Input-constrained robotic arm tracking control methods, systems, devices, and media

Abstract

This invention discloses a method, system, device, and medium for tracking control of a robotic arm based on input constraints, relating to the field of intelligent control technology. The method includes the following steps: acquiring physical characteristic data and preset performance indicators of the robotic arm; constructing a constrained system model of the robotic arm based on the physical characteristic data and preset performance indicators; performing an equivalent system transformation on the constrained system model to obtain an unconstrained system model; constructing the Hamilton-Jacobi-Bellman equation based on the unconstrained system model and the optimal control strategy of the robotic arm; solving the Hamilton-Jacobi-Bellman equation using an adaptive dynamic programming method to obtain the optimal control law, and controlling the robotic arm according to the optimal control law. This invention solves the technical problem that existing robotic arm control methods cannot achieve optimal control while satisfying preset performance indicator constraints and overcoming asymmetric input limitations.

Description

Technical Field

[0001] This invention relates to the field of intelligent control technology, and in particular to a method, system, device and medium for tracking control of a robotic arm with limited input. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the continuous advancement of technology, research on intelligent control of robotic arms has become increasingly mature, leading to higher standards for the control precision of robotic arms. To improve the control precision of robotic arms, performance requirements are typically set. Therefore, incorporating preset performance indicators into the controller design process is of great significance. Optimal control is a control strategy that considers both system control performance and energy-saving effects. The motion process of a robotic arm is a highly coupled nonlinear system, which poses a significant challenge to traditional optimal control methods. Furthermore, in industrial production, due to the influence of many practical factors such as voltage, weather, and temperature, the input is often not symmetrical. To improve the safety of robotic arm system applications, it is essential to consider asymmetric input limitations.

[0004] Therefore, how to achieve optimal control while meeting preset performance constraints and considering asymmetric input limitations during the control of a robotic arm has become an urgent problem to be solved. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method, system, device, and medium for tracking control of a robotic arm based on input constraints, thereby solving the technical problem that existing robotic arm control methods cannot achieve optimal control while meeting preset performance constraints and overcoming asymmetric input limitations.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0007] The first aspect of this invention provides a tracking control method for a robotic arm based on input constraints, comprising the following steps:

[0008] Acquire the physical characteristics data and preset performance indicators of the robotic arm;

[0009] Based on physical property data and preset performance indicators, a constrained system model of the robotic arm is constructed.

[0010] The constrained system model is transformed into an equivalent system model to obtain an unconstrained system model.

[0011] Based on the unconstrained system model and the optimal control strategy of the robotic arm, the Hamilton-Jacobi-Bellman equation is constructed; where the optimal control strategy is the optimal control strategy of the robotic arm constrained by asymmetric input.

[0012] The Hamilton-Jacobi-Bellman equations are solved using an adaptive dynamic programming method to obtain the optimal control law, which is then used to control the robotic arm.

[0013] Furthermore, the specific steps for constructing the constrained system model of the robotic arm based on physical characteristic data and preset performance indicators are as follows:

[0014] Establish the state-space equation of the robotic arm based on physical property data;

[0015] Define a preset performance function based on preset performance indicators;

[0016] Construct a constrained system model based on the state-space equations and preset performance functions.

[0017] Furthermore, the specific steps for establishing the state-space equation of the robotic arm based on physical characteristic data are as follows:

[0018] The dynamic model of the robotic arm is obtained by modeling the physical property data;

[0019] The dynamic model is transformed based on the physical characteristics of the robotic arm to obtain its state-space equations. Further, the specific steps for constructing the Hamilton-Jacobi-Bellman equations based on the unconstrained system model and the optimal control strategy of the robotic arm are as follows:

[0020] The cost function is defined based on the unconstrained system model and the optimal control strategy of the robotic arm constrained by asymmetric input;

[0021] The Hamilton-Jacobi-Bellman equation is constructed based on the cost function.

