Predictive time tracking control method for free-floating space manipulator system

Abstract

This application relates to a predetermined-time tracking control method for a free-floating space manipulator system, and pertains to the field of trajectory tracking control technology for manipulator systems. The aim is to address the poor stability and low robustness of free-floating space manipulator systems when facing model uncertainties and external disturbances. This application establishes a dynamic model of the space manipulator in free-floating mode; designs a nonlinear disturbance observer based on predetermined-time convergence; constructs piecewise continuous sliding mode variables based on the dynamic model; constructs a non-singular predetermined-time sliding mode controller based on the dynamic model, the nonlinear disturbance observer, and the piecewise continuous sliding mode variables; and utilizes the non-singular predetermined-time sliding mode controller to perform predetermined-time trajectory tracking control on the free-floating space manipulator system.

Description

Technical Field

[0001] This application belongs to the field of trajectory tracking and control technology for robotic arm systems. Background Technology

[0002] As human exploration of space deepens, the complexity and diversity of space missions are increasing year by year. Free-floating space robotic arms, characterized by their flexible operation, long endurance, and high load capacity, are widely used in space missions such as on-orbit assembly, on-orbit maintenance, and target acquisition.

[0003] Because the base floats in a microgravity environment and only the joints are controlled, the space robotic arm system is highly dynamically coupled. The movement of the robotic arm causes changes in the base's attitude and center of mass, which in turn affects the positioning and attitude fixation of the end effector, making its dynamic modeling, path planning, and control more complex and difficult than that of traditional robots. Furthermore, space robotic arms face more complex and harsher operating environments; any unknown disturbance can lead to the failure of the space mission, requiring the robot to have strong robustness and reliable control capabilities. Therefore, how to ensure high-precision tracking control of a free-floating space robotic arm in complex and changing environments has become a research hotspot. Summary of the Invention

[0004] This application aims to address the issues of poor stability and low robustness of free-floating space robotic arm systems when faced with model uncertainties and external disturbances. A predetermined time tracking control method for free-floating space robotic arm systems containing model uncertainties and external disturbances is provided.

[0005] This application provides a predetermined time tracking control method for a free-floating space robotic arm system.

[0006] Establish a dynamic model of the space robotic arm in free-floating mode;

[0007] Design a nonlinear perturbation observer based on predetermined time convergence;

[0008] Construct piecewise continuous sliding mode variables based on the aforementioned dynamic model;

[0009] A non-singular predetermined time sliding mode controller is constructed based on the dynamic model, the nonlinear disturbance observer, and the piecewise continuous sliding mode variables, and the non-singular predetermined time sliding mode controller is used to perform predetermined time trajectory tracking control on the free-floating space robotic arm system.

[0010] In one possible design, establishing the dynamic model of the space robotic arm in free-floating mode includes:

[0011] Construct a dynamic model of a spatial robotic arm in joint space under free-floating mode;

[0012] By treating parameter uncertainties and external disturbances as lumped disturbances, the dynamic model of the space manipulator in the joint space under the free-floating mode is transformed to obtain the dynamic model of the space manipulator under the free-floating mode.

[0013] In one possible design, the expression for the dynamic model of the space manipulator in joint space in the free-floating mode is:

[0014] ,

[0015] in, , and These are the angle vector, angular velocity vector, and joint acceleration vector of the robotic arm joint, respectively. Input torque for the control of the robotic arm joints. External disturbances The inertia matrix of a free-floating space robotic arm system. Let be the matrix of centrifugal force and Coriolis force.

[0016] In one possible design, the expression for the dynamic model of the space manipulator in the free-floating mode is:

[0017] ,

[0018] in, and Let be the state variables of a free-floating space robotic arm system, and have , ;

[0019] and They are respectively and Standard items;

[0020] Let be the lumped disturbance term of the free-floating space robotic arm system, and its expression is:

[0021] ,

[0022] and They are respectively and Error term.

[0023] In one possible design, the design is based on the expression of a nonlinear perturbation observer that converges over a predetermined time:

[0024] ,

[0025] in, and These are the angular velocities of the robotic arm joints. and lumped disturbance term The observation error,

[0026] and These are the angular velocities of the robotic arm joints. and lumped disturbance term The estimated value.

[0027] In one possible design, constructing piecewise continuous sliding mode variables based on the dynamic model includes:

[0028] The tracking error model of the free-floating space manipulator system is constructed with the goal of ensuring that the angle vectors of the manipulator joints of the free-floating space manipulator system can track their expected values.

