Robot control method and system based on predefined time control obstacle function

Abstract

The invention relates to the technical field of control engineering, in particular to a robot control method and system based on a predefined time control obstacle function, and the method comprises the steps: constructing a high-order control obstacle function; constructing a robot dynamic model; the robot dynamic model is converted into a nonlinear affine system standard form with uncertain items; designing a predefined time adaptive law, and constructing a high-order adaptive control barrier function; and controlling the robot by adopting the high-order self-adaptive control obstacle function. According to the embodiment of the invention, the parameter adaptive law with the predefined time convergence characteristic is designed, so that the estimation of the uncertain parameter is quickly converged within the set time, and the response speed and decision accuracy of the control barrier function are remarkably improved. According to the embodiment of the invention, accurate uncertain boundary knowledge is not required, and even if the estimation of the upper bound is relatively conservative, the system can still realize a non-conservative control effect on the premise of ensuring safety.

Description

Technical Field

[0001] This invention relates to the field of control engineering technology, and more specifically to a robot control method and system based on a predefined time control obstacle function. Background Technology

[0002] The development of robotics technology has enabled it to play an increasingly important role in industrial production and human life, and the complex surrounding environments and tasks have also placed new demands on its safety performance. To avoid damage to objects, robot destruction, and threats to human safety caused by collisions and exceeding speed limits, constraint control with safety as its goal has been extensively studied. Light-duty robots, as core equipment in welding, painting, inspection, and medical assistance, are characterized by small workloads, susceptibility to uncertainties in dynamic parameters, and nonlinear friction. Traditional model-based control methods struggle to achieve reliable safety constraints while maintaining accuracy. Model predictive control (MPC), while capable of handling hard constraints in multi-input / output systems, still has limitations in real-time performance and handling model uncertainties. The obstacle Lyapunov function (BLF) method was initially used to ensure bounded states, but it suffers from initial value sensitivity, a surge in boundary control variables, and difficulties in handling multiple constraints. Control obstacle functions (CBF), based on forward invariance, can achieve safety constraints without altering the inner loop structure, but its performance is highly dependent on model accuracy. In recent years, robust CBF and adaptive CBF have improved the system's ability to constrain under model uncertainty. However, how to achieve high accuracy and high relative safety control in lightly loaded robots with dynamic uncertainty and affected by friction remains an unsolved problem. Summary of the Invention

[0003] The purpose of this invention is to provide a robot control method and system based on a predefined time control obstacle function, in order to solve the technical problem that existing technologies cannot simultaneously meet the requirements of real-time performance, model robustness, high-order safety constraints and smooth performance in light-load robot scenarios.

[0004] To achieve the above objectives, embodiments of the present invention provide a robot control method based on a predefined time-controlled obstacle function, comprising: Construct higher-order control barrier functions; Construct a robot dynamics model; The robot dynamics model is transformed into the standard form of a nonlinear affine system with uncertainties; Design a predefined time-adaptive law and construct a higher-order adaptive control barrier function, including: The adaptive law of parameters in the system analysis process is defined according to formulas (6) and (7). (6) (7) in, For parameter adaptive law, For predetermined parameters, For parameters, This is an auxiliary matrix constructed based on the filtered information. As an auxiliary variable, The weighted error norm; The robot is controlled using the aforementioned high-order adaptive control obstacle function.

[0005] Optionally, a higher-order control barrier function is constructed, including: Construct scalar functions and define safe sets; Given a First-order differentiable function and differentiable extension Class function Define the function set as follows: ,(1); The corresponding definition of the zero superlevel set is: (2); Design a set of control constraints for higher-order control barrier functions.

[0006] Optionally, the robot dynamics model is transformed into the standard form of a nonlinear affine system with uncertainties, including: Construct an uncertain nonlinear affine control system based on formula (3): (3) in, Let be the state vector of the system. , , For local Lipschitz functions To control the quantity, A constant matrix representing uncertain parameters or disturbances; The state of the uncertain nonlinear affine control system Measurable feedback control law Bounded; Unknown parameters The set to which it belongs It is known and is a compact set and a convex set; the parameter regression matrix in the uncertain nonlinear affine control system It provides continuous motivation.

