Fractional order interval type-2 fuzzy sliding mode space robot tracking control method

Abstract

The application provides a fractional order interval bivalent fuzzy sliding mode space manipulator tracking control method, relates to the space manipulator control technical field, and solves the problems that the existing space manipulator controller is difficult to simultaneously realize high-precision stable control, dynamic trajectory optimization, intelligence ability distribution and strong environment adaptability. The method comprises the following steps: establishing a dynamics model of a space manipulator, constructing a fractional order interval bivalent fuzzy sliding mode controller according to the dynamics model, and determining a joint control torque of the space manipulator based on the constructed fractional order interval bivalent fuzzy sliding mode controller to realize tracking control of the space manipulator. The application realizes high-precision stable control, dynamic trajectory optimization, intelligence ability distribution and strong environment adaptability of the existing space manipulator controller, and further improves in-orbit operation performance of the space manipulator, and the space manipulator can better meet the requirements of tracking control accuracy and stability. The application can be applied to space manipulator control.

Description

Technical Field

[0001] This invention relates to the field of space robotic arm control technology, and more specifically, to a fractional-order interval type-II fuzzy sliding mode space robotic arm tracking control method. Background Technology

[0002] In space exploration, astronauts face harsh conditions such as space radiation, microgravity, and extreme temperatures during extravehicular activities (EVAs), which not only reduces mission efficiency but also seriously threatens their safety. With the rapid development of space technology, the application of space robots is becoming increasingly widespread. A space robot is a special type of robot used to assist or replace humans in performing tasks such as EVAs and explorations in the space environment. Among them, the space robotic arm, similar to a human arm, consists of a base and multiple links. It not only helps astronauts move but also performs operations such as equipment installation, maintenance, and replacement, thereby reducing astronauts' EVA time and ensuring their safety. Furthermore, the space robotic arm possesses powerful capture, rendezvous, and docking capabilities as well as heavy-load transport capabilities, making it an indispensable piece of equipment in the construction, maintenance, and operation of the space station.

[0003] The controller of a space robotic arm is the core component for achieving precise and reliable operation. However, space dynamics is characterized by strong nonlinearity, strong coupling, and time-varying parameters. Traditional fixed-model control methods are difficult to adapt to on-orbit conditions. Under heavy load handling and precise docking scenarios, oscillations and shocks are prone to occur, affecting operational safety. At the same time, existing algorithms have insufficient energy consumption optimization. Trajectory planning and force distribution for multi-task switching rely on experience or offline calculations, which cannot respond to sudden working conditions in real time, resulting in increased energy consumption and longer task cycles. Furthermore, the controller has poor robustness to progressive disturbances such as equipment aging, joint friction, and thermal deformation, and lacks an adaptive adjustment mechanism, making it difficult to simultaneously achieve high precision, low energy consumption, and strong anti-disturbance performance. Summary of the Invention

[0004] The problem solved by this invention is that existing space robotic arm controllers are unable to simultaneously achieve high-precision stable control, dynamic trajectory optimization, intelligent force distribution, and strong environmental adaptability.

[0005] To address the aforementioned problems, this invention provides a fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method, system, electronic device, and storage medium.

[0006] In a first aspect, the present invention provides a fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method, comprising:

[0007] Establish a dynamic model of the space robotic arm;

[0008] Based on the aforementioned dynamic model, a fractional-order interval type-II fuzzy sliding mode controller is constructed.

[0009] The control torque of the robotic arm joints is determined by constructing a fractional-order interval type II fuzzy sliding mode controller to achieve tracking control of the spatial robotic arm.

[0010] Optionally, constructing a fractional-order interval type-II fuzzy sliding mode controller based on the dynamic model includes:

[0011] A dynamic model of a space robotic arm is established, wherein the space robotic arm includes a floating base, flexible joints, and flexible links, and the dynamic model includes the six-degree-of-freedom motion equations of the floating base and the coupled dynamic equations of the robotic arm with flexible joints and flexible links;

[0012] Obtain the angular velocity and angular acceleration of the floating base, and solve the six-degree-of-freedom motion equations;

[0013] Based on the six-degree-of-freedom motion equations and the coupled dynamics equations of the robotic arm, a fractional-order interval type II fuzzy sliding mode controller is constructed, wherein the input of the fractional-order interval type II fuzzy sliding mode controller is the sliding surface, and the adjustment parameter is the sliding mode reaching law.

