Self-adaptive preset time period event trigger control method for floating-based space robot

Abstract

The invention discloses a self-adaptive preset time period event trigger control method for a floating-based space robot. The method comprises the steps of firstly establishing a space robot dynamic model; secondly, introducing a nonlinear mapping function and a barrier Lyapunov function, converting a state constraint control problem into an unconstrained stability problem, and ensuring that a tracking error is converged within a preset time; furthermore, a periodic event triggering mechanism is designed, and through discrete sampling and triggering condition judgment, the updating frequency of a control signal is greatly reduced, and communication resources are saved; and meanwhile, the uncertainty of the system model is adaptively compensated by adopting a radial basis function neural network. According to the method, the control problem of the free floating space robot in the aspects of state constraint, resource saving and preset time performance is effectively solved, and the reliability, safety and engineering practicability of the system are improved.

Description

Adaptive Preset Time Period Event Triggering Control Method for Floating Base Space Robots Technical Field

[0001] This invention relates to the field of spacecraft control and robotics, and in particular to an adaptive preset time period event triggering control method for floating-based space robots. Background Technology

[0002] With the rapid development of aerospace technology, space robots play an irreplaceable role in missions such as on-orbit servicing, satellite maintenance, and space station construction. Floating-based space robot systems, due to their free-floating base, are typical underactuated systems with nonholonomic constraints. A strong coupling dynamic relationship exists between the robotic arm's motion and the carrier's attitude, posing significant challenges to control system design. In actual space missions, the space robot's joint angles, angular velocities, and other state variables must be strictly constrained within preset ranges due to physical limitations and operational safety requirements. Traditional control methods often struggle to explicitly handle these state constraints, posing a risk of system state out-of-bounds errors. Furthermore, space robots typically exchange data with ground stations or other spacecraft via wireless communication, making communication bandwidth extremely valuable. Traditional time-triggered control methods require updating control signals at a fixed high frequency, consuming significant communication bandwidth and computational resources, especially when the system state tends towards stability, making such high-frequency updates unnecessary.

[0003] While existing control methods based on Lyapunov stability theory exist, they still suffer from the following shortcomings: 1. The system convergence time heavily depends on the initial state, making it impossible to achieve precise convergence within a preset time; 2. It is difficult to effectively handle state constraint problems, leading to the risk of system state out-of-bounds errors; 3. Control signals require continuous or high-frequency updates, resulting in wasted communication and computing resources; 4. Insufficient robustness to system model uncertainties and external disturbances. Summary of the Invention

[0004] To address the above problems, this invention provides an adaptive preset time period event-triggered control method for a floating-based space robot. This method ensures that the state variables of the space robot always meet preset constraints, significantly reduces the update frequency of control signals to save resources, and guarantees that the tracking error of the system converges to an adjustable residual set within a preset time.

[0005] This invention provides an adaptive preset time period event-triggered control method for a floating-based space robot, comprising: S1, establishing a dynamic model of the floating-based space robot based on the Lagrange second kind equation, and setting state constraints of the system so that the joint angles and angular velocities are always within preset constraint boundaries; S2, defining the trajectory tracking error of the system, and introducing a nonlinear mapping function to transform the tracking error, constructing an unconstrained error variable, so that the actual tracking error converges to a specified residual set within a preset convergence time; S3, based on the error variable, constructing a first obstacle Lyapunov function, and designing a first virtual control law to stabilize the dynamics of the error variable, ensuring that the state constraints of the original system are not violated; S4, based on the error... S5. Based on the second virtual control law, design a periodic event triggering mechanism. This mechanism determines whether to update the control signal according to the triggering condition at discrete sampling times, generates intermediate control commands and the final actual control input acting on the system; S6. For the error variables and neural network weight estimation errors, construct a second Lyapunov function and design a neural network adaptive update law to adjust the neural network weights online to approximate the unknown terms of the system; S7. Construct a total Lyapunov function containing all error variables and parameter estimation errors. Based on Lyapunov stability theory, prove that all signals in the closed-loop system are uniformly bounded and that the tracking error converges within the preset convergence time.