[0007] Optionally, the robot dynamics model is transformed into the standard form of a nonlinear affine system with uncertainties, including: A filter is introduced to perform first-order filtering on the uncertain nonlinear affine control system. Construct an auxiliary matrix based on the filtered information. sum vector ; Define auxiliary variables To obtain the parameter estimation error The linear equation: (4) The robot dynamics model is adapted to an uncertain nonlinear affine control system according to formula (5). (5) in, These are the position, velocity, and acceleration vectors, respectively. The nominal inertia matrix, For the nominal Coriolis matrix, This is the nominal gravity vector. For the reconstructed regression matrix, For input torque vector, For an unknown constant vector; The parameter mapping relationship between the uncertain nonlinear affine control system and the robot dynamics model is obtained as follows: , , in, .

[0008] Optionally, a predefined time-adaptive law is designed, and a higher-order adaptive control barrier function is constructed, including: Obtain the derivative of the Lyapunov function; Obtain the upper bound estimate of the parameter error; A higher-order adaptive control barrier function is constructed based on the adaptive law and the upper bound estimate of the parameter error.

[0009] Optionally, obtaining the derivative of a Lyapunov function includes: Lyapunov functions are obtained based on formulas (6) and (7). The derivative of (8) in, For Lyapunov functions The derivative of .

[0010] Optionally, obtaining an upper bound estimate of the parameter error includes: According to formula (8), when When the time function is obtained, it can be represented by formula (9): (9) in Thus, we can obtain formulas (10) to (12): (10) (11) (12) because Unknown, definition The expression for the upper bound of the parameter error can be obtained as follows: (13) Solve equation (13) to obtain the steady-state time function: , (14).

[0011] Optionally, a higher-order adaptive control barrier function is constructed based on the adaptive law and the upper bound estimate of the parameter error, including: Consider the higher-order adaptive control barrier function ,as well as Defined system state security set If the higher-order adaptive control barrier function Compared to uncertain nonlinear affine control systems, it has The order of relative degree, and the existence of Extensions of differentiability Class function Then for the domain All inside Control input The following conditions must be met: (15) in, These are the parameter estimates updated by the parameter adaptation law. This is the time-varying upper bound estimate of the parameter error. , and They represent along , and about functions Li's derivative; The set of local Lipschitz continuous control laws is obtained according to formula (16): , (16).

[0012] Optionally, the control law is subjected to real-time quadratic programming based on formulas (17) and (18): (17) (18) in, For safety control input, This is the trajectory tracking control law.

[0013] On the other hand, the present invention provides a robot control system based on a predefined time control obstacle function, the system including a processor configured to perform any of the methods described in the robot control method based on the predefined time control obstacle function.

[0014] The beneficial effects of this invention are: This invention, considering system uncertainties, constructs a high-order adaptive control barrier function that can simultaneously constrain state variables with different relative degrees, such as robot input, velocity, and position, achieving multiple safety guarantees under complex dynamics. For critical situations where the robot's initial state may be at the safety boundary but tends towards an unsafe region, this invention designs a parameter adaptive law with predefined time convergence characteristics, enabling the estimation of uncertain parameters to converge rapidly within a set time, significantly improving the response speed and decision accuracy of the control barrier function. Furthermore, compared to robust control methods that rely on prior information about uncertain upper bounds, this invention does not require precise knowledge of the uncertain boundary. Even with a conservative estimate of the upper bound, the system can still achieve non-conservative control effects while ensuring safety, enhancing the system's adaptability and reliability in real-world environments.

[0015] Other features and advantages of the embodiments of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0016] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings: Figure 1 A flowchart illustrating a robot control method based on a predefined time-controlled obstacle function according to an embodiment of the present invention; Figure 2 A flowchart of a dynamic model conversion method according to an embodiment of the present invention; Figure 3 A flowchart illustrating a method for constructing a high-order adaptive control barrier function according to an embodiment of the present invention; Figure 4This is a control block diagram of a predefined time-based high-order adaptive control barrier function according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the Cartesian space trajectory of a robot end effector under a circular task according to an embodiment of the present invention. Figure 6 This is a schematic diagram illustrating the estimation of unknown parameters of a robot under a circular task according to an embodiment of the present invention. Figure 7 This is a schematic diagram of the time-domain trajectory of a robot end effector under a sinusoidal velocity task according to an embodiment of the present invention. Detailed Implementation

[0017] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.