[0022] Furthermore, the specific steps for defining the cost function based on the unconstrained system model and the optimal control strategy of the robotic arm constrained by asymmetric input are as follows:

[0023] Based on the position tracking error defined by the unconstrained system model, the augmented state and the positive definite term due to the asymmetric input design are obtained;

[0024] A cost function is defined by combining the augmented state, the positive definite term designed due to asymmetric input, and the optimal control strategy of the robotic arm.

[0025] Furthermore, the specific steps for constructing the Hamilton-Jacobi-Bellman equation based on the cost function are as follows:

[0026] Define the Hamiltonian function and the optimal cost function based on the cost function;

[0027] The optimal cost function is solved using the Bellman optimality principle to obtain the optimal solution of the optimal cost function;

[0028] Substituting the optimal solution into the Hamiltonian function yields the Hamilton-Jacobi-Bellman equation.

[0029] Furthermore, the Hamilton-Jacobi-Bellman equations are solved using an adaptive dynamic programming method based on a neural network architecture to obtain the optimal control law.

[0030] A second aspect of the present invention provides a robotic arm tracking control system based on input constraints, comprising:

[0031] The data acquisition module is used to acquire the physical characteristic data and preset performance indicators of the robotic arm;

[0032] The model building module is used to construct a constrained system model of the robotic arm based on physical property data and preset performance indicators.

[0033] The system transformation module is used to perform equivalent system transformation on the constrained system model to obtain the unconstrained system model;

[0034] The equation construction module is used to construct the Hamilton-Jacobi-Bellman equations based on the unconstrained system model and the optimal control strategy of the robotic arm; where the optimal control strategy is the optimal control strategy of the robotic arm constrained by asymmetric input.

[0035] The optimal control module is used to solve the Hamilton-Jacobi-Bellman equations using an adaptive dynamic programming method to obtain the optimal control law, and then control the robotic arm according to the optimal control law.

[0036] A third aspect of the present invention provides an apparatus including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the input-constrained robotic arm tracking control method described in the first aspect of the present invention.

[0037] A fourth aspect of the present invention provides a medium having a program stored thereon, which, when executed by a processor, implements the steps in the input-constrained robotic arm tracking control method described in the first aspect of the present invention.

[0038] The above one or more technical solutions have the following beneficial effects:

[0039] This invention discloses a method, system, device, and medium for tracking control of a robotic arm based on input constraints. It fully analyzes the constraints of preset performance indicators and considers asymmetric input limitations during the control process. Optimal control is achieved while ensuring the preset performance indicators, resulting in high-precision control of the robotic arm. The method of this invention enables the robotic arm's system output to effectively track the reference signal and ensures that tracking errors meet preset requirements, thus improving control accuracy. It also overcomes the asymmetric input constraints that robotic arms may face in real-world scenarios and has energy-saving effects.

[0040] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0041] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0042] Figure 1 This is a flowchart illustrating the robotic arm tracking control method in Embodiment 1 of the present invention;

[0043] Figure 2 This is a convergence curve diagram for evaluating network weights in Embodiment 1 of the present invention;

[0044] Figure 3 The reference signal x in Embodiment 1 of the present invention d A graph showing the tracking effect against system state x;

[0045] Figure 4 This is a graph showing the tracking error e1 versus the preset performance boundary in Embodiment 1 of the present invention.

[0046] Figure 5 This is a graph showing the tracking error e2 versus the preset performance limit in Embodiment 1 of the present invention.

[0047] Figure 6 This is a graph of the controller in an asymmetric restricted input according to Embodiment 1 of the present invention;

[0048] Figure 7 This is a schematic diagram of the functional modules of the robotic arm control device in Embodiment 2 of the present invention;

[0049] Figure 8 This is a schematic diagram of the hardware structure of the robotic arm control device in Embodiment 3 of the present invention. Detailed Implementation

[0050] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0051] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0052] Example 1:

[0053] Analysis of existing technologies reveals that fast-response, high-precision position tracking control has always been a research hotspot for robotic arms. Currently, most robotic arm tracking control methods remain at the stage of ensuring asymptotic convergence of tracking errors, exhibiting problems such as slow response speed and excessive overshoot. To further improve the control accuracy of robotic arms, it is usually necessary to impose requirements on performance indicators such as convergence rate, maximum overshoot, and steady-state error. Therefore, incorporating preset performance indicators into the controller design process is of great significance. Meanwhile, in industrial production, due to various practical factors and considerations for system application safety, asymmetric input limitations must be taken into account.