[0014] Optionally, the six-degree-of-freedom equation of motion is specifically expressed as follows:

[0015] ,

[0016] ,

[0017] In the formula, The inertia matrix of the floating base. For the mass of the floating base, The angular velocity of the floating base is... Let be the angular acceleration of the floating base. express The cross product matrix, Let be the displacement of the floating base. The displacement of the floating base and the force exerted on the floating base by the attitude actuator, The displacement of the floating base and the torque exerted on the floating base by the attitude actuator are the following: The force exerted by the robotic arm on the floating base, The torque exerted by the robotic arm on the floating base.

[0018] Optionally, a PD controller may also be included.

[0019] The PD controller controls and adjusts the position and attitude of the floating base based on the six-degree-of-freedom motion equations, specifically as follows:

[0020] ,

[0021] In the formula, To control the quantity, , These are the forces and torques exerted on the floating base by the displacement and attitude actuators, respectively. It is a proportional gain matrix. The differential gain matrix is... Let be the error vector of the attitude and position of the floating base. It is the first derivative of the error vector.

[0022] Optionally, the sliding surface is specifically expressed as follows:

[0023] ,

[0024] In the formula, Let c be the sliding surface, and c be the sliding surface gain parameter. , This refers to the angular error, which is the difference between the expected joint angle and the actual joint angle of the space robotic arm. is the first derivative of the angle error.

[0025] Optionally, the sliding mode reaching law is specifically expressed as:

[0026] ,

[0027] In the formula, For the sliding mode reaching law, , It is a sharp value obtained after fuzzy control defuzzification. The order of a fractional power function. The sliding surface, This is an adjustable parameter.

[0028] Optionally, the determination of the joint control torque of the robotic arm based on the construction of a fractional-order interval type-II fuzzy sliding mode controller is specifically expressed as follows:

[0029] ,

[0030] In the formula, This refers to the joint control torque of the robotic arm; For the generalized coordinates of the robotic arm; The derivative of the joint angle; These are the sliding surface gain parameters; The time derivative of the desired joint angle; This refers to the error angular velocity; The sliding surface; This refers to the sliding mode reaching law; The inertia matrix of the robotic arm; The matrix represents the centrifugal force and the Coriolis force. Here is the stiffness matrix; Let be the motion equivalent moment vector of the floating base.

[0031] In a second aspect, the fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control system of the present invention includes:

[0032] The data acquisition unit is used to establish the dynamic model of the space robotic arm;

[0033] The data processing unit is used to construct a fractional-order interval type II fuzzy sliding mode controller based on the dynamic model.

[0034] The data analysis unit is used to determine the joint control torque of the robotic arm based on the construction of a fractional-order interval type II fuzzy sliding mode controller, so as to realize the tracking control of the space robotic arm.

[0035] Thirdly, the electronic device of the present invention includes: a processor and a memory, the memory being used to store a computer program;

[0036] When the computer program is loaded by the processor, it causes the processor to execute the above-described fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method.

[0037] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method.

[0038] The fractional-order interval type II fuzzy sliding mode space manipulator tracking control method, system, electronic device, and storage medium of this invention establish a dynamic model of the space manipulator, which can accurately reflect the real motion characteristics and flexible vibration coupling relationship of the space manipulator in a microgravity environment. By constructing a fractional-order interval type II fuzzy sliding mode controller, online dynamic adjustment of the sliding mode reaching law is realized, so that the control action can be nonlinearly amplified or compressed according to the actual state, effectively improving the stability, accuracy, and speed of sliding mode control. Finally, the precise joint control torque of the manipulator is obtained. Compared with the prior art, it has the advantages of shorter joint angle adjustment time, smaller steady-state error, and smaller time multiplication absolute error integral index, which can better meet the requirements of space manipulator for tracking control accuracy and stability. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating the fractional-order interval type II fuzzy sliding mode spatial robotic arm tracking control method in an embodiment of the present invention.

[0040] Figure 2This is a schematic diagram of a space robotic arm in an embodiment of the present invention;

[0041] Figure 3 This is one of the angle output curves of joint 1 in the embodiments of the present invention;

[0042] Figure 4 This is one of the angle output curves of joint 2 in the embodiments of the present invention;

[0043] Figure 5 This is the second example of the angle output curve of joint 1 in this embodiment of the invention;

[0044] Figure 6 This is the second example of the angle output curve of joint 2 in this embodiment of the invention;

[0045] Figure 7 This is a graph showing the angle error of joint 1 in an embodiment of the present invention.

