CN113814983A - Multi-single-arm manipulator system control method and system - Google Patents

Abstract

The invention relates to a multi-single-arm manipulator system control method and system, comprising the following steps: establishing a state dynamics model of the multiple-single-arm manipulator; The transformed tracking error; the identification model and the disturbance observer are obtained according to the obtained state dynamics model; the virtual controller is obtained according to the preset finite-time performance function, the transformed tracking error and the disturbance observer; the control signal to the virtual controller Filtering is performed to obtain new state variables; the controller of the multi-single-arm manipulator system is obtained according to the new state variables, the identification model and the disturbance observer, and the method of the invention has a good control effect.

Description

A multi-single-arm manipulator system control method and system

technical field

The invention relates to the technical field of industrial process control, in particular to a control method and system for a multi-single-arm manipulator system.

Background technique

With the continuous progress of modern technology, manipulators are widely used, such as machinery manufacturing, electronic processing, metallurgy, aerospace and so on. Robotic hands can replace humans to complete repetitive and heavy manual labor in harmful environments. However, with the rapid development of manipulators, the single-arm manipulator gradually shows the limitations of poor flexibility and low work efficiency, while the collaborative operation of multiple single-arm manipulators has the characteristics of low communication cost, high flexibility and robustness, and can complete complex and diverse tasks. Therefore, it is of great significance to study the design of the output consistent controller of the multi-arm manipulator. One manipulator in the multi-single-arm manipulator collaborative control system is used as the "leader", and some manipulators that can receive the output signal of the "leader" or adjacent manipulators are used as "followers", in which all "followers" can track the leader. The output signal of the user, so as to achieve the control goal of consistent output.

In practical applications, the multi-single-arm manipulator has high requirements on system performance due to external conditions, and the output error of the manipulator needs to meet certain constraints within a limited time. By selecting the preset finite-time performance function and error transformation, when the manipulator output error approaches the boundary conditions, the controller gain becomes larger, so that the output error cannot reach its limit boundary. The inventor found that the finite time of the existing finite-time controller design method is affected by the initial value of the system and the design parameters, which is complicated to determine.

The system model of the multi-arm manipulator often has unknown nonlinearity. As a common method to deal with nonlinearity, fuzzy logic system is widely used in the design of the controller. The inventor found that most of the existing approximation methods using fuzzy logic systems cannot accurately approximate the unknown nonlinearity of the system, thus resulting in weak controller robustness and poor control effect.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the prior art and provide a method for obtaining a controller of a multi-single-arm manipulator system, so that the fuzzy logic system can accurately approximate the unknown nonlinearity of the system and the tracking error can be converged in a limited time.

To achieve the above object, the present invention adopts the following technical solutions:

In a first aspect, an embodiment of the present invention provides a method for controlling a multi-single-arm manipulator system, including the following steps:

Establish the state dynamics model of the multi-arm manipulator;

According to the consistent tracking error model of the multi-single-arm manipulator and the constructed preset finite time performance function, the error transformation is performed to obtain the transformed tracking error;

Obtain the identification model and the disturbance observer according to the obtained state dynamics model;

The virtual controller is obtained according to the preset finite-time performance function, the transformed tracking error and the disturbance observer;

Filter the control signal of the virtual controller to obtain a new state variable;

According to the new state variables, identification model and disturbance observer, the controller of the multi-arm manipulator system is obtained, and the obtained controller is used to output the control signal.

Optionally, a system model of the single-arm manipulator is established, and the system model of the single-arm manipulator is converted to obtain a state dynamics model of the single-arm manipulator system.

Optionally, a first-order low-pass filter is used to filter the control signal of the virtual controller.

Optionally, the compensated tracking error is obtained according to the compensation signal, the second error surface is obtained according to the new state variable, and the controller is obtained according to the compensated tracking error, the second error surface, the identification model and the disturbance observer.

Optionally, a consistent tracking error model of the multi-single-arm manipulator is obtained according to the knowledge of graph theory.

Optionally, a preset finite-time performance function is obtained according to the finite time during which the consistent tracking error is stable.

Optionally, the disturbance observer includes a connecting rod angular velocity disturbance observer and a connecting rod angular acceleration disturbance observer of the single-arm manipulator.

Optionally, the unknown nonlinear function of the fuzzy logic system approximation system is obtained according to the basis function vector, the optimal weight vector and the approximation error, and the identification model is obtained according to the dynamic model of the multi-single-arm manipulator system.

Optionally, use a Gaussian function to obtain basis function vectors.