[0054] Furthermore, control places higher demands on its energy consumption. Reducing the control cost of robotic arms and minimizing energy consumption is particularly important for current technology. Optimal control is a class of control strategies that consider both system control performance and energy-saving effects. Research shows that the motion process of the robotic arm in the system is a highly coupled nonlinear system, which poses a significant challenge to traditional optimal control methods.

[0055] For optimal control problems of strongly nonlinear systems, adaptive dynamic programming is a viable solution. Based on this design technique, the resulting optimal controller ensures both system stability and optimal system performance. However, for the high-precision tracking control of robotic arms, overcoming asymmetric input limitations and designing an optimal controller that meets preset performance constraints remains a pressing issue.

[0056] Given that existing robotic arm tracking control methods cannot achieve optimal control while satisfying preset performance constraints and overcoming asymmetric input limitations, Embodiment 1 of this invention provides a robotic arm tracking control method based on input constraints, such as... Figure 1 As shown, it includes the following steps:

[0057] S100: Acquires physical characteristic data and preset performance indicators of the robotic arm.

[0058] In one specific implementation, the characteristics of the robotic arm are related to the relationship between displacement control and force control. To simplify the study, this embodiment uses a controller to control it, which is equivalent to a robotic arm.

[0059] Physical characteristic data refers to the mechanical characteristics corresponding to the hardware structure of the robotic arm, such as the robotic arm's own mass, damping, spring constant, and control input parameters. Preset performance indicators refer to the parameters required for the robotic arm to achieve preset performance control, such as the tracking error requirement. The tracking error is the difference between the robotic arm's output signal and the input signal that needs to be tracked; the tracking error indicator can be a range value.

[0060] S200: Construct a constrained system model of the robotic arm based on physical property data and preset performance indicators.

[0061] S210: Establish the state-space equations of the robotic arm based on physical characteristic data. When constructing the state-space equations based on the physical characteristic data of the robotic arm, a dynamic model can be established first and then converted into the form of state-space equations. Alternatively, pre-defined programs or methods, such as some existing modeling software, can be used to directly input the physical characteristic data to obtain the corresponding state-space equations.

[0062] In one specific implementation, a dynamic model is established and then transformed into the form of state-space equations:

[0063] S211: Model the physical property data to obtain the dynamic model of the robotic arm.

[0064] In this embodiment, the physical characteristics of the robotic arm are to be obtained, including the total mass Mg of the robotic arm, the damping coefficient B of the robotic arm, the total rotational inertia J of the motor, and the control input u(t) from the control device to the robotic arm. The physical characteristics of the robotic arm are modeled to obtain the following dynamic model:

[0065]

[0066] Where Mg represents the total mass of the robotic arm itself, and q represents the rotation angle of the robotic arm. Represents the angular velocity of the robotic arm. Let denot angular acceleration, B represent the damping of the robotic arm, J represent the total rotational inertia of the motor, u(t) represent the control input, and t represent time.

[0067] S212: The dynamic model is transformed according to the physical characteristics of the robotic arm to obtain the state-space equation of the robotic arm.

[0068] In this embodiment, based on the physical characteristics of the robotic arm, the equations of the dynamic model obtained from modeling can be transformed into state-space equations. Specifically, after the control device acquires the physical characteristic data of the robotic arm, it can construct a constrained system model of the robotic arm. This model can be a dynamic model or a model of state equations. When constructing state-space equations based on the physical characteristic data of the robotic arm, a dynamic model can be established first and then converted into the form of state-space equations. Alternatively, a pre-defined program or method, such as some existing modeling software, can be used to directly input the physical characteristic data to obtain the corresponding state-space equations.