[0046] Figure 8 This is a graph showing the angle error of joint 2 in an embodiment of the present invention. Detailed Implementation

[0047] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the accompanying drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0048] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0049] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to"; the term "based on" means "at least partially based on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments"; and the term "optionally" means "optional embodiments". Definitions of other terms will be given in the following description. It should be noted that the concepts of "first," "second," etc., mentioned in this invention are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.

[0050] It should be noted that the terms "a" and "a plurality of" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0051] The names of the messages or information exchanged between the multiple devices in the embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of these messages or information.

[0052] To address the problems existing in the prior art, this embodiment provides a fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method, system, electronic device, and storage medium.

[0053] Combination Figure 1 As shown in the figure, the fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method of the present invention provided in this embodiment includes:

[0054] Establish a dynamic model of the space robotic arm;

[0055] Based on the aforementioned dynamic model, a fractional-order interval type-II fuzzy sliding mode controller is constructed.

[0056] The control torque of the robotic arm joints is determined by constructing a fractional-order interval type II fuzzy sliding mode controller to achieve tracking control of the spatial robotic arm.

[0057] Specifically, in combination Figure 2 As shown, the space robotic arm in this embodiment is designed to be unaffected by external forces such as gravity, and all joints are rotatable. Specifically, a three-dimensional floating space robotic arm with flexible joints and flexible links is used as the controlled object, and its dynamic model is established. Among them, joint 2 of the robotic arm is a flexible joint, and link 2 is a flexible rod.

[0058] Specifically, the dynamic equations of the robotic arm with flexible joints and flexible links are as follows:

[0059] ,

[0060] In the formula, For the generalized coordinates of the robotic arm, This is the joint control torque vector. The derivative of the joint angle. Let be the second derivative of the joint angle. The inertia matrix, The vectors of centrifugal force and Coriolis force. Here is the stiffness matrix. This is the equivalent torque exerted by the base motion on the joints of the robotic arm.

[0061] Generalized coordinates as follows:

[0062] ,

[0063] In the formula, They are respectively Figure 2 The angles of joint 1 and joint 2 of the robotic arm. These are the coordinates of the first three modal modes of the flexible link of the robotic arm.

[0064] This embodiment divides the spatial robotic arm into a separate operation form consisting of a floating base and the robotic arm (flexible joints and flexible rods). This avoids the computational burden caused by an excessively high dimensional single controller, while also achieving decoupling optimization of base stability and robotic arm end-effector tracking.

[0065] Optionally, constructing a fractional-order interval type-II fuzzy sliding mode controller based on the dynamic model includes:

[0066] A dynamic model of a space robotic arm is established, wherein the space robotic arm includes a floating base, flexible joints, and flexible links, and the dynamic model includes the six-degree-of-freedom motion equations of the floating base and the coupled dynamic equations of the robotic arm with flexible joints and flexible links;

[0067] Obtain the angular velocity and angular acceleration of the floating base, and solve the six-degree-of-freedom motion equations;

[0068] Based on the six-degree-of-freedom motion equations and the coupled dynamics equations of the robotic arm, a fractional-order interval type II fuzzy sliding mode controller is constructed, wherein the input of the fractional-order interval type II fuzzy sliding mode controller is the sliding surface, and the adjustment parameter is the sliding mode reaching law.

[0069] Specifically, in space robot or spacecraft dynamics, the motion state of a rigid body in three-dimensional space is determined by 6 independent motion parameters (degrees of freedom), including: 3 translational degrees of freedom (describing the positional movement of the object along the X, Y, and Z axes); and 3 rotational degrees of freedom (describing the attitude rotation of the object around the X, Y, and Z axes, usually represented by Euler angles or angular velocity vectors).

[0070] Optionally, the six-degree-of-freedom equation of motion is specifically expressed as follows:

[0071] ,

[0072] ,

[0073] In the formula, The inertia matrix of the floating base. For the mass of the floating base, The angular velocity of the floating base is... Let be the angular acceleration of the floating base. express The cross product matrix, Let be the displacement of the floating base. The displacement of the floating base and the force exerted on the floating base by the attitude actuator, The displacement of the floating base and the torque exerted on the floating base by the attitude actuator are the following: The force exerted by the robotic arm on the floating base, The torque exerted by the robotic arm on the floating base.