[0018] It should be noted that the acquisition, transmission, storage, use, and processing of data in the technical solution of this application all comply with relevant laws and regulations. In the embodiments of this application, certain existing industry solutions such as software, components, and models may be mentioned. These should be considered exemplary, intended only to illustrate the feasibility of implementing the technical solution of this application, and do not imply that the applicant has already used or necessarily used such solutions.

[0019] like Figure 1 The diagram shows a flowchart of a robot control method based on a predefined time-controlled obstacle function according to an embodiment of the present invention. Figure 1 The control method may include the following steps: In step S10, a higher-order control barrier function is constructed; In step S11, a robot dynamics model is constructed; In step S12, the robot dynamics model is transformed into the standard form of a nonlinear affine system with uncertain terms; In step S13, a predefined time adaptive law is designed, and a high-order adaptive control barrier function is constructed; In step S14, the robot is controlled using the higher-order adaptive control obstacle function.

[0020] In such Figure 1 In the robot control method based on a predefined time-controlled obstacle function, step S10 is used to construct a higher-order control obstacle function. In this embodiment, a nonlinear affine control system is considered: (19), of which It is a state vector. It is a control input. and It is a local Lipschitz vector field.

[0021] The nonlinear affine control system (19) is positively complete, that is, given the control variable... Given an initial state x(0) ∈ D, the solution x(t) is a unique solution in the maximum time domain I(x0) = [0, +∞). Define a scalar function. If the safety state of the nonlinear affine control system (19) is available Hyperlevel set representation: (20) Then it is called For the safety set of the nonlinear affine control system (19).

[0022] If the state x(t, x0) of the nonlinear affine control system (19) originates from S, i.e., x0 = x(0) ∈ S, and for all t ∈ I(x0), x(t) ∈ S, then the set S is forward invariant with respect to the nonlinear affine control system (19). Furthermore, if the set S is forward invariant, then the nonlinear affine control system (19) is safe with respect to the set S.

[0023] After constructing the scalar function and defining the safety set, the higher-order control barrier function (HOCBF) is constructed. Specifically, in this example, the method for constructing the higher-order control barrier function can be given a... First-order differentiable function and differentiable extension Class function Define the function set as follows: (twenty one) That is, abbreviated as: (1) Correspondingly, a series of zero superlevel sets are defined as: (2) Given a nonlinear affine control system (19) and a First-order differentiable function If a differentiable extension exists. Class function And a satisfaction The opening episode , satisfying: (1) exist The middle has relative order (2) For ,have (22). Function That is, the nonlinear affine control system (19) (order) HOCBF, where For function Along the vector field The Lie derivative is expressed as , It satisfies formula (2). It satisfies formula (21).

[0024] Consider a HOCBF that satisfies the above definition. Any local Lipschitz continuous control law All of these can make the set S invariant in the forward direction with respect to the nonlinear affine control system (19), where, (23), that is It is the set of control constraints for higher-order control barrier functions.

[0025] Step S11 is used to construct the robot's dynamics model. For a common robotic arm system, its dynamic equations can be given by the following equation: ,(twenty four) in, These are the position, velocity, and acceleration vectors, respectively. These are inertia, the Coriolis matrix, gravity, and the input torque vector, respectively.

[0026] Dynamic parameters are usually not known precisely; parameter uncertainty can be described as follows: (25) in, This is the nominal value. This is an uncertain term.

[0027] There exists a vector that depends on the structural parameters of the manipulator. This makes the dynamic matrix satisfy the following relationship: (26) in, This is the regression matrix.

[0028] Step S12 is used to transform the robot dynamics model into the standard form of a nonlinear affine system with uncertainties. In this embodiment, the specific method for this dynamics model transformation in step S12 can be of various forms known to those skilled in the art. In one example of the present invention, step S12 may include, for example... Figure 2 The steps shown are described. Figure 2 In this context, step S12 may include: In step S20, key assumptions are established; In step S21, auxiliary variables are defined based on the filter; In step S22, the robot dynamics model is transformed into the standard form of a nonlinear affine system with uncertainties.