In a second aspect, an embodiment of the present invention provides a multi-arm manipulator system control system, including:

Modeling module: used to establish the state dynamics model of the multi-arm manipulator system;

Tracking error acquisition module: It is used to perform error transformation according to the consistent tracking error model of the multi-single-arm manipulator and the constructed finite-time performance function, and obtain the transformed tracking error;

Identification model and disturbance observer acquisition module: used to obtain identification model and disturbance observer according to the obtained state dynamics model;

Virtual controller acquisition model: used to obtain a virtual controller according to the preset finite-time performance function, the transformed tracking error and the disturbance observer;

State variable acquisition module: used to filter the control signal of the virtual controller to obtain new state variables;

Control module: used to obtain the controller of the multi-arm manipulator system according to the new state variables, identification model and disturbance observer, and use the obtained controller to output control signals.

Beneficial effects of the present invention:

1. The method of the present invention, by using the recognition model, enables the fuzzy logic system to accurately approximate the unknown nonlinear function of the system, so that the controller obtained according to the recognition model has stronger robustness and better control effect.

2. The method of the present invention obtains an error variation model according to the consistent tracking error of the multi-single-arm manipulator and the constructed finite-time performance function, so that the consistent tracking error satisfies the constraints and reaches a stable state within a preset time, and then It is guaranteed that the multi-arm manipulator can effectively track the given signal, and the limited time setting of this method is more flexible, independent of the initial value of the system and the setting parameters.

3. In the method of the present invention, by designing a disturbance observer, the problem of time-varying disturbance is taken into consideration, so that the obtained controller can meet the requirements of the multi-single-arm manipulator working in a more complex environment.

4. The method of the present invention filters the control signal of the virtual controller, introduces the dynamic surface technology to solve the "computation explosion" problem existing in the traditional backstepping method, and eliminates the filter error caused by the dynamic surface technology through the error compensation model. influences.

Description of drawings

The accompanying drawings that constitute a part of the present application are used to provide further understanding of the present application, and the schematic embodiments and descriptions of the present application are used to explain the present application and do not constitute a limitation to the present application.

1 is a flowchart of a control method according to Embodiment 1 of the present invention;

FIG. 2 is a communication topology diagram between the single-arm manipulators in Embodiment 1 of the present invention;

3 is a control flow chart of the i-th single-arm manipulator preset limited time in Embodiment 1 of the present invention;

4 is a tracking effect diagram of a simulation test in Embodiment 1 of the present invention;

5 is a schematic diagram of the tracking error of the simulation test in Embodiment 1 of the present invention;

6 is a schematic diagram of the observation results of the time-varying disturbance d _i,1 in the simulation test of Embodiment 1 of the present invention;

FIG. 7 is a schematic diagram of the estimation result of the unknown nonlinear function and the time-varying disturbance f _i,2 +d _i,2 in the simulation test system of Embodiment 1 of the present invention.

Detailed ways

Example 1

This embodiment provides a method for controlling a multi-single-arm manipulator system, where the multiple-single-arm manipulator system includes a leading manipulator and N following manipulators, where the following manipulators are single-arm manipulators with unknown nonlinearity and time-varying disturbance, As shown in Figure 1, the control method includes the following steps:

Step 1: Establish the state dynamics model of the multi-arm manipulator.

The specific method is as follows: the system model of the single-arm manipulator as a follower manipulator has been widely recognized in related fields. As shown in Figure 1, the system model of the i-th single-arm manipulator in the follower manipulator is:

分别为单臂机械手的连杆的转角位置、角速度和角加速度，m_i为连杆总质量，M_i为连杆总转动惯量，g为重力加速度，D_i为总阻尼系数，l_i为从关节轴到连杆质心的距离。in,

are the angular position, angular velocity and angular acceleration of the connecting rod of the single-arm manipulator, m _i is the total mass of the connecting rod, M _i is the total moment of inertia of the connecting rod, g is the gravitational acceleration, D _i is the total damping coefficient, l _i is the Distance from joint axis to link center of mass.

The steps of establishing the state dynamics model are as follows:

Step 1.1: Establish the knowledge of graph theory describing the communication relationship between multiple single-arm manipulators:

为边的集合，(v_i,v_j)∈E表示机械手i能接收到机械手j的信息。机械手i的邻接节点集合表示为N_i＝{v_j∈|(v_i,v_j)∈E,i≠j}。定义权重邻接矩阵为

