A rigid robot arm angular position tracking control method

Abstract

The application relates to the technical field of rigid robot control, in particular to a rigid robot mechanical arm angle position tracking control method, which can effectively solve the problems of waste of communication resources of the rigid robot, influence of actuator faults and dead zone constraints, and ensure that the rigid robot mechanical arm realizes accurate angle position tracking.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of rigid robot control, in particular to a rigid robot mechanical arm angle position tracking control method. BACKGROUND

[0002] The mechanical arm is the main component of the robot, which is a kind of high-precision, multi-input and multi-output, high nonlinearity, strong coupling complex system that can automatically complete some repetitive tasks according to the control signal. As an important part of modern automation industry, the mechanical arm has the characteristics of flexible operation, high efficiency, accuracy and reliability, and has been widely applied and popularized in the fields of production and manufacturing, medical treatment and other fields.

[0003] However, due to the environment of the mechanical arm, system model uncertainty and other interference factors, the mechanical arm often cannot make correct instructions. On the one hand, after long time and high precision continuous operation of the mechanical arm, the actuator will fail due to aging of part of the components or external interference, so that the tracking control effect is not ideal; on the other hand, the communication between the actuator and the control device in the mechanical arm system is continuous, which means that the tracking control needs to be calculated and run in real time, which puts forward higher requirements on the computing power and storage capacity of the computer, and also causes the wear and tear of the system structure and the waste of communication resources, thereby causing the mechanical arm to have poor tracking effect, inaccurate tracking data and other problems. SUMMARY

[0004] The purpose of the present application is to provide a rigid robot mechanical arm angle position tracking control method.

[0005] The technical scheme of the present application is as follows:

[0006] The present application provides a rigid robot mechanical arm angle position tracking control method, comprising the following steps:

[0007] Step 1: taking the mechanical arm angle position, the mechanical arm angular velocity and the armature current as the state quantity respectively, considering the influence of actuator failure and dead zone constraint, establishing the state space model of the rigid robot mechanical arm driven by the direct current motor;

[0008] Step 2: for the state space model, designing a funnel conversion function and a command filter, based on the funnel variable and the command filter output, obtaining an error system model through equivalent coordinate transformation;

[0009] Step 3: under the condition of limited communication resources, considering the error system model, using Lyapunov stability theory and backstepping method technology, designing a self-triggering adaptive fault-tolerant controller;

[0010] Step 4: By adjusting the design parameters in the self-triggered adaptive fault-tolerant controller in Step 3, the output voltage of the DC motor is controlled to make the tracking error not exceed the funnel boundary, realizing accurate tracking of the angular position of the rigid robot manipulator.

[0011] As a preferred scheme of the present application, the state space model of the rigid robot manipulator driven by the DC motor in Step 1 is:

[0012]

[0013] where q, are the angular position and angular velocity of the manipulator, I is the armature current, V e is the output voltage of the DC motor, J, K r , m, L o , M o , R o , L, R, K B , B0 are the nominal values of the moment of inertia, electromechanical conversion coefficient, link mass, link length, load mass, load radius, armature inductance, armature resistance, back electromotive force coefficient and viscous friction coefficient at the joint, respectively. m represents the model uncertainty term in the rigid robot manipulator control system. Considering the effects of actuator faults and dead-zone constraints, the output voltage expression is where π k is the unknown sensitivity parameter of the kth actuator, v k , is the unknown dead-zone constraint parameter, u dk is the control input torque.

[0014] As a preferred scheme of the present application, the specific process of Step 2 is:

[0015] Step 2.1, based on the state space model established in Step 1, define q = x1, I = x3, and the derivative is:

[0016]

[0017] where,

[0018] Step 2.2, define the angular position tracking error e1 = x1 - x d , where x d is the angular position reference trajectory. The funnel conversion function and command filter are designed as follows:

[0019]

[0020]

[0021] x i，c (0) = a i (0), i = 1, 2,

[0022] where e1is the angular position tracking error, z1is the angular position related error variable, is the funnel boundary, is the adjustable parameter of the funnel boundary, a1is the convergence rate of the funnel boundary, a i is the virtual control input signal, x i，c is the output signal of the command filter, τ i * is the filter gain, x i，c (0) and a i (0) are the initial value of the command filter state and the initial value of the virtual control input signal, respectively, t is time.