[0029] In such Figure 2 In the method shown, step S20 is used to establish key assumptions. Because in real-world applications, the model parameters of robot systems are often difficult to measure directly, or the measurement cost is too high, an unavoidable deviation exists between the dynamic model and the real system. When model errors exist, the resulting uncertainties have a significant impact on the performance of the control system. This problem is particularly critical in robot safety-related tasks: if the system's own safety constraints are violated, it may lead to a shortened lifespan of structural components or direct damage to parts; and if external safety boundaries are breached, it may seriously threaten the lives of personnel. Therefore, to address the above issues, in this example, a perturbation system with uncertainties can be considered: (3) in, Given the local Lipschitz regression matrix, This is a constant matrix representing uncertain parameters or disturbances. For disturbances... The following conditions are allowed when hour, ,Right now It neither disappears nor is small enough.

[0030] To ensure the effective design of the adaptive law, the following assumptions can be made in this example: Assumption 1: The state of the uncertain nonlinear affine control system (3) Measurable feedback control law Bounded.

[0031] Assumption 2: Unknown parameters The set to which it belongs It is known and is a compact set and a convex set.

[0032] Assumption 3: The parameter regression matrix in the uncertain nonlinear affine control system (3) It provides continuous motivation.

[0033] Assumption 2 implies that the parameter estimates can be constrained within the set, i.e. ,in Let the parameter estimation vector be the vector. Then, we can define: (1) If for any parameter vector... ,have ,in for The Archimedes norm is then called the Archimedes norm. For parameter estimation error The upper bound is denoted as (2) For a matrix function If there is a time period and a sufficiently small number ,satisfy ,So Continuous incentives.

[0034] Assumption 3 states that the continuous excitation condition guarantees that the linear equations in the control system have a unique solution.

[0035] Consider satisfying system If this system is stable in a fixed time, and the stable time function is... satisfy If the origin of this system is defined as time-stable, then the system is said to be time-stable. For predefined time.

[0036] Step S21 is used to define auxiliary variables based on the filter. To achieve predefined time stability of parameter estimation, the following is the basic work for system analysis. First, a first-order filter is performed on the uncertain nonlinear affine control system (3): (27) in, , for The filter variable, The filter design parameters, along with the sampling period, determine the filter's cutoff frequency. An auxiliary integral regression matrix is ​​defined. sum vector : (28) in, For the gain parameter, define a parameter error information. Auxiliary variables : (4) Step S22 is used to transform the robot dynamics model into the standard form of a nonlinear affine system with uncertainties. Specifically, in this example, this can be achieved by decoupling, transforming equation (24) into its nominal form with uncertainties: (29) To avoid affecting the regression matrix Mid-angular acceleration term Applications, definitions: (30) At this point, formula (29) can be written as: (5) In the formula Equation (31) can be used to solve the problem: (31) Right now (32) Finally, the expressions related to the dynamic model (5) in the uncertain nonlinear affine control system (3) are as follows: .in, .

[0037] Step S13 is used to design a predefined time-adaptive law and construct a higher-order adaptive control barrier function. In this embodiment, the specific method for constructing the higher-order adaptive control barrier function in step S13 can be of various forms known to those skilled in the art. In one example of the present invention, step S13 may include, for example... Figure 3 The steps shown are described. Figure 3 In this context, step S13 may include: In step S30, the adaptive law is designed and the derivative of the Lyapunov function is obtained; In step S31, the upper bound estimate of the parameter error is obtained; In step S32, a higher-order adaptive control barrier function is constructed based on the adaptive law and the upper bound estimate of the parameter error.

[0038] In such Figure 3 In the method shown, step S30 is used to design the adaptive law. Consider the uncertain nonlinear affine system (3) obtained from the robot dynamics system (24), if the filter and auxiliary vector of the system... Defined by formulas (27), (28) and (4), and whose parameter adaptive law satisfies: (6) In the formula For predetermined parameters, For parameters, Defined as: (7) Then for any initial error , At a predefined time It converges to zero.

[0039] The proof is as follows: The Lyapunov function is: (33) By taking the derivative and combining formulas (4), (6), and (7), we can obtain: (8).