[0029] Based on the tracking error model, a piecewise continuous sliding mode variable is designed.

[0030] In one possible design, the objective of the free-floating space robotic arm system can be expressed as follows:

[0031] ,

[0032] in, , and These are the angle vector, angular velocity vector, and joint acceleration vector of the robotic arm joint, respectively. for Expected value and They are respectively and Standard items, The inertia matrix of a free-floating space robotic arm system. The matrix of centrifugal force and Coriolis force. Input torque for the control of the robotic arm joints. This is the lumped disturbance term for the free-floating space robotic arm system.

[0033] In one possible design, the tracking error model expression of the free-floating space robotic arm system is:

[0034] ,

[0035] in, This refers to the angular error of the robotic arm joints. for The second derivative, for The second derivative of .

[0036] In one possible design, the expression for the piecewise continuous sliding mode variable is:

[0037] ,

[0038] in, For piecewise continuous sliding mode variables; for The first derivative;

[0039] intermediate variables exist: ;

[0040] , , and All are sliding surface gain coefficients, and we have: , , , , , and All are sliding mode variable parameters. , , ;

[0041] intermediate variables , ;

[0042] To adjust the parameters; It is a very small positive number; The upper bound of the predetermined time for the trajectory tracking error of the free-floating space robotic arm system to converge to 0; Represents a symbolic function.

[0043] In one possible design, the expression for the non-singular predetermined-time sliding mode controller is:

[0044] ,

[0045] Among them, intermediate variables ;

[0046] and They are respectively and Standard items, The inertia matrix of a free-floating space robotic arm system. The matrix represents the centrifugal force and the Coriolis force.

[0047] intermediate variables The first derivative of , and we have:

[0048] ;

[0049] , , and All are sliding surface gain coefficients, and we have: , , , , , and All are sliding mode variable parameters. , , ;

[0050] intermediate variables exist: , , ;

[0051] It is a very small positive number; The upper bound of the predetermined time for the trajectory tracking error of the free-floating space robotic arm system to converge to 0;

[0052] For lumped disturbance terms The estimated value; , and These are the angle vector, angular velocity vector, and joint acceleration vector of the robotic arm joint, respectively. Let be the second derivative of the expected value of the angle vector of the robotic arm joint;

[0053] , , and All are gain coefficients of non-singular sliding mode controllers. , , , , , and These are all parameters for non-singular sliding mode controllers. , , ;

[0054] For piecewise continuous sliding mode variables; To adjust the parameters; Represents a symbolic function; For the sliding mode variables to converge from the initial state to the sliding surface The upper limit of the scheduled time.

[0055] The beneficial effects of this application are:

[0056] This application improves the robustness and stability of the space robotic arm system in free-floating mode, while considering both model uncertainties and external disturbances. The control mechanism consists of a predetermined-time observer and a predetermined-time sliding mode controller. The predetermined-time observer estimates the lumped disturbances of the system, including model uncertainties and external disturbances. A non-singular predetermined-time sliding mode controller is designed to enable the system to converge within a preset time range. The upper bound of the convergence time is fully set by the user and is independent of the initial state. Simulation results show that this application enables the output trajectory of the space robotic arm system to exhibit better dynamic and steady-state performance. Attached Figure Description

[0057] Figure 1 This is a schematic diagram illustrating the principle of a predetermined time control scheme based on a predetermined time observer.

[0058] Figure 2 Waveforms of the tracking trajectory of joint 1 angle of a space manipulator under different initial errors;

[0059] Figure 3 Waveforms of the tracking trajectory of joint 2 angle of a space manipulator under different initial errors;

[0060] Figure 4 The waveforms of the tracking error of joint 1 angle of the space manipulator under different initial errors are shown.

[0061] Figure 5 The waveforms of the tracking error of joint 2 angle of the space manipulator under different initial errors are shown.

[0062] Figure 6 Waveforms of sliding mode variables of joint 1 of a space manipulator under different initial errors;

[0063] Figure 7 Waveforms of sliding mode variables of joint 2 of a spatial robotic arm under different initial errors;

[0064] Figure 8 The waveform of the joint control torque of the space manipulator under large initial error;

[0065] Figure 9 Waveform of the floating trajectory of the space manipulator base under large initial error;

[0066] Figure 10 The waveform of the lumped disturbance observed by the space manipulator under large initial error;

[0067] Figure 11 The waveform diagram shows the observation error of the space robot under large initial error. Detailed Implementation

[0068] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other.