[0023] Step 2.3, based on the designed funnel switching function and the command filter, the following equivalent coordinate transformation is performed:

[0024]

[0025] where z1, z2, z3are the angular position, angular velocity and armature current related error variables, respectively, ξ1, ξ2, ξ3are the error compensation signals, v1, v2, v3are the angular position, angular velocity and armature current compensation tracking errors, respectively, a 1，c , a 2，c is the output of the command filter.

[0026] As a preferred scheme of the present application, the specific process of step 3 is as follows:

[0027] Step 3.1, based on step 2.3, a Lyapunov function is constructed:

[0028]

[0029] where η K , η P , Γ1, Γ2 are positive design parameters, is the neural network weight error, is the parameter estimation error.

[0030] Step 3.2, the virtual control input signal is designed:

[0031]

[0032] where k1, k2, k3, l1 are positive design parameters.

[0033] Step 3.3, the error compensation signal is designed:

[0034]

[0035] Step 3.4, design a self-triggered adaptive fault-tolerant controller:

[0036]

[0037] where u ck is the kth controller input signal, is the estimation vector of K, K = [K1, K 21 , K 22 ] T is the unknown vector containing fault information, ∏ = [∏1, ∏ 21 , ∏ 22 ] T is the control input signal vector in the dynamics model, ∏1= α3, ∏ 21 = ∏ 22 = 1, and α3is a virtual control input signal. k is the kth actuator dead-zone constraint slope. k is the kth actuator unknown sensitivity parameter. Based on the adaptive fault-tolerant controller, a continuous input signal ω(t) is constructed:

[0038]

[0039] where ω(t) is the continuous control input signal, s G , ι, and s m are self-triggered design parameters.

[0040] Step 3.5, according to the rigid robot arm angle position tracking control method of claim 1, characterized in that the continuous control input signal satisfies u dk (t) is the actual input of the rigid robot arm control system at time t k , s G , s D , and s Λ are self-triggered design parameters, is the derivative of the continuous control input ω(t) at time t k , when t ∈ [t k , t k+1 ], u dk (t) = ω(t k ), t is time, t k represents the time when the kth trigger of the controller occurs, and t k+1 is the time when the k+1th trigger of the controller occurs, [t k , tk+1 ) is the time interval between the k+1th self-triggering and the kth self-triggering of the controller. The design parameter adaptive law includes a controller parameter adaptive law dead-zone parameter adaptive law and a neural network weight update adaptive law The expressions are respectively:

[0041]

[0042]

[0043]

[0044] wherein η K , m K , η P , m P , Γ, σ are positive design parameters. As a preferred scheme of the present application, the specific process of step 4 is:

[0045] Step 4.1, adjust the parameters so that ensure that the derivative of the Lyapunov function is negative outside the residual set.

[0046] Step 4.2, by proving that the Lyapunov function is bounded, the boundedness of the error variable related to the angular position is obtained, and then the output voltage of the permanent magnet brush motor is controlled to make the tracking error not exceed the funnel boundary, so as to realize accurate tracking of the angular position of the rigid robot arm.

[0047] The present application has the following beneficial effects:

[0048] The rigid robot arm angular position tracking control method provided by the present application considers the case that the system contains modeling uncertainty, input dead zone and actuator fault, and realizes accurate tracking of the angular position of the rigid robot arm by controlling the output voltage of the DC motor to make the tracking error not exceed the funnel boundary.

[0049] Compared with the existing time-triggered control and periodic-triggered control, the self-triggering mechanism designed in the present application avoids unnecessary calculation, improves calculation efficiency, and makes the system more stable and reliable. At the same time of realizing high-performance tracking, the self-triggering mechanism avoids frequent updating of control input, reduces the accumulation of tracking error, and improves the tracking accuracy of the system. Compared with the existing event-triggered control, the self-triggering mechanism designed in the present application does not need to monitor whether the tracking error meets the triggering condition at all times, and the next triggering time only depends on the state information of the current triggering time, thereby further saving communication resources. At the same time, the constant s ΛAvoiding long time controller stagnation update, the transient performance of the system is improved.