[0006] Furthermore, the dynamic model is as follows: The state constraint conditions are as follows: ;in, The joint angle vector; This is the joint angular velocity vector; This is the joint angular acceleration vector; The inertial matrix is ​​symmetric and positive definite. It is a vector containing both Coriolis force and centrifugal force; This is the input vector for the control torque; These are the preset constraint boundaries.

[0007] Furthermore, the construction process of the error variable is as follows: Define the tracking error. ,in Let q be the desired trajectory, and q be the joint angle vector; define And combined with the aforementioned dynamic model, we obtain: ;in, It is the inverse of the inertia matrix; It is a column vector containing Coriolis force and centrifugal force; It is the angular velocity vector; Let be the angular acceleration vector; then the tracking error The tracking error is transformed to obtain: ;in, This is the first virtual control law; Z is a nonlinear mapping function; Z1 is the first-step error variable, i.e., the joint tracking error after coordinate transformation, and... z2 is the error variable for the second step, i.e., the actual joint speed versus the first virtual control law. The deviation between them, and n represents the number of joints in the system.

[0008] Furthermore, the nonlinear mapping function is defined as: Where T is the preset convergence time; t is the time variable; For design parameters, ; For residual coefficients, The nonlinear mapping function satisfies a strictly monotonically increasing property, ensuring that the actual tracking error u converges to the specified residual set after reaching a preset convergence time. ,in Let z1 be the constraint boundary.

[0009] Furthermore, S3 specifically includes: the first barrier Lyapunov function. The expression is: ;in, For z1, the constraint boundary; Differentiation yields: ;in, It is an intermediate variable, and ;u i Let be the tracking error of the i-th joint; Let the derivative of the desired trajectory of the i-th joint with respect to time be given; design the first virtual control law. for: Where c1 is the positive design parameter.

[0010] Furthermore, based on the error variable and the first virtual control law, a second virtual control law is designed. : ;in, The weights are estimated for an ideal neural network; S represents the set of Gaussian functions. c1 is a matrix composed of the diagonal elements of matrix M; c2 represents positive design parameters. Let z2 be the constraint boundary.

[0011] Furthermore, the design of the periodic event triggering mechanism specifically includes: control signals. The update pattern is as follows: ;in, To be at the sampling time The intermediate control quantity calculated in real time is designed as follows: ; Where h is the monitoring period of the event-triggered control strategy; These are positive design parameters, and ; It is a natural number; the triggering condition is: ;in, To trigger error, .

[0012] Furthermore, the second Lyapunov function The expression is: ;in, For adaptive gain; It is the difference between the ideal weight value and the online estimate; the adaptive update law of the neural network. Designed as follows: Where ρ is the robustness parameter, and .

[0013] Furthermore, the total Lyapunov function V is defined as: Its derivative satisfies: ;in, , All are constants.

[0014] Compared with the prior art, the beneficial effects of the present invention are: 1. The present invention designs the virtual control law, the parameter adaptive update law and the neural network weight update law in a unified framework, and rigorously proves the global stability of the closed-loop system through the composite Lyapunov function, thus solving the performance conflict problem caused by the independent design of each subsystem in the traditional method.

[0015] 2. This invention innovatively adopts a periodic event triggering mechanism, updating the control signal only when the triggering conditions are met, which significantly reduces the communication load and saves communication and computing resources compared to traditional time-triggered control.

[0016] 3. This invention, through the design of a nonlinear mapping function, enables the system tracking error to converge within a preset time, and the convergence time is independent of the initial state, which greatly enhances the accuracy and reliability of space mission planning.

[0017] 4. By combining adaptive neural network technology, this invention can approximate and compensate for system model uncertainties, parameter changes and external disturbances in real time, thereby enhancing the robustness and adaptability of the control system in complex spatial environments.

