A design method for preset performance trajectory tracking controller of a two-degree-of-freedom manipulator

Abstract

A design method for a preset performance trajectory tracking controller for a two-degree-of-freedom manipulator is proposed. The state space equation is established based on the dynamic model of the two-degree-of-freedom manipulator. The reference trajectory is tracked according to the output trajectory to generate a tracking error. The tracking error is limited to the envelope of the fixed-time preset performance function, and the tracking error constrained by the inequality is converted into an unconstrained equivalent error. The two-degree-of-freedom manipulator system is divided into two-level subsystems, and a virtual controller and a first adaptive law are designed to make the first-level subsystem stable in fixed time. A fixed-time self-trigger preset performance trajectory tracking controller and a second adaptive law are designed to make the entire two-degree-of-freedom manipulator system stable in fixed time, and the controller gain is determined to complete the design of the fixed-time self-trigger preset performance trajectory tracking controller. This trajectory tracking controller improves the anti-interference and response speed of the two-degree-of-freedom manipulator system, and meets the preset tracking performance requirements within any time.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical arm control, and in particular to a design method for a preset performance trajectory tracking controller of a two-degree-of-freedom mechanical arm. Background Art

[0002] With the continuous advancement of technology, robotic arms have become an important tool to replace humans in repetitive, persistent, precise and dangerous tasks, and have been widely used in industrial automation production, medical treatment, semiconductor manufacturing and space exploration. Nowadays, the requirements for the operational capabilities of robotic arms are also increasing. Most work scenarios have high control accuracy requirements. If the expected accuracy is not achieved, serious economic and safety accidents will occur. It should be pointed out that the trajectory tracking control of the robotic arm is the basis for completing the above complex control problems. Based on this, it is necessary to design a fast and high-precision trajectory tracking controller. In addition, most existing controller design methods often ignore the fact that the trajectory tracking error needs to meet the requirements of transient performance and steady-state performance at the same time during the convergence process. Some core indicators including convergence time, maximum overshoot and steady-state accuracy cannot be guaranteed at the same time. Therefore, how to improve the transient performance and steady-state performance of the tracking error is a task of great significance.

[0003] In addition, when performing tasks, the robot arm needs to transmit and calculate external information in real time, and most robot arm controllers are based on time-triggered control strategies. The disadvantage of this method is that the system control signal is continuously updated, which will undoubtedly lead to a waste of system communication resources and mechanical wear of the actuator. Furthermore, during the transmission process, most of the control signals are encoded as 8-bit or 16-bit digital signals. When packet loss, delay, blocking and other problems inevitably occur during network transmission, the tracking performance of the robot arm will be greatly affected. Therefore, how to reduce the update frequency of the control signal and reduce data transmission problems is very important both in theory and in practice. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a design method of a preset performance trajectory tracking controller of a two-degree-of-freedom robotic arm, which improves the response speed and tracking performance of the two-degree-of-freedom robotic arm system.

[0005] In order to achieve the above technical purpose, the technical solution adopted is: a design method for a preset performance trajectory tracking controller of a two-degree-of-freedom manipulator, comprising the following steps:

[0006] Step 1: Establish the state space equation based on the dynamic model of the two-degree-of-freedom manipulator;

[0007] Step 2: Based on the state space equation of step 1, the reference trajectory is tracked according to the output trajectory of the two-degree-of-freedom manipulator to generate a tracking error e1i (t), by establishing an inequality relationship, the tracking error is limited to a fixed time preset performance function η i The error conversion function Ξ is established within the envelope of i (ε i (t)) and the equation relationship e 1i (t) = η i (t)Ξ i (ε i (t)), the tracking error constrained by the inequality is converted into an unconstrained equivalent error. The tracking error of the two-degree-of-freedom manipulator system after the equivalent transformation is:

[0008] Step 3: According to the tracking error of the two-degree-of-freedom manipulator system after the equivalent transformation obtained in step 2, the coordinate transformation is constructed based on the adaptive backstepping control method, and the two-degree-of-freedom manipulator system is divided into two-level subsystems. For the first-level subsystem, a virtual controller α1 and the first adaptive law are designed to make it stable in fixed time. Then the controller gain to be designed for the first-level subsystem is obtained. For the second-level subsystem, combined with the self-triggering control mechanism, a fixed-time self-triggering preset performance trajectory tracking controller τ(t) and a second adaptive law are designed to make the entire two-degree-of-freedom manipulator system stable in fixed time. Then the controller gain to be designed for the second-level subsystem is obtained, completing the design of the fixed-time self-triggered preset performance trajectory tracking controller.

