Extensible cooperative anti-interference control method for motion-limited multiple mechanical arms

Abstract

The invention discloses an extensible cooperative anti-interference control method for motion-limited multiple mechanical arms, and relates to the technical field of cooperative control of the multiple mechanical arms. The method comprises the steps that a dynamic model of the multi-mechanical-arm system under external disturbance is established; the dynamic model of the multi-mechanical-arm system under external disturbance is converted into a dynamic model of a generalized multi-agent system; determining a topological structure of a communication network of the generalized multi-agent system and accessible information of each agent, and introducing local exchange information of an extensible generalized cooperative control protocol; obtaining key parameters of an extensible generalized cooperative control protocol by using a kinetic model of the generalized multi-agent system; and an extensible generalized cooperative control protocol is designed, so that the multi-mechanical-arm system realizes anti-interference synchronization of positions and speeds of all joints under external disturbance. According to the method, limited movement of the mechanical arms can be processed at the same time, cooperation of the multiple mechanical arms is achieved, the anti-interference capacity is achieved, and efficient and stable operation of a multi-mechanical-arm system can be achieved.

Description

Technical Field

[0001] This invention relates to the field of multi-manipulator cooperative control technology, specifically to a scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators. Background Technology

[0002] Collaborative control technology for robotic arms has wide applications in industrial automation and service robots. For example, in industrial or public area cleaning operations, multiple robotic arms can cover a larger work area through collaboration, effectively improving cleaning efficiency. However, the physical structure of any robotic arm limits the range of motion of its joints; each joint has a defined maximum and minimum displacement limit. During multi-robotic arm collaborative operations, factors such as complex task processes, heavy loads, and tight coupling between multiple robotic arms can cause one or more joints of the robotic arm to approach or even exceed its physical limits during dynamic operation. Once joint displacement exceeds the limit, it can lead to the failure of the current collaborative task and damage to the workpiece, or even permanent mechanical damage to the robotic arm itself, and may even cause a production safety accident.

[0003] by Figure 1 Taking the three-link cleaning planar robotic arm shown as an example, this type of robotic arm always has two core constraints during its movement: (1) the joint displacement constraint is that the sum of the angles of the three joints is always 180 degrees to adapt to the operation scenario of planar cleaning; (2) the range of motion of the robotic arm in the horizontal axis direction is clearly limited and cannot break through the preset boundary. These constraints make the motion states of each joint of the robotic arm mutually coupled and no longer independent, thus describing the dynamic characteristics of the entire multi-robotic arm system as a generalized multi-agent system, that is, there are constraints between the system state variables through algebraic equation relationships. This characteristic is significantly different from the conventional multi-agent system where the states are completely independent.

[0004] In practical industrial applications, the number of robotic arms in a multi-arm collaborative system may need to be dynamically increased or decreased depending on different task requirements. For example, on an industrial assembly line, when faced with a sudden increase in assembly tasks or the need for collaborative assembly of complex workpieces, a robotic arm may need to be temporarily added for auxiliary operations. However, traditional centralized control methods require redesigning dedicated controllers for a specific number of robotic arms, lacking the flexibility to cope with dynamic changes in system scale. While some distributed control methods can reduce the computational burden on the central node, their control laws are usually tightly coupled with the network topology and the number of robots among the multiple robotic arms; when the system scale changes, the controller often needs to be redesigned and its parameters retuned, lacking "plug-and-play" scalability. This deficiency limits the further promotion and application of multi-arm systems in flexible manufacturing and other scenarios.

[0005] Furthermore, robotic arms in real-world working environments such as cleaning operations are frequently subjected to various external disturbances, such as dynamic changes in workload, wind interference, uneven ground conditions, and nonlinear disturbances like friction between robotic arm joints. These external disturbances severely degrade the control performance of multi-robotic arm collaborative systems, leading to increased coordination errors between robotic arms, system-wide oscillations, and even instability in severe cases. Moreover, when multi-robotic arm systems are modeled as generalized multi-agent systems, the motion constraints of the robotic arms are transformed into algebraic equations, resulting in stronger nonlinear coupling between system state variables. This further increases the design difficulty of robust anti-interference control protocols, ultimately making it difficult for existing control methods to simultaneously meet the system's requirements for robustness and scalability. Summary of the Invention

[0006] Therefore, the purpose of this invention is to provide a scalable cooperative control method that can simultaneously handle motion constraints, achieve multi-manipulator collaboration, and possess disturbance rejection capabilities, namely, a scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators. The aim is to ensure that the multi-manipulator system can still achieve efficient and stable operation under motion-constrained conditions by modeling the multi-manipulator system as a generalized multi-agent system.

