Fault-tolerant state quantitative control method based on flexible joint mechanical arm

Abstract

The invention discloses a fault-tolerant state quantitative control method based on a flexible joint mechanical arm, and relates to the field of state quantitative control of flexible joint mechanical arms. Comprising the steps that a, a state space model of a flexible joint mechanical arm system is established; b, defining a radial basis function neural network of an approximate unknown term; c, defining a uniform quantizer; d, error transformation of an unquantized flexible joint mechanical arm system is defined; e, deriving an unquantized error variable; f, constructing an unquantized virtual controller and an adaptive rate; g, designing an unquantized actual anti-interference fault-tolerant controller; and h, designing a quantized controller and an adaptive rate. According to the controller designed by the invention, the tracking performance of the flexible joint mechanical arm with a quantitative state can be ensured, fault-tolerant control is realized, and the system efficiency is improved.

Description

Technical Field

[0001] The invention discloses a fault-tolerant state quantization control method based on a flexible joint mechanical arm, and relates to the field of flexible joint mechanical arm state quantization control. Background Art

[0002] With the continuous development of global science and technology, the requirements for robot performance are gradually increasing. Flexible manipulators have the characteristics of high load-to-weight ratio, high adaptability, and strong safety, and are often used in medical, aviation, manufacturing, service and other fields. Among them, flexible joint robots have high dynamic force control and high-precision position control accuracy due to the flexibility of their joints, which is particularly prominent in manipulators and has attracted the attention of scholars.

[0003] Although flexible joint robots have many advantages, their nonlinear, high-order, and strong-coupling characteristics are also complex. The existing modeling problems are more important for further research on flexible joint robots. At present, the Lagrange equation, the Newton-Euler equation, and the Kane equation are the main modeling tools. First, some control methods are proposed to study their tracking control problems, such as adaptive control, feedback linearization control, and singular perturbation control. Subsequently, a series of intelligent algorithms are provided, including adaptive backstepping control, adaptive sliding mode control, and model predictive control. In addition, all states become discontinuous through the quantizer, and the derivative of the state does not exist, which is difficult to apply to backstepping design. Especially in controller design, the virtual controller and the real controller inevitably contain discontinuous state vectors, and the time derivative cannot be obtained. Therefore, in order to solve the state quantization problem of the flexible joint robot system, it is necessary to overcome the discontinuity problem caused by the quantizer. Summary of the invention

[0004] The present invention proposes a fault-tolerant state quantization control method based on a flexible joint manipulator. In order to solve the discontinuity problem caused by quantization, a design similar to backstepping is used here, which brings the additional advantage of relative simplicity to the designed controller. With the help of performance function and quantizer, the method effectively saves bandwidth while ensuring the realization of transient and steady-state performance. In addition, by approximating the unknown function with a neural network, the global Lipschitz condition of full-state quantization is eliminated. Finally, it is proved that all errors of the closed-loop system remain within the pre-designed performance function range.

[0005] The present invention provides a fault-tolerant state quantization control method based on a flexible joint mechanical arm, comprising:

[0006] a. Establish the state space model of the flexible joint manipulator system;

[0007] b. Define a radial basis neural network that approximates the unknown terms;

[0008] c. Define uniform quantizer;

[0009] d. Define the error transformation of the unquantized flexible joint manipulator system;

[0010] e. Derivative of the unquantized error variable;

[0011] f. Construct an unquantized virtual controller and adaptive rate;

[0012] g. Design unquantized practical anti-interference fault-tolerant controller;

[0013] h. Design quantized controller and adaptation rate.