[0069] In one specific implementation, let x1 = q, The state-space equation of the robotic arm is obtained as follows:

[0070]

[0071]

[0072] Assume the input signal that the robotic arm needs to track is x. d Its first derivative Second derivative If all of these exist, then we can obtain a compact structure of the state-space equations for the robotic arm, that is, the formula for the constrained system model is expressed as:

[0073]

[0074] in,

[0075] S220: Define a preset performance function based on preset performance indicators.

[0076] Preset performance control is a practical technique that can predetermine dynamic performance indicators such as convergence speed and control accuracy. It can keep the tracking error of the robotic arm within a finite range composed of two specified performance functions, thereby ensuring the high dynamic performance of the robotic arm.

[0077] In this embodiment, the tracking error of the robotic arm is the difference between the output signal x and the input signal to be tracked, and it is defined as:

[0078] e(t) = [e1, e2, ..., e n ] T

[0079] =[x1-x d1 x2-x d2 , ..., x n -x dn ] T

[0080] Among them, e i (t) represents the difference between the tracking signal and the tracked signal, i.e., the tracking error.

[0081] To ensure that the tracking error achieves the specified transient and steady-state performance, and to constrain the tracking error within a specified range. The preset performance function, determined based on the preset performance indicators of the robotic arm, is as follows:

[0082]

[0083] Where, δ i,min δ i,max ,ν i η i,0 , and η i,∞ All are positive design parameters and can be set according to actual needs.

[0084] The purpose of the preset performance function is to limit the tracking error to a settable range, which can be adjusted by adjusting the design parameters in the function.

[0085] S230: Construct a constrained system model based on the state-space equations and preset performance functions.

[0086] S300: Perform an equivalent system transformation on the constrained system model to obtain an unconstrained system model.

[0087] In this embodiment, to achieve the goal of high-precision control, a system conversion technique based on a preset performance function is employed. For the output signal of the robotic arm, a smooth, strictly increasing function is introduced:

[0088]

[0089] Among them, z i This represents the unconstrained tracking error after conversion;

[0090] And there are:

[0091] e i (t)=η i (t)k i (z i ),

[0092] The constrained tracking error can be converted into the unconstrained tracking error using the following conversion method:

[0093]

[0094] The derivative of the unconstrained error after transformation is:

[0095]

[0096] in The original system is represented by the transformed unconstrained error.

[0097]

[0098] Where u is the control input, x d This is an ideal signal.

[0099] To facilitate the design of the tracking controller, this embodiment employs an augmented state matrix:

[0100] The transformed augmented system compact set form is:

[0101]

[0102] in

[0103]

[0104]

[0105] By utilizing system transformation techniques to address problems with pre-defined performance constraints, and by defining a nonlinear mapping function based on pre-defined performance indices, a constrained system model can be transformed into an unconstrained equivalent system model. The control strategy designed for the transformed unconstrained system model ensures that the tracking error of the robotic arm remains within a finite range defined by the pre-defined performance function, thereby effectively improving control accuracy.

[0106] S400: Based on the unconstrained system model and the optimal control strategy of the robotic arm, the Hamilton-Jacobi-Bellman equation is constructed; where the optimal control strategy is the optimal control strategy of the robotic arm constrained by asymmetric input.

[0107] S410: To balance control accuracy and the energy consumed by the control input, thereby achieving the goal of optimal control, a cost function is defined. Specifically, the cost function is defined based on the unconstrained system model and the optimal control strategy of the robotic arm constrained by asymmetric input.

[0108] S411: Define the position tracking error based on the unconstrained system model, and obtain the augmented state and the positive definite term due to the asymmetric input design.

[0109] In this embodiment, a new augmented matrix is ​​defined for the transformed unconstrained system model. The so-called asymmetric input constraint means that the control input to the controlled object is u. min <u<u max and||u min ||≠||u max ||, where u minu represents the minimum value of the input limit. max This represents the maximum value of the input limit.

