Multi-agent formation control method based on performance and safety decoupling control

Abstract

The invention provides a multi-agent formation control method and device based on performance and security decoupling control, electronic equipment and a readable storage medium. According to the method, a nominal controller meeting performance constraints is designed based on PPC; and the nominal controller adopts a time-varying performance function with an auxiliary variable and is used for limiting the tracking error to evolve within a predefined dynamic limit. And designing a control barrier function (CBF) as a safety constraint, taking an intelligent agent control input smaller than a known scalar as an input saturation constraint condition, modeling a quadratic programming problem, and solving a safety control quantity closest to a nominal control quantity output by a nominal controller. And adjusting an auxiliary variable of the time-varying performance function according to the difference of the sum so as to relieve the conflict between the performance and the security and eliminate the control singularity. The multi-agent formation control method can solve the problem of multi-agent formation control under the condition that performance, safety and input constraints exist at the same time.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent control technology, specifically relating to a multi-agent formation control method, device, electronic device, and storage medium based on performance and safety decoupling control. Background Technology

[0002] Formation control has long been a core research topic in collaborative multi-robot systems due to its wide range of practical applications in areas such as collaborative transport, search and rescue missions, precision agriculture, and space missions. As these systems gradually move from laboratory environments to complex real-world scenarios, they inevitably face multi-layered constraints—from performance guarantees and operational safety requirements to hardware resource limitations—which must be considered and satisfied simultaneously. Achieving reliable formation control under such diverse and often conflicting constraints remains a significant and incompletely solved problem in this field.

[0003] To address the formation control problem under the aforementioned multiple constraints, the following research schemes are currently available: Solution 1: In the literature (Huang Y, Meng Z, Dimarogonas D V. Prescribed performanceformation control for second-order multi-agent systems with connectivity and collision constraints[J]. Automatica, 2024, 160: 111412.), prescribed performance control (PPC) is used to ensure topological connectivity between agents while achieving formation control. Considering collision avoidance between agents, safety constraints are modeled using a control barrier function (CBF), and a collision-avoiding safety controller is obtained using quadratic programming (QP). However, since this method only connects the CBF in series with the PPC, the resulting controller may not meet the performance requirements, causing control singularity problems.

[0004] Scheme 2: In the literature (Wang P, Yong K, Chen M, et al. Output-feedback flexible performance-based safe formation for underactuated unmanned surface vehicles[J]. IEEE Transactions on Intelligent Vehicles, 2022, 8(3): 2437-2447.), the artificial potential field method is integrated into the controller design of PPC, which realizes the maintenance of connectivity between agents, collision avoidance between agents and between agents and obstacles, and uses an auxiliary system to correct the performance function. However, this method does not consider the input saturation situation in practical applications, and there may be control inputs with large amplitude values.

[0005] Option 3: The literature (Yong K, Chen M, Shi Y, et al. Flexible performance-based robust control for a class of nonlinear systems with input saturation[J].Automatica, 2020, 122: 109268.) proposes an auxiliary system to handle the conflict between input saturation and performance constraints. However, the input design of this auxiliary system does not consider the interaction between multi-agent systems, nor does it consider the issue of safety constraints.

[0006] Considering the constraints of transient and steady-state performance, obstacle avoidance and collision avoidance, and input saturation in multi-agent system formation, existing methods typically transform safety constraints into constraints on formation errors, and then design specific performance functions to ensure the system simultaneously meets these constraints. The limitation of this approach is that the design of the performance function must not only consider the performance the system should meet, but also characterize the boundary of the tracking error when the system satisfies the constraints. On the one hand, safety constraints generally involve the coupling of multi-channel errors, while the performance function constrains each dimension of the error individually, increasing the complexity of the performance function design. On the other hand, when performance indicators and safety constraints conflict, the design of the performance function often introduces conservatism into the system. Therefore, no existing technology can solve the multi-agent formation control problem when performance, safety, and input constraints coexist without complex modeling. Summary of the Invention

[0007] In view of this, the present invention provides a multi-agent formation control method, apparatus, electronic device and readable storage medium based on performance and safety decoupling control. This method can solve the multi-agent formation control problem when performance, safety and input constraints exist simultaneously.

[0008] The first aspect of the present invention provides a multi-agent formation control method based on performance and safety decoupling control, comprising: A nominal controller that meets performance constraints is designed based on the preset performance control PPC. The nominal controller uses a time-varying performance function with auxiliary variables to limit the formation tracking error of the agent within a predefined dynamic limit. We design a control barrier function (CBF) as a safety constraint, and use the agent's control input being less than a known scalar as an input saturation constraint. We then model a quadratic programming problem to find the control quantity that most closely approximates the nominal controller output. Safety control quantity ; According to the nominal control quantity and safety control quantity To mitigate the conflict between performance and safety and eliminate control singularity, the auxiliary variables of the time-varying performance function are adjusted to address the differences.

