0078]

[0079] in, Indicates time, This represents the angular displacement of the drive motor rotor. This represents the angular velocity of the drive motor rotor. This represents the angular acceleration of the drive motor rotor. This represents the inertial torque of the drive motor. This represents the nonlinear damping term of the drive motor (including Coriolis force, centrifugal force, and viscous friction). Represents nonlinear frictional torque. This represents the input torque of the load. Wherein, , This represents the lower limit of the angular displacement of the drive motor rotor. This indicates the upper limit of the angular displacement of the drive motor rotor.

[0080] When transforming the displacement of the drive motor from a bounded domain to an unbounded domain, let:

[0081]

[0082]

[0083] in, Indicates angular displacement The corresponding unconstrained state variables (angular displacement) (The unconstrained state variables obtained after being restricted to a preset travel range). Indicates angular displacement The corresponding unconstrained expected trajectory (including angular displacement) The unconstrained expected trajectory obtained after conversion within a preset travel range. express The target location or desired trajectory, when hour, ;when , ;when , .

[0084] For all (Indicates angular displacement) (can take any real number), has We can obtain:

[0085]

[0086] Taking the first derivative of formula (4) yields:

[0087]

[0088] Taking the second derivative of formula (4) yields:

[0089]

[0090] Therefore, substituting formulas (5) and (6) into formula (1) yields:

[0091]

[0092] After simplifying formula (7), we can obtain:

[0093]

[0094] in, This represents the original control input (the input torque of the load). Nonlinear scaling transformation.

[0095] Therefore, the dynamic model of the drive motor under inequality constraints can be expressed as:

[0096]

[0097]

[0098]

[0099]

[0100] in, Indicates time, Indicates angular displacement The corresponding unconstrained state variables, express The derivative with respect to time corresponds to the angular velocity. Transformation form, express The second derivative with respect to time corresponds to angular acceleration. Transformation form, The functional form representing the inertia matrix of the mechanical system containing the drive motor after transformation. The functional form representing the Coriolis force and centrifugal force terms. The functional form representing gravity, friction, and transformation terms. This represents the input torque of the load. This represents the inertia matrix of the mechanical system containing the drive motor after transformation. This represents the inertia matrix of the drive motor. Represents Coriolis force and centrifugal force. This represents the nonlinear damping torque. This represents gravity, friction, and conversion terms. Represents nonlinear frictional torque. This represents the inertia of the drive motor. This indicates the upper limit of the angular displacement of the drive motor rotor. This represents the lower limit of the angular displacement of the drive motor rotor.

[0101] In one embodiment of the present invention, such as Figure 4 As shown, when constructing a dynamic model of a drive motor with parameter uncertainties based on the dynamic model of the drive motor under inequality constraints, the geometric constraints are first handled by coordinate transformation, and then parameter uncertainties are introduced into the physical coordinate system to establish a robust dynamic model for the final control law design (i.e., a dynamic model of a drive motor with parameter uncertainties).

[0102] When using coordinate transformation to process geometric constraints, based on the unbounded domain transformation of inequality constraints, first define bounded constraints (i.e., formula (1)), then introduce coordinate transformation (i.e., formula (2)), and finally construct the dynamic model of the drive motor under the transformed inequality constraints (i.e., formula (9)).

[0103] When introducing parameter uncertainties into the mechanical system containing the drive motor in the physical coordinate system, the physical coordinate system and angular displacement are determined by reverting to the physical coordinate system and introducing parameter uncertainties. angular velocity and angular acceleration Then, the uncertainty parameters of the mechanical system in which the drive motor is located are introduced. And the uncertainty parameters of the mechanical system in which the drive motor is located. By embedding these components into each part of the dynamic model of the drive motor under inequality constraints (i.e., formula (9)), a dynamic model of the mechanical system containing the drive motor with parameter uncertainties is constructed:

[0104]

[0105] in, Indicates time, This represents the angular displacement of the drive motor rotor. This represents the angular velocity of the drive motor rotor. This represents the angular acceleration of the drive motor rotor. This represents the uncertainty parameter of the mechanical system in which the drive motor is located. This represents the input torque of the load. This represents the inertia matrix of the mechanical system containing the drive motor after transformation. Represents Coriolis force and centrifugal force. Represents nonlinear frictional force. It represents gravity, friction, and conversion terms.