[0018] 5. By employing the obstacle Lyapunov function method, this invention strictly ensures that the system's full state variables always meet the preset constraints, effectively avoiding state out-of-bounds errors and ensuring the safe operation of the space robot. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this drawing or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this drawing. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0020] Figure 1 is a flowchart of the method of the present invention; Figure 2 is a plan view of the space robot in the present invention; Figure 3 is a flowchart of the periodic event triggering mechanism; Figure 4 is a tracking curve of the space robot carrier's attitude angle; Figure 5 is a tracking curve of joint 1 of the space robot carrier; Figure 6 is a tracking curve of joint 2 of the space robot carrier; Figure 7 is a tracking error curve of the space robot's attitude angle; Figure 8 is a tracking curve of joint angle 1 of the space robot. Tracking error curve; Figure 9 shows the joint angle of the space robot. Tracking error curve; Figure 10 is a comparison of the communication performance between event-triggered control and traditional periodic control. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. All other embodiments obtained by those skilled in the art based on the embodiments provided by this invention without inventive effort are within the scope of protection of this invention.

[0022] This invention provides an adaptive preset time period event triggering control method for a floating-based space robot, as shown in Figure 1. Specifically, it includes the following steps: S1, establishing a dynamic model of the floating-based space robot based on the second type of Lagrange equations, and setting state constraints of the system so that the joint angles and angular velocities are always within the preset constraint boundaries.

[0023] The controlled object of this invention is a rigid-arm floating-base space robot system, as shown in Figure 2. It consists of a free-floating carrier, two linked robotic arms, two rotary joints, and two joint actuators. The lengths of link one and link two are respectively... and The attitude angle of the carrier is ,joint and joints The rotation angle is and OXY is the system's inertial coordinate system. It is a moving coordinate system fixed on a carrier or robotic arm.

[0024] The system dynamics model is based on the second kind of Lagrange equation, and its expression is: ;in, Let be an angle vector, and ; Let be the angular velocity vector, and ; Let be the angular acceleration vector, and ; The inertial matrix is ​​symmetric and positive definite. It is a column vector containing Coriolis force and centrifugal force; This is the control torque input vector, i.e., the system input.

[0025] The state constraints of the system are: ;in, , The predefined constraint boundary, and This indicates that constraints are imposed on the joint angle and joint angular velocity.

[0026] S2 defines the system's trajectory tracking error. ,in The desired trajectory.

[0027] definition And combined with the system dynamics model, we get: ;in, It is the inverse of the inertia matrix; It is a column vector containing Coriolis force and centrifugal force; It is the angular velocity vector; This is the angular acceleration vector.

[0028] Then tracking error And perform the following coordinate transformations: Where z1 is the first-step error variable, i.e., the joint tracking error after coordinate transformation, and z2 is the error variable for the second step, i.e., the actual joint speed versus the first virtual control law. The deviation between them, and n is the number of joints in the system; It is a nonlinear mapping function; This is the first virtual control law, used to ensure that the system's state constraints and preset performance are met.

[0029] To ensure that the tracking error reaches the predetermined accuracy residual set within the specified convergence time, a nonlinear mapping function is used. Defined as: Where T is the preset convergence time; t is the time variable; For design parameters, ; For residual coefficients, The nonlinear mapping function enables the tracking error u to converge within a preset convergence time T.

[0030] when When, taking the derivative of the nonlinear mapping function, we get: It can be seen that, Nonlinear mapping function It satisfies the strict monotonically increasing property, and It is continuously differentiable. It is bounded in the interval [0, T).

[0031] The value is taken after the preset convergence time T. So that the actual tracking error u is within Converging to the specified residual set ,in Let z1 be the constraint boundary.

[0032] Lemma 1: For and The following inequalities are satisfied: .

[0033] S3, based on the error variable z1, and according to Lemma 1, define the first barrier Lyapunov function. for: ;in, ,and .

[0034] The options are as follows: These are the necessary state constraints to be met, because , We can obtain: Furthermore, since λ is a monotonically increasing function with a minimum value of 1, therefore It is a new constraint boundary derived to ensure the original state constraints.

[0035] Pick The time derivative is obtained as follows: ;in, It is an intermediate variable, and ;u i It is a component of u.

[0036] Design the first virtual control law for: Where c1 is the positive design parameter.