[0014] Furthermore, in step (a), the Euler-Lagrange energy modeling method is used for the flexible joint manipulator system, and its dynamic model equation is expressed as:

[0015]

[0016] Where l∈R n is the angular position of the connecting rod, is the angular velocity of the connecting rod, is the angular acceleration of the connecting rod, l m ∈R n is the angular position of the motor, represents the angular velocity of the motor, represents the angular acceleration of the motor, is a positive definite symmetric inertia matrix, is the vector containing the centripetal force and the Coriolis force, G(l)∈R n represents the gravity vector, represents the friction term, K=diag(K1,…,K n ) represents R n×n Joint stiffness is a positive definite matrix, J = diag(J1,…,J n )∈R n×n represents the positive motor inertia matrix, B = diag(B1,…,B n )∈R n×n represents the natural damping term, u f =u0+u * ∈R n is the actual input, u0 is the designed controller, u * is the additive fault degree encountered by the controller. After transformation, the following expression can be obtained:

[0017]

[0018] in

[0019] Furthermore, in step (b), a radial basis function neural network θ is designed. T ψ(X) satisfies the following conditions,

[0020] f(X)=θ T ψ(X)+σ(X),|σ(X)|≤∈,

[0021] where X∈R n is the input of the neural network, θ∈R r is the optimal weight vector, r is the number of nodes, and θ is defined as is an estimate of θ, σ(X) is defined as the estimation error, and the Gaussian basis function is ψ(X)=[ψ1(X),ψ(X)2,…,ψ r (X)], where τ i Represents the width, a i =[a i1 ,a i2 ,…,a in ],i=1,,r is the center of the Gaussian function.

[0022] Further, in step (c), a uniform quantizer for quantizing the state signal is defined as

[0023]

[0024] By using the above quantization criteria, all state variables are uniformly quantized, where r>0 is the length of the quantization level, Q1=r, Q i+1 =Q i +r.

[0025] Further, in step (d), an error variable is defined by a fault-tolerant state quantization control method of a flexible joint manipulator.

[0026]

[0027] Among them, z1 represents the tracking error, α i represents the virtual controller, and further defines the error transformation variable as

[0028]

[0029] Among them, A>1 is the designed parameter, Represents the error z i The boundary, i0 , i∞ , μ i are all designed positive constants.

[0030] Furthermore, in step (e), the four error variables are derived separately,

[0031]

[0032] in, Represents the derivative of the virtual controller.

[0033] Furthermore, in step (f), in order to design the adaptive rate, virtual and actual controllers, the Lyapunov candidate function is designed by backstepping. In the backstepping process, the virtual controller α j (j=1,2,3) is constructed as,

[0034]

[0035] At the same time, the adaptive rate

[0036] The design is as follows,

[0037]

[0038] in are the parameters to be designed.

[0039] Further, in step (g), the quantized controller and the adaptive rate are designed. After the state is quantized by the quantizer, the error transformation variable in

[0040]

[0041] According to the similar method mentioned above, the error variable after design quantization is as follows:

[0042]

[0043] In the above formula, α i It is a virtual controller designed based on the quantized state. The specific expression is:

[0044]

[0045] The controller designed based on the quantized state and the adaptive rate are,

[0046]

[0047] According to the designed controller and adaptive rate, the impact of the fault is effectively handled.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows: the fault-tolerant state quantization control method based on the flexible joint manipulator provided by the present invention designs an effective adaptive fault-tolerant controller containing quantized states for the mathematical model of the manipulator system containing flexible joints. The reference of the performance function limits the error between the motion trajectory of the manipulator and the reference trajectory to a safe range, improves the tracking control accuracy of the manipulator, and reduces the influence of additive faults on the actuator, ensuring the stable operation of the system. First, according to the flexible joint manipulator model, it is accurately modeled to obtain a more practical system. Secondly, with the help of adaptive control and stability theory in the sense of Lyapunov, using performance functions and uniform quantizers, an adaptive fault-tolerant controller is designed for the system under consideration. The controller involved can not only ensure accurate tracking control in the case of containing quantized states, but also reduce the influence of actuator failures, save communication resources, and reduce the communication burden. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is the trajectory of the actual control input given by the present invention;

[0050] Figure 2 The tracking trajectory of the connecting rod provided by the present invention;

[0051] Figure 3 It is the tracking error trajectory under the preset performance function provided by the present invention;

[0052] Figure 4 is the trajectory of the connecting rod angular velocity provided by the present invention;

[0053] Figure 5 This is the trajectory of the adaptation rate given by the present invention. DETAILED DESCRIPTION

[0054] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0055] The present invention provides a fault-tolerant state quantization control method based on a flexible joint mechanical arm, which is specifically implemented through the following steps.

