Design Method and System of Distributed Interval Observer Based on Multi-Robot Model

Abstract

This application discloses a design method and system for a distributed interval observer based on a multi-arm robot model. The method includes: acquiring the working state of a single-arm robot model; obtaining the state-space equation of the single-arm robot model based on its working state; transforming the state-space equation of the single-arm robot model to construct a multi-arm robot model; establishing a distributed interval observer for the multi-arm robot model based on a first theoretical framework network; and obtaining observation data through the distributed interval observer. This invention employs an interval estimation method to solve the problem of finding the optimal solution when the state equation and measurement equation of a nonlinear system cannot be expressed analytically. This ensures the minimum variance of the system's state variables, causing the error between the original state trajectory of the multi-arm robot system and the state trajectory of the distributed interval observer (DIO) to converge to a very small bound, thus ensuring the effectiveness of the DIO.

Description

Technical Field

[0001] This invention relates to the field of multi-manipulator system control, and in particular to a design method and system for a distributed interval observer based on a multi-manipulator model. Background Technology

[0002] With the continuous development and application of robotics technology, robotic arms have become one of the most commonly used robots in the field of industrial automation. As a complex dynamic system, the control and observation problems of robotic arms have become a research hotspot. Currently, the main methods used for the control and observation of robotic arms include model predictive control, adaptive control, and interval observers. Meanwhile, in recent years, multi-agent systems based on Euler-Lagrange theory have also received increasing research attention, mainly used to simulate some typical real-world industrial systems, such as multi-armed robots, mobile robots, and spacecraft.

[0003] Since the concept of multi-agent systems was introduced in the field of control theory, academic research on multi-agent systems has developed significantly. Based on the centralized control of traditional general systems, multi-agent systems can be extended to distributed systems, evolving into distributed control. Simultaneously, from the perspective of the information flow direction designed in the control process, control methods can be broadly divided into two categories: centralized control strategies and distributed control strategies. In centralized control structures, the system is required to have a global "master," that is, possessing global system information. The main problems of centralized control are computational complexity and system fragility. Distributed methods mainly utilize local information to execute global cluster control, thus exhibiting better system robustness and flexibility. It should be noted that multi-agent systems with Euler dynamics exhibit stronger uncertainty and nonlinearity. Multi-agent systems described by the Euler-Lagrange equations are called multi-Euler-Lagrange systems (ELSs), but unfortunately, methods used in general linear and nonlinear systems cannot be directly extended to such multi-agent systems.

[0004] Multi-Euler-Lagrange systems have been widely used in many real mechanical models. However, in experiments, the variables in some specific mechanical systems cannot be directly obtained. Many researchers have proposed design schemes for system observers and solved some problems. For example, the literature [Stamnes, ...] [N.; Aamo, OM; Kaasa, GOA constructive speed observer design for general Euler-Lagrange systems. Automatica 148 2011, 47, 2233–2238.] This paper proves the existence of a globally exponentially convergent speed observer for general Euler-Lagrange systems. The key to this result is a function defined by certain integrals that cannot be solved a priori and may not have explicit analytical solutions.

[0005] Secondly, in the literature [Cai, H.; Huang, J. The leader-following consensus for multiple uncertain Euler-Lagrange systems with a distributed adaptive observer. In Proceedings of the 2015 IEEE 7th International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE 163 Conference on Robotics, Automation and Mechatronics (RAM). IEEE, 2015, pp. 218–223.], the authors and their team designed a distributed adaptive observer for uncertain multi-agent systems (MELs) and designed a leader-follow consensus protocol based on DO. Furthermore, in the literature [Zhang Z, Yang G. Distributed fault detection and isolation for multiagent systems: An interval observer approach[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, 50(6): 2220-2230.], the authors proposed a method for designing DIOs and applied them to multiagent systems to address the problem of fault diagnosis and isolation when encountering external attacks.

[0006] In terms of modeling methods, since multi-robot models have multiple subsystems, appropriate system theory is needed to fit reality. Existing literature shows that most models use centralized observers to analyze the robot system, neglecting the observation of individual states, parameters, and their errors in a multi-dimensional system. This introduces uncertainties and errors between the model and reality. This invention combines distributed interval observers with the multi-robot model to overcome the errors between state observations and reality in the multi-robot model.