[0050] The rigid robot manipulator angle position tracking control method provided by the application improves the transient performance of the system and overcomes the influence of model uncertainty on the system by introducing a funnel transformation function and a radial basis neural network function. BRIEF DESCRIPTION OF DRAWINGS

[0051] The scheme and advantages of the application will become clear to those skilled in the art from the following detailed description of the preferred embodiments. The drawings are only for the purpose of illustrating the preferred embodiments and are not considered to be limiting on the application. In the drawings, case one is the rigid robot manipulator system with actuator fault compensation and funnel transformation function constraint; case two is the rigid robot manipulator system without actuator fault compensation; and case three is the rigid robot manipulator system without funnel transformation function constraint. The specific description is as follows:

[0052] Figure 1 The control block diagram of the rigid robot manipulator of the application;

[0053] Figure 2 The tracking error curve e1 and the reference signal curve y of 0s-20s in case one and case two of the application d schematic diagram;

[0054] Figure 3 The tracking error curve e1 and the reference signal curve y of 0s-20s in case one and case three of the application d schematic diagram;

[0055] Figure 4 The angle position attitude curve x1 and the reference signal curve y of 0s-20s in case one of the application d schematic diagram;

[0056] Figure 5 The actual control input curve schematic diagram based on self-triggered control of 0s-20s in case one of the application;

[0057] Figure 6 The parameter adaptive law curve of 0s-20s in case one of the application DETAILED DESCRIPTION

[0058] Embodiments of the present application are described in detail below with reference to the attached drawing figures, wherein the examples of the embodiments are shown.

[0059] A rigid robot manipulator angular position tracking control method, the specific steps are as follows:

[0060] Step 1: taking the manipulator angular position, the manipulator angular velocity and the armature current as the state variables respectively, considering the influence of actuator faults and dead zone constraints, a state space model of the rigid robot manipulator driven by a DC motor is established;

[0061] Step 2: for the state space model, a funnel transformation function and a command filter are designed, and based on the funnel variable and the command filter output, an error system model is obtained through equivalent coordinate transformation;

[0062] Step 3: under the condition of limited communication resources, considering the error system model, a self-triggered adaptive fault-tolerant controller is designed by using Lyapunov stability theory and backstepping method technology;

[0063] Step 4: by adjusting the design parameters in the self-triggered adaptive fault-tolerant controller in step 3, the output voltage of the DC motor is controlled to make the tracking error not exceed the funnel boundary, so as to realize accurate tracking of the angular position of the rigid robot manipulator.

[0064] Step 1:

[0065] Based on the dynamics model of the rigid robot manipulator, a rigid robot manipulator control system containing model uncertainty, actuator faults and dead zone constraints is constructed, and according to the balance equation of the armature voltage and the torque balance equation, the following state space model is established:

[0066]

[0067] Wherein, q, are the angular position and angular velocity of the manipulator, I is the armature current, V e is the output voltage of the DC motor, J, K τ , m, L o , M o , R o , L, R, K B , B0 are the nominal values of the moment of inertia, the electromechanical conversion coefficient, the link mass, the link length, the load mass, the load radius, the armature inductance, the armature resistance, the back electromotive force coefficient and the joint viscous friction coefficient, respectively, and t is the time. m Δ k represents the model uncertainty in the rigid robot manipulator control system. Considering the influence of actuator faults and dead zone constraints, the output voltage expression is Wherein, π k is the unknown sensitivity parameter of the kth actuator, vk , is an unknown dead-zone constraint parameter, u dk is the control input torque.

[0068] Let J = 1.625 x 10 -3 Kg·m 2 , m = 0.506 Kg, M o = 0.434 Kg, L o = 0.305 m, R o = 0.023 m, G = 9.8 N / Kg, B o = 16.25 x 10 -3 N·m·s / rad, K r = 0.90 N·m / A, π k = 0.8. Δ m represents the model uncertainty term in the rigid robotic manipulator control system, The above parameter values are empirical data, widely used, and have high modeling accuracy.