[0007] The technical solution of this invention is:

[0008] A scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators, comprising the following steps:

[0009] Step 1: Based on the physical structure of each motion-constrained robotic arm in the multi-robotic arm system, establish a dynamic model of the multi-robotic arm system under external disturbances;

[0010] Step 2: Describe the multi-manipulator system under external disturbance as a linear generalized multi-agent system, thereby transforming the dynamic model of the multi-manipulator system under external disturbance into the dynamic model of the generalized multi-agent system.

[0011] Step 3: Determine the topology of the communication network of the generalized multi-agent system and the information accessible to each agent, and introduce local information exchange of a scalable generalized cooperative control protocol;

[0012] Step 4: Obtain key parameters of the scalable generalized cooperative control protocol using the dynamic model of the generalized multi-agent system;

[0013] Step 5: Based on the information accessible to each agent, the local exchange information of the scalable generalized cooperative control protocol, and key parameters, design a scalable generalized cooperative control protocol to enable the multi-manipulator system to achieve disturbance-resistant synchronization of the position and velocity of each joint under external disturbances.

[0014] Furthermore, according to the scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators, step 1 further includes the following steps:

[0015] Step 1.1: Establish the dynamic equations of the single-joint confined robotic arm under study;

[0016] Step 1.2: Locally linearize the dynamic equations of the single-joint constrained manipulator established in Step 1.1 around the equilibrium point of the single manipulator;

[0017] Step 1.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] A multi-arm system is established by constructing several physically identical joint-restricted robotic arms. Considering external disturbances, each joint-restricted robotic arm in this multi-arm system is treated as an intelligent agent, and the first joint-restricted robotic arm of this multi-arm system is established. The dynamic equations of a constrained robotic arm.

[0018] Furthermore, according to the scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators described above, the first... The dynamic equations of a constrained robotic arm are as follows:

[0019] (5) (6)

[0020] in Let be the output vector of the multi-arm robotic system, which is the th Positional deviation of the robotic arm Speed ​​deviation and constraint deviation Through the coefficient matrix The result of linear combination; It is a positive definite inertia matrix; It is the damping and gyroscope matrix; These are the stiffness and circulation matrices; It is the force distribution matrix; It is the Jacobian matrix of the constraint equations; and It is the coefficient matrix of the constraint equations; It is the first The position deviation vector of the robotic arm; It is the first The velocity deviation vector of each robotic arm; It is the first The acceleration deviation vector of each robotic arm; It is the first The input force deviation vector of a known control input for a robotic arm; It is the first The constraint force deviation vector of each robotic arm; Representing the External disturbances to a robotic arm and satisfying ; It is the coefficient matrix of the external disturbance and is related to Matchable.

[0021] Furthermore, based on the aforementioned scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators, the dynamic model of the generalized multi-agent system, i.e., the agent... The specific dynamic model is as follows:

[0022] (7)

[0023] in, It is the first The state variables of each agent; It is the first Control input variables of the intelligent agent; It is the first The measurement output variables of each agent; These are all coefficient matrices, as detailed below:

[0024] (8)

[0025] This indicates that the external disturbance and the control input are compatible.

[0026] Furthermore, according to the scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators, step 3 further includes the following steps:

[0027] Step 3.1: Determine the topology of the communication network of the generalized multi-agent system and the information accessible to each agent;

[0028] The topology of the communication network of the generalized multi-agent system is as follows: And satisfy ,in Indicates having a A set of nodes and a graph containing directed spanning trees; the information accessible to each agent is:

[0029] (9)

[0030] in, Topology graph The weight of the middle edge, and ;

[0031] Step 3.2: Introduce the following local information exchange method for the scalable generalized cooperative control protocol:

[0032] (12)

[0033] in, and These are variables generated internally within the scalable generalized cooperative control protocol.

[0034] Furthermore, according to the scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators described above, the parameter matrix is ​​obtained in step 4. and The method is as follows: by performing a non-singular transformation on the state variables of the generalized multi-agent system, the coefficient matrix of the generalized multi-agent system is obtained. The parameters can be obtained by transforming them into the equivalent standard decomposition form shown in equation (13). and ;

[0035] (13)

[0036] in, yes An identity matrix of 3D; yes A 3D matrix; yes An identity matrix of dimension 1.