[0037] Based on the above formula, we obtain: .

[0038] The purpose of designing the first virtual control law is to handle joint angle state constraints, ensuring that the joint angles do not exceed physical constraints, guiding convergence within a preset time, ensuring that the tracking error converges to the residual set within a specified time, and ensuring... The time derivative contains a negative definite term, which is also the basis of hierarchical control.

[0039] S4. Based on the error variable z2 and the first virtual control law, design the second virtual control law. for: ;in, Let M be a matrix consisting of the diagonal elements; This is a crossover error cancellation term, used to ensure... Negative definite; This is the error suppression term, which rapidly suppresses the error variable z2 through the proportional term. For neural network compensation terms, this refers to unknown nonlinear terms in the system model. Provide compensation; Let z2 be the constraint boundary; The weights of the ideal neural network are estimated; S represents the set of Gaussian functions; c2 represents the positive design parameters; design the second virtual control law. The purpose is to handle the state constraints of angular velocity and stabilize the error variable z2.

[0040] S5. To further conserve system network bandwidth resources, reduce the transmission frequency of control signals, and avoid continuous monitoring, the following periodic event-triggered control strategy was designed, as shown in Figure 3, to generate intermediate control commands. and actual control input And at discrete sampling times ( Determine the triggering condition and update the control signal.

[0041] in The following design is proposed: ; ; Where h is the monitoring period of the event-triggered control strategy; These are positive design parameters, and ; It is a natural number.

[0042] It has a built-in saturation mechanism and uses a smooth hyperbolic tangent function to eliminate chattering. It is calculated only at the trigger time, saving communication resources.

[0043] The designed trigger conditions are: ;in, To trigger error, .

[0044] During the trigger interval Within this period, the system did not trigger a control update, i.e. For any scalar , any The following strict equivalence relation holds: ,Right now ,have ,in .

[0045] The above equivalence relation is proven to hold in the following manner: Assume it exists. , making Taking the absolute value and applying the triangle inequality, we get... ;because ,get ;therefore Established.

[0046] make Then for any Existence function Make .

[0047] On the other hand, this method employs zero-order hold (ZOH) for the actual input, meaning that within the trigger interval: ;therefore, The sign is fixed within the interval.

[0048] definition Then for any There is a strict equation: ;make Then there are still And obtain the equation representing the triggering error: ;Right now ;and , satisfy , .

[0049] S6, Construct the second Lyapunov function for: ;in, For adaptive gain; The difference between the ideal weight value and the online estimate. , For ideal weight values, Yes The online estimate.

[0050] Because the second-order state variables of the system must satisfy ,for It can be known ,because , It is a bounded function. and It exists, therefore it is constant. Also exists .based on It can be known .therefore, It can be represented as .

[0051] right Differentiation yields: A radial basis function neural network is introduced to approximate the unknown function of the system. The radial basis function neural network is represented as: ;in, It is a nonlinear function; is the input to the radial basis function neural network; W represents the weights of the neural network. This represents the set of Gaussian functions, where N is the number of nodes in the neural network.

[0052] The specific expression is: ;in, Let represent the center value of the Gaussian function; b is the width of the radial range of the Gaussian function; the approximate value of the Gaussian function can be expressed as: ;in, It represents the approximate error and is bounded in the compact set.

[0053] Ideal weight vector Defined as: It can be seen that, Minimize the error.

[0054] To avoid online estimation of high-dimensional weight vectors To reduce computational complexity, scalarization is used, and unknown scalar parameters are defined. ;use An online estimate of this can be obtained from the Cauchy–Schwarz inequality: According to Young's inequality (Lemma 2), for any have: .

[0055] Therefore, regarding The unknowns are all scalars This is expressed as a scalar upper bound that compresses the unknown weight vector to a form that can be adaptively estimated.

[0056] Design an adaptive update law for neural networks for: Where ρ is the robustness parameter, and .

[0057] S7, Design of the overall Lyapunov function This proves that all signals in the closed-loop system are consistent and eventually bounded, and that the tracking error converges within a preset convergence time.