[0056] Step a. Establish a dynamic model of the flexible joint robot system. By constructing the energy relationship between the kinetic energy and potential energy of the flexible joint robot system, the flexible joint robot is modeled based on the Euler-Lagrange energy modeling method, and its dynamic differential equation is expressed as:

[0057]

[0058] Where l∈Rn is the angular position of the connecting rod, is the angular velocity of the connecting rod, is the angular acceleration of the connecting rod, l m ∈R n is the angular position of the motor, represents the angular velocity of the motor, represents the angular acceleration of the motor, is a positive definite symmetric inertia matrix, is the vector containing the centripetal force and the Coriolis force, G(l)∈R n represents the gravity vector, represents the friction term, K=diag(K1,…,K n )∈R n×n is a positive definite matrix representing the joint stiffness,

[0059] J=diag(J1,…,J n )∈R n×n represents the positive motor inertia matrix, B = diag(B1,…,B n )∈R n×n represents the natural damping term, u f =u0+u * ∈R n is the actual input, u0 is the designed controller, u * is the additive fault level encountered by the controller. By defining the following transformation, we can get the following expression,

[0060]

[0061] in,

[0062] Step b. A radial basis function neural network θ T ψ(X) satisfies the following conditions:

[0063] f(X)=θ T ψ(X)+σ(X),|σ(X)|≤∈,

[0064] where X∈R n is the input of the neural network, θ∈R r is the optimal weight vector, r is the number of nodes, and θ is defined as is an estimate of θ, σ(X) is defined as the estimation error, and the Gaussian basis function is ψ(X)=[ψ1(X),ψ(X)2,…,ψ r (X)], where τ i Represents the width, a i =[a i1 ,a i2 ,…,ain ], i = 1,…, r is the center of the Gaussian function.

[0065] Step c. The uniform quantizer for quantizing the state signal is defined as

[0066]

[0067] Using the above quantization criteria, all state variables are uniformly quantized, where r>0 is the length of the quantization level, Q1=r, Q i+1 =Q i +r.

[0068] Step d. Define the following error variable,

[0069]

[0070] Among them, z1 represents the tracking error, α i represents the virtual controller, and further defines the error transformation variable as

[0071]

[0072] Among them, A>1 is the designed parameter, Represents the error z i The boundary, i0 , i∞ , μ i are all designed positive constants.

[0073] Step e. Solve the derivatives of the four error variables.

[0074]

[0075] in, Represents the derivative of the virtual controller.

[0076] Step f. In the backstepping design process of the controller, a Lyapunov candidate function is selected at each step to construct a virtual controller until the real controller and the adaptive rate are designed in the last step. The virtual controller α j (j=1,2,3) is constructed as,

[0077]

[0078] At the same time, the adaptive rate

[0079] The design is as follows,

[0080]

[0081] in are the parameters to be designed.

[0082] Step g. After state quantization, the quantized controller and adaptive rate are designed below. The error transformation variable after quantization is in

[0083]

[0084] According to the similar method mentioned above, the error variable after design quantization is as follows:

[0085]

[0086] In each step It is a virtual controller designed based on the quantized state. The specific expression is:

[0087]

[0088] The controller designed based on the quantized state and the adaptive rate are,

[0089]

[0090] According to the designed controller and the adaptive rate, the additive fault of the actuator is transformed into a radial basis function neural network. Approximation is carried out to effectively deal with the impact of the fault.

[0091] The present invention is further described below through a specific embodiment of the present invention. In this embodiment, the system parameters shown in Table 1 and the design parameters given during simulation are set.