如果(v_i,v_j)∈E，那么a_i,j>0；否则a_i,j＝0。假设拓扑图中不存在自环，即a_i,i＝0，

定义节点i的入度矩阵为

入度对角矩阵R＝diag{b₁,b₂,...,b_N}，则图G的拉普拉斯矩阵为L＝R-A。定义H＝diag{a_1,0,a_2,0,...,a_N,0}，如果节点i能接收到领导者0的信息，则a_i,0>0；否则，a_i,0＝0；In order to describe the communication relationship between the manipulators in the topology diagram of Figure 2, it is necessary to introduce the relevant knowledge of algebraic graph theory. A directed graph is defined as G=(V, E, A). Among them, V=(v ₁ ,v ₂ ,...,v _N ) is a non-empty set of N manipulators,

is a set of edges, (vi , v _j )∈E means that robot i can receive the information of robot _j . The set of adjacent nodes of robot i is expressed as N _i ={v _j ∈|(v _i ,v _j )∈E,i≠j}. Define the weight adjacency matrix as

If (v _i , v _j )∈E, then a _i,j >0; otherwise a _i,j =0. Assuming that there is no self-loop in the topology graph, that is, a _i,i =0,

Define the in-degree matrix of node i as

In-degree diagonal matrix R=diag{b ₁ ,b ₂ ,...,b _N }, then the Laplacian matrix of graph G is L=RA. Define H=diag{a _1,0 ,a _2,0 ,...,a _N,0 }, if node i can receive the information of leader 0, then a _i,0 >0; otherwise, a _{i, 0} = 0;

Step 1.2: Convert the modeled system model of the single-arm manipulator to a state dynamic mechanical model:

单臂机械手的连杆的转角位置和角速度，系统未知非线性函数

d_i,1(t),d_i,2(t)代表未知时变扰动。Among them, x _i,1 =q _i,1 ,

The angular position and angular velocity of the link of the single-arm manipulator, the system is unknown nonlinear function

d _i,1 (t),d _i,2 (t) represent unknown time-varying disturbances.

Step 2: Obtain the tracking error according to the consistent tracking error model of the multi-single-arm manipulator and the constructed finite-time performance function, and perform coordinate transformation to obtain the transformed tracking error.

Step 2.1: Define the i-th multi-single-arm manipulator consistent tracking error model as follows:

Among them, y _i represents the output of the link angle position of the i-th manipulator, y ₀ represents the link angle position of the leading manipulator as the reference signal for system tracking, a _i,0 , a _i,j contain the communication information between the manipulators, Defined by the above graph theory knowledge;

Step 2.2 Design a preset finite time performance function:

为设计参数；T_i为跟踪误差稳定的有限时间，可灵活设置，与系统初值无关，确定方法比较简单。in,

is the design parameter; T _i is the limited time for the stability of the tracking error, which can be set flexibly and has nothing to do with the initial value of the system, and the determination method is relatively simple.

In step 2.3, the following error changes are made to obtain the transformed tracking error.

Step 3: Design a recognition model based on a fuzzy logic system according to the state dynamics model obtained in step 1, and design a disturbance observer according to the state dynamics model obtained in step 1.

Step 3.1 Design the fuzzy logic system to approximate the unknown nonlinear function of the system:

The unknown nonlinear function of the system is:

为最优权值向量，θ_i,2为基函数向量，ε为逼近误差。in,

is the optimal weight vector, θ _i,2 is the basis function vector, and ε is the approximation error.

Choose basis function vectors:

Among them, N is the number of fuzzy rules, using the following Gaussian function:

为中心点，o_i为高斯函数宽度。in,

is the center point, and o _i is the width of the Gaussian function.

Step 3.2: Design a recognition model according to the designed fuzzy logic system approximating the unknown nonlinear function of the system.

The designed recognition model is:

是最优权值向量

的估计值，

是对扰动d_i，2的估计值，

为预测状态，β_i，2,γ_i，2,δ_i，2>0为待设计参数。in,

is the optimal weight vector

the estimated value of ,

is an estimate of the disturbance di _,2 ,

is the predicted state, β _{i, 2} , γ _{i, 2} , δ _{i, 2} >0 are the parameters to be designed.

The disturbance observers designed in step 3.3 include the link angular velocity disturbance observer and the link angular acceleration disturbance observer of the single-arm manipulator.

Among them, the connecting rod angular velocity disturbance observer is:

The connecting rod angular acceleration disturbance observer is:

和

是对扰动d_i，1，d_i，2的观测值，s_i，1和s_i，2为扰动观测器辅助系统状态根据扰动观测器设计的导数来变换,λ_i，1,λ_i，2>0为待设计参数。in,

and

is the observed value of the disturbance di _,1 ,di _,2 , s _i,1 and s _i,2 are the disturbance observer auxiliary system state and transform according to the derivative designed by the disturbance observer, λ _i,1 ,λ _{i, 2} > 0 is the parameter to be designed.