[0074] Specifically, the physical structure of the space manipulator in this embodiment includes a floating base, flexible joints, and flexible links. Based on these components, six-degree-of-freedom motion equations for the floating base and coupled dynamic equations for the manipulator with flexible joints and links are established. This embodiment fully considers the floating effect of the base and the flexible deformation of the joints and links under microgravity conditions. Compared to traditional rigid models or fixed base models, it is closer to the actual physical system, providing a high-fidelity mathematical model foundation for the accurate derivation of subsequent control torques.

[0075] This embodiment obtains the angular velocity of the floating base. By combining angular acceleration with the base mass *m* to solve the translational equations, and through real-time solving of the six-degree-of-freedom motion equations, the forces and torques generated by the floating base motion, as well as the equivalent torque of the floating base motion reaction on the robotic arm, are accurately calculated, and the interference of base floating on the robotic arm motion is quantified. Based on the solution results of the six-degree-of-freedom motion equations, the robotic arm dynamics equations are derived, incorporating the influence of base motion into the calculation of the robotic arm control torque in the form of equivalent torque, thereby effectively compensating for the nonlinear interference caused by base floating and flexible coupling. The output joint control torque has a clear physical meaning, enabling more precise driving of the robotic arm joints and improving the control accuracy and system stability of the space robotic arm tracking control.

[0076] Optionally, a PD controller may also be included.

[0077] The PD controller controls and adjusts the position and attitude of the floating base based on the six-degree-of-freedom motion equations, specifically as follows:

[0078] ,

[0079] In the formula, To control the quantity, , These are the forces and torques exerted on the floating base by the displacement and attitude actuators, respectively. It is a proportional gain matrix. The differential gain matrix is... Let be the error vector of the attitude and position of the floating base. It is the first derivative of the error vector.

[0080] Specifically, both the proportional gain moment and the differential gain matrix are 6x6 diagonal matrices.

[0081] Specifically, this embodiment uses a PD controller to achieve six degrees of freedom control over the position and attitude of the floating base.

[0082] The base attitude and position PD control law is as follows In this embodiment, the elements of the proportional and differential gain matrices are obtained by engineering tuning based on the system response characteristics.

[0083] This embodiment employs a PD controller to achieve six-degree-of-freedom control of the floating base's position and attitude. The control law takes the base's position and attitude error and its time derivative as input. Through engineering tuning, the elements of the proportional and differential gain matrices are obtained based on the system's response characteristics. The control quantities include the forces and torques acting on the base. Compared to the complex nonlinear strategies commonly used in the field of space robotics, such as the torque calculation method, backstepping method, or adaptive control, the PD control structure is simple, the physical meaning of the parameters is clear, and the computational load is small. It can ensure base stability without the need for precise solution of the system dynamics model, providing quasi-static base constraints for the fractional-order interval type II fuzzy sliding mode control of the robotic arm joints. At the same time, the hierarchical architecture of the six-degree-of-freedom control of the base and the high-precision control of the robotic arm joints effectively avoids the problem of excessively high controller dimensionality caused by unified modeling, achieving synergistic optimization of overall platform stability and accurate end-effector trajectory tracking while reducing the computational burden.

[0084] Optionally, the sliding surface is specifically expressed as follows:

[0085] ,

[0086] In the formula, Let c be the sliding surface, and c be the sliding surface gain parameter. , This refers to the angular error, which is the difference between the expected joint angle and the actual joint angle of the space robotic arm. is the first derivative of the angle error.