[0110] And define the positive definite terms for the asymmetric input design. for:

[0111]

[0112] in, m is the number of control inputs u, s is the integration variable, and tanh is the hyperbolic tangent function.

[0113] S412: Define the cost function by combining the augmented state, the positive definite term designed due to asymmetric input, and the optimal control strategy of the robotic arm.

[0114] In this embodiment, the optimal control strategy for the robotic arm refers to a control method that enables the system to achieve optimal performance within a certain time frame, given a system model, performance indicators, and constraints. The objective of optimal control is typically to maximize or minimize a specific performance indicator, such as minimizing energy consumption, maximizing system stability, or transferring the system from an initial state to a target state within a finite time. In this embodiment, the optimal control strategy is determined based on the actual control task, and then the following cost function is obtained.

[0115] To ensure system stability, a discount factor ρ is introduced, and the cost function V(X(t)) is defined as follows:

[0116]

[0117] in, It is a positive definite matrix, which can be set according to actual needs. t is the time variable and τ is the integration variable.

[0118] S420: By deriving the Hamilton-Jacobi-Bellman equations based on the cost function defined by the optimal control strategy, the optimal control problem can be transformed into solving the Hamilton-Jacobi-Bellman equations. Specifically, the Hamilton-Jacobi-Bellman equations are constructed based on the cost function.

[0119] S421: Define the Hamiltonian function and the optimal cost function based on the cost function.

[0120] The cost function is defined as the Hamiltonian function as follows:

[0121]

[0122] in,

[0123] In optimal control, the cost function must be minimized to achieve the desired control accuracy with minimal control input. In this embodiment, the optimal cost function is defined as:

[0124]

[0125] Where Ω represents the set of permissible control strategies for the robotic arm, and V * (X) satisfies V * (0) = 0.

[0126] S422: Solve the optimal cost function using the Bellman optimality principle to obtain the optimal solution of the optimal cost function.

[0127] According to the Bellman optimality principle, we can obtain:

[0128]

[0129] in,

[0130] Depend on The optimal solution for the optimal cost function can be obtained as follows:

[0131]

[0132] S423: Substitute the optimal solution into the Hamiltonian function to obtain the Hamilton-Jacobi-Bellman equation.

[0133] In this embodiment, the optimal solution u * Substituting (t) into the Hamiltonian function, we obtain the Hamilton-Jacobi-Bellman equation as follows:

[0134]

[0135] S500: Solve the Hamilton-Jacobi-Bellman equations using an adaptive dynamic programming method to obtain the optimal control law, and control the robotic arm according to the optimal control law.

[0136] S510: The Hamilton-Jacobi-Bellman equations are solved using an adaptive dynamic programming method based on a neural network architecture to obtain the optimal control law.

[0137] In this embodiment, a single-network evaluation network is established based on a neural network architecture, with the optimal cost function V. * (X) can be evaluated as a network approximation as:

[0138]

[0139]

[0140] in, For the ideal weight vector, For the basis function vector, The approximation error is given by m, which represents the number of nodes in the neural network.

[0141] make The optimal cost function can be estimated as follows: (This represents an estimate of the ideal weights.)

[0142]

[0143]

[0144] Then the approximate optimal control law can be obtained as follows:

[0145]

[0146] Thus, the control equipment can control the robotic arm according to the optimal control law, ensuring optimal control based on preset performance indicators, and achieving high-precision control of the system.

[0147] The optimal control law is approximated by a single-network adaptive dynamic programming method to achieve control of the robotic arm. A single evaluation network is used to approximate the optimal cost function. Compared with the traditional execution-evaluation dual network structure, this method helps to reduce the amount of computation and memory requirements.

[0148] Alternatively, the weight update law of the designed evaluation network can be:

[0149]

[0150] in, The design parameter is positive and can be set according to actual needs.