[0037] Furthermore, according to the scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators, in step 4, the control gain parameter matrix... The control gain parameter matrix is ​​obtained through equation (14). Obtained through equation (15);

[0038] (14)

[0039] (15)

[0040] By independently selecting a suitable scalar This will suppress the impact of disturbances on synchronization accuracy to an arbitrary desired level.

[0041] Furthermore, according to the scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators, the scalable generalized cooperative control protocol is as follows:

[0042] (16)

[0043] in, and These are internal variables of the scalable generalized cooperative control protocol; and It is the derivative of the internal variables of the scalable generalized cooperative control protocol.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] (1) The present invention establishes a dynamic model based on the physical structure of a multi-manipulator that is restricted by external disturbances, and describes the multi-manipulator system as a generalized multi-agent system. It determines the communication topology and the information accessible to the agents, uses the knowledge of the agent model itself to obtain the key parameters of the designed scalable generalized cooperative control protocol, and designs a scalable generalized cooperative control protocol with extended functions based on local information interaction.

[0046] (2) The scalable generalized cooperative control protocol designed in this invention interacts with the state information of its neighbors based solely on the agent's own dynamic model knowledge. By constructing a cooperative control protocol with disturbance suppression capabilities, it achieves distributed cooperative disturbance rejection control that does not rely on global network information. This protocol fundamentally overcomes the scale vulnerability of traditional cooperative control methods, enabling multi-manipulator systems to remain stable without redesigning or tuning the controller when the network scale changes dynamically or the communication topology changes, thus giving multi-manipulator systems true "plug-and-play" scalability.

[0047] (3) The disturbance suppression mechanism embedded in the scalable generalized cooperative control protocol designed in this invention can actively estimate and compensate for complex external disturbances in the operation of a multi-manipulator system, suppressing the impact of disturbances on synchronization accuracy to an arbitrary desired level. This method successfully integrates the physical constraint of motion limitation into the framework of a generalized multi-agent system, and achieves disturbance-resistant synchronization of joint positions and velocities in a multi-manipulator system under any communication network containing a directed spanning tree, without violating displacement constraints.

[0048] In summary, this invention provides a cooperative control solution for multi-manipulator systems that need to operate stably for a long time in complex environments with dynamic expansion, uncertain disturbances, and inherent physical constraints. This solution combines strong robustness, high scalability, and engineering applicability. It can effectively overcome the risk of control instability when the scale of the multi-manipulator system changes dynamically, and can suppress the impact of external disturbances on synchronization performance to any desired level. It has strong engineering applicability and robustness. Attached Figure Description

[0049] Figure 1 This is a model diagram of a multi-manipulator system consisting of multiple planar manipulators with restricted displacement of three-bar joints;

[0050] Figure 2 This is a flowchart of the scalable cooperative disturbance rejection control method for motion-restricted multi-manipulators of the present invention;

[0051] Figure 3 This invention is in A diagram of a scalable, generalized cooperative control protocol architecture for synchronization in a meaningful sense;

[0052] Figure 4 This is an 8-node communication topology diagram of the multi-robotic arm system in this embodiment of the invention;

[0053] Figure 5 This is a 20-node communication topology diagram of the multi-robotic arm system in this embodiment of the invention;

[0054] Figure 6 This is a state response curve of the 8-node multi-manipulator system without external disturbance in an embodiment of the present invention;

[0055] Figure 7 This is a synchronization error response curve of the 8-node multi-manipulator system without external disturbance in an embodiment of the present invention;

[0056] Figure 8 This is an example of an 8-node multi-robotic arm system with external disturbances in this embodiment of the invention. State response curve diagram under the condition;

[0057] Figure 9 This is an example of an 8-node multi-robotic arm system with external disturbances in this embodiment of the invention. In the case of Synchronization error response curve in the sense of the present;

[0058] Figure 10 This is an example of an 8-node multi-robotic arm system with external disturbances in this embodiment of the invention. State response curve diagram under the condition;

[0059] Figure 11 This is an example of an 8-node multi-robotic arm system with external disturbances in this embodiment of the invention. In the case of Synchronization error response curve in the sense of the present;