[0106] like Figure 4 As shown, a second-order form of the servo constraint for the mechanical system containing the drive motor with parameter uncertainties is constructed based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainties:

[0107] Under sufficiently smooth conditions, the constraint equations of the mechanical system containing the drive motor are as follows:

[0108]

[0109] in, Indicates time, This represents the angular displacement of the drive motor rotor. This represents the position constraint transformation matrix (or Jacobian matrix of the position constraint) in the constraint equation of the drive motor. This represents the position constraint transformation vector in the constraint equation of the drive motor.

[0110] The performance of the second-order servo constraint is derived from the first-order constraint, as follows:

[0111]

[0112] in, This indicates the drive motor index (joint index). This represents the total number of degrees of freedom in the mechanical system containing the drive motor. This represents the angular displacement of the drive motor rotor. Indicates time, express The Middle Line 1 Column elements, The row index representing the servo constraint. Indicates the first The generalized coordinate components corresponding to each servo constraint Indicates the number of servo constraints.

[0113] For the time in formula (15) Differentiation yields:

[0114]

[0115] in, Indicates the index of the drive motor. This represents the total number of degrees of freedom in the mechanical system containing the drive motor. This represents the angular displacement of the drive motor rotor. Indicates time, express The Middle Line 1 Column elements, Indicates the first The generalized coordinate components corresponding to each servo constraint.

[0116] Formula (16) can be written as:

[0117]

[0118] in, Indicates the index of the drive motor. This represents the total number of degrees of freedom in the mechanical system containing the drive motor. This represents the angular displacement of the drive motor rotor. Indicates time, Represents the acceleration constraint transformation matrix The line, number Column elements, This represents the angular velocity of the drive motor rotor. Indicates the first The generalized velocity corresponding to each servo constraint.

[0119] Then, regarding the time in formula (17) Differentiation yields:

[0120]

[0121] in, Indicates the index of the drive motor. This represents the total number of degrees of freedom in the mechanical system containing the drive motor. This represents the angular displacement of the drive motor rotor. Indicates time, Represents the acceleration constraint transformation matrix The line, number Column elements, Indicates the first The angular velocity of the rotor of the drive motor. Indicates the first The angular acceleration of the rotor of the drive motor. Indicates the first The generalized velocity corresponding to each servo constraint.

[0122] Formula (18) can be written as:

[0123]

[0124] in, Indicates the index of the drive motor. This represents the total number of degrees of freedom in the mechanical system containing the drive motor. This represents the angular displacement of the drive motor rotor. Indicates time, Represents the acceleration constraint transformation matrix The line, number Column elements, Indicates the first The angular acceleration of the rotor of the drive motor. Indicates the first The generalized coordinate components corresponding to each servo constraint.

[0125] Formula (19) shows the second-order constraint representation of the servo constraint of the mechanical system in which the drive motor is located.

[0126] Based on the derivation results of formulas (14)-(19), the constraint equations of the mechanical system containing the drive motor are shown:

[0127]

[0128]

[0129] make , Indicates the number of servo constraints. This represents the total number of degrees of freedom in the mechanical system containing the drive motor. Indicates angular displacement dependent on generalized coordinates and time generalized speed, , Indicates angular displacement dependent on generalized coordinates angular velocity and time Expected acceleration, .

[0130] The constraint forces of the mechanical system containing the drive motor under uncertain conditions are as follows:

[0131]

[0132] in, This represents the ideal constraint force required by the mechanical system containing the drive motor. Indicates angular displacement dependent on generalized coordinates and time The nominal inertia matrix of the mechanical system containing the drive motor after conversion. express The square root matrix, express The inverse matrix, Indicates angular displacement dependent on generalized coordinates and time The acceleration constraint transformation matrix, Indicates angular displacement dependent on generalized coordinates angular velocity and time State variables, Indicates angular displacement dependent on generalized coordinates angular velocity and time Coriolis force and centrifugal force, Indicates angular displacement dependent on generalized coordinates and time The inverse inertial matrix of the mechanical system containing the drive motor after transformation. Indicates angular displacement dependent on generalized coordinates and time The nominal gravity, friction, and conversion terms. Indicates angular displacement dependent on generalized coordinates and time The nominal nonlinear frictional force.