[0069] Step 2:

[0070] Based on the state space model established in step 1, define q = x1, I = x3, and the derivative is:

[0071]

[0072] wherein, Define the angular position tracking error e1 = x1 - x d , wherein x d (t) is the angular position reference trajectory. The funnel transfer function and the command filter are designed as follows:

[0073]

[0074]

[0075]

[0076] wherein, z1 is an error variable related to the angular position, e1 is the position tracking error, is the funnel boundary, is the adjustable parameter of the funnel boundary, a1 is the funnel boundary convergence rate, α i is the virtual control input signal of the dynamic model, x i，c is the output signal of the command filter, τ i * is the filter gain, x i，c (0) and α i(0) are the initial values of the command filter state and the initial values of the control input signal of the dynamic model, respectively. Based on the designed funnel transformation function and the command filter, the following equivalent coordinate transformation is performed:

[0077]

[0078] where z1, z2, z3 are the angular position, angular velocity and armature current related error variables, respectively, ξ1, ξ2, ξ3 are the error compensation signals, v1, v2, v3 are the angular position, angular velocity and armature current compensation tracking errors, respectively, and α 1，c , α 2，c is the command filter output.

[0079] Step 3:

[0080] The angular position tracking control of the traditional rigid robot arm system requires that the tracking error of the target trajectory must be limited within the constraint boundary range. However, due to the existence of actuator faults and dead zone constraints in the system, the tracking error may violate the performance boundary when a fault occurs, resulting in singular phenomenon and causing the traditional control algorithm to fail.

[0081] To solve this technical problem, a funnel transformation function is introduced to make the system have good transient performance. In addition, a self-triggered adaptive fault-tolerant controller is designed using Lyapunov theory and backstepping technology, which ensures that the angular position tracking error of the system will not violate the performance boundary when a fault occurs, so that the system has good steady-state performance while greatly saving communication resources. The specific operation process of step 3 is as follows:

[0082] Taking the derivative of the angular position related error variable gives:

[0083]

[0084] where The following candidate Lyapunov function V1 is constructed:

[0085]

[0086] Taking the derivative of V1 gives:

[0087]

[0088] The Young inequality is:

[0089]

[0090] where a, b, p, q are all positive real numbers, and satisfy The Young inequality is used to process the strong coupling term existing in the rigid robot manipulator control system and the nonlinear term such as the neural network weight value, so that the control mechanism design of the rigid robot manipulator control system is simplified, and a more accurate error tracking range is obtained.

[0091] The virtual control signal and the error compensation signal are designed as follows:

[0092]

[0093]

[0094] The above formula is substituted into the derivative of the candidate Lyapunov function , and the Young inequality is further used to shrink as follows:

[0095]

[0096] The candidate Lyapunov function V1 and the angular velocity related error variable and the neural network weight value estimation are combined to construct the following candidate Lyapunov function V2:

[0097]

[0098] wherein Γ1 is a positive design parameter, is a neural network weight error, is a neural network weight estimation. The radial basis neural network is used to extract, classify and approximate the influence of the model uncertainty, actuator failure and dead zone constraint existing in the system, map the system model data, and realize the simplified processing of the data. The adaptive neural network tracking controller is used in the radial basis neural network, so that the radial basis neural network can be conveniently used in the rapid calculation and processing of the rigid robot manipulator system.

[0099] The derivative of the candidate Lyapunov function V2 is obtained as follows:

[0100]

[0101] The following virtual control signal, error compensation signal and neural network weight value update adaptive law are designed:

[0102]

[0103]

[0104]

[0105] The above formula is substituted into the derivative of the candidate Lyapunov function , and the Young inequality is further used to shrink as follows:

[0106]

[0107] where k2 and σ1 are controller and neural network gains, respectively 1m is the neural network weight estimation error upper bound.

[0108] The candidate Lyapunov function V2 is combined with the armature current related error variable, the neural network weight estimation, and the adaptive parameter estimation to construct the following Lyapunov function V3:

[0109]

[0110] where Γ2, η P , η K are positive design parameters, is the neural network weight estimation error, is the neural network weight estimation. is the parameter estimation error, is the adaptive parameter estimation value.