[0060] Figure 12 This is a state response curve of the 20-node multi-manipulator system without external disturbance in an embodiment of the present invention;

[0061] Figure 13 This is a synchronization error response curve of the 20-node multi-manipulator system without external disturbance in an embodiment of the present invention;

[0062] Figure 14 This is a multi-robotic arm system with 20 nodes and external disturbances in an embodiment of the present invention. State response curve diagram under the condition;

[0063] Figure 15This is a multi-robotic arm system with 20 nodes and external disturbances in an embodiment of the present invention. In the case of Synchronization error response curve in the sense of the present;

[0064] Figure 16 This is a multi-robotic arm system with 20 nodes and external disturbances in an embodiment of the present invention. State response curve diagram under the condition;

[0065] Figure 17 This is a multi-robotic arm system with 20 nodes and external disturbances in an embodiment of the present invention. In the case of Synchronization error response curve in the context of the law. Detailed Implementation

[0066] To facilitate understanding of this application, a more comprehensive description of this application will be provided below with reference to the accompanying drawings.

[0067] Figure 2 This is a flowchart of the scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators provided by the present invention. Figure 2 As shown, the scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators includes the following steps:

[0068] Step 1: Based on the physical structure of each motion-constrained robotic arm in the multi-robotic arm system, establish a dynamic model of the multi-robotic arm system under external disturbances;

[0069] Step 1.1: This embodiment considers a type of joint-constrained robotic arm, and the dynamic equation of a single robotic arm is described in the following form:

[0070] (1)

[0071] in, It is the joint displacement vector of the robotic arm; It is the velocity vector of the robotic arm joint motion; It is the acceleration vector of the robotic arm joint motion; It is the constraint function that restricts the movement of the robotic arm; It is the known control torque acting on the joint; It is a Lagrange multiplier vector; It is a general constraint and ; It is a quality matrix; It is the centrifugal Coriolis vector; It is the vector of gravitational acceleration.

[0072] Step 1.2: Locally linearize the dynamic equations of the single robotic arm near its equilibrium point.

[0073] First, its Cartesian coordinate system model is established.

[0074] remember Let be the vector formed by the position and orientation of the end effector of a single robotic arm in Cartesian coordinates. Then, in the Cartesian coordinate system, through the Jacobian matrix... ,make The resulting dynamic equations in the Cartesian coordinate system are:

[0075] (2)

[0076] The equilibrium point of linearization is selected as And the nominal control input required to maintain the balance of a single robotic arm at this equilibrium point is The force required to maintain the constraints at this equilibrium point is .

[0077] Define position deviation Speed ​​deviation , acceleration deviation Constraint deviation and control input deviation They are as follows:

[0078] , (3)

[0079] The dynamic equations of a single robotic arm are obtained in Cartesian space, linearized around the equilibrium point. The specific linearized model is as follows:

[0080] (4)

[0081] in, It is a positive definite inertial matrix. It is the damping and gyroscope matrix. These are the stiffness and circulation matrices. It is the force distribution matrix. It is the Jacobian matrix of the constraint equations. and It is the coefficient matrix of the constraint equations.

[0082] Step 1.3: Considering external disturbances, treat a single constrained robotic arm as an intelligent agent. These agents interact with each other through a communication network. A multi-arm system is established by constructing several physically identical restricted robotic arms. The first robotic arm in this multi-arm system... The dynamic equations of a constrained robotic arm are composed of the following equations (5) and (6):

[0083] (5)

[0084] in It is the first The position deviation vector of the robotic arm It is the first The velocity deviation vector of the robotic arm It is the first The acceleration deviation vector of each robotic arm, It is the first The input force deviation vector of a robotic arm with known control inputs. It is the first The constraint force deviation vector of each robotic arm. This represents an external disturbance consisting of load variations, inter-joint friction, and unmodeled dynamics (i.e., the complex dynamic characteristics of the mechanical structure itself that are not described due to model idealization) and satisfies , It is the coefficient matrix of the external disturbance and is related to It is possible to match the coefficient matrix of the multi-arm robotic system (5), which is a known constant matrix.

[0085] The first of the multi-robotic arm system The output vector of the robotic arm It is the first Positional deviation of the robotic arm Speed ​​deviation and constraint deviation Through the coefficient matrix The results of the linear combination are as follows:

[0086] (6)

[0087] Step 2: The multi-manipulator system under external disturbance is described by a linear generalized multi-agent system, namely a generalized state-space multi-agent system, thereby transforming the dynamic model of the multi-manipulator system under external disturbance into the dynamic model of the generalized multi-agent system.