[0058] Differentiating with respect to V, we get: .

[0059] For the first virtual control law Differentiation yields: .

[0060] Will Substitute From the derivative formula, we get: .

[0061] By approximating the nonlinear term in the above equation using an RBF radial basis neural network, we can obtain: .

[0062] This represents the upper bound of the approximation error of the neural network, which, combined with the two formulas above, yields: .

[0063] in ,based on We can obtain: .

[0064] Lemma 2: For We can obtain: ;in, .

[0065] Using the inequalities of Lemma 2, we can obtain: ;in, .

[0066] Lemma 3: For , Establish the following inequalities: ;in, .

[0067] By processing the above formula, we can obtain: .

[0068] For any real number They all (If tanh has the same sign as the independent variable), then we have: ; combination Therefore, we get: The final result is: .

[0069] Formula Substituting into the above formula, we get: .

[0070] Combining Lemma 3, we get: .

[0071] and Finally, we get: .

[0072] right Further processing yielded: .

[0073] Substituting the designed second virtual control law into the above formula, we get: .

[0074] Substituting the adaptive weight update law into the equation and simplifying, we get: .

[0075] Finally, the derivative of the total Lyapunov function is obtained as follows: .

[0076] According to Lemmas 1 and 2: , , ,get: .

[0077] and Finally, we get: ;in, .

[0078] The final result is: ;in, .

[0079] Lemma 4: Consider the system For smooth positive functions When the following inequalities hold, the nonlinear system For semi-globally consistent bounded limits: ;in, It is a constant.

[0080] Based on the above analysis, it is proven According to Lemma 4, , , Both are bounded, as can be seen from the coordinate transformation formula in S2. ,because It is a bounded variable and design parameters It is composed of, so it can be guaranteed. The boundedness of . Due to It is possible to know Similar to this analysis process, , It is a bounded, periodic-time triggered control strategy with control inputs. It is also bounded. Therefore, we can conclude that all signals in the system are bounded and uniformly stable.

[0081] Based on the properties of the barrier Lyapunov function, we have and Because the design parameters are , , , Therefore, based on the nonlinear mapping function, the full-state constraint requirements are met, resulting in: .

[0082] This means that the tracking error u of the robotic arm under consideration i The residual set converges to the predetermined accuracy within the specified convergence time T. .

[0083] Because a periodic event-triggered control strategy is adopted, the system monitors the triggering conditions only at discrete sampling times and decides whether to update the control signal accordingly; this process is discontinuous. Furthermore, as shown in S4, the monitoring period h of the selected event-triggered control strategy is related to the minimum event time of the event triggering method. This is relevant and corresponds to the proposed periodic event triggering control strategy. The corresponding event triggering control strategy is shown below: .

[0084] In addition, the actual input of this method is obtained by zero-order hold (ZOH): ;because exist Since it is not differentiable at a given point, we introduce the upper right Dini derivative: For absolute value functions, there is a standard inequality: Therefore, we can conclude that: .

[0085] The following definition is given: Because of the boundedness of the barrier and the closed loop, All variables in the set are bounded within the compact set, and exist. For a constant, such that .

[0086] At each trigger moment have The derivative of the trigger error is within the interval between two triggers. Integrating within the interval, the accumulated amount of the triggering error satisfies: .

[0087] Error reset after triggering ,get: The system at the trigger time Instantly and before the update, the following conditions must be met: Therefore, based on the event-triggered control strategy, we can conclude that: .

[0088] The event-triggered control strategy will be verified periodically, and the sampling period h can be selected to be less than or equal to the lower bound of the time interval. The selection of the sampling period h must satisfy the following conditions: , Based on the aforementioned analysis, and considering the maximum sampling period, event-triggered control has a lower bound on the minimum event interval time. And satisfy This prevented Zeno's behavior.