[0087] Specifically, this embodiment defines the sliding surface as a linear combination of the angle error and its time derivative. Compared to the existing technology that only includes a linear combination of the angle error and its first derivative, this structure is simpler and the physical meaning is clearer. Compared to existing higher-order sliding surfaces (such as those containing higher-order error derivatives or fractional-order differential operators), it avoids complex differential operations and noise amplification problems. At the same time, the gain parameter c, which is greater than zero, can be flexibly adjusted according to the system response characteristics to achieve a balance between error convergence speed and overshoot. Compared to conventional methods, this embodiment directly uses the difference between the expected joint angle and the actual joint angle of the space manipulator as the error signal, clearly defining the core objective of joint tracking. Compared to the method of using the end effector pose error as input, it does not require complex solutions, significantly reducing the computational load, and is more suitable for space manipulator systems with flexible joints and floating base coupling. In this embodiment, the sliding surface serves as the core state variable of the fractional-order interval type II fuzzy sliding surface controller, providing a unique input (sliding surface value) for subsequent operations. This allows the fuzzy rules to adaptively adjust the fractional order according to the degree to which the system deviates from the equilibrium position. The clear value z, combined with the sliding mode approach law, ensures that the control state converges to the sliding surface and tracks stably within a finite time, providing a state constraint basis for outputting precise control torque of the robotic arm joints, and improving the speed, accuracy and robustness of the tracking control of the space robotic arm as a whole.

[0088] Optionally, the sliding mode reaching law is specifically expressed as:

[0089] ,

[0090] In the formula, For the sliding mode reaching law, , It is a sharp value obtained after fuzzy control defuzzification. The order of a fractional power function. The sliding surface, This is an adjustable parameter.

[0091] Specifically, traditional sliding mode control uses a fixed sign function sign(s) as the constant velocity term, whose amplitude remains constant. This causes a sharp jump in control torque when the system crosses the sliding surface, leading to inherent chattering problems. In contrast, this embodiment replaces the fixed sign function with a nonlinear reaching term, allowing the amplitude of the sliding mode reaching law to change continuously according to the system state, fundamentally reducing chattering. Compared to conventional methods that directly use fuzzy output as equivalent control or switching gain, maintaining a linear relationship between fuzzy output and actual control action, this embodiment introduces fractional power operations. When the power At this time, the relationship between the control action and the sharpness value z is no longer linear, but rather nonlinearly amplified or compressed according to the output magnitude; that is, when When the value is large, the exponentiation operation amplifies it, accelerating the convergence speed when it is far from the equilibrium position. When the power operation is small, it is compressed, reducing the control amplitude when approaching the equilibrium position, thereby achieving an adaptive balance between convergence speed and steady-state accuracy. This embodiment retains the robustness of sliding mode control to system uncertainties and external disturbances, and significantly improves the dynamic quality of the system through fractional power nonlinear mapping. It provides a high-quality approach law basis for the subsequent derivation of precise manipulator joint control torque. Overall, it enables the space manipulator to exhibit superior performance in tracking control with shorter settling time, smaller steady-state error, and weaker chattering.

[0092] In one embodiment, sliding mode control is an advanced control strategy widely used in the field of engineering control, possessing advantages such as fast dynamic response, simple implementation, and intuitive parameter adjustment. The goal of sliding mode control is to bring the system state [a set of variables that can completely describe the current motion of the space robot arm, i.e., a state vector containing the robot arm's generalized coordinates (rigid joint angles + flexible link modal coordinates) and their time derivatives (angular velocity + modal velocity)] to and stabilize on the sliding surface. The sliding mode reaching law directly determines that the system state approaches the sliding surface from any initial position. Dynamic quality.

[0093] The traditional sliding mode control exponential approach law is as follows:

[0094] ,

[0095] In the formula, It is an adjustable parameter. .

[0096] This embodiment uses fuzzy control output. The constant velocity term directly replaces the exponential reaching law of traditional sliding mode control. ,Right now

[0097] ,

[0098] In the formula, , This is a sharpened value obtained after defuzzification in fuzzy control. Unlike traditional fuzzy control, fractional-order fuzzy control performs a power function operation on the sharpened value obtained after defuzzification by the fuzzy controller. When the order of the power function... At the same time, control action and The relationship between them is no longer linear, but rather non-linear, depending on the output size, which can be amplified or compressed.

[0099] Optionally, the determination of the joint control torque of the robotic arm based on the construction of a fractional-order interval type-II fuzzy sliding mode controller is specifically expressed as follows:

[0100] ,

[0101] In the formula, This refers to the joint control torque of the robotic arm; For the generalized coordinates of the robotic arm; The derivative of the joint angle; These are the sliding surface gain parameters; The time derivative of the desired joint angle; This refers to the error angular velocity; The sliding surface; This refers to the sliding mode reaching law; The inertia matrix of the robotic arm; The matrix represents the centrifugal force and the Coriolis force. Here is the stiffness matrix; Let be the motion equivalent moment vector of the floating base.