[0007] In research, researchers mostly focus on the stable control and convergence speed of multi-agent systems. However, for systems under disturbance, the greater concern is ensuring the system state remains at an ideal level of control accuracy and robustness, rather than convergence speed. Multi-agent systems exhibit uncertainty and nonlinearity, with uncontrollable factors beyond human intervention, leading to instability in observer design. Therefore, considering the effectiveness of system interval estimation and the stability of DIO design during system modeling has both practical and theoretical significance. Summary of the Invention

[0008] (a) Technical problems to be solved

[0009] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a distributed interval observer design method and system based on a multi-manipulator model to solve the technical problems of the prior art. On the one hand, most of them use centralized observers to model and analyze their manipulator systems, while ignoring the observation of individual states and parameters and their errors of multi-dimensional systems, which makes the model and reality have uncertainties and errors. On the other hand, the existing multi-agent system has uncertainties and nonlinearities, and there are uncontrollable factors that are not human-made, which makes the observer design unstable.

[0010] (II) Technical Solution

[0011] To achieve the above objectives, the first aspect of the present invention provides a design method for a distributed interval observer based on a multi-manipulator model.

[0012] A second aspect of the present invention provides a distributed interval observer system based on a multi-robotic arm model.

[0013] In view of this, according to a first aspect of the embodiments of this application, a method for designing a distributed interval observer based on a multi-robotic arm model is proposed, the method comprising:

[0014] Obtain the working state of the single robotic arm model, and derive the state-space equation of the single robotic arm model based on the working state of the single robotic arm model.

[0015] The state-space equations of the single-arm robotic model are transformed to construct a multi-arm robotic model.

[0016] A distributed interval observer for the multi-robotic arm model is established based on the first theoretical framework network.

[0017] Observational data were obtained using a distributed interval observer with a multi-robotic arm model.

[0018] In one implementation, the working state of a single robotic arm model is obtained, and the state-space equation of the single robotic arm model is obtained based on the working state of the single robotic arm model, including:

[0019] The state-space equation is:

[0020]

[0021] where x i1 =q i , h(x i1 )=M(x i1 ) -1 f(x) i1 ,x i2 )=-M(x i1 ) -1 (C(x i1 ,x i2 )x i2 +G(x i1 )). q i ∈R n M represents a generalized coordinate vector. i (q i )∈R n×n Represents the inertia matrix. G(q) represents the matrix of Coriolis force and centripetal force. i )∈R n Represents the gravity vector, u i ∈R n The vector representing the generalized control input force.

[0022] In one implementation, the state-space equations of the single-arm robotic model are transformed to construct a multi-arm robotic model, including:

[0023] For model matrix A∈R n×n Perform equivalent transformations using linear transformations. The state-space equations of the constructed robotic arm model are as follows:

[0024]

[0025] in, C = [I n×n 0 n×n ]∈Rn×2n ,

[0026] In one implementation, a distributed interval observer for the multi-robotic arm model is established based on a first theoretical framework network, including:

[0027] The first theoretical framework network is a theoretical network framework based on multi-Euler-Lagrange systems. When designing a multi-manipulator distributed interval observer, two methods for designing the observer gain are designed using monotonic system theory and Lyapunov stability theory.

[0028] The observer design values ​​for each single robotic arm model are as follows:

[0029]

[0030] Among them, matrices L, M, and and Υ, and satisfy Make Π satisfy the Metzler matrix.

[0031]

[0032] In one implementation, observation data is obtained through a distributed interval observer using a multi-robotics model, including:

[0033] The dynamic equation of the distributed interval observer of the multi-manipulator model is:

[0034]

[0035] in,

[0036] The dynamic equation of the distributed interval observer error model of the multi-manipulator model is:

[0037]

[0038] For the multi-arm robotic model, the initial state satisfies the inequality:

[0039] Among them, the formula (4) gives And z(t) satisfy for all t≥0,

[0040] For the multi-arm robotic model, an additional observer gain L is defined. i , Υ i and M i The Lyapunov function is defined as follows: V(t) and Equivalence, explanation The system is designed with stable interval observers.

[0041] In one implementation, the multi-arm model includes at least two single-arm models.

[0042] In one implementation, the observation data is bounded and stable.

[0043] According to a second aspect of the embodiments of this application, a distributed interval observer system based on a multi-robotic arm model is proposed, comprising:

[0044] The single robotic arm model state space equation acquisition module is used to acquire the working state of the single robotic arm model and obtain the state space equation of the single robotic arm model based on the working state of the single robotic arm model.