[0133] It should be noted that, and It serves to map variables with different degrees of freedom and different inertial scales to the same energy space.

[0134] Based on the characteristics of the mechanical system containing the drive motor and the servo constraint characteristics, certain assumptions are proposed, including:

[0135] (1) For any ,as well as , ,in, This represents the uncertainty parameter of the mechanical system in which the drive motor is located. express It can take any constant. Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The converted inertia matrix of the mechanical system containing the drive motor;

[0136] (2) Formula (21) ( They exhibit consistency in terms of constraints, among which, Indicates angular displacement dependent on generalized coordinates angular velocity and time The acceleration constraint transformation matrix, express The derivative matrix, Indicates angular displacement dependent on generalized coordinates angular velocity and time Expected acceleration;

[0137] (3) For any given Acceleration constraint transformation matrix Full rank, thus indicating the product It is reversible;

[0138] (4) Given the assumptions in (3), for a given positive definite weight matrix ,make:

[0139]

[0140] in, Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The weighted acceleration energy function used for optimized control. Indicates the definition symbol, Indicates angular displacement dependent on generalized coordinates and time The positive definite weighted matrix, express The transpose of the matrix, Indicates angular displacement dependent on generalized coordinates and time The acceleration constraint transformation matrix, Indicates angular displacement dependent on generalized coordinates and time The nominal inertia matrix of the mechanical system containing the drive motor after conversion. Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The feedback control gain matrix, Indicates angular displacement dependent on generalized coordinates and time The drive motor has an inertia matrix that does not exhibit uncertainty. Let represent a positive definite weight matrix. There exists... This makes it possible for all All of them have:

[0141]

[0142] in, Represents the smallest number. Represents the smallest eigenvalue. Indicates the number of servo constraints. express transpose, Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The weighted acceleration energy function used for optimized control. Uncertainty boundary parameters of inertial systems The estimated value, in the absence of uncertainty, .

[0143] Since the boundaries of uncertainty have not yet been determined, Similarly, there is no definite value. In situations where there is no uncertainty in the system, one can choose... .

[0144] Under the above assumptions, and considering the uncertainties in the mechanical system containing the drive motor, the error presented in the control is: (Error vector).

[0145] Based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainty and the second-order constraint form of the servo constraint of the mechanical system containing the drive motor, the uncertainty part of formula (13) is decomposed, and an inequality constraint control model is established according to the above-established assumptions.

[0146] After analyzing formula (13), for , , and Decompose (for each item in formula (13)) , , , The constraints are decomposed into "nominal + uncertainty" to construct the subsequent robust constraint controller, as shown below:

[0147]

[0148] in, This represents the inertia matrix of the mechanical system containing the drive motor after transformation. This represents the nominal inertia matrix of the mechanical system containing the drive motor after conversion. This represents the uncertainty part of the inertia matrix of the mechanical system containing the drive motor after transformation. This represents the actual constraint force required by the mechanical system containing the drive motor. This represents the nominal actual constraint force required by the mechanical system containing the drive motor. This represents the nominal actual constraint force required by the mechanical system containing the drive motor. This represents the ideal constraint force required by the mechanical system containing the drive motor. This represents the nominal ideal constraint force required by the mechanical system containing the drive motor. The uncertainty of the ideal constraint force required by the mechanical system in which the drive motor is located. , and This refers to the nominal (known) part of the dynamic model of the mechanical system containing the drive motor, which has parameter uncertainties. , , For the uncertainty (unknown disturbance part) in the drive motor constraint system, and , , , , , All are continuous, let:

[0149]

[0150] in, The inertia matrix represents the inertia matrix of the drive motor, indicating that there is no uncertainty. This represents the nominal inertia inverse matrix of the mechanical system containing the drive motor after conversion. The inertia matrix representing the absence of uncertainty in the drive motor. The uncertain part, This represents the inverse inertia matrix of the mechanical system containing the drive motor after transformation. Represents the feedback control gain matrix. This represents the nominal inertia matrix of the mechanical system containing the drive motor after conversion. This represents the identity matrix. It should be noted that the drive motor does not have an uncertain inertia matrix. There is no inherent uncertainty. yes The uncertainty lies in the relationship between the actual inertia of the drive motor and its ideal model. Unknown deviations between them.