[0102] Specifically, the expression for the joint control torque of the robotic arm in this embodiment is derived based on the dynamic model of the space robotic arm and fully includes the inertial force term. Centrifugal force and Coriolis force terms Stiffness force term and the base motion equivalent moment term This method comprehensively compensates for the nonlinear dynamic effects caused by the floating base, flexible joints, and flexible linkages. Compared to existing approximate models or simplified control schemes that ignore flexible modes, it significantly improves the physical accuracy of control torque calculation and system matching. Compared to conventional sliding mode control laws, this expression directly embeds the sliding surface and its reaching law into the calculation of the inertial force term. The combination of these terms transforms the convergence requirements of sliding mode control into specific control torque commands, enabling the system state to rapidly converge to the sliding surface and stably track along the dynamic trajectory designed by the reaching law; simultaneously, the expression retains complete dynamic coupling terms. and By eliminating the interference of nonlinear centrifugal force, Coriolis force and elastic restoring force on tracking accuracy through feedforward compensation, it has a faster response speed and smaller steady-state error compared with the existing sliding mode controller that only relies on error feedback.

[0103] This embodiment enables the final output joint control torque to possess precise dynamic physical meaning, fast sliding mode convergence performance, and strong robust adaptive capability, thereby achieving high-precision, fast-response, and low-jitter tracking control of the space robot arm under conditions of base floating, flexible vibration, and parameter uncertainty.

[0104] In summary, this embodiment addresses the requirements of stability, accuracy, and speed in the sliding mode control system of a space robotic arm by constructing a fractional-order interval type-II fuzzy controller. This enables online dynamic adjustment of the sliding mode control reaching law. The interval type-II fuzzy controller uses the sliding surface... For input, and fractional order For output. In this embodiment, five fuzzy subsets are selected: NB, NS, ZO, PS, and PB. The membership function of a base-width isosceles triangle is used, as shown in the following formula:

[0105] ,

[0106] ,

[0107] In the formula, x is the independent variable of the function. For a certain fuzzy subset, These correspond to NB, NS, ZO, PS, and PB, respectively. They are respectively The upper and lower bound membership function output values, Let x be the x-coordinate of the center of the isosceles triangle. Let be a constant representing the width of the isosceles triangle, satisfying The fuzzy adaptive rules are shown in Table 1. Taking the last column of Table 1 as an example, the corresponding fuzzy rule is: If s is PB, then z is PB and is PS.

[0108] Table 1 Fuzzy Rules

[0109]

[0110] The interval type-2 fuzzy controller in this embodiment does not have an output membership function. The output intervals of the five interval type-2 fuzzy subsets are shown in Table 2. To output the lower bound of the interval, This is the upper bound of the output interval.

[0111] Table 2 Output Range

[0112]

[0113] The interval type-2 reduction defuzzification algorithm used in this embodiment is as follows:

[0114] The sliding surface is the sharpness value input for the fuzzy system, and a total of [number] are set. Fuzzy rules, in this embodiment Through fuzzy reasoning, we obtain the first... Triggering range of a fuzzy rule for:

[0115] ,

[0116] The upper and lower bounds of the trigger interval for:

[0117] ,

[0118] ,

[0119] In the formula, For the fuzzy subset corresponding to this fuzzy rule, taking the last column of Table 1 as an example, for this fuzzy rule, =PB, This represents the lower bound membership function value of the corresponding fuzzy subset. This represents the membership function value of the upper bound of the corresponding fuzzy subset.

[0120] No. Fuzzy rule output range for

[0121] ,

[0122] In the formula, To output the lower bound of the interval, This is the upper bound of the output interval.

[0123] Then, based on the following formula, the set center algorithm is used to reduce the form and obtain two set centers. :

[0124] ,

[0125] ,

[0126] in, and The transition point is obtained through the KM iteration method.

[0127] The average of the two centers in the above formula is the sharpness value. .

[0128] In another embodiment, to verify and demonstrate the effectiveness of the fractional-order interval type-II fuzzy sliding mode controller and the floating base PD control in this embodiment, the following simulation experiment was conducted. The parameters of the space manipulator are shown in Table 3, and the parameters of the interval type-II fuzzy membership function are as follows: See Table 4.

[0129] Table 3. Specific values ​​of various physical quantities of the two-bar linkage robotic arm.