[0088] Step 2.1: Determine the state vector of the dynamic model of the generalized multi-agent system.

[0089] The state of a generalized multi-agent system is determined by the first... Positional deviation of the robotic arm Speed ​​deviation and constraint deviation Composition, specifically , , ,Right now The control input is .

[0090] Step 2.2: Describe the multi-manipulator system subjected to external disturbances as a linear generalized state-space multi-agent system.

[0091] The intelligent agents of the generalized multi-agent system The specific dynamic model is as follows:

[0092] (7)

[0093] in, It is the first The state variables of an agent, It is the first The control input variables of the intelligent agent, It is the first The measurement output variables of each agent These are all coefficient matrices, as follows:

[0094] (8)

[0095] This indicates that the external disturbance and the control input are compatible.

[0096] Step 3: Determine the topology of the communication network of the generalized multi-agent system and the information accessible to each agent, and introduce local information exchange between agents;

[0097] Step 3.1: Determine the topology of the communication network of the generalized multi-agent system and the information accessible to each agent.

[0098] make Indicates having a A set of graphs containing nodes and a directed spanning tree (i.e., a directed tree containing all nodes of the graph), representing the topology of the communication network involved in this invention. The dynamic model of this generalized multi-agent system incorporates relative information from the communication network. Specifically, the communication network represents the agents. Please provide the following information:

[0099] (9)

[0100] This information is from intelligent agents The linear combination of its own output relative to the outputs of other agents, where, and .

[0101] The topology of a communication network can be represented by a weighted graph. This can be described as follows: nodes correspond to agents in the network, and edge weights are determined by coefficients. Given the weighted graph Laplace matrix Specifically:

[0102] (10)

[0103] It can be rewritten in the following form:

[0104] (11)

[0105] Step 3.2: Introduce the following local information exchange method for the scalable generalized cooperative control protocol:

[0106] (12)

[0107] in, and These are variables generated internally by the Scalable Generalized Cooperative Control Protocol and are defined in step 5.1.

[0108] Step 4: Obtain key parameters of the scalable generalized cooperative control protocol using the dynamic model of the generalized multi-agent system;

[0109] Step 4.1: Obtain the parameter matrix of the control protocol and .

[0110] First, by performing a non-singular transformation on the state variables of the generalized multi-agent system, the coefficient matrix of the generalized multi-agent system is obtained. It is transformed into its equivalent standard decomposition form, with the following specific expression:

[0111] (13)

[0112] in, yes An identity matrix of 3D; yes A 3D matrix; yes A 3D identity matrix; thus obtaining the parameters of a scalable generalized cooperative control protocol. and .

[0113] Step 4.2: Obtain the control gain parameter matrix of the scalable generalized cooperative control protocol. and .

[0114] Control gain parameter matrix It satisfies the following generalized Riccati equation:

[0115] (14)

[0116] Control gain parameter matrix Satisfies the following generalized equation:

[0117] (15)

[0118] This allows us to obtain the key parameter matrix of the scalable generalized cooperative control protocol. .

[0119] By selecting an appropriate scalar This will suppress the impact of disturbances on synchronization accuracy to an arbitrary desired level.

[0120] Step 5: Based on the information accessible to each agent, the local exchange information of the scalable generalized cooperative control protocol, and key parameters, design a scalable generalized cooperative control protocol to enable the multi-manipulator system to achieve disturbance-resistant synchronization of the position and velocity of each joint under external disturbances.

[0121] according to Figure 3 As shown in A scalable generalized cooperative control protocol architecture for synchronization in the sense of the word is proposed, and a specific scalable generalized cooperative control protocol is designed.

[0122] The following specific scalable generalized cooperative control protocol is designed:

[0123] (16)

[0124] in, and These are internal variables of the scalable generalized cooperative control protocol; and It is the derivative of the internal variables of the scalable generalized cooperative control protocol; communication between agents Set as Therefore, equation (12) is transformed into equation (17).

[0125] (17)

[0126] Derived from the designed scalable generalized cooperative control protocol Figure 3 One implementable coefficient matrix for the control protocol is as follows:

[0127] (18)

[0128] (19)

[0129] Obtain regular pulse-free and in A stable synchronization error system in the sense of the present can realize the anti-disturbance synchronization of the position and velocity of each joint of multiple robotic arms under external disturbances.