[0151] so:

[0152]

[0153] in, This represents the nominal inertia inverse matrix of the mechanical system containing the drive motor after conversion. The inertia matrix represents the inertia matrix of the drive motor, indicating that there is no uncertainty. The inertia matrix representing the absence of uncertainty in the drive motor. The uncertain part, This represents the feedback control gain matrix.

[0154] An inequality constraint control model is constructed based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainties (Equation (13)), the second-order constraint form of the servo constraint of the mechanical system containing the drive motor, and the constraint force of the mechanical system containing the drive motor under uncertainties (Equation (22)). :

[0155]

[0156] in,

[0157]

[0158]

[0159]

[0160] in, ,

[0161]

[0162]

[0163] choose , so that:

[0164]

[0165] in, This represents the angular displacement of the drive motor rotor. This represents the angular velocity of the drive motor rotor. Indicates time, Represents the ideal constraint term. This represents the initial condition compensation term. This represents the uncertainty suppression term. This represents the ideal constraint force required by the mechanical system containing the drive motor. This represents the control gain coefficient. Indicates angular displacement dependent on generalized coordinates and time The nominal inertia matrix of the mechanical system containing the drive motor after conversion. express The transpose of the matrix, Indicates angular displacement dependent on generalized coordinates and time The acceleration constraint transformation matrix, Represents a positive definite weight matrix The reverse, Represents the error vector. Indicates angular displacement dependent on generalized coordinates angular velocity and time The weighted terms of the Lyapunov function, Indicates angular displacement dependent on generalized coordinates angular velocity and time The damping coefficient, Indicates angular displacement dependent on generalized coordinates angular velocity and time The uncertainty boundary parameters of the mechanical system in which the drive motor is located. Indicates angular displacement dependent on generalized coordinates and time Uncertainty boundary parameters of inertial systems The estimated value, Represents positive numbers. Indicates angular displacement dependent on generalized coordinates angular velocity and time The error vector, Indicates the reference trajectory term. This represents the acceleration constraint transformation matrix. The inertia matrix representing the absence of uncertainty in the drive motor. The uncertain part, The inertia matrix represents the inertia matrix of the drive motor, indicating that there is no uncertainty. Represents Coriolis force and centrifugal force. This represents gravity, friction, and conversion terms. Representing Coriolis force and centrifugal force The uncertain part, Representing gravity, friction, and conversion terms The uncertain part.

[0166] The upper limit of the expression is precisely defined in formula (34) by choosing an arbitrarily small positive constant (an arbitrarily small parameter). High-performance constraints can be achieved, however, positive constants The value cannot be decreased indefinitely; control gain coefficient The choice of [specific factor] affects the convergence speed of the mechanical system containing the drive motor; a higher [specific factor]... A certain value can facilitate faster convergence, but it requires increased control expenditure. Therefore, it is necessary to choose an appropriate value based on actual requirements. value.

[0167] This invention provides an embodiment for a stability analysis of the constructed robust constraint tracking controller for uncertainty.

[0168] Specifically, the final uniform stability bound of the constructed uncertainty-oriented robust constraint tracking controller is analyzed using the Lyapunov function shown in Equation (35):

[0169]

[0170] in, Represents the Lyapunov function. Represents the error vector transpose, Represents a positive definite weight matrix. This represents the error vector.