[0009] A 1-bit encoding and decoding mechanism is designed according to the triggering conditions of the self-triggering control mechanism.

[0010] The specific implementation form of the triggering condition of the self-triggering control mechanism is to calculate the next triggering time of the control signal according to the current information of the system controller, encode it according to the difference between the previous triggering time and the next triggering time of the control signal, and encode the control signal as 1 when the difference is greater than zero. On the contrary, when the difference is less than zero, the control signal is encoded as 0. The encoded signal is then transmitted to the decoder for decoding to obtain the actual control signal, which is then transmitted to the actuator of the two-degree-of-freedom robotic arm system.

[0011] The beneficial effects of the present invention are:

[0012] 1. This method does not require an accurate two-degree-of-freedom robotic arm system model and prior knowledge of disturbances. Through online identification, the system model is gradually improved. The designed fixed-time self-triggering preset performance trajectory tracking controller solves the problem that the upper bound of the system's stable time cannot be determined when the initial position is unknown in the traditional control scheme. It ensures that all signals of the two-degree-of-freedom robotic arm closed-loop system are fixed-time bounded. At the same time, the upper bound of the system's stable time can be estimated and is independent of the system's initial position conditions, and improves the anti-interference and response speed of the two-degree-of-freedom robotic arm system.

[0013] 2. Different from the traditional exponential preset performance function, the time for the tracking error to converge to the preset performance interval cannot be quantitatively expressed. The higher the set stability accuracy, the longer the convergence time. Only when the time tends to infinity can the tracking error converge to the preset performance interval. The present invention introduces a fixed time preset performance function to ensure that within any time to be set, the tracking error can converge to the envelope (performance interval) of the performance function, meet the preset tracking performance requirements, and effectively improve the transient performance and steady-state performance of the system. The maximum overshoot, convergence time and steady-state accuracy of the system can be arbitrarily designed according to actual needs, which can meet the performance requirements in different situations.

[0014] 3. Combined with the self-triggering control mechanism, a fixed-time self-triggering preset performance trajectory tracking controller is designed to effectively avoid the continuous updating of the two-degree-of-freedom robot arm controller signal. While realizing the indirect updating of the controller signal, it still ensures that the output trajectory of the two-degree-of-freedom robot arm system can quickly track the reference trajectory.

[0015] 4. Based on the triggering conditions of the self-triggering mechanism, a 1-bit encoding and decoding mechanism is designed. When the control signal is updated, only 1-bit encoding signal needs to be transmitted, which reduces the occurrence rate of failures such as packet loss, blocking and hysteresis during signal transmission, and improves the accuracy of control signal transmission, thereby ensuring the tracking performance of the two-degree-of-freedom robotic arm system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a schematic diagram of a two-degree-of-freedom robotic arm;

[0017] Figure 2 It is a schematic diagram of the design flow of a fixed-time self-trigger preset performance tracking controller and a 1-bit encoding and decoding mechanism for a two-degree-of-freedom manipulator;

[0018] Figure 3 It is a structural diagram of the trajectory tracking control method of a two-degree-of-freedom manipulator;

[0019] Figure 4 is the tracking error trajectory diagram of the first manipulator of the two-degree-of-freedom manipulator;

[0020] Figure 5 is the tracking error trajectory diagram of the second manipulator of the two-degree-of-freedom manipulator;

[0021] Figure 6 is the control input curve diagram of the first manipulator of the two-degree-of-freedom manipulator;

[0022] Figure 7 is the control input curve diagram of the second manipulator of the two-degree-of-freedom manipulator;

[0023] Figure 8 is the trigger interval diagram of the control input of the first arm of the two-degree-of-freedom robot;

[0024] Fig. 9 is a trigger interval diagram of the control input of the second arm of a two-degree-of-freedom robot;

[0025] Fig.10 is the first robot tracking error trajectory diagram including sampling error;

[0026] Fig.11 It is the tracking error trajectory of the second robot including sampling error. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0028] A method for designing a preset performance trajectory tracking controller for a two-degree-of-freedom robotic arm comprises the following steps:

[0029] Step 1.1, according to Figure 1 The schematic diagram of the two-degree-of-freedom robotic arm is shown, and its dynamic model is described as follows:

[0030]

[0031] Where: M(ω,t) is the inertia matrix; is the centrifugal-Coriolis force matrix; G(ω,t) is the gravity vector; Δ(t) is the disturbance vector; u(t) is the control force vector; ω, and Represent the position vector, velocity vector and acceleration vector respectively; t is time; m1 and m2 represent the mass of the first robot arm and the second robot arm respectively; l1 and l2 represent the length of the first robot arm and the second robot arm respectively; g is the gravitational acceleration; ω1, and Respectively represent the position, velocity and acceleration of the first robot arm; ω2, and The position, velocity and acceleration of the second robot arm; u1(t) and u2(t) represent the input signals of the first robot arm and the second robot arm respectively. For simplicity, let M(ω,t) = M, G(ω,t)=G,Δ(t)=Δ.

[0032] For subsequent analysis, the following state space equation is established based on the dynamic model of the two-degree-of-freedom robotic arm system in formula (1):

[0033]

[0034] Where: f2(x1,x2,t)=M -1 (-CG-Δ), g2(x1,x2,t)=M -1 , y1 is the output trajectory of the two-degree-of-freedom robot. For simplicity, let f2(x1,x2,t)=f2, g2(x1,x2,t)=g2.

[0035] Step 1.2: Based on the state space equation obtained in step 1.1, the main control goal of the two-DOF manipulator trajectory tracking control is to output the trajectory y1 to track the reference trajectory y as much as possible. d =[y 1d y 2d ] T ,y 1d is the reference trajectory of the first robot arm, y 2d is the reference trajectory of the second robot arm, which will generate a tracking error e 1i (t) = x 1i -y id In order to make the tracking error have good transient performance and steady-state performance (shorter convergence time, smaller overshoot and higher steady-state accuracy), the following fixed time preset performance function η is introduced i (t)(i=1,2) to constrain the tracking error e 1i (t):

[0036]

[0037] Where: η i,0 and η i,∞are the initial value and steady-state value of the fixed-time performance function, T i is the convergence time to be designed. The fixed-time preset performance function is a monotonically decreasing, continuous and differentiable function. The performance envelope is artificially designed using the convergence characteristics of the fixed-time preset performance function, and the tracking error is constrained within the performance function envelope, thereby meeting the preset tracking performance requirements.

[0038] In order to achieve the purpose of controlling the tracking error constraint, the tracking error is limited to a fixed time preset performance function η by establishing the following inequality relationship: i Within the envelope of (t):

[0039] -ζ i,min η i (t)≤e 1i (t)≤ζ i,max η i (t) (4)

[0040] Where: i.min >0,ζ i.max >0, and satisfies -ζ i,min η i (0)≤e 1i (0)≤ζ i,max η i (0), where e 1i (0) is the tracking error at the initial moment, η i (0) = η i,0 .

[0041] Furthermore, in order to avoid the increase in controller design complexity and difficulty caused by the introduction of a fixed-time preset performance function, the following error conversion function Ξ is established: i (ε i (t)) and the equation relationship e 1i (t) = η i (t)Ξ i (ε i (t)), converting the tracking error subject to inequality constraints into an unconstrained equivalent error:

[0042]

[0043] Where: ε i (t) is the conversion error. The tracking error of the system after equivalent transformation is:

[0044] Step 1.3: Based on the tracking error of the system after equivalent transformation obtained in step 1.2, the following coordinate transformation is constructed based on the adaptive backstepping control method:

[0045]

[0046] Where: The two-degree-of-freedom manipulator system is divided into two-level subsystems, and the error variables z1 and z2 are introduced. The corresponding subsystems are stabilized by the designed virtual controller, so that the error variables z1 and z2 tend to be stable. Finally, the actual controller τ(t) is designed to ensure the fixed-time stability of the two-degree-of-freedom manipulator system, and then the controller gain to be designed is determined to achieve the tracking of the reference trajectory within a fixed time. First, a continuous and positive Lyapunov function is constructed for the first-level subsystem, and the virtual controller α1 and the first adaptive law that make the first-level subsystem fixed-time stable are designed. Based on the fixed-time stability of the first-level subsystem, the Lyapunov function of the second-level subsystem is constructed, and the actual controller τ(t) and the second adaptive law are further designed. The fixed-time stability of the entire closed-loop system is guaranteed, and the controller gain is obtained on the basis of the stability of the closed-loop system to achieve effective tracking of the reference trajectory.