[0130]

[0131] Table 4. Parameters of Interval Type II Fuzzy Membership Function

[0132]

[0133] Simulation verification shows that the controller in this embodiment can simultaneously meet the control requirements of the space robot arm's joint angles and the base's posture. (Desired position of the floating base) Desired attitude angle It reaches and stabilizes at the desired value in approximately 120 seconds. (Desired angle of the space robotic arm joint) The joint angle output of the space robotic arm is as follows: Figure 3 and Figure 4 The legend "FSMC" represents the output angle curve of fractional-order interval type II sliding mode control, and "SMC" represents the output angle curve of traditional sliding mode control.

[0134] The control performance indicators are shown in Table 5. In the table, ts1 represents the settling time of joint 1 (2%), and ITAE1 represents the ITAE index of joint 1. The smaller the value of this index, the better the control effect. ts2 and ITAE2 are calculated similarly. The expression for calculating ITAE is as follows: In the formula, Let T be the absolute value of the error, and T be the upper bound time for the ITAE integral.

[0135] Table 5 Joint Angle Tracking Performance Indicators

[0136]

[0137] For the four control performance indicators of the robotic arm's two joints (ITAE and settling time) in the fuzzy sliding mode control method, the present embodiment outperforms the traditional sliding mode control method. This indicates that the adaptive adjustment of the sliding mode control reaching law by the interval type-II fuzzy control can improve the sliding mode control performance. The output angle curve shows that the fractional-order interval type-II fuzzy sliding mode control is faster than the traditional sliding mode control.

[0138] Next, a ramp response simulation test is conducted, where it is expected that both joints of the robotic arm rotate at a uniform speed of 0.5 rad / s, while the desired position and attitude angle of the base remain unchanged. The joint angle output of the spatial robotic arm is as follows: Figure 5 and Figure 6 Angular error such as Figure 7 and Figure 8 The ITAE metrics are shown in Table 6.

[0139] Table 6 Joint Angle ITAE Index

[0140]

[0141] In summary, although the angle error in this embodiment is greater than that of the traditional sliding mode control method in the initial stage of control, the angle error of the traditional sliding mode control method is difficult to converge to 0. Joint 1 always has an error of about 0.01 rad, joint 2 exhibits chattering, and the mean error is not zero in the later stage. The fractional-order interval type II sliding mode controller of this embodiment has a smaller steady-state error and a smaller ITAE compared to the traditional sliding mode method, and can better meet the control accuracy requirements. The simulation results show that the fractional-order interval type II fuzzy sliding mode controller of this embodiment has certain advantages over the traditional sliding mode controller, whether for step signal tracking or ramp signal tracking.

[0142] This invention also provides a fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control system, comprising:

[0143] The data acquisition unit is used to establish the dynamic model of the space robotic arm;

[0144] The data processing unit is used to construct a fractional-order interval type II fuzzy sliding mode controller based on the dynamic model.

[0145] The data analysis unit is used to determine the joint control torque of the robotic arm based on the construction of a fractional-order interval type II fuzzy sliding mode controller, so as to realize the tracking control of the space robotic arm.

[0146] The fractional-order interval type II fuzzy sliding mode spatial manipulator tracking control system of the present invention has the same advantages over the prior art as the aforementioned fractional-order interval type II fuzzy sliding mode spatial manipulator tracking control method, and will not be repeated here.

[0147] This invention also provides an electronic device, including: a processor and a memory, wherein the memory is used to store computer programs;

[0148] When the computer program is loaded by the processor, it causes the processor to execute the fractional-order interval type-II fuzzy sliding mode spatial manipulator tracking control method as described above.

[0149] The electronic device of the present invention has the same advantages over the prior art as the aforementioned fractional-order interval type II fuzzy sliding mode spatial manipulator tracking control method over the prior art, and will not be repeated here.

[0150] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the fractional-order interval type II fuzzy sliding mode spatial robotic arm tracking control method as described above.

[0151] The computer-readable storage medium of the present invention has the same advantages over the prior art as the aforementioned fractional-order interval type II fuzzy sliding mode spatial manipulator tracking control method over the prior art, and will not be repeated here.