Step 4: Obtain the virtual controller according to the preset finite-time performance function, the transformed tracking error and the disturbance observer

The designed virtual controller is:

k_i,1>0为设计参数。in,

k _i,1 > 0 are design parameters.

反复微分而引起“微分爆炸”问题。因此引入动态面技术，动态面将虚拟控制器的信号输入到一个一阶低通滤波器，得到新的状态变量

代替第一个虚拟控制器进行下一步计算，这样处理的优点在于减小多单臂机械手系统的计算量，具体的，包括以下步骤：The control method of this embodiment is designed based on the backstepping method, while the traditional backstepping method requires the virtual controller

Repeated differentiation causes the "differential explosion" problem. Therefore, the dynamic surface technology is introduced. The dynamic surface inputs the signal of the virtual controller into a first-order low-pass filter to obtain new state variables.

Instead of the first virtual controller to perform the next calculation, the advantage of this processing is to reduce the calculation amount of the multi-arm manipulator system. Specifically, it includes the following steps:

Step 4.1 uses a first-order low-pass filter to filter the control signal of the virtual controller.

The designed first-order low-pass filter is:

τ_i，1>0为设计参数。Among them, get the new state variable

τ _{i, 1} > 0 is a design parameter.

Step 4.2 In order to eliminate the influence of the filtering error, the tracking error after transformation is compensated, and the tracking error after compensation is defined as:

v _i,1 =ξ _i,1 -z _i,1

Among them, z _i,1 is the compensation signal designed for the filtering error.

The derivative of the compensation signal designed in step 4.3 is:

Step 4.4: Define the second error surface according to the new state variables as:

Step 5: Obtain the controller of the multi-arm manipulator system according to the new state variables, recognition model and disturbance observer.

The controller _ui is:

Among them, k _i,2 > 0 are design parameters.

The realization process of the whole control method is shown in Fig. 3.

Use the control signal output by the controller to control the system to work, and detect whether the tracking error meets the requirements. If the requirements are not met, the above steps are repeated to form a closed-loop system until the requirements are met.

In a simulation test of this embodiment:

The control goal of the simulation experiment is to make the angle q _i of the connecting rod track the given trajectory signal y ₀ =0.5sin(t)+sin(0.5t), considering the unknown time-varying disturbance, in order to verify the effectiveness of the method, it can be assumed as d _i,1 =sin(t)-0.5sin(1.5t); di _,2 =-0.8[sin(t-0.6)-sin(t-0.8)].

According to the actual system, the relevant parameters are the total mass of the connecting rod m _i = 2kg, the total moment of inertia of the connecting rod M _i = 2kg·m ² , the acceleration of gravity g = 10m/s ² , the total damping coefficient D _i = 2, from the joint axis to The distance _li = 1m from the center of mass, the system is unknown nonlinear function

w_i,2(0)＝[0,0,0,0,0,0,0,0,0,0]；

The initial conditions of the simulation are: x _i,1 (0)=[0.1,0.2,0.1,0.3]; _xi,2 (0)=[0.2,0.1,0.2,0]; _si,1 (0)=[ 0,0,0,0]; _si,2 (0)=[0,0,0,0];

w _i,2 (0)=[0,0,0,0,0,0,0,0,0,0];

The relevant parameters are set as follows: ρ _i,0 =1; ρ _i,T =0.05; T _i =0.1; β _i,2 =1; γ _i,2 =50; δ _i,2 =20;λ _i,1 =10; λ _i,2 =10; ki _,1 =20; ki _,2 =20; τ _i,1 =0.005.

The simulation results are shown in Figure 4-7. Figure 4 shows the tracking effect of the multi-single-arm manipulator, and a given trajectory y ₀ is tracked in a very short time. It can be seen from the tracking error performance constraint diagram in Fig. 5 that the preset finite time performance constraint method constrains the consistent tracking error within a specified boundary and reaches a stable state at a given time. Figure 6 is a schematic diagram of the observation results of the time-varying disturbance di _,1 , which can accurately estimate the time-varying disturbance. Figure 7 is a schematic diagram of simultaneously estimating the unknown nonlinear function of the system and the time-varying disturbance f _i,1 +d _i,1 . The combination of the fuzzy logic system and the disturbance observer can accurately estimate the unknown part of the system f _i,1 +d _i,1 . Therefore, numerical simulations demonstrate the effectiveness of the proposed control method.

To sum up, the method of this embodiment has the following advantages:

(1) Design a preset finite-time performance constraint method to make the consistent tracking error meet the external constraints and reach a stable state within the required finite time.