[0130] make

[0131]

[0132] The synchronization error system is obtained as follows:

[0133] (20)

[0134] in , .

[0135] The synchronization error system is obtained to be regular and pulse-free and in Stable in a meaningful sense.

[0136] This invention was tested using the MATLAB simulation platform to obtain the position and velocity variation curves of each joint in the multi-robotic arm system, thereby verifying the effectiveness of the method. Specific embodiments are described below.

[0137] This embodiment employs multi-robotic arm systems consisting of 8 and 20 motion-restricted robotic arms, respectively. First, each robotic arm is considered as an intelligent agent, and a system is created as follows: Figure 4 and 5 The 8-node and 20-node topology diagrams shown illustrate that the designed protocol is scalable, i.e., it is compatible with the topology of the communication network and the number of agents. Irrelevant. Figure 4 and 5 The middle circle indicates the first There are 8 robotic arms, and the connections between the robotic arms represent communication relationships. The weight of each edge is 1. It can be seen that the topology graphs of 8 nodes and 20 nodes are both directed weighted graphs with directed spanning trees.

[0138] according to Figure 4 Given the topology graph, the Laplace matrix of the 8-node topology graph can be calculated as follows:

[0139]

[0140] according to Figure 5 The Laplace matrix of the given topology graph, specifically for a 20-node topology graph, is as follows:

[0141]

[0142] The specific expression for the coefficient matrix of the constructed generalized multi-agent system is as follows:

[0143]

[0144]

[0145]

[0146] The generalized finite poles of each agent are specifically:

[0147] For an 8-node topology, the external disturbances for each robotic arm are as follows:

[0148]

[0149]

[0150] For a 20-node topology, the external perturbations for each robotic arm are as follows:

[0151]

[0152]

[0153]

[0154] The coefficient matrix of the generalized multi-agent system The equivalent standard decomposition form is shown in the following expression:

[0155]

[0156] Then the parameter matrix of the scalable generalized cooperative control protocol can be obtained. and Specifically

[0157]

[0158] The parameters given in this embodiment By solving the generalized algebraic Riccati equation, the gain matrix of the scalable generalized cooperative control protocol is obtained. as follows:

[0159]

[0160] for and Solving the generalized equations separately yields the gain parameters of the scalable generalized cooperative control protocol. They are respectively:

[0161]

[0162]

[0163] In the simulation, due to the large number of nodes, the initial states of the generalized multi-agent system are not listed individually in this paper. The simulation results are as follows: Figure 6-17 As shown. By Figure 6 , 7 As can be seen from 12 and 13, for communication topologies with 8 nodes and 20 nodes, under the condition of no external disturbance, all five states of all agents are synchronized, and the synchronization error is... Eventually, the value approaches zero. This means that the positions and speeds of the robotic arm's joints are synchronized.

[0164] Figure 8 , 9 Figures 10 and 11 show that, under an 8-node communication topology, eight robotic arms subjected to external disturbances can achieve [the desired result]. Pose synchronization in the sense of meaning, and when Increasing the value from 2 to 20 reduces the impact of disturbances on the position and speed of the robotic arm joints. Using the same key parameters of the same scalable generalized cooperative control protocol described above, [the following is achieved / implemented]... Figure 14 , 15 From points 16 and 17, we can see that in a 20-node communication topology, the 20 robotic arms, even under external disturbances, also achieve [the same functionality / operation]. Synchronization in a meaningful sense. Simulation results show that the protocol design is independent of the communication network topology and is scalable. Therefore, it can be implemented through a one-time protocol design for topologies containing any number of agents. State synchronization in a meaningful sense. Simulation results also show that by adding The value can be achieved with higher precision. State synchronization in the sense of the present invention. Therefore, the scalable generalized cooperative control protocol designed in this invention is applicable to any communication topology containing a directed spanning tree and has no limit on the number of agents.

[0165] It should be understood that, inspired by the technical concept of this invention, those skilled in the art can make various improvements or modifications based on the above content without departing from the scope of this invention, and these modifications still fall within the protection scope of this invention.