[0089] In summary, by introducing an obstacle Lyapunov function to handle system state constraints, designing a periodic event triggering mechanism to reduce communication load, combining a nonlinear mapping function to achieve convergence within a preset time, and using an adaptive neural network to compensate for system uncertainties, it is possible to significantly reduce the control signal update frequency while strictly ensuring that the system state does not exceed the limits. This ensures that the floating space robot achieves high-precision trajectory tracking control within a preset time, while effectively saving communication and computing resources.

[0090] Figure 2 is a plan view of the space robot in this invention. The system consists of a freely floating carrier. Rigid connecting rod composition, and The components are connected using rigid joints. The symbols in the diagram are defined as follows: For the system's inertial coordinate system, For split The system is in the moving coordinate system. Motion in a plane Link The axis of symmetry; For the system's overall centroid, As the centroid of the carrier, and With respect to the center of rotation of the carrier coincide, Link The center of mass; For each component Relative to the origin of the inertial coordinate system The radius vector; the split The masses are respectively The moment of inertia is ; The center of the rotational hinge; For the carrier attitude angle, Link Joint angle; and The distance between them is , and The distance between them is , The length is .

[0091] Taking the space robot shown in Figure 2 as an example, a program was written in MATLAB to simulate and verify the feasibility of the adaptive preset time event triggering control method for space robots with state constraints proposed in this invention.

[0092] The system physical parameters are shown in Table 1 below, and the controller parameters are shown in Table 2 below. The initial state of the system (unit: radians) is as follows: , , The desired trajectory (in radians) of the space robot joints is: .

[0093] Table 1 System Physical Parameters

[0094] Table 2 Controller Parameters

[0095] Figures 4-6 show the performance of the space robot's posture and joint angle tracking. The proposed periodic event-triggered control strategy achieves rapid convergence in a short time, demonstrating excellent tracking performance. This rapid convergence characteristic not only improves the system's response speed but also ensures the stability and reliability of the control process.

[0096] Figures 7-9 show the tracking errors of the space robot's posture and joint angles, depicting the error variations of the posture angles and joint angles. Simulation results show that the tracking errors of the three joint angles remain at a low level and do not exceed the preset output error constraint range. This phenomenon fully verifies the effectiveness and robustness of the proposed control algorithm.

[0097] Figure 10 shows a comparison of communication performance between event-triggered control and traditional periodic control. Compared to a 1ms communication cycle, it can save 90.9% of communication resources, 72.7% compared to a 3ms communication cycle, 54.5% compared to a 5ms communication cycle, and 36.3% compared to a 7ms communication cycle. The number of event triggers is 2727, with a trigger rate of 9.09%. The results indicate that the proposed event-triggered control can significantly reduce communication load while maintaining control performance.

[0098] It should be noted that the present invention is not limited to the above-described embodiments. The above embodiments are merely examples, and any embodiments that have the same structure and perform the same effects as the technical concept within the scope of the present invention are included within the scope of the present invention. Furthermore, various modifications that can be conceived by those skilled in the art to the embodiments, and other ways of constructing by combining some of the constituent elements of the embodiments, without departing from the spirit of the present invention, are also included within the scope of the present invention.

Claims

1. A method for adaptive preset time period event triggering control of a floating base space robot, characterized in that, include: S1. Establish a dynamic model of the floating space robot based on the second type of Lagrange equations and set state constraints for the system to ensure that joint angles and angular velocities remain within preset constraint boundaries. S2. Define the system's trajectory tracking error and introduce a nonlinear mapping function to transform the tracking error, constructing an unconstrained error variable so that the actual tracking error converges to a specified residual set within a preset convergence time. S3. Based on the error variable, construct a first obstacle Lyapunov function and design a first virtual control law to stabilize the dynamics of the error variable, ensuring that the state constraints of the original system are not violated. S4. Based on the error variable and the first virtual control law, design a second virtual control law. S5. Based on the second virtual control law, a periodic event triggering mechanism is designed. This mechanism determines whether to update the control signal according to the triggering condition at discrete sampling times, generates intermediate control commands and the final actual control input acting on the system; S6. For the error variables and neural network weight estimation errors, a second Lyapunov function is constructed, and an adaptive update law for the neural network is designed to adjust the neural network weights online to approximate the unknown terms of the system; S7. A total Lyapunov function containing all error variables and parameter estimation errors is constructed. Based on Lyapunov stability theory, it is proved that all signals in the closed-loop system are uniformly bounded eventually, and the tracking error converges within the preset convergence time.