[0040] According to the literature "Predefined-Time Robust Stabilization of RoboticManipulators" For steady-time function The upper bound of the law is such that the adaptive law (6) converges to its truth value in a predefined time, thus having a predefined time. ,Right now .

[0041] Step S31 is used to obtain the upper bound estimate of the parameter error. Specifically, in this example, according to formula (8), when When the time function is obtained, it can be represented by formula (9): (9) in, Thus, we can obtain formulas (10) to (12): (10) (11) (12) because Unknown, definition The expression for the upper bound of the parameter error can be obtained as follows: (13) Solve equation (13) to obtain the steady-state time function: (14).

[0042] steady-state time function The explicit solution shows that It is related to the initial estimation error, and only if... .

[0043] Step S32 is used to construct a higher-order adaptive control barrier function based on the adaptive law and the upper bound estimate of the parameter error. Specifically, in this example, consider an uncertain system (3) and a set defined by equations (1) and (2). With vector field If it exists Extensions of differentiability Class function ,satisfy: (1) If Compared to system (3), it has Rank relative degree; (2)

[0044] (15) in, Updated by the adaptive law (6), From formula (13). Then The predefined time-high-order adaptive control barrier function (PTHOaCBF) for system (3).

[0045] In formula (15) This ensures system safety even with initial estimation errors, and its value decreases to zero upon reaching a steady time, avoiding the over-conservatism of PTHOaCBF.

[0046] Consider PTHOaCBF Any local Lipschitz continuous control law All of these can make set S invariant in the forward direction with respect to system (3), where: (16) According to the literature "High Order Robust Adaptive Control Barrier Functions and Exponentially Stabilizing Adaptive Control Lyapunov Functions", it is only necessary to prove... This will guarantee PTHOACBF The proof regarding the forward invariance of system (3) is as follows: (34) therefore .

[0047] Furthermore, to minimize the impact on control performance while ensuring system safety, a QP-based method is adopted to minimize the norm difference between the feedback control input and the safety input: (17) (18) in, For safety control input, This is the trajectory tracking control law.

[0048] Step S14 is used to control the robot using a higher-order adaptive control obstacle function. Specifically, in this example, the predefined time-based higher-order adaptive control obstacle function control block diagram is as follows: Figure 4 As shown.

[0049] The robot control method based on a predefined time-controlled obstacle function in this invention is compared with commonly used control methods in the field, such as... Figure 5 The figure shows the Cartesian space trajectory of the robot's end effector under a circular task. As can be seen from the figure, compared to other methods, the robot control method based on a predefined time-controlled obstacle function in this invention exhibits accurate safety performance. The estimation of unknown robot parameters under a circular task is as follows: Figure 6 As shown. The time-domain trajectory of the robot's end effector under a sinusoidal velocity task is as follows. Figure 7 As shown.

[0050] On the other hand, the present invention provides a robot control system based on a predefined time control obstacle function, the system including a processor configured to perform any of the methods described in the robot control method based on the predefined time control obstacle function.

[0051] The beneficial effects of this invention are: This invention, considering system uncertainties, constructs a high-order adaptive control barrier function that can simultaneously constrain state variables with different relative degrees, such as robot input, velocity, and position, achieving multiple safety guarantees under complex dynamics. For critical situations where the robot's initial state may be at the safety boundary but tends towards an unsafe region, this invention designs a parameter adaptive law with predefined time convergence characteristics, enabling the estimation of uncertain parameters to converge rapidly within a set time, significantly improving the response speed and decision accuracy of the control barrier function. Furthermore, compared to robust control methods that rely on prior information about uncertain upper bounds, this invention does not require precise knowledge of the uncertain boundary. Even with a conservative estimate of the upper bound, the system can still achieve non-conservative control effects while ensuring safety, enhancing the system's adaptability and reliability in real-world environments.