[0171] For Lyapunov functions Taking the derivative, we get the following:

[0172]

[0173] in, This represents the time derivative of the Lyapunov function. Represents the error vector transpose, This represents the acceleration constraint transformation matrix. This represents the angular acceleration of the drive motor rotor. Represents generalized speed. This represents the inertia matrix of the mechanical system containing the drive motor after transformation. This represents the inverse inertia matrix of the mechanical system containing the drive motor after transformation. Represents Coriolis force and centrifugal force. This represents gravity, friction, and conversion terms. Represents nonlinear frictional force. Represents the control weighting matrix. This represents the control weighted inverse matrix. Represents the ideal constraint term. This represents the initial condition compensation term. This represents the uncertainty suppression term. The inertia matrix represents the inertia matrix of the drive motor, indicating that there is no uncertainty. This indicates the nominal Coriolis force and centrifugal force (the nominal portion of the Coriolis force and centrifugal force). This indicates the nominal gravity, friction, and conversion terms (the nominal portion of gravity, friction, and conversion terms). This indicates the nominal nonlinear friction force (the nominal portion of the nonlinear friction force). This represents the uncertainty in the Coriolis force and the centrifugal force C. This represents the uncertainty in gravity, friction, and the transformation term G. This represents the uncertainty of the nonlinear frictional force F. This represents the uncertain part of the inertial matrix E, which indicates that the drive motor has no uncertainty.

[0174] (1) After determining the mechanical system:

[0175]

[0176] therefore,

[0177]

[0178] (2) From formula (34), we can obtain:

[0179]

[0180] (3) From formula (30) - formula (33), we can obtain:

[0181]

[0182] in, Represents the error vector transpose, Represents a positive definite weight matrix. This represents the acceleration constraint transformation matrix. The inertia matrix represents the inertia matrix of the drive motor, indicating that there is no uncertainty. This represents the initial condition compensation term. This represents the control gain coefficient. This represents the nominal control weighting matrix. express The transpose of the matrix, Represents a positive definite weight matrix The reverse.

[0183] (4) Through From formula (24) and formula (31) - formula (33), we can obtain:

[0184]

[0185] in, Represents the error vector transpose, Represents a positive definite weight matrix. This represents the acceleration constraint transformation matrix. The inertia matrix represents the inertia matrix of the drive motor, indicating that there is no uncertainty. The inertia matrix representing the absence of uncertainty in the drive motor. The uncertain part, This represents the uncertainty suppression term. Represents the feedback control gain matrix. This represents the nominal inertia matrix of the drive motor. express The transpose of the matrix, Represents a positive definite weight matrix The reverse, This represents the weighted terms of the Lyapunov function. Represents the damping coefficient. This represents the uncertainty boundary parameters of the mechanical system containing the drive motor. express transpose, This represents the actual constraint force required by the mechanical system containing the drive motor. express transpose, Represents the smallest eigenvalue. Indicates the number of servo constraints. Uncertainty boundary parameters of inertial systems The estimated value.

[0186] From formula (23), formula (28) - formula (30), we can obtain:

[0187]

[0188] in, This represents the time derivative of the Lyapunov function. Represents the error vector. This represents the uncertainty boundary parameters of the mechanical system containing the drive motor. This represents the control gain coefficient. This represents the weighted terms of the Lyapunov function. Uncertainty boundary parameters of inertial systems The estimated value, This represents the damping coefficient.

[0189] in, ( Represents the damping coefficient. This represents a pre-set positive small constant (error threshold).

[0190]

[0191] in, ,

[0192]

[0193] The magnitude of the final consistent bounded error of the closed-loop control system for the drive motor ( ).

[0194] The embodiments of this invention simulate the constructed robust constraint tracking controller for uncertainty, and compare it with a traditional PID (Proportional-Integral-Derivative) controller and a controller without inequality constraints. Controller and None Item Controller comparison (see) Figure 5 and Figure 6 This verifies the effectiveness of the proposed controller. Specifically, such as... Figure 5 The simulation results of the sinusoidal signal under different algorithms are shown below. Figure 6 The simulation results of the step signal shown are compared under different algorithms. Through comparison... Figure 5 and Figure 6 The simulation results show that the method in the embodiment of the present invention achieves better control performance than the other three methods (PID, LQR (Linear Quadratic Regulator), and BLF (Barrier Lyapunov Function)), proving the effectiveness and superiority of the design method of the present invention.