Claims

1. A scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators, characterized in that, The method includes the following steps: Step 1: Based on the physical structure of each motion-constrained robotic arm in the multi-robotic arm system, establish a dynamic model of the multi-robotic arm system under external disturbances; Step 2: Describe the multi-manipulator system under external disturbance as a linear generalized multi-agent system, thereby transforming the dynamic model of the multi-manipulator system under external disturbance into the dynamic model of the generalized multi-agent system. Step 3: Determine the topology of the communication network of the generalized multi-agent system and the information accessible to each agent, and introduce local information exchange of a scalable generalized cooperative control protocol; Step 4: Obtain key parameters of the scalable generalized cooperative control protocol using the dynamic model of the generalized multi-agent system; Step 5: Based on the information accessible to each agent, the local exchange information of the scalable generalized cooperative control protocol, and key parameters, design a scalable generalized cooperative control protocol to enable the multi-manipulator system to achieve disturbance-resistant synchronization of the position and velocity of each joint under external disturbances.

2. The scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators according to claim 1, characterized in that, Step 1 further includes the following steps: Step 1.1: Establish the dynamic equations of the single-joint confined robotic arm under study; Step 1.2: Locally linearize the dynamic equations of the single-joint constrained manipulator established in Step 1.1 around the equilibrium point of the single manipulator; Step 1.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require A multi-arm system is established by constructing several physically identical joint-restricted robotic arms. Considering external disturbances, each joint-restricted robotic arm in this multi-arm system is treated as an intelligent agent, and the first joint-restricted robotic arm of this multi-arm system is established. The dynamic equations of a constrained robotic arm.

3. The scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators according to claim 2, characterized in that, The first The dynamic equations of a constrained robotic arm are as follows: （5） （6） in Let be the output vector of the multi-arm robotic system, which is the th Positional deviation of the robotic arm Speed ​​deviation and constraint deviation Through the coefficient matrix The result of linear combination; It is a positive definite inertia matrix; It is the damping and gyroscope matrix; These are the stiffness and circulation matrices; It is the force distribution matrix; It is the Jacobian matrix of the constraint equations; and It is the coefficient matrix of the constraint equations; It is the first The position deviation vector of the robotic arm; It is the first The velocity deviation vector of each robotic arm; It is the first The acceleration deviation vector of each robotic arm; It is the first The input force deviation vector of a known control input for a robotic arm; It is the first The constraint force deviation vector of each robotic arm; Representing the External disturbances to a robotic arm and satisfying ; It is the coefficient matrix of the external disturbance and is related to Matchable.

4. The scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators according to claim 3, characterized in that, The dynamic model of the generalized multi-agent system is the agent. The specific dynamic model is as follows: （7） in, It is the first The state variables of an agent; It is the first Control input variables of the intelligent agent; It is the first The measurement output variables of each agent; These are all coefficient matrices, as detailed below: （8） This indicates that the external disturbance and the control input are compatible.

5. The scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators according to claim 4, characterized in that, Step 3 further includes the following steps: Step 3.1: Determine the topology of the communication network of the generalized multi-agent system and the information accessible to each agent; The topology of the communication network of the generalized multi-agent system is as follows: And satisfy ,in Indicates having a A set of nodes and a graph containing directed spanning trees; the information accessible to each agent is: （9） in, Topology graph The weight of the middle edge, and ; Step 3.2: Introduce the following local information exchange method for the scalable generalized cooperative control protocol: （12） in, and These are variables generated internally within the scalable generalized cooperative control protocol.

6. The scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators according to claim 5, characterized in that, In step 4, the parameter matrix is ​​obtained. and The method is as follows: by performing a non-singular transformation on the state variables of the generalized multi-agent system, the coefficient matrix of the generalized multi-agent system is obtained. The parameters can be obtained by transforming them into the equivalent standard decomposition form shown in equation (13). and ; （13） in, yes An identity matrix of dimensionality; yes A 3D matrix; yes An identity matrix of dimension 1.

7. The scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators according to claim 6, characterized in that, In step 4, the control gain parameter matrix The control gain parameter matrix is ​​obtained through equation (14). Obtained through equation (15); （14） （15） By independently selecting a suitable scalar This will suppress the impact of disturbances on synchronization accuracy to an arbitrary desired level.

8. The scalable cooperative disturbance rejection control method for motion-constrained multi-manipulators according to claim 7, characterized in that, The scalable generalized cooperative control protocol is as follows: （16） in, and These are internal variables of the scalable generalized cooperative control protocol; and It is the derivative of the internal variables of the scalable generalized cooperative control protocol.

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