[0052] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0053] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0054] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0055] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0056] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0057] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0058] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0059] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0060] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A robot control method based on a predefined time-controlled obstacle function, characterized in that, The method includes: Construct higher-order control barrier functions; Construct a robot dynamics model; The robot dynamics model is transformed into the standard form of a nonlinear affine system with uncertainties; Design a predefined time-adaptive law and construct a high-order adaptive control barrier function, including: The adaptive law of parameters in the system analysis process is defined according to formulas (6) and (7). ，（6） ，（7） in, For parameter adaptive law, For predetermined parameters, For parameters, This is an auxiliary matrix constructed based on the filtered information. As an auxiliary variable, The weighted error norm; The robot is controlled using the aforementioned high-order adaptive control obstacle function.

2. The control method according to claim 1, characterized in that, Constructing higher-order control barrier functions includes: Construct scalar functions and define safe sets; Given a First-order differentiable function and differentiable extension Class function Define the function set as follows: ，（1）； The corresponding definition of the zero superlevel set is: ，（2）； Design a set of control constraints for higher-order control barrier functions.

3. The control method according to claim 1, characterized in that, The robot dynamics model is transformed into the standard form of a nonlinear affine system with uncertainties, including: Construct an uncertain nonlinear affine control system based on formula (3): ，（3） in, Let be the state vector of the system. , , For local Lipschitz functions To control the quantity, A constant matrix representing uncertain parameters or disturbances; The state of the uncertain nonlinear affine control system Measurable feedback control law Bounded; Unknown parameters The set to which it belongs It is known and is a compact set and a convex set; the parameter regression matrix in the uncertain nonlinear affine control system It provides continuous motivation.

4. The control method according to claim 3, characterized in that, The robot dynamics model is transformed into the standard form of a nonlinear affine system with uncertainties, including: A filter is introduced to perform first-order filtering on the uncertain nonlinear affine control system. Construct an auxiliary matrix based on the filtered information. sum vector ; Define auxiliary variables To obtain the parameter estimation error The linear equation: ，（4） The robot dynamics model is adapted to an uncertain nonlinear affine control system according to formula (5). ，（5） in, These are the position, velocity, and acceleration vectors, respectively. The nominal inertia matrix, For the nominal Coriolis matrix, This is the nominal gravity vector. For the reconstructed regression matrix, For input torque vector, For an unknown constant vector; The parameter mapping relationship between the uncertain nonlinear affine control system and the robot dynamics model is obtained as follows: ， ， in, .

5. The control method according to claim 1, characterized in that, Design a predefined time-adaptive law and construct a high-order adaptive control barrier function, including: Obtain the derivative of the Lyapunov function; Obtain the upper bound estimate of the parameter error; A higher-order adaptive control barrier function is constructed based on the adaptive law and the upper bound estimate of the parameter error.

6. The control method according to claim 5, characterized in that, To obtain the derivative of a Lyapunov function, including: Lyapunov functions are obtained based on formulas (6) and (7). The derivative of ，（8） in, For Lyapunov functions The derivative of .

7. The control method according to claim 6, characterized in that, Obtaining the upper bound estimate of the parameter error includes: According to formula (8), when When the time function is obtained, it can be represented by formula (9): ，（9） in Thus, we can obtain formulas (10) to (12): ，（10） ，（11） （12） because Unknown, definition The expression for the upper bound of the parameter error can be obtained as follows: （13） Solve equation (13) to obtain the steady-state time function: ，（14）。 8. The control method according to claim 5, characterized in that, Based on the adaptive law and the upper bound estimate of the parameter error, a higher-order adaptive control barrier function is constructed, including: Consider the higher-order adaptive control barrier function ,as well as Defined system state security set If the higher-order adaptive control barrier function Compared to uncertain nonlinear affine control systems, it has The order of relative degree, and the existence of Extensions of differentiability Class function Then for the domain All inside Control input The following conditions must be met: ，（15） in, These are the parameter estimates updated by the parameter adaptation law. This is the time-varying upper bound estimate of the parameter error. , and They represent along , and about functions Li's derivative; The set of local Lipschitz continuous control laws is obtained according to formula (16): ，（16）。 9. The control method according to claim 8, characterized in that, The control law is subjected to real-time quadratic programming based on formulas (17) and (18): ，（17） ，（18） in, For safety control input, This is the trajectory tracking control law.

10. A robot control system based on a predefined time-controlled obstacle function, characterized in that, The system includes a processor configured to perform the method as described in any one of claims 1 to 9.

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