[0047] Step 1.4: Based on the coordinate transformation constructed in step 1.3, construct the following continuous and positive Lyapunov function V1 for the first-level subsystem of the two-degree-of-freedom manipulator:

[0048]

[0049] Where: ρ1 is a positive constant, represents the estimation error, is the estimated value of the ideal weight vector θ1, is the estimated error, and κ1 is an unknown constant.

[0050] Furthermore, by taking the derivative of the Lyapunov function V1 of the first-level subsystem with respect to time, we can obtain:

[0051]

[0052] Where: in is the reference trajectory y d The derivative of .

[0053] For the nonlinear function in the above formula The radial basis function neural network technique is used to approximate Specifically, it can be expressed as:

[0054]

[0055] Where: represents the ideal weight vector, Indicates that the input is The radial basis function, Represents the approximation error and satisfies is a normal number, represent The transpose of .

[0056] By using Young's inequality and constructing the following virtual controller α1 and the first adaptive law Ensure the first-level subsystem is stable at fixed time:

[0057]

[0058]

[0059] Where: and γ 1i (i=1,2,j=1,2,3) is the positive controller gain to be designed, in It is represented as a diagonal matrix, max{*} means taking the maximum value in *, and ||·|| means the Frobenius norm of vector ·.

[0060] The designed virtual controller α1 and the first adaptive law Substituting into formula (8), we can get:

[0061]

[0062] Where: κ1=min{k 1i}(i=1,2), and ι is a positive constant, and min{*} represents the minimum value among *.

[0063] Based on Lyapunov's fixed-time stability theory, it is proved that the designed virtual controller α1 and the first adaptive law The first-level subsystem of the two-degree-of-freedom manipulator system can be stabilized in fixed time, and then the virtual controller α1 and the first adaptive law can be obtained. On the basis of ensuring the fixed time stability of the first-level subsystem, the actual controller τ(t) and the second adaptive law are further designed. This enables the entire closed-loop system (two-degree-of-freedom robotic arm system) to achieve fixed-time stability.

[0064] Step 1.5: Based on step 1.4 (if the first-level subsystem is unstable, the second-level subsystem will also be unstable), construct a continuous and positive definite Lyapunov function V2 of the second-level subsystem:

[0065]

[0066] Where: ρ2 is a positive constant, is the estimation error and satisfies is the estimated value of the ideal weight vector θ2, and κ2 is an unknown constant.

[0067] Furthermore, by taking the derivative of formula (12) with respect to time t, we can obtain:

[0068]

[0069] Where: in is the derivative of α1. Use radial basis neural network to approximate nonlinear terms The specific form is as follows:

[0070]

[0071] Where: represents the ideal weight vector, represent The transpose of represents the radial basis function, is the input vector of the radial basis function, Represents the error generated by the radial basis neural network approximation process and satisfies Is a normal number.

[0072] By using Yong's inequality, we define Where max{*} means taking the maximum value among *, the second adaptive law The design is as follows:

[0073]

[0074] Where: ρ2, γ 21 and γ 22 is the positive controller gain to be designed.

[0075] Since most robot arm controllers are based on a time-triggered control framework, the disadvantage of this control method is that the system control signal is continuously updated, which will undoubtedly lead to a waste of system communication resources and cause mechanical wear of the actuator. In order to solve this problem, the present invention introduces a self-triggering control mechanism into the fixed-time trajectory tracking controller design, and calculates the next triggering time of the control signal based on the information of the previous triggering time. When the designed triggering condition (16) is met, the control signal will be updated and transmitted to the actuator, reducing the update frequency of the control signal and the wear of the actuator. The self-triggering controller is designed as follows:

[0076]

[0077]

[0078]

[0079] Where: τ(t)=[τ1(t) τ2(t)] T , τ1(t) is the actual controller of the first robot arm, τ2(t) is the actual controller of the second robot arm, t i,k and t i,k+1 is a positive integer, μ i >0 and satisfies Represented as control signal u i (t) absolute value of the derivative, Indicates the time interval between two consecutive trigger control signals. and Indicates the rate of change of the control signal interval, σ i , μ i , and is the positive controller gain to be designed.