[0152] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for tracking and controlling a fractional-order interval type-II fuzzy sliding mode spatial robotic arm, characterized in that, The method includes: Establish a dynamic model of the space robotic arm; Based on the aforementioned dynamic model, a fractional-order interval type-II fuzzy sliding mode controller is constructed. The control torque of the robotic arm joints is determined by constructing a fractional-order interval type II fuzzy sliding mode controller to achieve tracking control of the spatial robotic arm.

2. The fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method according to claim 1, characterized in that, The construction of a fractional-order interval type-II fuzzy sliding mode controller based on the dynamic model includes: A dynamic model of a space robotic arm is established, wherein the space robotic arm includes a floating base, flexible joints, and flexible links, and the dynamic model includes the six-degree-of-freedom motion equations of the floating base and the coupled dynamic equations of the robotic arm with flexible joints and flexible links; Obtain the angular velocity and angular acceleration of the floating base, and solve the six-degree-of-freedom motion equations; Based on the six-degree-of-freedom motion equations and the coupled dynamics equations of the robotic arm, a fractional-order interval type II fuzzy sliding mode controller is constructed, wherein the input of the fractional-order interval type II fuzzy sliding mode controller is the sliding surface, and the adjustment parameter is the sliding mode reaching law.

3. The fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method according to claim 2, characterized in that, The specific expression of the six-degree-of-freedom motion equations is as follows: ， ， In the formula, The inertia matrix of the floating base. For the mass of the floating base, The angular velocity of the floating base is... Let be the angular acceleration of the floating base. express The cross product matrix, Let be the displacement of the floating base. The displacement of the floating base and the force exerted on the floating base by the attitude actuator, The displacement of the floating base and the torque exerted on the floating base by the attitude actuator are the following: The force exerted by the robotic arm on the floating base, The torque exerted by the robotic arm on the floating base.

4. The fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method according to claim 2, characterized in that, It also includes a PD controller, The PD controller controls and adjusts the position and attitude of the floating base based on the six-degree-of-freedom motion equations, specifically as follows: ， In the formula, To control the quantity, , These are the forces and torques exerted on the floating base by the displacement and attitude actuators, respectively. It is a proportional gain matrix. The differential gain matrix is... Let be the error vector of the attitude and position of the floating base. It is the first derivative of the error vector.

5. The fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method according to claim 2, characterized in that, The sliding surface is specifically expressed as follows: ， In the formula, Let c be the sliding surface, and c be the sliding surface gain parameter. , The angle error is the difference between the expected joint angle and the actual joint angle of the space robotic arm. is the first derivative of the angle error.

6. The fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method according to claim 2, characterized in that, The sliding mode reaching law is specifically expressed as follows: ， In the formula, For the sliding mode reaching law, , It is a sharp value obtained after fuzzy control defuzzification. The order of a fractional power function. The sliding surface, This is an adjustable parameter.

7. The fractional-order interval type-II fuzzy sliding mode spatial robotic arm tracking control method according to claim 1, characterized in that, The specific expression for determining the joint control torque of the robotic arm based on the constructed fractional-order interval type-II fuzzy sliding mode controller is as follows: ， In the formula, This refers to the joint control torque of the robotic arm; For the generalized coordinates of the robotic arm; The derivative of the joint angle; These are the sliding surface gain parameters; The time derivative of the desired joint angle; This refers to the error angular velocity; The sliding surface; This refers to the sliding mode reaching law; The inertia matrix of the robotic arm; The matrix represents the centrifugal force and the Coriolis force. Here is the stiffness matrix; Let be the motion equivalent moment vector of the floating base.

8. A fractional-order interval type-two fuzzy sliding mode spatial robotic arm tracking control system, characterized in that, include: The data acquisition unit is used to establish the dynamic model of the space robotic arm; The data processing unit is used to construct a fractional-order interval type II fuzzy sliding mode controller based on the dynamic model. The data analysis unit is used to determine the joint control torque of the robotic arm based on the construction of a fractional-order interval type II fuzzy sliding mode controller, so as to realize the tracking control of the space robotic arm.

9. An electronic device, characterized in that, include: Processor and memory, the memory being used to store computer programs; When the computer program is loaded by the processor, it causes the processor to execute the fractional-order interval type-II fuzzy sliding mode spatial manipulator tracking control method as described in any one of claims 1-7.

10. 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 fractional-order interval type-II fuzzy sliding mode spatial manipulator tracking control method as described in any one of claims 1-7.

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