[0009] Preferably, based on the nominal control quantity and safety control quantity The difference is used to adjust the auxiliary variable of the time-varying performance function as follows: According to the intelligent agent i nominal control quantity and safety control quantity The differences, and combined with intelligent agents i Number of neighbors , construct adjustment amount This adjustment is used to update the auxiliary variables, and then the time-varying performance function, avoiding issues caused by the nominal control quantity. and safety control quantity The different control singularities caused by these differences.

[0010] Preferably, the time-varying performance function used by the nominal controller is constructed in the following way: Formation error for each agent Transform into unconstrained variables :

[0011] in Represents dimensions; and It is a time-varying performance function that satisfies the following equation:

[0012]

[0013] in, It is an exponentially decreasing time-varying performance function; The auxiliary variable is represented as:

[0014] in, ; It is an intermediate variable. It is the control gain matrix; Representing variables Initial value; Auxiliary variables to be designed:

[0015] in, Represents the retained vector Non-negative elements remain unchanged, and the rest are 0; ; here, and To be based on the nominal control quantity and safety control quantity The difference is used to construct the part of the time-varying performance function to adjust the time-varying performance function.

[0016] Preferably, the design control barrier function CBF serves as a safety constraint as follows: Based on the relative positions and relative velocities between agents, construct CBFs between agents and between agents and obstacles, as safety constraints for solving the quadratic programming problem of safety control quantities.

[0017] Preferably, when the quadratic programming problem is unsolvable, the control strategy is switched, and the agent decelerates to 0 with maximum acceleration in the current velocity direction.

[0018] According to a second aspect of the present invention, a multi-agent formation control device based on performance and safety decoupling control is provided, the device comprising a nominal controller, a safety controller, and a time-varying performance function update module; The nominal controller is a nominal controller designed based on a preset performance control PPC to meet performance constraints. This nominal controller employs a time-varying performance function with auxiliary variables to limit the evolution of the agent's formation tracking error within predefined dynamic limits; the nominal output of the nominal controller... Provided to the safety controller and variable performance function update module; The safety controller uses the control barrier function CBF as a safety constraint and the agent's control input being less than a known scalar as an input saturation constraint to model a quadratic programming problem, solving for the closest approximation to the nominal control output of the nominal controller. Safety control quantity Safety control quantity The output is given to the agent for execution and also provided to the variable performance function update module; The variable performance function update module is used to update the nominal control quantity. and safety control quantity The differences are used to adjust the auxiliary variables of the time-varying performance function to alleviate the conflict between performance and safety and eliminate control singularity; the adjusted time-varying performance function is used to update the nominal controller.

[0019] Preferably, the variable performance function update module updates the nominal control quantity. and safety control quantity The difference is addressed by adjusting the auxiliary variables of the time-varying performance function as follows: According to the intelligent agent i nominal control quantity and safety control quantity The differences, and combined with intelligent agents i Number of neighbors , construct adjustment amount The adjustment amount is used as the input to the auxiliary variable dynamics to update the auxiliary variable in real time, thereby updating the time-varying performance function and thus alleviating the conflict between performance and safety.

[0020] Preferably, the safety controller uses a collision avoidance and obstacle avoidance CBF constructed based on the relative position and relative speed between agents, and between agents and obstacles.

[0021] According to a third aspect of the present invention, an electronic device is provided, comprising: a processor and a memory, the memory storing a program or instructions executable on the processor, wherein the program or instructions, when executed by the processor, implement the steps of the multi-agent formation control method based on performance and security decoupling control as described in any one of the first aspects.

[0022] According to a fourth aspect of the present invention, a readable storage medium is provided having a program or instructions stored thereon, which, when executed by a processor, implement the steps of the multi-agent formation control method based on performance and security decoupling control as described in any one of the first aspects.

[0023] Beneficial effects: (1) This method can handle the multi-agent formation control problem under various constraints, including transient and steady-state performance constraints, safety constraints and input saturation constraints. It adopts a modular design approach, which effectively avoids the complexity of controller design.

[0024] (2) This method determines the optimal expression of the auxiliary variable through derivation. The auxiliary system constructed using the auxiliary variable quantitatively characterizes the performance loss caused by ensuring safety and limiting input. It can effectively avoid the control singularity problem that may occur when there is a conflict between performance constraints and safety constraints and input saturation, and has more practical application significance. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the multi-agent formation control scheme based on performance and safety decoupling control of the present invention.