[0080] In order to introduce the self-triggering controller, the following equation relationship and time-varying function ξ are constructed: 1i (t i,k )=ξ 2i (t i,k )=0,ξ 1i (t i,k+1 )=ξ 2i (t i,k+1 )=±1, and satisfy |ξ 1i (t)|≤1 and |ξ 2i (t)|≤1,

[0081]

[0082] Combining formula (15) and formula (18), and using the second adaptive law and the actual controller τ(t), we can get:

[0083]

[0084] Where: κ2= g 2, ι is a positive constant, g 2 and are the upper and lower bounds of g2 respectively, and min{*} represents the minimum value among *.

[0085] For the second-level subsystem of the two-degree-of-freedom manipulator, the designed actual controller τ(t) and the second adaptive law are used The second-level subsystem of the two-degree-of-freedom manipulator system achieves fixed-time stability, and then obtains the actual controller τ(t) and the second adaptive law The control gain of

[0086] Furthermore, in order to prove the fixed-time stability of the entire closed-loop system, the first-level subsystem Lyapunov function V1 and the second-level subsystem Lyapunov function V2 are combined to construct the following total Lyapunov function:

[0087] V=V1+V2 (20)

[0088] By taking the derivative of formula (20) with respect to time, we can obtain:

[0089]

[0090] Where:

[0091] According to formula (21), the designed virtual controller α1, the actual controller τ(t), and the first adaptive law and the second adaptive law It is ensured that all signals of the two-DOF manipulator closed-loop system are fixed-time bounded, and the upper bound of its stable fixed time is Where 0<Λ<1; and at the fixed time to be set T i The tracking error of the system is 1i (t) Converge to the envelope of the performance function and meet the preset tracking performance requirements.

[0092] According to the above analysis, since all signals of the two-DOF manipulator closed-loop system are fixed-time bounded, the input signal u(t) is bounded, and further we can get It is also bounded, that is, the lower limit of the time interval between two consecutive trigger controls satisfies t * =t i,k+1 -t i,k >0, effectively avoiding the Zeno effect.

[0093] So far, the design of a fixed-time self-triggering preset performance trajectory tracking controller for a two-degree-of-freedom robotic arm system has been completed. Furthermore, considering the 8-bit or 16-bit encoding mechanism adopted by most actual systems, each transmission of the control signal will occupy a large amount of network bandwidth channels, which may cause a network burden. To address this problem, the present invention designs a 1-bit encoding and decoding mechanism between the controller and the actuator of the two-degree-of-freedom robotic arm. According to the triggering condition of the self-triggering control mechanism, when the control signal is updated, only a 1-bit digital signal (0 or 1) needs to be transmitted, which reduces unnecessary occupation of network channels and reduces the incidence of faults such as packet loss, blocking and hysteresis during signal transmission. The accuracy of control signal transmission is improved, thereby ensuring the tracking performance of the two-degree-of-freedom robotic arm system. The design steps of the 1-bit encoding and decoding mechanism are as follows:

[0094] Step 2.1: According to the triggering conditions of the self-triggering control mechanism, whenever the triggering conditions are met, the control signal is updated, and then encoded according to the difference between the last triggering moment and the next triggering moment of the control signal. When the difference is greater than zero, the control signal is encoded as 1. On the contrary, when the difference is less than zero, the control signal is encoded as 0. The encoder design is as follows:

[0095]

[0096] Step 2.2: Encoder output m i Transmitted to the decoder through the network channel, the decoder is designed as follows:

[0097]

[0098] Where: is the latest control signal stored in advance, μ i Is a normal number.

[0099] The robustness analysis of the designed 1-bit encoding and decoding mechanism is divided into the following two cases: Case 1: In this case, the two consecutive trigger intervals will not be destroyed, and the controller and actuator of the two-degree-of-freedom robotic arm system will get the same control signal

[0100] Case 2: In this case, the sampler may generate a random sampling error during the sampling process. At this time, there is an error in the signal between the controller and the decoder. Therefore, the present invention uses the random error in the simulation experiment. To simulate random sampling errors, At this time, by selecting the control parameters and Ensure the fixed time stability of the two-degree-of-freedom robotic arm system.