[0069] Traditional control methods such as PID control, sliding mode control, and backstepping control, while effective, are mostly asymptotically stable, meaning the error converges to zero in infinite time. Finite-time control can guarantee that the spacecraft's attitude state converges to an equilibrium point within a finite time, but the upper bound of the convergence time depends on the initial state. Some researchers have proposed fixed-time control strategies to solve the trajectory tracking control problem of uncertain robot systems. The system can converge within a fixed time and is independent of the initial state. However, it is difficult to obtain an explicit relationship between the fixed upper bound of the convergence time and the adjustable parameters, and the controller design is complex, resulting in less than ideal application performance. Therefore, predetermined-time control has received widespread attention from some researchers. The upper bound of the convergence time in predetermined-time control is entirely set by the user and is independent of the initial conditions, reducing the complexity of controller design. Subsequently, researchers proposed various predetermined-time control algorithms, but few have been applied to space robotic arm systems, and they have not considered modeling errors.

[0070] In summary, the convergence time of current finite-time control algorithms is affected by the initial state of the system, fixed-time control algorithms are complex to design, and most existing predetermined-time control methods have not been applied to space robotic arm systems.

[0071] In view of this, the present application provides a predetermined time tracking control method for a free-floating space robotic arm system to solve the above-mentioned problems. The solution of the present application embodiment will be described in detail below.

[0072] The predetermined time tracking control method for a free-floating space robotic arm system described in this embodiment is characterized by comprising:

[0073] Establish a dynamic model of the space robotic arm in free-floating mode;

[0074] Design a nonlinear perturbation observer based on predetermined time convergence;

[0075] Construct piecewise continuous sliding mode variables based on the aforementioned dynamic model;

[0076] A non-singular predetermined time sliding mode controller is constructed based on the dynamic model, the nonlinear disturbance observer, and the piecewise continuous sliding mode variables, and the non-singular predetermined time sliding mode controller is used to perform predetermined time trajectory tracking control on the free-floating space robotic arm system.

[0077] In one implementation, establishing the dynamic model of the space robotic arm in free-floating mode includes:

[0078] Construct a dynamic model of a spatial robotic arm in joint space under free-floating mode;

[0079] By treating parameter uncertainties and external disturbances as lumped disturbances, the dynamic model of the space manipulator in the joint space under the free-floating mode is transformed to obtain the dynamic model of the space manipulator under the free-floating mode.

[0080] In one embodiment, the expression for the dynamic model of the space robotic arm in the joint space in the free-floating mode is:

[0081] ,

[0082] in, , and These are the angle vector, angular velocity vector, and joint acceleration vector of the robotic arm joint, respectively. Input torque for the control of the robotic arm joints. External disturbances The inertia matrix of a free-floating space robotic arm system. Let be the matrix of centrifugal force and Coriolis force.

[0083] In one implementation, the expression for the dynamic model of the space robotic arm in the free-floating mode is:

[0084] ,

[0085] in, and Let be the state variables of a free-floating space robotic arm system, and have , ;

[0086] and They are respectively and Standard items;

[0087] Let be the lumped disturbance term of the free-floating space robotic arm system, and its expression is:

[0088] ,

[0089] and They are respectively and Error term.

[0090] In one implementation, the design is based on the expression for a nonlinear perturbation observer that converges over a predetermined time:

[0091] ,

[0092] in, and These are the angular velocities of the robotic arm joints. and lumped disturbance term The observation error,

[0093] and These are the angular velocities of the robotic arm joints. and lumped disturbance term The estimated value.

[0094] In one implementation, constructing piecewise continuous sliding mode variables based on the dynamic model includes:

[0095] The tracking error model of the free-floating space manipulator system is constructed with the goal of ensuring that the angle vectors of the manipulator joints of the free-floating space manipulator system can track their expected values.

[0096] Based on the tracking error model, a piecewise continuous sliding mode variable is designed.

[0097] In one implementation, the objective of the free-floating space robotic arm system can be expressed as follows:

[0098] ,

[0099] in, , and These are the angle vector, angular velocity vector, and joint acceleration vector of the robotic arm joint, respectively. for Expected value and They are respectively and Standard items, The inertia matrix of a free-floating space robotic arm system. The matrix of centrifugal force and Coriolis force. Input torque for the control of the robotic arm joints. This is the lumped disturbance term for the free-floating space robotic arm system.