[0092] Table 1 System parameters and design parameters

[0093] <![CDATA[m1]]> <![CDATA[m2]]> <![CDATA[l1]]> <![CDATA[l2]]> <![CDATA[J1]]> <![CDATA[J2]]> <![CDATA[K1]]> <![CDATA[K2]]> 1 5.8 2 1.72 0.006 0.006 110 110 <![CDATA[B1]]> <![CDATA[B2]]> <![CDATA[θ c 2]]> <![CDATA[k1]]> <![CDATA[k2]]> <![CDATA[k3]]> <![CDATA[k4]]> <![CDATA[r1]]> 0.5 0.5 0.1 12 92 5 9 0.01 <![CDATA[r2]]> <![CDATA[c1]]> <![CDATA[c2]]> <![CDATA[θ c 1]]> 0.01 2 2 0.1

[0094] The initial value of the system is selected as x = [0, 0, 0, 0, 0, 0, 0] T ; The expected trajectory is selected as y r1 =2.5sin(1.31t-1.4)+3.2,y r2 =2.7sin(1.35t+1.4)-3.1. Under the effect of the designed adaptive fault-tolerant quantitative control scheme, the tracking trajectory of the actual controller, the connecting rod, the tracking error trajectory under the preset performance function, the trajectory of the connecting rod angular velocity, and the trajectory of the adaptive rate are respectively as follows: Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown. Figure 1 and Figure 2 It can be concluded that Figure 1describes the trajectory of the actual control input, Figure 2 The proposed design can ensure good tracking performance, thus ensuring the stability of the rehabilitation robot during operation. Figure 3 It can be seen that the tracking error converges to the vicinity of the origin, indicating that the designed fault-tolerant quantitative controller ensures that the tracking error is constrained within a certain area and achieves a good tracking effect. Figure 4 and Figure 5 The quantization of the connecting rod angular velocity and the size of the adaptive rate can be seen respectively, indicating that the proposed control design scheme can save communication resources and reduce the communication burden.

[0095] This method is close to the real problem and designs an adaptive fault-tolerant state quantization controller for the flexible joint robot arm model. Compared with the prior art, the technical solution provided by the present invention has the following effects:

[0096] (1) This study proposes for the first time a low-complexity performance tracking control scheme for a flexible joint manipulator based on a full-state quantized signal. In order to solve the discontinuity problem caused by quantization, existing results often use command filtering technology, which invisibly increases the dimension of the dynamic equations in the closed-loop system. In contrast, a backstepping-like design is used here, which brings the additional advantage that the designed controller is relatively simple. With the help of the performance function and the quantizer, this method effectively saves bandwidth while ensuring the realization of transient and steady-state performance. In addition, by approximating the unknown function with a neural network, the global Lipschitz condition is eliminated. Finally, this application also proves that all errors of the closed-loop system remain within the pre-designed performance function range.

[0097] (2) For a flexible joint robot arm, a reference trajectory needs to be set before working, so as to facilitate tracking of the working trajectory of the robot arm, so as to ensure that the robot arm works according to the operating steps. However, in reality, due to the influence of some external and internal factors, it is inevitable that the tracking path of the robot arm will deviate from the reference trajectory when working, and even in some extreme cases, the tracking error is too large, resulting in poor working efficiency of the robot arm. Therefore, in order to solve this problem, the present invention introduces a performance function. The designed performance function fully considers the error limit between the trajectory of the robot arm when working and the reference trajectory, and proposes a constraint control scheme to ensure that the control target can be stably achieved, which has important practical significance.

[0098] (3) For a flexible joint robot arm, the actuator is an indispensable part of the normal operation of the robot arm, because the actuator controls the normal operation of the robot arm and plays a vital role. However, in reality, the actuator is often in some extreme environments or harsh working conditions, which may cause the actuator to fail, which may cause the control process to deviate from the desired goal. Therefore, the present invention takes into account the additive fault conditions of the actuator and designs an effective fault tolerance scheme, so that even if the actuator fails, the control goal can still be achieved.

[0099] (4) With the advancement of science and technology, how to save communication resources as much as possible and reduce the computational burden is an issue that must be considered. The main focus of existing methods such as command filtering and dynamic surface in saving resources is to avoid multiple derivations of the virtual controller during the backstepping process, which causes a large amount of computational burden. The difference is that the present invention introduces a uniform quantizer to quantize all the states of the system. By using the quantized state signal combined with a backstepping-like method, the controller and the adaptive rate are designed to save communication resources and realize a fault-tolerant state quantization control method based on a flexible joint manipulator.

[0100] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above-mentioned technical features. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also regarded as the protection scope of the present invention.