(2) Establish a recognition model based on fuzzy logic system, so that the fuzzy logic system can accurately approximate the unknown nonlinearity of the system. The problem of unknown model of the controlled system is solved, and the designed controller enhances the robustness of the controlled system and can be extended to a wider range of systems.

(3) The designed disturbance observer can effectively compensate the influence of time-varying disturbance, making the multi-arm manipulator suitable for more complex environments.

Example 2:

This embodiment discloses a multi-single-arm manipulator system control system, including:

Modeling module: used to establish the state dynamics model of the multi-arm manipulator system;

Tracking error acquisition module: It is used to perform coordinate transformation according to the consistent tracking error model of the single-arm manipulator and the constructed finite-time performance function to obtain the transformed tracking error;

Identification model and disturbance observer acquisition module: used to obtain identification model and disturbance observer according to the obtained state dynamics model;

Virtual controller acquisition model: used to obtain a virtual controller according to the preset finite-time performance function, the transformed tracking error and the disturbance observer;

State variable acquisition module: used to filter the control signal of the virtual controller to obtain new state variables;

Control module: used to obtain the controller of the multi-arm manipulator system according to the new state variables, recognition model and disturbance observer.

Although the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, they do not limit the scope of protection of the present invention. Those skilled in the art should understand that on the basis of the technical solutions of the present invention, those skilled in the art do not need to pay creative efforts. Various modifications or variations that can be made are still within the protection scope of the present invention.

Claims (10)

1. a multi-arm manipulator system control method, is characterized in that, comprises the following steps: Establish the state dynamics model of the multi-arm manipulator; Perform error transformation according to the consistent tracking error model of the single-arm manipulator and the constructed preset finite-time performance function, and obtain the transformed tracking error; Obtain the identification model and the disturbance observer according to the obtained state dynamics model; The virtual controller is obtained according to the preset finite-time performance function, the transformed tracking error and the disturbance observer; Filter the control signal of the virtual controller to obtain a new state variable; According to the new state variables, identification model and disturbance observer, the controller of the multi-arm manipulator system is obtained, and the controller is used to output control signals. 2. a kind of multi-single-arm manipulator system control method as claimed in claim 1 is characterized in that, establishing the system model of one-arm manipulator, converting the system model of one-arm manipulator, and obtaining the state dynamics of one-arm manipulator system Model. 3 . The method for controlling a multi-single-arm manipulator system according to claim 1 , wherein a first-order low-pass filter is used to filter the control signal of the virtual controller. 4 . 4. A multi-arm manipulator system control method as claimed in claim 1, characterized in that, the tracking error after compensation is obtained according to the compensation signal, the second error surface is obtained according to the new state variable, and the tracking error after compensation is obtained according to the compensation signal. The error, the second error surface, the recognition model, and the disturbance observer get the controller. 5 . The method for controlling a multi-single-arm manipulator system according to claim 1 , wherein a consistent tracking error model of the single-arm manipulator is obtained according to the knowledge of graph theory. 6 . 6 . The method for controlling a multi-single-arm manipulator system according to claim 1 , wherein the preset finite-time performance function is obtained according to the finite time during which the consistent tracking error is stable. 7 . 7 . The method for controlling a multi-arm manipulator system according to claim 1 , wherein the disturbance observer comprises a connecting rod angular velocity disturbance observer and a connecting rod angular acceleration disturbance observer of the single-arm manipulator. 8 . 8. a kind of multi-arm manipulator system control method as claimed in claim 1 is characterized in that, obtains the unknown nonlinear function of fuzzy logic system approximation system according to basis function vector, optimal weight vector and approximation error, The state dynamics model of the single-arm manipulator is identified as the model. 9 . The method for controlling a multi-arm manipulator system according to claim 8 , wherein the basis function vector is obtained by using a Gaussian function. 10 . 10. A multi-single-arm manipulator system control system, characterized in that, comprising: Modeling module: used to establish the state dynamics model of the multi-arm manipulator system; Tracking error acquisition module: It is used to perform coordinate transformation according to the consistent tracking error model of the single-arm manipulator and the constructed finite-time performance function to obtain the transformed tracking error; Identification model and disturbance observer acquisition module: used to obtain the identification model and disturbance observer according to the obtained state dynamics model; Virtual controller acquisition model: used to obtain a virtual controller according to the preset finite-time performance function, the transformed tracking error and the disturbance observer; State variable acquisition module: used to filter the control signal of the virtual controller to obtain new state variables; Control module: used to obtain the controller of the multi-arm manipulator system according to the new state variables, identification model and disturbance observer, and use the controller to output control signals.

Images