[0195] In this embodiment of the invention, new dynamic equations are obtained by applying inequality constraints to the drive motor system. Then, the nominal controller (ideal constraint force term) of the system is written from the dynamic equations, objective constraints, and assumptions. Then, based on the system error, a controller (initial condition compensation term) is proposed to compensate for the incompatibility of initial conditions. Then, based on the design, a controller (uncertainty suppression term) is proposed to solve the uncertainty problem. Then, the stability of the designed controller was analyzed using Lyapunov functions to determine that the designed controller achieved uniform boundedness and uniform eventual boundedness. Finally, experiments were conducted to verify the effectiveness of the controller.

[0196] Figure 7 The process of constructing an inequality constraint control model according to an embodiment of the present invention is illustrated.

[0197] This invention constructs a special tangent function as shown in formula (3) to transform the constrained displacement of the drive motor into an unconstrained variable in an unbounded domain. Based on this, formula (13) (a dynamic model of the mechanical system containing the drive motor with parameter uncertainties) is constructed. Based on formula (13), formula (19) (a second-order representation of the servo constraint equation of the mechanical system containing the drive motor) and the constraint force of the mechanical system containing the drive motor under uncertainties, an inequality constraint control model is established. The established inequality constraint control model satisfies the needs of inequality constraints and accurate trajectory tracking under the influence of uncertainties. The proposed method is based on joint module constraints considering inequality constraints, and the actual angular displacement is forcibly restricted within the constraint boundary. Lyapunov theory is used to prove that the proposed method is uniformly bounded, and is uniform and ultimately bounded. Under the influence of uncertainties, it simultaneously satisfies the needs of inequality constraints and accurate trajectory tracking. When the angular displacement is far from the boundary, the control focus is on trajectory tracking. When the angular displacement is close to the boundary, the control focus is on generating greater gain to make the state move away from the boundary and move towards the desired trajectory.

[0198] This invention provides a computer-readable storage medium.

[0199] In this embodiment, a computer program is stored on a computer-readable storage medium. When the computer program is executed by a processor, it implements the inequality constraint control method for a friction stir welding robot with complex curved surfaces as described above.

[0200] This invention provides a controller.

[0201] In this embodiment, the controller may include a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, it implements the inequality constraint control method for friction stir welding robots with complex curved surfaces as described above.

[0202] Figure 8 This is a structural block diagram of the controller according to an embodiment of the present invention.

[0203] like Figure 8 As shown, the controller 500 includes a processor 501 and a memory 503. The processor 501 and the memory 503 are connected, for example, via a bus 502. Optionally, the controller 500 may also include a transceiver 504. It should be noted that in practical applications, the transceiver 504 is not limited to one, and the structure of the controller 500 does not constitute a limitation on the embodiments of the present invention.

[0204] Processor 501 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this invention. Processor 501 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0205] Bus 502 may include a pathway for transmitting information between the aforementioned components. Bus 502 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 502 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 8 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0206] The memory 503 stores a computer program corresponding to the inequality constraint control method for a friction stir welding robot with complex curved surfaces according to the above embodiments of the present invention. This computer program is executed by the processor 501. The processor 501 executes the computer program stored in the memory 503 to implement the content shown in the aforementioned method embodiments.

[0207] The controller 500 includes, but is not limited to, mobile terminals such as mobile phones, laptops, digital radio receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), and in-vehicle terminals (such as in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers. Figure 8 The controller 500 shown is merely an example and should not be construed as limiting the functionality and scope of use of embodiments of the present invention.