[0100] In one embodiment, the tracking error model expression of the free-floating space robotic arm system is:

[0101] ,

[0102] in, This refers to the angular error of the robotic arm joints. for The second derivative, for The second derivative of .

[0103] In one implementation, the expression for the piecewise continuous sliding mode variable is:

[0104] ,

[0105] in, For piecewise continuous sliding mode variables; for The first derivative;

[0106] intermediate variables exist: ;

[0107] , , and All are sliding surface gain coefficients, and we have: , , , , , , ;

[0108] intermediate variables , ;

[0109] To adjust the parameters; It is a very small positive number; The upper bound of the predetermined time for the trajectory tracking error of the free-floating space robotic arm system to converge to 0; Represents a symbolic function.

[0110] In one implementation, the expression for the non-singular predetermined time sliding mode controller is:

[0111] ,

[0112] Among them, intermediate variables ;

[0113] and They are respectively and Standard items, The inertia matrix of a free-floating space robotic arm system. The matrix represents the centrifugal force and the Coriolis force.

[0114] intermediate variables The first derivative of , and we have:

[0115] ;

[0116] , , and All are sliding surface gain coefficients, and we have: , , , , , , ;

[0117] intermediate variables exist: , , ;

[0118] It is a very small positive number; The upper bound of the predetermined time for the trajectory tracking error of the free-floating space robotic arm system to converge to 0;

[0119] For lumped disturbance terms The estimated value; , and These are the angle vector, angular velocity vector, and joint acceleration vector of the robotic arm joint, respectively. Let be the second derivative of the expected value of the angle vector of the robotic arm joint;

[0120] , , and All are gain coefficients of non-singular sliding mode controllers. , , , , , , ;

[0121] For piecewise continuous sliding mode variables; To adjust the parameters; Represents a symbolic function; For the sliding mode variables to converge from the initial state to the sliding surface The upper limit of the scheduled time.

[0122] To further illustrate the implementation scheme of this application, Figure 1 A predetermined time tracking control method for a free-floating space robotic arm system is provided, comprising steps one through five, wherein the numbering of the steps does not necessarily restrict their execution order. Each step is described in detail below:

[0123] Step 1: Establish a dynamic model of the space robotic arm in free-floating mode, and treat model uncertainties and external disturbances as lumped disturbances.

[0124] The dynamic model of the space robotic arm in free-floating mode in joint space is represented as follows:

[0125] (1),

[0126] In the formula, , and These represent the angle vector, angular velocity vector, and joint acceleration vector of the robotic arm joint, respectively. Input torque for joint control. Represents external disturbances. Symmetric positive definite matrix. Here is the inertia matrix of the robotic arm system. Let be the matrices of centrifugal force and Coriolis force, and let their expressions be as follows:

[0127] (2),

[0128] in, for Standard items, for Error term, for Standard items, for Error term, and All of these are modeling error coefficients.

[0129] This embodiment addresses a space robotic arm system with parameter uncertainties and external disturbances. First, it defines the system state variables. , The dynamic model of the space robotic arm can be transformed into the following formula:

[0130] (3),

[0131] in, For the lumped disturbance term of the system, in free-floating mode, the base of the space robotic arm is not subjected to torque, only the joints are controlled, and the momentum of the system is conserved throughout the motion.

[0132] Step 2: Design a nonlinear perturbation observer that converges within a predetermined time, then estimate the lumped perturbation of the system, and use Lyapunov's stability theorem to prove that the perturbation observation error can converge within a predetermined time.

[0133] The specific form of the nonlinear observer based on predetermined time convergence is as follows:

[0134] (4),

[0135] In the formula, and These represent the observation errors for joint velocity and lumped disturbance, respectively. It is joint velocity The estimated value, It is a lumped disturbance term The estimated value.

[0136] Based on this, the update rate of the nonlinear perturbation observer is designed as follows:

[0137] (5),

[0138] in, , , , , , and All of these are gain coefficients of nonlinear perturbation observers. , and These are all nonlinear disturbance observer parameters. , , , , , , , Intermediate variables for adjusting parameters , This is the upper bound of the convergence time when the observation error approaches 0.

[0139] Based on the designed observer, i.e., formula (5), it can be proven through Lyapunov stability that the observation error will be within the predetermined time. It converges to 0.