[0101] To illustrate the control effect of the scheme of the present invention in detail, a simulation experiment will be carried out in MATLAB. The parameters of the two-degree-of-freedom manipulator system are designed as follows: reference trajectory Initial Position m1=m2=1kg, l1=1m, l2=0.5m, g=9.8m / s 2 , T i =1s,η i (0) = η i,0 =1,η i,∞ =0.05,ζ i,max =ζ i,min =1,(i=1,2), the tracking error will be e 1i Constrained within the range of (-0.05, 0.05), the control gain is selected as shown in Table 1 below:

[0102] Table 1: Control gains

[0103]

[0104] The following results were obtained through simulation experiments using MATLAB: Figure 4 and Figure 5 It can be concluded that the output trajectory y1 of the two-degree-of-freedom robotic arm system can quickly track the reference trajectory y d , and the tracking error is within the preset fixed time T i =1s, converges to the envelope of the fixed time performance function; Figure 6 and Figure 7 The control input diagrams for the first and second robotic arms are shown respectively. It can be concluded from the simulation diagram that the continuous updating of the control signal is effectively avoided, the burden of network communication is alleviated, and the wear of the actuator is reduced; Figure 8 and Fig. 9 The trigger time interval diagram of the control signal shows that the Zeno effect is effectively avoided. Fig.10 and Fig.11 It can be concluded that even if random sampling errors are introduced The fixed-time stability of the closed-loop system can still be guaranteed, and it converges to the preset performance range within the preset fixed time. Through simulation experimental results, it is concluded that the fixed-time self-triggering preset performance trajectory tracking controller designed by the present invention realizes the fixed-time stability of the closed-loop system, and the upper limit of the stability time is independent of the initial position conditions of the system; by adjusting the design parameters of the fixed-time preset performance function, the tracking performance requirements under different circumstances are met; combined with the self-triggering control technology, the continuous update of the system control signal is effectively avoided, the update frequency of the control signal and the wear of the actuator are reduced; based on the triggering conditions of the self-triggering control, a 1-bit encoding and decoding mechanism is designed to reduce the unnecessary occupation of the network channel and effectively alleviate the pressure on the network bandwidth.

[0105] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for designing a preset performance trajectory tracking controller for a two-degree-of-freedom robotic arm, characterized in that: The following steps are involved: Step 1: Establish the state space equation based on the dynamic model of the two-degree-of-freedom manipulator; Step 2: Based on the state space equation of step 1, the reference trajectory is tracked according to the output trajectory of the two-degree-of-freedom manipulator to generate a tracking error e 1i (t), by establishing an inequality relationship, the tracking error is limited to a fixed time preset performance function η i The error conversion function Ξ is established within the envelope of i (ε i (t)) and the equation relationship e 1i (t) = η i (t)Ξ i (ε i (t)), the tracking error constrained by the inequality is converted into an unconstrained equivalent error. The tracking error of the two-degree-of-freedom manipulator system after the equivalent transformation is: Step 3: According to the tracking error of the two-degree-of-freedom manipulator system after the equivalent transformation obtained in step 2, the coordinate transformation is constructed based on the adaptive backstepping control method, and the two-degree-of-freedom manipulator system is divided into two-level subsystems. For the first-level subsystem, a virtual controller α1 and the first adaptive law are designed to make it stable in fixed time. Then the controller gain to be designed for the first-level subsystem is obtained. For the second-level subsystem, combined with the self-triggering control mechanism, a fixed-time self-triggering preset performance trajectory tracking controller τ(t) and a second adaptive law are designed to make the entire two-degree-of-freedom manipulator system stable in fixed time. Then the controller gain to be designed for the second-level subsystem is obtained, completing the design of the fixed-time self-triggered preset performance trajectory tracking controller.

2. The method for designing a preset performance trajectory tracking controller for a two-degree-of-freedom robotic arm according to claim 1, characterized in that: A 1-bit encoding and decoding mechanism is designed according to the triggering condition of the self-triggering control mechanism.

3. The method for designing a preset performance trajectory tracking controller for a two-degree-of-freedom robotic arm as claimed in claim 2, characterized in that: The specific implementation form of the triggering condition of the self-triggering control mechanism is to calculate the next triggering time value of the control signal according to the current information of the system controller, encode the control signal according to the difference between the previous triggering time and the next triggering time, and encode the control signal as 1 when the difference is greater than zero. On the contrary, when the difference is less than zero, the control signal is encoded as 0. The encoded signal is then transmitted to the decoder for decoding to obtain the actual control signal, which is then transmitted to the actuator of the two-degree-of-freedom robotic arm system.

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