2. The adaptive preset time period event triggering control method for a floating base space robot according to claim 1, characterized in that, The dynamic model is as follows: The state constraint conditions are as follows: ;in, Let be the joint angle vector, and n be the number of joints in the system; This is the joint angular velocity vector; This is the joint angular acceleration vector; The inertial matrix is ​​symmetric and positive definite. It is a vector containing both Coriolis force and centrifugal force; This is the input vector for the control torque; These are the preset constraint boundaries.

3. The adaptive preset time period event triggering control method for a floating base space robot according to claim 1, characterized in that, The construction process of the error variable is as follows: Define the tracking error. ,in Let q be the desired trajectory, and q be the joint angle vector; define And combined with the aforementioned dynamic model, we obtain: ;in, It is the inverse of the inertia matrix; It is a column vector containing Coriolis force and centrifugal force; It is the angular velocity vector; It is the angular acceleration vector; The control torque input vector is used; therefore, the tracking error... The tracking error is transformed to obtain: ;in, This is the first virtual control law; Z is a nonlinear mapping function; Z1 is the first-step error variable, i.e., the joint tracking error after coordinate transformation, and... z2 is the error variable for the second step, i.e., the actual joint speed versus the first virtual control law. The deviation between them, and n represents the number of joints in the system.

4. The adaptive preset time period event triggering control method for a floating base space robot according to claim 3, characterized in that, The nonlinear mapping function is defined as follows: Where T is the preset convergence time; t is the time variable; For design parameters, ； The residual coefficient is... The nonlinear mapping function satisfies a strictly monotonically increasing property, ensuring that the actual tracking error u converges to the specified residual set after reaching a preset convergence time. ,in Let z1 be the constraint boundary.

5. The adaptive preset time period event triggering control method for a floating base space robot according to claim 1, characterized in that, Specifically, S3 includes: the first barrier Lyapunov function. The expression is: Among them, z 1i This is the error variable for the first step; For z 1i The constraint boundary; n is the number of joints in the system; for Differentiation yields: ;in, It is an intermediate variable, and ;u i Let be the tracking error of the i-th joint; Let z be the derivative of the expected trajectory of the i-th joint with respect to time; 2i The error variable for the second step; design the first virtual control law. for: Where c1 is the positive design parameter.

6. The adaptive preset time period event triggering control method for a floating base space robot according to claim 1, characterized in that, Design a second virtual control law based on the error variable and the first virtual control law. ： ;in, The weights are estimated for an ideal neural network; S represents the set of Gaussian functions. c2 is a matrix consisting of the diagonal elements of matrix M; c2 represents positive design parameters; z 2i z is the error variable for the second step. 1i This is the error variable for the first step; Let z2 be the constraint boundary; It is a nonlinear mapping function; For z 1i The constraint boundary.

7. The adaptive preset time period event triggering control method for a floating base space robot according to claim 6, characterized in that, The designed periodic event triggering mechanism specifically includes: control signals. The update pattern is as follows: ;in, To be at the sampling time The intermediate control quantity calculated in real time is designed as follows: ； Where h is the monitoring period of the event-triggered control strategy; These are positive design parameters, and ； It is a natural number; the triggering condition is: ;in, To trigger error, 。 8. The adaptive preset time period event triggering control method for a floating base space robot according to claim 6, characterized in that, The second Lyapunov function The expression is: ;in, For adaptive gain; It is the difference between the ideal weight value and the online estimate; n is the number of joints in the system; neural network adaptive update law Designed as follows: Where ρ is the robustness parameter, and 。 9. The adaptive preset time period event triggering control method for a floating base space robot according to claim 1, characterized in that, The total Lyapunov function V is defined as follows: ； Its derivative satisfies: ;in, 、 All are constants; The first barrier is the Lyapunov function; This is the second barrier Lyapunov function.

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