[0045] The multi-arm robotic model construction module is used to transform the state space equation of the single-arm robotic model to construct a multi-arm robotic model.

[0046] The observer framework design module is used to establish a distributed interval observer for the multi-manipulator model based on the first theoretical framework network.

[0047] The observer data calculation module is used to obtain observation data through a distributed interval observer using a multi-robotic arm model.

[0048] According to a third aspect of the embodiments of this application, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of a distributed interval observer design method based on a multi-manipulator model as described in any of the preceding claims.

[0049] According to a fourth aspect of the embodiments of this application, a non-transitory computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the steps of a distributed interval observer design method based on a multi-manipulator model as described in any of the preceding claims.

[0050] (III) Beneficial Effects

[0051] The beneficial effects of this invention are:

[0052] This invention provides a distributed interval observer design method and system based on a multi-manipulator model. First, the multi-manipulator model is modeled, and the nonlinear model is linearized and simplified to construct the state-space equations commonly used in control theory. Simultaneously, graph theory knowledge is integrated into the system to form a cluster system. This type of system has wide applicability. Furthermore, a DIO framework is constructed, and a distributed interval observer is designed to estimate the unknown parameters and state variables of each sub-model. At the same time, the interval estimation method is used to solve the problem of finding the optimal solution when the state equations and measurement equations of the nonlinear system cannot be analytically expressed, thus ensuring the minimum variance of the system state variables. This ensures that the error between the original state trajectory of the multi-manipulator model and the state trajectory of the DIO converges to a very small bound, guaranteeing the effectiveness of the DIO. An additional observation gain is innovatively added, providing a strong guarantee for the adjustability of the design and the final solution, thereby ensuring the stability of the DIO. This distributed interval observer design based on a multi-manipulator model makes the system more stable and can better perform state estimation and parameter analysis on multi-manipulator systems with uncertainties. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0054] Figure 1 A flowchart illustrating a distributed interval observer design method based on a multi-robotic arm model provided in this application;

[0055] Figure 2 A schematic diagram of a single robotic arm model structure for a distributed interval observer based on a multi-robotic arm model provided in this application;

[0056] Figure 3 This application provides a schematic diagram of the topology of a distributed interval observer system based on a multi-robotic arm model. Detailed Implementation

[0057] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0058] This application addresses the technical problems in existing technologies. Firstly, most models and analyses of robotic arm systems employ centralized observers, neglecting the observation of individual states, parameters, and errors in multi-dimensional systems. This leads to uncertainties and errors between the model and reality. Secondly, existing multi-agent systems exhibit uncertainty and nonlinearity, with uncontrollable factors beyond human intervention, resulting in instability in observer design. Therefore, this application provides a distributed interval observer design method and system based on a multi-robotic arm model.

[0059] The method and system of the present invention will be further described below with reference to specific embodiments.

[0060] Firstly, such as Figure 1 As shown, this application provides a design method for a distributed interval observer based on a multi-robotic arm model, the method comprising:

[0061] S100, Obtain the working state of the single robotic arm model, and obtain the state space equation of the single robotic arm model based on the working state of the single robotic arm model.

[0062] In step S100, a single robotic arm model is first established, and its schematic diagram is shown below. Figure 2 As shown, this is a 2-DOF robotic arm model with a directed graph. Table 1 provides a description of the relevant parameters of this robotic arm model.

[0063] Table 1. Description of relevant parameters for the robotic arm model.

[0064] symbol meaning Numerical <![CDATA[I1]]> Moment of inertia of link 1 <![CDATA[61.25×10 -3 kgm 2 ]]> <![CDATA[I2]]> Moment of inertia of link 2 <![CDATA[20.42×10 -3 kgm 2 ]]> <![CDATA[m1]]> Mass of Link 1 2kg <![CDATA[m2]]> Linkage 2 mass 0.85kg l1 Length of Link 1 0.35m <![CDATA[l2]]> Length of Link 2 0.31m <![CDATA[l c1 ]]> Center of mass of link 1 0.175m <![CDATA[l c2 ]]> Center of mass of link 2 0.155m g gravitational acceleration <![CDATA[9.81m / s 2 ]]>

[0065] The state-space equations are obtained through calculation, and the specific steps include:

[0066] The ELS expression for a second-order dynamical system is given as follows:

[0067]

[0068] Where, q i ∈R n M represents a generalized coordinate vector. i (q i )∈R n×n Represents the inertia matrix. G(q) represents the matrix of Coriolis force and centripetal force. i )∈R n Represents the gravity vector, u i ∈R n The vector representing the generalized control input force;

[0069] Equation (6) is transformed as follows:

[0070]

[0071] where x i1 =q i , h(x i1 )=M(x i1 ) -1 f(x) i1 ,x i2 )=-M(x i1 ) -1 (C(x i1 ,x i2 )x i2 +G(x i1 Under the above state reconstruction, joint displacements are measurable. The spatial state equations can be obtained as follows:

[0072]

[0073] in, C = [I n×n 0 n×n ]∈ Rn×2n ,

[0074] In this embodiment, graphs are an effective tool for characterizing the topological structure between adjacent nodes in a multi-agent network. In this invention, the graphs studied are all directed graphs, denoted by G = (ν, ε, A). This directed graph contains many nodes, also referred to as individual agents, denoted as ν = {ν1, ν2, ..., ν...}. n}, where ν is a set of finitely many non-empty nodes. It is the set of edges in a directed graph, where two nodes form an edge, i.e., e. ij =(ν i ,ν j Let the set of these edges be denoted as a finite set ε. According to the relationship between edges and vertices, the edge set satisfies... A∈R n×n =[a ij ] represents the adjacency matrix, where a ij This represents the weight of edge (j,i). If a ij =a ji If so, the directed graph can be considered as an undirected graph. Generally, each node has no spin, therefore, a ii =0. For a path, taking point k to point l as an example, {(v k ,v k+1 ),(v k+1 ,v k+2 ),...,(v k+m ,v l )} is a valid path from point k to point l.

[0075] For any point ν in the network i The out-degree of a point refers to the number of edges originating from that point, while the in-degree refers to the number of edges ending at that point.

[0076] A network is called a balanced network when all points in the network have the same out-degree and in-degree.

[0077] For an undirected graph, if any two points in the graph can always find a path to the other, then such a graph is called strongly connected.

[0078] For a directed graph, if there exists an edge from vertex ν... i Start to point ν j That's all, so let's get to point ν. i It is point ν j A parent node. If a directed graph has only one root node (i.e., it has no parent node), and all other nodes have exactly one parent node, then the directed graph is called a directed tree. If the spanning subgraph of a graph is a directed graph, then the tree is called a spanning tree.

[0079] The degree matrix D of G is a diagonal matrix, where the diagonal elements are the degrees of each vertex, denoted as . The Laplace matrix is: L = DA, L = [l ij ]∈R n×n ,in,

[0080]

[0081] In this embodiment, through this construction, it is easy to obtain that the Laplacian matrix L has an eigenvector corresponding to an eigenvalue of zero, which is 1 / N. Furthermore, if the graph is strongly connected, then 0 = λ1(G) ≤ λ2(G) ≤ … ≤ λ N (G), where λ i (G) is the eigenvector of L.

[0082] In this embodiment, the present invention establishes a robotic arm cluster model based on graph theory and control theory, where i in the system represents the state-space equation of the i-th robotic arm.

[0083] In this embodiment, for matrix E, E + Let max{0,E}, where E - =E + -E. For a real symmetric matrix O∈R n×n O > 0 (O < 0) indicates that matrix O is positive (negative) definite, and He(O) = O T +O.

[0084] The lemma used in this embodiment is as follows:

[0085] Lemma 1: G is a strongly connected graph, and r i (i = 1, ..., N) represents the left eigenvector with eigenvalue 0, and R = diag{r1, ..., r2} N}, then RL+L T ≥0 is true;

[0086] Lemma 2: If G is strongly connected, the generalized algebraic connectivity of G can be expressed as:

[0087]

[0088] If the topology is balanced, then matrix R = r1I N ,but

[0089] Lemma 3: If φ(x) i If x is a globally differentiable Lipschitz function, then there exist two increasing Lipschitz functions f(x). i ) and g(x i ), so that:

[0090] φ(x i )=f(x i )-g(x i );

[0091] Lemma 4: For φ(x) in Lemma 3 i There exists a global Lipschitz function. satisfy:

[0092]

[0093] Lemma 5, for φ(x) in Lemma 4 i ), and There exists a matrix F i ∈{1,2,3,4}, satisfying:

[0094]

[0095] in, e i =x i - x i and

[0096] Lemma 6: Given a constant matrix A∈R m×n and a vector ζ∈R n×1 ,if If it is established, then

[0097]

[0098] S200, the state space equation of the single robotic arm model is transformed to construct a multi-robotic arm model;

[0099] In this embodiment, the multi-arm robotic model includes at least two single-arm robotic models;

[0100] In this embodiment, for the model matrix A∈R n×n Perform an equivalent transformation using the linear transformation z. i =Hx i The state-space equations of the constructed robotic arm model are as follows:

[0101]

[0102] in, C = [I n×n 0 n×n ]∈R n×2n ,

[0103] S300, The multi-robotic arm model is used to establish a distributed interval observer for the multi-robotic arm model based on the first theoretical framework network;

[0104] In this embodiment, the first theoretical framework network is a theoretical network framework based on multiple Euler-Lagrange systems. When designing the multi-manipulator distributed interval observer, two methods for designing the observer gain are designed using the monotonic system theory method and the Lyapunov stability theory method.

[0105] In this embodiment, the observer design values ​​for each single robotic arm model are as follows:

[0106]

[0107] Among them, matrices L, M, and and Υ And satisfy Make Π satisfy the Metzler matrix.

[0108]

[0109] S400 obtains observation data through a multi-robotic arm model distributed interval observer;

[0110] In this embodiment, the following assumptions and notes are made for the construction of the DIO framework:

[0111] Assume that the initial state of system (3) satisfies the following inequalities

[0112]

[0113] Assume that there exist matrices L, M, and Υ Such that Π satisfies the Metzler matrix.

[0114]

[0115] in, Assume that the topological graph in 3 is considered to be balanced and strongly connected.

[0116] Note 1: In order to estimate the nonlinear function φ i The boundary of (x) is defined by us.

[0117]

[0118] In the formula and z i (t) represents z i The estimated value of (t), H a =H -1 .

[0119] Under Lemma 6, we can obtain the following inequality:

[0120]

[0121] Note 2: After coordinate transformation, the conclusion of Lemma 5 takes the following form:

[0122]

[0123] Where, N i =F i H(i=1,2,3,4) is a constant matrix.

[0124] In order to achieve The observer design values ​​for each sub-model were constructed as follows:

[0125]

[0126] In this embodiment, the boundedness design process of DIO is as follows:

[0127] From the DIO of each sub-model, the dynamic equation of the multi-manipulator model distributed interval observer error model of the i-th subsystem is:

[0128]

[0129] Under assumption 3, the dynamic equations of the entire model are expressed as:

[0130]

[0131] in,

[0132] The dynamic equations of the global observer are:

[0133]

[0134] in

[0135] Theorem 1 If Assumptions 1-2 hold, then z(t) and z(t) given in (4) satisfy

[0136] Proof: The dynamics of the global error system is given by

[0137]

[0138] By definition, we can obtain the derivative of ∈(t):

[0139]

[0140] in

[0141] The proofs of validity in (3) and (4) are equivalent to the proof of the nonnegativity of the error system. Through the above process, we can obtain... and It is obvious that we can obtain from hypothesis 1 and e (0)≥0. By assumption 2, we obtain that Π is Metzler. First, considering the theory of monotonic systems, ∈(t)≥0 holds, which means that for all cases t≥0,

[0142] In this embodiment, the process of DIO stability design is as follows:

[0143] After proving the boundedness of DIO, we proceed to design the observer gain L. i , Υ i and M i This is to ensure the stability of DIO.

[0144] Theorem 2: Given a positive definite matrix P = P T And a constant τ≥0, if such a solution exists.

[0145]

[0146] Among them, L i =P -1 Q i , Υ i =P -1 W i M i -1 =P is the observation gain, γ is the coupling strength, then (4) is the DIO of (8).

[0147] Proof: The Lyapunov function can be defined as follows: The derivative of V(t) can then be written as:

[0148]

[0149] In the formula

[0150]

[0151] By Lemma 2, we can obtain

[0152]

[0153]

[0154] Consider M i =P -1 , can be written as

[0155]

[0156] Note We have

[0157]

[0158] in,

[0159]

[0160] Note 3: To meet the requirements of the LMI toolbox, Applied to Ω, the result is

[0161]

[0162] From this, we can obtain V(t) and Equivalence, explanation and This ensures the stability of DIO.