[0026] Figure 2 This is a simulation diagram showing the tracking trajectories of four intelligent agents in formation. Figure 3 The graph shows the tracking error and performance function changes of the four agents in the simulation. Figure 4 This is a graph showing the changes between the nominal and actual inputs of the four agents in the simulation. Figure 5 The diagram shows the CBF changes of the four agents in the simulation. Figure 6 This is a formation tracking diagram of four drones in an obstacle-prone environment. Figure 7 The flight path and formation diagram of four drones; Figure 8 The tracking error curves and performance function curves for a formation of four drones; Figure 9 Nominal and actual input curves for four drones; Figure 10 This is a block diagram of the multi-agent formation control device based on performance and safety decoupling control according to the present invention.

[0027] Figure 11 This is a schematic diagram of the hardware structure of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0028] This invention provides a multi-agent formation control scheme based on performance and safety decoupling control. It aims to meet the performance indicators of the agent formation tracking system while achieving safe collision avoidance between multiple agents and between agents and environmental obstacles. It also considers input saturation constraints, thereby solving the multi-agent formation control problem when performance, safety, and input constraints coexist. It is suitable for practical application scenarios where agents have input constraints.

[0029] This method considers N agents, one of which is the leader and the rest are followers. The leader can obtain the desired time-varying trajectory and its derivative information, and each agent obtains the position and velocity of its neighboring agents through communication.

[0030] In this invention, for formation tracking control, a nominal controller based on Preset Performance Control (PPC) is designed. Given time-varying trajectory information, the formation error of each agent satisfies the constraints of a time-varying performance function. This time-varying performance function constraint uses a time-varying performance function with auxiliary variables. This invention improves the auxiliary variables in the time-varying performance function based on the optimal control quantity to be calculated. (i.e., safety control quantity) and nominal output quantity of the nominal controller. The system constructs an auxiliary system based on the differences in the real-time state, continuously updating the auxiliary variables of each agent, thereby updating the performance function of PPC, achieving a balance between performance and safety, and avoiding control singularity problems.

[0031] Nominal controller output This invention provides a safety controller. The safety controller of this invention considers the distances between agents and between agents and obstacles, designs a control obstacle function (CBF) based on the maximum braking concept, and constructs a quadratic programming problem to obtain the optimal control input for the agents. .

[0032] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0033] Figure 1 This illustrates the principle of a multi-agent formation control scheme based on performance and safety decoupling control, as described in an embodiment of the present invention. Combined with... Figure 1 The specific steps in this embodiment of the invention are as follows: Step 1: Design the nominal controller: This step designs a preset performance controller with a variable performance function as the nominal controller to ensure that the formation error meets the performance constraints.

[0034] consider Several agents are grouped together, and the kinematic model of each agent is represented by the following second-order system: (1) in, The ID number representing the intelligent agent. N The total number of intelligent agents. These are the agent's position, velocity, and acceleration, respectively. express 3D real vector . express The first derivative of acceleration. As input, and with saturation constraints as follows:

[0035] in Represents the infinite norm, It is a scalar; the condition shown in formula (2) serves as the input saturation constraint on the agent input when solving the security controller below.

[0036] exist In a group of intelligent agents, there is one leader and the rest... Each agent is a follower, and the leader receives information about the desired time-varying trajectory and its derivative. Each agent interacts with its neighbors through a connected undirected graph. The formation error for each agent is defined as follows:

[0037] in Representing intelligent agents i The set of neighboring agent IDs, including agent 0, which is a virtual agent representing the desired trajectory. Representing intelligent agents i and j The weights between them Indicate if they are neighbors, otherwise . Indicates the relative positions between intelligent agents. This represents the expected relative position between intelligent agents.

[0038] To design a formation controller that meets performance constraints, the formation error is first considered. Transform into unconstrained variables , , :

[0039] in Represents dimensions; and It is a time-varying performance function that satisfies the following equation: (5) in It is an exponentially decreasing time-varying performance function:

[0040] in These are the initial and final state performance function values, respectively. It is a scalar that controls the rate at which the performance function decreases.

[0041] It is an auxiliary variable, and its dynamics satisfy: (7) in . It is an intermediate variable. It is the control gain matrix. Representing intelligent agents i The number of neighbors. Representing variables Initial value; The input for the auxiliary system (7) to be designed.

[0042] Based on the transformed variables in (4), design a system that... Stable nominal controller Using the backstep method, first find Derivative:

[0043] Design virtual control input to enable Stable, virtual control input is as follows:

[0044] in It is a positive definite gain matrix.