[0111] When t∈[t k , t k+1 ), the derivative of Lyapunov function V3 is:

[0112]

[0113] The following self-triggered mechanism is designed:

[0114] u dk (t)=ω(t s ),

[0115]

[0116] It can be seen that when t∈[t k , t k+1 ), there is |ω(t)-u dk (t)|≤s G |u dk (t)|+s D holds. Let φ1(t s )=φ2(t s )=0, φ1(t s+1 )=φ2(t s+1 )=±1 and |φ1(t)|≤1, |φ2(t)|≤1, holds. The continuous input signal ω(t) is constructed as:

[0117]

[0118] where ω(t) is the continuous control input signal, s​G i and s m is a self-triggered design parameter.

[0119] Substitute the continuous input signal u dk into the equation:

[0120]

[0121] Design a self-triggered adaptive fault-tolerant controller:

[0122]

[0123] wherein u ck is the kth controller input signal, is an estimated vector of K, K = [K1, K 21 , K 22 ] T is an unknown vector containing fault information, ∏ = [∏1, ∏ 21 , ∏ 22 ] T is a vector containing the control input signal in the dynamics model, ∏1 = α3, ∏ 21 = ∏ 22 = 1, and α3 is a virtual control input signal. k is the kth actuator dead-zone constraint slope. k is the kth actuator unknown sensitivity parameter.

[0124] Substitute u ck into the equation:

[0125]

[0126] Design the following virtual control signal, error compensation signal, neural network weight update adaptive law, and parameter adaptive law:

[0127]

[0128] wherein k3, σ2, m K , m P , and l1 are positive design parameters. Substitute the above equation into , and further adjust it using Young's inequality to obtain:

[0129]

[0130] wherein

[0131] Integrate the above equation to obtain:

[0132] ​

[0133] According to Lyapunov function theory, V3, V i (i = 1, 2, 3), is bounded, so x1, x2, x3, ξ1, ξ2, ξ3 are bounded, further α1, α2, α3, u ck , ω, u dk are bounded, so all signals in the closed-loop system are bounded; on the other hand, the continuous control input signal satisfies where u dk is the actual input of the rigid robot manipulator control system at time t k , and is the derivative of the continuous control input ω(t) at time t k . Since is bounded, there is t k+1 -t k > 0, thereby avoiding Zeno behavior.

[0134] By introducing a self-triggering mechanism in the system, designing a continuous control input signal that satisfies the self-triggering condition can effectively reduce the number of updates and calculations of the control mechanism state, save system resources, and improve the reliability and stability of the control system. Compared with the traditional event-triggered control scheme, the self-triggering mechanism directly calculates the next triggering time from the current time information, avoiding the problem of excessive frequent controller response. In addition, by introducing a constant s Λ to control the length of the triggering interval, the problem of system performance degradation caused by long-term stagnation of the controller is avoided.

[0135] To verify the effectiveness of the rigid robot manipulator angular position tracking control method proposed in the present application, the rigid robot manipulator system with modeling uncertainty, actuator fault input dead zone is considered, and the case without actuator fault compensation and without applying funnel conversion function constraint is compared. In the drawings, case one is the rigid robot manipulator system with actuator fault compensation and funnel conversion function constraint; case two is the rigid robot manipulator system without actuator fault compensation; case three is the rigid robot manipulator system without funnel conversion function constraint. The specific description is as follows:

[0136] Figure 1 is the control block diagram of the rigid robot manipulator of the present application;

[0137] Figure 2 The tracking error curve e1 and the reference signal curve y dFig. 1 is a schematic diagram. In the figure, the solid line is a schematic diagram of the tracking error curve variation of the rigid robot manipulator system with actuator fault compensation and funnel switching function constraints (case one), the dashed line is a schematic diagram of the tracking error curve variation of the rigid robot manipulator system without actuator fault compensation (case two), and the thick dotted line is the funnel switching function boundary As can be seen from the figure, the controller without actuator fault compensation causes the system tracking error curve to gradually diverge, resulting in the system output being difficult to track the reference signal in time, and a large position tracking error being generated. In contrast, the designed control scheme (case one) ensures that the tracking error is always constrained within the funnel boundary, and accurate angular position trajectory tracking is achieved.