[0140] Step 3: Based on the spatial robotic arm dynamics model established in Step 1, construct piecewise continuous sliding mode variables to avoid singularities in sliding mode control. Specifically, this includes:

[0141] Step 3.1. Define the control objective: For a space robotic arm system in free-floating mode containing model uncertainties and friction, determine the system state variables... Able to track expectations :

[0142] (6),

[0143] Step 3.2: Transform the model to obtain the tracking error model of the robotic arm system:

[0144] (7),

[0145] Step 3: Design segmented continuous sliding surfaces Specific form:

[0146] (8),

[0147] in, (9);

[0148] , , and All are sliding surface gain coefficients. , , , , , , ; , and All of these are sliding mode variable parameters designed. , , intermediate variables , , It is a very small positive number. This is the upper bound of the predetermined time for the trajectory tracking error of the robotic arm system to converge to 0.

[0149] Step 4: Based on the space robotic arm model and predetermined time observer designed in Steps 1 and 2, and combined with Step 3, design a novel non-singular predetermined time sliding mode controller so that the system can achieve rapid convergence within a predetermined time independent of the initial state.

[0150] The specific form of the pre-set time non-singular sliding mode controller is as follows:

[0151] (10)

[0152] in, , , and All are gain coefficients of non-singular sliding mode controllers. , , , , , , ; , and These are all parameters for non-singular sliding mode controllers. , , ; The sliding mode variables converge from the initial state to the sliding surface. The upper limit of the scheduled time.

[0153] Step 5: Use Lyapunov's stability theorem to prove the stability of the system.

[0154] According to Lyapunov's stability theorem and the predetermined time convergence theorem, the upper bound of the convergence time of the predetermined time control scheme designed in this embodiment is:

[0155] for ,have:

[0156] (11),

[0157] In the formula, The upper bound of the convergence time for the space robotic arm system in the preset free-floating mode to track the desired trajectory.

[0158] The effectiveness of this embodiment is verified through simulation results. For the two-degree-of-freedom spatial robotic arm system, the desired trajectory is selected as follows: The external disturbance acting at the joint is To further verify the effectiveness of the present invention, three sets of simulation experiments were set up to compare and analyze the tracking performance of the space robot under no initial error (Group A, initial error of 0 rad), small initial error (Group B, initial error of 0.2 rad), and large initial error (Group C, initial error of 1 rad). The specific control parameters are shown in Table 1.

[0159] Table 1

[0160]

[0161] Figures 2 to 7 The joint angle tracking waveform, tracking error waveform, and sliding mode variable waveform of the space robot under the proposed control scheme are shown under three different initial errors. Figures 8 to 11 The waveforms of the joint control torque, base floating trajectory, disturbance observation, and observation error of the space manipulator under large initial errors are shown. Experimental results demonstrate that the predetermined-time non-singular sliding mode control method based on a predetermined-time observer proposed in this invention achieves convergence and high-precision trajectory tracking of the space manipulator system within a predetermined time, and the angle tracking error is within... The rad-level readings verified the effectiveness of the invented control algorithm.

[0162] In summary, this embodiment proposes a novel predetermined-time nonsingular sliding mode control scheme based on a predetermined-time observer to address the trajectory tracking problem of a free-floating space manipulator system. By designing a nonlinear disturbance observer to compensate for lumped disturbances and designing corresponding sliding mode variables, the controlled object achieves rapid convergence within a predetermined time range, ensuring accurate trajectory tracking of the desired space manipulator system with model uncertainties and external disturbances in base-floating mode.

[0163] While specific embodiments of this application have been described herein with reference to them, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A predetermined time tracking control method for a free-floating space robotic arm system, characterized in that, include: Establish a dynamic model of the space robotic arm in free-floating mode; Design a nonlinear perturbation observer based on predetermined time convergence; Construct piecewise continuous sliding mode variables based on the aforementioned dynamic model; A non-singular predetermined time sliding mode controller is constructed based on the dynamic model, the nonlinear disturbance observer, and the piecewise continuous sliding mode variables, and the non-singular predetermined time sliding mode controller is used to perform predetermined time trajectory tracking control on the free-floating space robotic arm system.

2. The predetermined time tracking control method for a free-floating space robotic arm system according to claim 1, characterized in that, The establishment of the dynamic model of the space robotic arm in free-floating mode includes: Construct a dynamic model of a spatial robotic arm in joint space under free-floating mode; By treating parameter uncertainties and external disturbances as lumped disturbances, the dynamic model of the space manipulator in the joint space under the free-floating mode is transformed to obtain the dynamic model of the space manipulator under the free-floating mode.