Claims

1. A fault-tolerant state quantization control method based on a flexible joint robot arm, characterized in that: The following steps are included: a. Establish the state space model of the flexible joint manipulator system; b. Define a radial basis neural network that approximates the unknown terms; c. Define uniform quantizer; d. Define the error transformation of the unquantized flexible joint manipulator system; e. Derivative of the unquantized error variable; f. Construct an unquantized virtual controller and adaptive rate; g. Design unquantized practical anti-interference fault-tolerant controller; h. Design quantized controller and adaptation rate.

2. A fault-tolerant state quantization control method based on a flexible joint robot arm according to claim 1, characterized in that: In step (a), based on the energy relationship between the kinetic energy and potential energy of the flexible joint manipulator system, the lower limb rehabilitation robot with flexible joints is modeled by using the Euler-Lagrangian energy modeling method, and its dynamic model equation is expressed as: Where l∈R n is the angular position of the connecting rod, l∈R n is the angular velocity of the connecting rod, is the angular acceleration of the connecting rod, l m ∈R n is the angular position of the motor, represents the angular velocity of the motor, represents the angular acceleration of the motor, is a positive symmetric inertia matrix, C(l,l) is a vector containing the centripetal force and the Coriolis force, G(l)∈R n represents the gravity vector, represents the friction term, K=diag(K1,…,K n ) represents the joint stiffness, which is positive definite R n×n Matrix, J = diag(J1,…,J n )∈R n×n represents the positive motor inertia matrix, B = diag(B1,…,B n )∈R n×n represents the natural damping term, u f =u0+u * ∈R n is the actual input, u0 is the designed controller, u * is the additive fault degree encountered by the controller; after transformation, the following expression is obtained, in, 3. The fault-tolerant state quantization control method based on a flexible joint robot arm according to claim 2 is characterized in that: In step (b), there is a radial basis function neural network θ T ψ(X) satisfies the following conditions, f(X)=θ T ψ(X)+σ(X),|σ(X)|≤∈, where X∈R n is the input of the neural network, θ∈R r is the optimal weight vector, r is the number of nodes, and θ is defined as is an estimate of θ, σ(X) is defined as the estimation error, and the Gaussian basis function is ψ(X)=[ψ1(X),ψ(X)2,…,ψ r (X)], where τ i Represents the width, a i =[a i1 ,a i2 ,…,a in ], i = 1,…, r is the center of the Gaussian function.

4. The fault-tolerant state quantization control method based on a flexible joint robot arm according to claim 3 is characterized in that: In step (c), the uniform quantizer of the quantized state signal is defined as By using the above quantization criteria, all state variables are uniformly quantized, where r>0 is the length of the quantization level, Q1=r, Q i+1 =Q i +r.

5. The fault-tolerant state quantization control method based on a flexible joint robot arm according to claim 4 is characterized in that: In step (d), define the error variable, Among them, z1 represents the tracking error, α i represents the virtual controller, and further defines the error transformation variable as Among them, A>1 is the designed parameter, Represents the error z i The boundary, i0 , i∞ , μ i are all designed positive constants.

6. The fault-tolerant state quantization control method based on a flexible joint robot arm according to claim 5 is further characterized in that: In step (e), the four error variables are differentiated separately, in, Represents the derivative of the virtual controller.

7. The fault-tolerant state quantization control method based on a flexible joint robot arm according to claim 6 is characterized in that: In step (f), the Lyapunov candidate function is constructed by backstepping to design a virtual controller, and the real controller and the adaptive rate are designed in the last step, where the virtual controller α j (j=1,2,3) is constructed as, At the same time, the adaptive rate The design is as follows, in are the parameters to be designed.

8. The fault-tolerant state quantization control method based on a flexible joint robot arm according to claim 7 is further characterized in that: In step (g), the quantized controller and the adaptive rate are designed. After the state is quantized by the quantizer, the error transformation variable in According to the above method, the error variable after design quantization is as follows: In the above formula It is a virtual controller designed based on the quantized state. The specific expression is: The controller designed based on the quantized state and the adaptive rate are, The impact of the fault is handled according to the designed controller and adaptive rate.

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