[0138] Figure 3 Fig. 2 is the tracking error curve el and the reference signal curve y under case one and case three from 0s to 20s d Fig. 1 is a schematic diagram. In the figure, the solid line is a schematic diagram of the tracking error curve variation of the rigid robot manipulator system with actuator fault compensation and funnel switching function constraints (case one), the dashed line is a schematic diagram of the tracking error curve variation of the rigid robot manipulator system without actuator fault compensation (case two), and the thick dotted line is the funnel switching function boundary As can be seen from the figure, the controller without actuator fault compensation causes the system tracking error curve to gradually diverge, resulting in the system output being difficult to track the reference signal in time, and a large position tracking error being generated. In contrast, the designed control scheme (case one) ensures that the tracking error is always constrained within the funnel boundary, and accurate angular position trajectory tracking is achieved.

[0139] Figure 4 Fig. 2 is the tracking error curve el and the reference signal curve y under case one and case three from 0s to 20s d Fig. 1 is a schematic diagram. In the figure, the solid line is a schematic diagram of the tracking error curve variation of the rigid robot manipulator system with actuator fault compensation and funnel switching function constraints (case one), the dashed line is a schematic diagram of the tracking error curve variation of the rigid robot manipulator system without actuator fault compensation (case two), and the thick dotted line is the funnel switching function boundary

[0140] Figure 5 Fig. 2 is the tracking error curve el and the reference signal curve y under case one and case three from 0s to 20s

[0141] Figure 6 Fig. 2 is the tracking error curve el and the reference signal curve y under case one and case three from 0s to 20s Dead zone parameter adaptive law Neural network weight update adaptive law Wherein the solid line is the curve change schematic diagram of the controller parameter adaptive law The dashed line is the curve change schematic diagram of the dead zone parameter adaptive law The dotted line is the curve change schematic diagram of the neural network weight update adaptive law From the figure, it can be seen that when in case one, the designed adaptive law is always maintained within a bounded range, and with the system running, the designed adaptive law can effectively estimate the unknown input dead zone parameter.

[0142] For a rigid robot arm system with model uncertainty, actuator failure and input dead zone, based on adaptive control theory, radial basis neural network technology and funnel transfer function method can effectively solve the existing problems. The control scheme has the following advantages: based on adaptive theory, the controller parameters of the system can be automatically adjusted online, adapting to the dynamic changes and uncertainties of the system; the motion and control strategy of the system can be adjusted in real time according to the feedback signal, so as to better adapt to the environment and improve the control precision; the self-triggering fault-tolerant control scheme designed in the application can effectively reduce the computational load and energy consumption of the system, and can adjust the system parameters according to the fault occurred in the system, thereby ensuring the safe operation of the system; the radial basis neural network technology can learn the dynamic behavior and response of the system, improve the intelligent level of the system, and at the same time, the radial basis neural network technology can adaptively adjust the parameters and model of the system to adapt to different environments and application occasions, ensure the stable and efficient operation of the system, and make the system have the characteristics of good tracking effect, high tracking data accuracy and the like.

Claims

1. A rigid robot arm angle position tracking control method, characterized by, The method comprises the following steps: Step 1: a state space model of a rigid robot arm driven by a direct current motor is established by taking the mechanical arm angular position, the mechanical arm angular velocity and the armature current as state variables, and considering the influence of actuator faults and dead zone constraints, and the rigid robot arm angular position tracking control method is characterized in that the state space model of the rigid robot arm driven by the direct current motor in step 1 is as follows: where q(t), ω(t) are the joint position and velocity, I(t) is the armature current, V(t) is the DC motor output voltage, e (t) is the DC motor output voltage, J, K τ , m, L o , M o , R o , L, R, K B , B0 are the nominal values of the moment of inertia, the electromechanical conversion coefficient, the link mass, the link length, the load mass, the load radius, the armature inductance, the armature resistance, the back electromotive force coefficient and the joint viscous friction coefficient, respectively, t is the time, Δ m represents the model uncertainty in the rigid robot manipulator control system, considering the influence of actuator faults and dead-zone constraints, the output voltage expression is where π k is the unknown sensitivity parameter of the kth actuator, ν k , is the unknown dead-zone constraint parameter, u dk is the control input torque;​ Step 2: a funnel transformation function and a command filter are designed for the state space model, and an error system model is obtained through equivalent coordinate transformation based on the output of the funnel transformation function and the command filter; Step 3: under the condition of limited communication resources, a self-triggered adaptive fault-tolerant controller is designed by using Lyapunov stability theory and backstepping technology, considering the error system model; Step 4: the design parameters in the self-triggered adaptive fault-tolerant controller in step 3 are adjusted to make the Lyapunov function in step 3 negative, so as to realize accurate tracking of the rigid robot arm angular position.