[0208] It should be noted that the logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0209] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0210] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0211] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0212] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0213] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0214] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0215] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. An inequality constraint control method for a friction stir welding robot with complex curved surfaces, characterized in that, The method includes: The angular displacement of the drive motor of the friction stir welding robot and the input torque of the load driven by the drive motor are collected. Using a pre-established inequality constraint control model, the drive motor is controlled based on the angular displacement and the input torque. The inequality constraint control model is determined by a dynamic model of the mechanical system containing the drive motor with parameter uncertainties, a second-order constraint form of the servo constraints of the mechanical system containing the drive motor, and constraint forces of the mechanical system containing the drive motor under uncertainties. The dynamic model of the mechanical system containing the drive motor with parameter uncertainties is constructed based on the dynamic model of the drive motor under inequality constraints. The second-order constraint form of the servo constraints of the mechanical system containing the drive motor is constructed based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainties under sufficiently smooth conditions. The dynamic model of the drive motor under inequality constraints is obtained by limiting the displacement of the drive motor within a preset stroke range while converting the displacement of the drive motor from a bounded domain to an unbounded domain, based on the dynamic model of the drive motor. The process of constructing the inequality constraint control model includes: Based on the dynamic model of the drive motor, the displacement of the drive motor is restricted within a preset stroke range, and the displacement of the drive motor is transformed from a bounded domain to an unbounded domain, thus obtaining the dynamic model of the drive motor under the inequality constraint. Based on the dynamic model of the drive motor under the inequality constraints, a dynamic model of the mechanical system containing the drive motor with parameter uncertainties is constructed. Based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainties, a second-order constraint form of the servo constraint of the mechanical system containing the drive motor is constructed under sufficiently smooth conditions. Based on the second-order constraint form of the servo constraint of the mechanical system containing the drive motor, the constraint force of the mechanical system containing the drive motor under uncertainties is constructed. Based on the characteristics of the mechanical system containing the drive motor and the servo constraint characteristics, assumptions and requirements are constructed. Based on the dynamic model of the mechanical system containing the drive motor with parameter uncertainty, the second-order constraint form of the servo constraint of the mechanical system containing the drive motor, and the constraint force of the mechanical system containing the drive motor under uncertainty, the uncertainty part in the dynamic model of the mechanical system containing the drive motor with parameter uncertainty is decomposed, and the inequality constraint control model is established according to the assumption requirements.

2. The inequality constraint control method according to claim 1, characterized in that, The expression for the dynamic model of the drive motor under the inequality constraint is as follows: in, Indicates time, Indicates angular displacement The corresponding unconstrained state variables, express The derivative with respect to time corresponds to the angular velocity. Transformation form, express The second derivative with respect to time corresponds to angular acceleration. Transformation form, The functional form representing the inertia matrix of the mechanical system containing the drive motor after transformation. The functional form representing the Coriolis force and centrifugal force terms. The functional form representing gravity, friction, and transformation terms. This represents the input torque of the load. This represents the inertia matrix of the mechanical system containing the drive motor after transformation. The inertia matrix represents the drive motor. Represents Coriolis force and centrifugal force. This represents the nonlinear damping torque. This represents gravity, friction, and conversion terms. This represents nonlinear frictional torque. This represents the inertia of the drive motor. This indicates the upper limit of the angular displacement of the drive motor rotor. This represents the lower limit of the angular displacement of the drive motor rotor.

3. The inequality constraint control method according to claim 2, characterized in that, The expression for the dynamic model of the mechanical system containing the drive motor with parameter uncertainties is: in, Indicates time, This represents the angular displacement of the drive motor rotor. This represents the angular velocity of the drive motor rotor. This represents the angular acceleration of the drive motor rotor. This represents the uncertainty parameter of the mechanical system in which the drive motor is located. This represents the input torque of the load. This represents the inertia matrix of the mechanical system containing the drive motor after transformation. Represents Coriolis force and centrifugal force. Represents nonlinear frictional force. It represents gravity, friction, and conversion terms.

4. The inequality constraint control method according to claim 3, characterized in that, The expression for the second-order constraint form of the servo constraint of the mechanical system containing the drive motor is as follows: in, Indicates the index of the drive motor. This represents the total number of degrees of freedom in the mechanical system containing the drive motor. This represents the angular displacement of the drive motor rotor. Indicates time, Represents the acceleration constraint transformation matrix The line, number Column elements, Indicates the first The angular acceleration of the rotor of the drive motor. Indicates the first The generalized coordinate components corresponding to each servo constraint.

5. The inequality constraint control method according to claim 4, characterized in that, The expression for the constraint force of the mechanical system containing the drive motor under uncertain conditions is as follows: in, This represents the ideal constraint force required by the mechanical system containing the drive motor. Indicates angular displacement dependent on generalized coordinates and time The nominal inertia matrix of the mechanical system containing the drive motor after conversion. express The square root matrix, express The inverse matrix, Indicates angular displacement dependent on generalized coordinates and time The acceleration constraint transformation matrix, Indicates angular displacement dependent on generalized coordinates angular velocity and time State variables, Indicates angular displacement dependent on generalized coordinates angular velocity and time Coriolis force and centrifugal force, Indicates angular displacement dependent on generalized coordinates and time The inverse inertial matrix of the mechanical system containing the drive motor after transformation. Indicates angular displacement dependent on generalized coordinates and time The nominal gravity, friction, and conversion terms. Indicates angular displacement dependent on generalized coordinates and time The nominal nonlinear frictional force.