[0151]

[0152] To verify the effectiveness of the robotic arm tracking control method provided in this embodiment, the following simulation experiment was conducted:

[0153] In the simulation experiment, the control objective was set to make the output signal of the robotic arm track the reference signal in the optimal way. Based on the actual system of the robotic arm, the total mass of the robotic arm itself is Mg = 10, the damping of the spring in the robotic arm is B = 2, and the total rotational inertia of the motor is J = 1. The preset performance errors eventually converge to -0.7 < e1 < 0.7 and -2 < e2 < 2, respectively. The initial state values ​​of the robotic arm are x1(0) = 0.1 and x2(0) = 0.1. The tracking signal x... d1 (0) = 0.4, x d2 (0) = 0.4. The function for evaluating the network is set as follows: Its initial weight is w c (0) = [0, 3000, 300, 0, 0, 0] T Finally converged to

[0154] [1.1993,2995.9,304.5066,0.0651,-4.8015,5.0840] T Additionally, the asymmetric input is set to u. min =-4, u max =5, ρ=0.6,

[0155] Choosing Lyapunov functions The results are analyzed by calculating the time derivative. The parameters are designed based on the actual conditions in the simulation experiment; examples are not given here. After analysis, we can obtain... According to Lyapunov's stability theorem, the tracking error z and the positive definite terms due to the asymmetric input design are... And the weight estimation error of the evaluation network. All signals are consistent and eventually bounded, meaning the output signal of the robotic arm system can track the reference signal, and the weights of the evaluation network can converge to near the ideal value, such as... Figure 2 The graph shows the convergence curve of the evaluation network weights. In the graph, the horizontal axis represents time in seconds (s), and the vertical axis represents the value of the evaluation network weights. As can be seen from the graph, the evaluation network can accurately approximate the cost function, and therefore the resulting control input u(t) can be considered optimal.

[0156] like Figure 3 The figure shows the reference signal x in this embodiment. d The graph is a curve representing the system state x. In the graph, the horizontal axis represents time in seconds (s), and the vertical axis represents the value corresponding to each curve; for example... Figure 4 The figure shown is a graph of the tracking error e1 versus the preset performance limit in this embodiment. In the figure, the horizontal axis represents time in seconds (s), and the vertical axis represents the value corresponding to each curve, such as... Figure 5 The figure shown is a graph of the tracking error e2 versus the preset performance limit in this embodiment.

[0157] In the graph, the horizontal axis represents time in seconds (s), and the vertical axis represents the values ​​corresponding to each curve. The preset performance boundary is the curve corresponding to the preset performance index value. Figures 3-5 It can be seen that the system state of the robotic arm corresponding to the output signal is consistent with the reference signal. This control method exhibits good tracking performance, and the tracking error meets the preset performance requirements, enabling high-precision control of the robotic arm. Figure 6The figure shows the control input under asymmetric input constraints in this embodiment. In the figure, the horizontal axis represents time in seconds (s), and the vertical axis represents the value corresponding to each curve, where u min u represents the minimum value in the control input limit. max This represents the maximum value in the control input limits. Figure 6 As can be seen, in this embodiment, the control input is effectively limited to the range between the maximum and minimum values.

[0158] The robotic arm tracking control method provided in this embodiment constructs a constrained system model of the robotic arm based on its physical characteristic data and preset performance indicators. This constrained system model is then transformed into an unconstrained system model through an equivalent system transformation. Next, the Hamilton-Jacobi-Bellman equation is constructed based on the unconstrained system model and the optimal control strategy for the robotic arm constrained by asymmetric input. The Hamilton-Jacobi-Bellman equation is solved using an adaptive dynamic programming method to obtain the optimal control law. This optimal control law controls the robotic arm, achieving high-precision control while ensuring preset performance indicators. The method of this invention enables the robotic arm to effectively overcome asymmetric input constraints while outputting an effective tracking reference signal, ensuring that tracking errors meet preset requirements, thus improving control accuracy and providing energy-saving effects.

[0159] Example 2:

[0160] Embodiment 2 of the present invention provides a robotic arm tracking control system based on input constraints, such as... Figure 7 As shown, it includes:

[0161] The data acquisition module is used to acquire the physical characteristic data and preset performance indicators of the robotic arm;

[0162] The model building module is used to construct a constrained system model of the robotic arm based on physical property data and preset performance indicators.