2. The rigid robotic manipulator angular position tracking control method of claim 1, wherein, The specific process of step 2 is as follows: Step 2.1, on the basis of the state space model established in Step 1, define q(t) = x1(t), I(t) = x3(t), and the derivative can be obtained: wherein Step 2.2, define the angular position tracking error e1(t) = x1(t) - x d (t), where x d (t) is the angular position reference trajectory, design the funnel transfer function and command filter as follows: x i,c (0) = a i (0), i = 1,2, where e1(t) is an angular position tracking error, z1(t) is an angular position related error variable, is a funnel boundary, is a funnel boundary adjustable parameter, a1 is a funnel boundary convergence rate, a i (t) is a virtual control input signal, x i,c (t) is an output signal of the command filter, τ i * is a filter gain, x i,c (0) and a i (0) are an initial value of the command filter state and an initial value of the virtual control input signal, respectively, t is time, and for convenience, the variable t is omitted hereinafter; Step 2.3: based on the designed funnel transformation function and command filter, the following equivalent coordinate transformation is performed: where z1, z2, z3 are angular position, angular velocity and armature current related error variables, respectively, and ξ1, ξ2, ξ3 are error compensation signals, and v1, v2, v3 are angular position, angular velocity and armature current compensation tracking errors, respectively, and α 1,c ,α 2,c is the command filter output.

3. The rigid robotic manipulator angular position tracking control method of claim 1, wherein, The specific process of step 3 is as follows: Step 3.1: on the basis of step 2.3, a Lyapunov function is constructed: where η K ,η P ,Γ1,Γ2 are positive design parameters, is the neural network weight error, is the parameter estimation error; Step 3.2: a virtual control input signal is designed: Wherein, k1, k2, k3, l1 are positive design parameters; Step 3.3: an error compensation signal is designed: Step 3.4: a self-triggered adaptive fault-tolerant controller is designed: where u ck is the kth controller input signal, is the estimated vector of K, K = [K1, K 21 , 22 ] T is the unknown vector containing fault information, Π = [Π1, Π 21 , Π 22 ] T is the vector of control input signals in the dynamics model, Π1= α3, Π 21 = Π 22 = 1, α3 is a virtual control input signal, υ k is the kth actuator dead-zone constraint slope, π k is the kth actuator unknown sensitivity parameter, based on the adaptive fault-tolerant controller, a continuous input signal ω(t) is constructed: where ω(t) is a continuous control input signal, s G , i and s m are self-triggered design parameters; The rigid robot manipulator angular position tracking control method according to claim 1, wherein the continuous control input signal satisfies u dk (t) is the actual input of the rigid robot manipulator control system at time t k s G , s D and s Λ are self-triggered design parameters, is the derivative of the continuous control input ω(t) at time t k , when t∈[t k , t k+1 ], u dk (t) = ω(t k ), t is time, t k represents the time when the kth trigger of the controller occurs, t k+1 is the time when the k+1th trigger of the controller occurs, [t k , t k+1 ] is the time interval between the k+1th self-trigger and the kth self-trigger of the controller, and the design parameter adaptive law comprises a controller parameter adaptive law a dead zone parameter adaptive law and a neural network weight update adaptive law , and their expressions are respectively: where η K ,m K ,η P ,m P ,Γ,σ are positive design parameters.

4. The rigid robotic manipulator angular position tracking control method of claim 1, wherein, The specific process of step 4 is as follows: Step 4.1, adjust parameters so that Guarantee Lyapunov function derivative negative outside the residual set; Step 4.2: by proving that the Lyapunov function is bounded, the boundedness of the error variable related to the angular position is obtained, and then the output voltage of the direct current motor is controlled to make the tracking error not exceed the funnel boundary, so as to realize accurate tracking of the rigid robot arm angular position.

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