6. The inequality constraint control method according to claim 5, characterized in that, The assumptions must include at least the following: (1) For any ,as well as , ,in, This represents the uncertainty parameter of the mechanical system in which the drive motor is located. express Take any constant, Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The converted inertia matrix of the mechanical system containing the drive motor; (2) They exhibit consistency in terms of constraints, among which, Indicates angular displacement dependent on generalized coordinates angular velocity and time The acceleration constraint transformation matrix, express The derivative matrix, Indicates angular displacement dependent on generalized coordinates angular velocity and time Expected acceleration; (3) For any given Acceleration constraint transformation matrix Full rank, reversible; (4) Given the assumptions in (3), for a given positive definite weight matrix ,make: in, Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The weighted acceleration energy function used for optimized control. Indicates the definition symbol, Indicates angular displacement dependent on generalized coordinates and time The positive definite weighted matrix, express The transpose of the matrix, Indicates angular displacement dependent on generalized coordinates and time The acceleration constraint transformation matrix, Indicates angular displacement dependent on generalized coordinates and time The nominal inertia matrix of the mechanical system containing the drive motor after conversion. Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The feedback control gain matrix, Indicates angular displacement dependent on generalized coordinates and time The drive motor has an inertia matrix that does not exhibit uncertainty. Let the positive definite weight matrix have the following properties: This makes it possible for all All of them have: in, Represents the smallest number. Represents the smallest eigenvalue. Indicates the number of servo constraints. express transpose, Indicates angular displacement dependent on generalized coordinates Uncertainty parameters and time The weighted acceleration energy function used for optimized control. Uncertainty boundary parameters of inertial systems The estimated value, in the absence of uncertainty, .

7. The inequality constraint control method according to claim 6, characterized in that, The inequality constraint control model for: in, in, , choose , so that: in, This represents the angular displacement of the drive motor rotor. This represents the angular velocity of the drive motor rotor. Indicates time, Represents the ideal constraint term. This represents the initial condition compensation term. This represents the uncertainty suppression term. This represents the ideal constraint force required by the mechanical system containing the drive motor. This represents the control gain coefficient. Indicates angular displacement dependent on generalized coordinates and time The nominal inertia matrix of the mechanical system containing the drive motor after conversion. express The transpose of the matrix, Indicates angular displacement dependent on generalized coordinates and time The acceleration constraint transformation matrix, Represents a positive definite weight matrix The reverse, Represents the error vector. Indicates angular displacement dependent on generalized coordinates angular velocity and time The weighted terms of the Lyapunov function, Indicates angular displacement dependent on generalized coordinates angular velocity and time The damping coefficient, Indicates angular displacement dependent on generalized coordinates angular velocity and time The uncertainty boundary parameters of the mechanical system in which the drive motor is located. Indicates angular displacement dependent on generalized coordinates and time Uncertainty boundary parameters of inertial systems The estimated value, Represents positive numbers. Indicates angular displacement dependent on generalized coordinates angular velocity and time The error vector, Indicates the reference trajectory term. This represents the acceleration constraint transformation matrix. The inertia matrix representing the absence of uncertainty in the drive motor. The uncertain part, The inertia matrix represents the inertia matrix of the drive motor, indicating that there is no uncertainty. Represents Coriolis force and centrifugal force. This represents gravity, friction, and conversion terms. Representing Coriolis force and centrifugal force The uncertain part, Representing gravity, friction, and conversion terms The uncertain part.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the inequality constraint control method for friction stir welding robots with complex curved surfaces as described in any one of claims 1-7.

9. A controller, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the computer program is executed by the processor, it implements the inequality constraint control method for a friction stir welding robot for complex curved surfaces as described in any one of claims 1-7.

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