[0163] The system transformation module is used to perform equivalent system transformation on the constrained system model to obtain the unconstrained system model;

[0164] The equation construction module is used to construct the Hamilton-Jacobi-Bellman equations based on the unconstrained system model and the optimal control strategy of the robotic arm; where the optimal control strategy is the optimal control strategy of the robotic arm constrained by asymmetric input.

[0165] The optimal control module is used to solve the Hamilton-Jacobi-Bellman equations using an adaptive dynamic programming method to obtain the optimal control law, and then control the robotic arm according to the optimal control law.

[0166] Example 3:

[0167] Embodiment 3 of the present invention provides a device including a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the input-constrained robotic arm tracking control method described in Embodiment 1 of the present invention.

[0168] In one specific implementation, the robotic arm control device refers to a terminal device or control device capable of data transmission. It can be a terminal device such as a mobile phone, computer, or embedded industrial computer, or a control device such as a controller or processor located within the system.

[0169] like Figure 8 The diagram shown is a schematic of the hardware structure of a robotic arm control device. The robotic arm control device may include: a processor 1001, such as a CPU (Central Processing Unit), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. Those skilled in the art will understand that... Figure 8 The hardware structure shown does not constitute a limitation on the robotic arm control device of the present invention, and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0170] Specifically, the communication bus 1002 is used to realize the connection and communication between these components; the user interface 1003 is used to connect to the client and communicate data with the client. The user interface 1003 may include output units, such as a display screen, and input units, such as a keyboard; the network interface 1004 is used to connect to the backend server and communicate data with the backend server. The network interface 1004 may include input / output interfaces, such as standard wired interfaces and wireless interfaces, such as Wi-Fi interfaces; the memory 1005 is used to store various types of data, such as instructions for any application or method in the robotic arm control device, as well as application-related data. The memory 1005 may be a high-speed RAM memory or a stable memory, such as a disk storage device; optionally, the memory 1005 may also be a storage device independent of the processor 1001. The memory 1005 may include an operating system, a network communication module, a user interface module, and a robotic arm control program. The processor 1001 is used to call the robotic arm control program stored in the memory 1005.

[0171] The memory is used to store various types of data, which may include, for example, instructions for any application or method in the robotic arm control device, as well as application-related data. The memory can be implemented using any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Random Access Memory (RAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disks, or optical disks. Optionally, the memory can also be a processor-independent storage device.

[0172] The processor is used to call the robotic arm control program stored in the memory and execute the robotic arm tracking control method as described above. The processor can be an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a digital signal processing device (DSPD), a programmable logic device (PLD), a field-programmable gate array (FPGA), a controller, a microcontroller, a microprocessor, or other electronic components, and is used to execute all or part of the steps of the various embodiments of the robotic arm tracking control method described above.

[0173] Example 4:

[0174] Embodiment 4 of the present invention provides a medium on which a program is stored. When the program is executed by a processor, it implements the steps in the input-constrained robotic arm tracking control method described in Embodiment 1 of the present invention.