3. The predetermined time tracking control method for a free-floating space robotic arm system according to claim 2, characterized in that, The expression for the dynamic model of the space robotic arm in the joint space under the free-floating mode is as follows: ， in, , and These are the angle vector, angular velocity vector, and joint acceleration vector of the robotic arm joint, respectively. Input torque for the control of the robotic arm joints. External disturbances The inertia matrix of a free-floating space robotic arm system. Let be the matrix of centrifugal force and Coriolis force.

4. The predetermined time tracking control method for a free-floating space robotic arm system according to claim 3, characterized in that, The expression for the dynamic model of the space robotic arm in the free-floating mode is as follows: ， in, and Let be the state variables of a free-floating space robotic arm system, and have , ; and They are respectively and Standard items; Let be the lumped disturbance term of the free-floating space robotic arm system, and its expression is: ， and They are respectively and Error term.

5. The predetermined time tracking control method for a free-floating space robotic arm system according to claim 1 or 4, characterized in that, The design is based on the expression of a nonlinear perturbation observer that converges within a predetermined time: ， in, and These are the angular velocities of the robotic arm joints. and lumped disturbance term The observation error, and These are the angular velocities of the robotic arm joints. and lumped disturbance term The estimated value.

6. The predetermined time tracking control method for a free-floating space robotic arm system according to claim 1, characterized in that, The step of constructing piecewise continuous sliding mode variables based on the dynamic model includes: The tracking error model of the free-floating space manipulator system is constructed with the goal of ensuring that the angle vectors of the manipulator joints of the free-floating space manipulator system can track their expected values. Based on the tracking error model, a piecewise continuous sliding mode variable is designed.

7. The predetermined time tracking control method for a free-floating space robotic arm system according to claim 6, characterized in that, The objective of the free-floating space robotic arm system can be expressed as follows: ， in, , and These are the angle vector, angular velocity vector, and joint acceleration vector of the robotic arm joint, respectively. for Expected value and They are respectively and Standard items, The inertia matrix of a free-floating space robotic arm system. The matrix of centrifugal force and Coriolis force. Input torque for the control of the robotic arm joints. This is the lumped disturbance term for the free-floating space robotic arm system.

8. The predetermined time tracking control method for a free-floating space robotic arm system according to claim 7, characterized in that, The tracking error model expression for the free-floating space robotic arm system is as follows: ， in, This refers to the angular error of the robotic arm joints. for The second derivative, for The second derivative of .

9. The predetermined time tracking control method for a free-floating space robotic arm system according to claim 8, characterized in that, The expression for the piecewise continuous sliding mode variable is: ， in, For piecewise continuous sliding mode variables; for The first derivative; intermediate variables exist: ; , , and All are sliding surface gain coefficients, and we have: , , , , , and All are sliding mode variable parameters. , , ; intermediate variables , ; To adjust the parameters; It is a very small positive number; The upper bound of the predetermined time for the trajectory tracking error of the free-floating space robotic arm system to converge to 0; Represents a symbolic function.

10. The predetermined time tracking control method for a free-floating space robotic arm system according to claim 1, 4, or 9, characterized in that, The expression for the non-singular predetermined time sliding mode controller is: ， Among them, intermediate variables ; and They are respectively and Standard items, The inertia matrix of a free-floating space robotic arm system. The matrix represents the centrifugal force and the Coriolis force. intermediate variables The first derivative of , and we have: ； , , and All are sliding surface gain coefficients, and we have: , , , , , and All are sliding mode variable parameters. , , ; intermediate variables exist: , , ; It is a very small positive number; The upper bound of the predetermined time for the trajectory tracking error of the free-floating space robotic arm system to converge to 0; For lumped disturbance terms The estimated value; , and These are the angle vector, angular velocity vector, and joint acceleration vector of the robotic arm joint, respectively. Let be the second derivative of the expected value of the angle vector of the robotic arm joint; , , and All are gain coefficients of non-singular sliding mode controllers. , , , , , and These are all parameters for non-singular sliding mode controllers. , , ; For piecewise continuous sliding mode variables; To adjust the parameters; Represents a symbolic function; For the sliding mode variables to converge from the initial state to the sliding surface The upper limit of the scheduled time.

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