[0163] Secondly, this application provides a distributed interval observer system based on a multi-robotic arm model, comprising:

[0164] The single robotic arm model state space equation acquisition module is used to acquire the working state of the single robotic arm model and obtain the state space equation of the single robotic arm model based on the working state of the single robotic arm model.

[0165] The multi-arm robotic model construction module is used to transform the state space equation of the single-arm robotic model to construct a multi-arm robotic model.

[0166] The observer framework design module is used to establish a distributed interval observer for the multi-manipulator model based on the first theoretical framework network.

[0167] The observer data calculation module is used to obtain observation data through a distributed interval observer using a multi-robotic arm model.

[0168] The effects of applying the aforementioned method in the above system can be found in the description of the aforementioned method embodiments, and will not be repeated here.

[0169] Thirdly, this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of a distributed interval observer design method based on a multi-manipulator model as described in any of the preceding claims.

[0170] Fourthly, this application provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of a distributed interval observer design method based on a multi-manipulator model as described in any of the preceding claims.

[0171] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims of this application.

Claims

1. A design method for a distributed interval observer based on a multi-robotic arm model, characterized in that, The method includes: Obtain the working state of the single robotic arm model, and derive the state-space equation of the single robotic arm model based on the working state of the single robotic arm model. The state-space equations of the single-arm robotic model are transformed to construct a multi-arm robotic model. A distributed interval observer for the multi-robotic arm model is established based on the first theoretical framework network; the first theoretical framework network is a theoretical network framework based on a multi-Euler-Lagrange system. Observational data was obtained using a distributed interval observer with a multi-robotic arm model. Specifically, establishing a distributed interval observer based on the multi-robotic arm model according to the first theoretical framework network includes: When designing a multi-manipulator distributed interval observer using the first theoretical framework, the monotonic system theory method and the Lyapunov stability theory method are used to calculate the observer gain matrix. The observer design values ​​for each single robotic arm model are as follows: Among them, matrices L, M, and and Υ And satisfy Make Π satisfy the Metzler matrix.

2. The method for designing a distributed interval observer based on a multi-robotic arm model as described in claim 1, characterized in that, Obtain the working state of the single robotic arm model, and derive the state-space equation of the single robotic arm model based on the working state of the single robotic arm model, including: The second-order dynamic multi-Euler-Lagrange system based on the single-manipulator model can be written as: Where q i ∈R n M represents a generalized coordinate vector. i (q i )∈R n×n Represents the inertia matrix. G(q) represents the matrix of Coriolis force and centripetal force. i )∈R n Represents the gravity vector, u i ∈R n A vector representing the generalized control input force; The above second-order powered single-arm manipulator model is transformed as follows: State x can then be obtained i Dynamic relationship: Therefore, the state-space equation of the single robotic arm model is: in, 3. The method for designing a distributed interval observer based on a multi-robotic arm model as described in claim 1, characterized in that, The state-space equations of the single-arm robotic model are transformed to construct a multi-arm robotic model, including: For model matrix A∈R n×n Perform an equivalent transformation using the linear transformation z. i =Hx i The state-space equations of the constructed robotic arm model are as follows: in 4. The method for designing a distributed interval observer based on a multi-robotic arm model as described in claim 1, characterized in that, The observation data obtained through the distributed interval observer of the multi-robotic arm model includes: The dynamic equation of the distributed interval observer of the multi-manipulator model is: in, The dynamic equation of the distributed interval observer error model of the multi-manipulator model is: For the multi-arm robotic model, the initial state satisfies the inequality: Equation (6) gives and z (t) satisfies the following condition for all t≥0. For the multi-robotic arm model, the observer gain L is defined. i , Υ i and M i The Lyapunov function is defined as follows: By proof illustrate and The system's designed interval observer is stable.

5. The method for designing a distributed interval observer based on a multi-robotic arm model as described in claim 1, characterized in that, The multi-arm robotic model includes at least two single-arm robotic models.

6. The method for designing a distributed interval observer based on a multi-robotic arm model as described in claim 1, characterized in that, The observation data is bounded and stable.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the distributed interval observer design method based on a multi-manipulator model as described in any one of claims 1 to 6.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of a distributed interval observer design method based on a multi-manipulator model as described in any one of claims 1 to 6.

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