[0175] The steps and methods involved in Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0176] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0177] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A tracking control method for a robotic arm based on input constraints, characterized in that, Includes the following steps: Acquire the physical characteristics data and preset performance indicators of the robotic arm; Based on physical property data and preset performance indicators, a constrained system model of the robotic arm is constructed. The constrained system model is transformed into an equivalent system model to obtain an unconstrained system model. Based on the unconstrained system model and the optimal control strategy of the robotic arm, the Hamilton-Jacobi-Bellman equations are constructed; wherein, the optimal control strategy is the optimal control strategy of the robotic arm constrained by asymmetric input. The specific steps for constructing the Hamilton-Jacobi-Bellman equations based on the unconstrained system model and the optimal control strategy of the robotic arm are as follows: The cost function is defined based on the unconstrained system model and the optimal control strategy of the robotic arm constrained by asymmetric input. The specific steps for defining the cost function based on the unconstrained system model and the optimal control strategy of the robotic arm constrained by asymmetric input are as follows: Based on the position tracking error defined in the unconstrained system model, the augmented state and the positive definite term due to asymmetric input design are obtained. For the transformed unconstrained system model, a new augmented matrix is ​​defined. The so-called asymmetric input constraint refers to the control of the controlled object being... and ,in This represents the minimum value of the input limit. Represents the maximum value of the input limit; And define the positive definite terms for the asymmetric input design. for: in, m is the number of control inputs u, s is the integration variable, and tanh is the hyperbolic tangent function; Combining the augmented state, the positive definite term designed due to asymmetric input, and the optimal control strategy of the robotic arm, a cost function is defined as follows: in, It is a positive definite matrix, which can be set according to actual needs, and t is a time variable. It is an integral variable; The Hamilton-Jacobi-Bellman equation is constructed based on the cost function; the specific steps for constructing the Hamilton-Jacobi-Bellman equation based on the cost function are as follows: Based on the cost function, the Hamiltonian function and the optimal cost function are defined. The cost function defines the Hamiltonian function as follows: in, ; The optimal cost function is: in, This represents the set of permitted control strategies for a robotic arm. satisfy ; Using the Bellman optimality principle, the optimal solution to the optimal cost function is obtained as follows: ; Substituting the optimal solution into the Hamiltonian function, we obtain the Hamilton-Jacobi-Bellman equation: ; The Hamilton-Jacobi-Bellman equations are solved using an adaptive dynamic programming method to obtain the optimal control law, which is then used to control the robotic arm. The optimal control law is as follows: 。 2. The robotic arm tracking control method based on input constraints as described in claim 1, characterized in that, The specific steps for constructing the constrained system model of the robotic arm based on physical characteristic data and preset performance indicators are as follows: Establish the state-space equation of the robotic arm based on physical property data; Define a preset performance function based on preset performance indicators; Construct a constrained system model based on the state-space equations and preset performance functions.

3. The robotic arm tracking control method based on input constraints as described in claim 2, characterized in that, The specific steps for establishing the state-space equation of the robotic arm based on physical property data are as follows: The dynamic model of the robotic arm is obtained by modeling the physical property data; The dynamic model is transformed based on the physical characteristics of the robotic arm to obtain the state-space equation of the robotic arm.

4. The robotic arm tracking control method based on input constraints as described in claim 1, characterized in that, The Hamilton-Jacobi-Bellman equations are solved using an adaptive dynamic programming method based on a neural network architecture to obtain the optimal control law.

5. A robotic arm tracking control system based on input constraints, used to execute a robotic arm tracking control method based on input constraints as described in any one of claims 1-4, characterized in that, include: The data acquisition module is used to acquire the physical characteristic data and preset performance indicators of the robotic arm; The model building module is used to construct a constrained system model of the robotic arm based on physical property data and preset performance indicators. The system transformation module is used to perform equivalent system transformation on the constrained system model to obtain the unconstrained system model; The equation construction module is used to construct the Hamilton-Jacobi-Bellman equations based on the unconstrained system model and the optimal control strategy of the robotic arm; where the optimal control strategy is the optimal control strategy of the robotic arm constrained by asymmetric input. The optimal control module is used to solve the Hamilton-Jacobi-Bellman equations using an adaptive dynamic programming method to obtain the optimal control law, and then control the robotic arm according to the optimal control law.

6. A computer-readable storage medium, characterized in that, It stores multiple instructions, which are adapted to be loaded and executed by the processor of the terminal device according to any one of claims 1-4, for the input-constrained robotic arm tracking control method.

7. A terminal device, characterized in that, The method includes a processor and a computer-readable storage medium, wherein the processor implements various instructions; and the computer-readable storage medium stores multiple instructions adapted to be loaded by the processor and executed by the processor for the input-constrained robotic arm tracking control method according to any one of claims 1-4.

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