[0045] To avoid complexity explosion, the tracking variables of the virtual controller are designed. The following dynamic equations are satisfied:

[0046] in It is an adjustable parameter. for The derivative of .

[0047] make , representing the error variable and the virtual control tracking error, respectively. The desired speed is defined as follows: .right Differentiating, we get:

[0048] Note that (11) does not explicitly contain And the number of individual neighbors right The evolution of the system also plays a role. If the input of the auxiliary system can be designed... make Once established, it can then be designed. make Stability. When designing the control input of an auxiliary system, it is necessary to consider not only the nominal control input. and security control The difference also needs to be considered in terms of the number of neighbors. The impact on stability. Therefore, based on the above relationship, the input of the auxiliary system (7) is designed as follows:

[0049] Then equation (7) can be written in the following form:

[0050] in The optimal safety controller obtained by (17); Represents the retained vector Non-negative elements remain unchanged, and the rest are 0; .

[0051] Based on this, the following nominal controller can be designed:

[0052] in It is a positive definite gain matrix.

[0053] Step 2: Design a safety controller to avoid collisions between agents and between agents and obstacles.

[0054] This step designs a control barrier function (CBF) as a safety constraint, uses the infinite norm of the agent's control input being less than a known scalar as an input saturation constraint, models a quadratic programming problem, and solves for the control quantity that most closely approximates the nominal controller output. Safety control quantity .

[0055] To avoid collisions between agents, for any two pairs of agents out of N agents ( i , j The absolute relative velocity between the two for:

[0056] in, For intelligent agents i and j The relative speed between them.

[0057] Considering agent input saturation, the following collision avoidance flow (CBF) is designed:

[0058] in It is the preset safe distance between intelligent agents. For maximum acceleration constraints.

[0059] Similarly, in order to achieve collision avoidance between the agent and obstacles, for those containing A collection of obstacles The first An obstacle, The obstacle avoidance CBF is designed as follows:

[0060] in It is a preset safe distance between the intelligent agent and the obstacle.

[0061] Based on the defined collision avoidance and obstacle avoidance CBF, the following quadratic programming problem is constructed to solve for the optimal safety control input:

[0062] Where: (a) represents the collision avoidance constraints between agents; (b) represents the collision avoidance constraints between agents and obstacles; and (c) represents the input saturation constraints of the agents. Specifically, , 。 . This represents the optimization variable to be solved.

[0063] Furthermore, to handle the possibility that the above quadratic programming might be unsolvable, the following switching strategy is designed: when (17) is unsolvable, the agent decelerates to 0 with maximum acceleration in the current velocity direction:

[0064] The control method proposed in this invention was simulated and tested in physical experiments.

[0065] Figure 2 The simulation demonstrates that a formation of four agents tracks a time-varying trajectory in an environment with obstacles, showing that the agents can form a formation and track the time-varying trajectory while avoiding obstacles in the environment.

[0066] Figure 3 The simulation demonstrates the changes in formation tracking errors and performance functions for four agents. The formation error of each agent evolves within a time-varying performance envelope, satisfying performance constraints. Furthermore, the upper and lower boundaries of the performance function adaptively change when avoiding obstacles, balancing performance and safety.

[0067] Figure 4 The simulation demonstrates the changes in the nominal control input and the optimal safety control input for the four agents. It is evident that the agent inputs consistently satisfy saturation constraints and differ from the nominal control inputs during obstacle avoidance, thus ensuring system safety.

[0068] Figure 5 The simulation shows the changes in the average and extreme values ​​of the CBF (Containment Risk Factor) of the four agents over time. It can be seen that the CBF value of each agent is strictly greater than 0, indicating that their respective security is guaranteed.

[0069] Figure 6 The experiment demonstrated four drones conducting a formation tracking test in an environment with obstacles.

[0070] Figure 7 The demonstration showcased the real-world formation and trajectory of four drones. The intelligent agent was able to avoid obstacles in the environment by changing its formation, ensuring safety. Furthermore, after navigating obstacles, the formation returned to a pre-defined configuration, meeting performance requirements.

[0071] Figure 8 The diagram illustrates the changes in the formation tracking error curves and performance functions of four UAVs in the x and y directions. It shows that the individual performance function boundaries adaptively adjust when obstacle avoidance and input saturation are present, and revert to the preset performance function when there are no obstacles or input saturation. Furthermore, the formation error always evolves within the performance constraints.

[0072] Figure 9 The diagram illustrates the changes in nominal control inputs and optimal safety control inputs for four drones. It demonstrates that nominal control can violate input constraints, while the actual safety control inputs applied to the agent strictly satisfy these constraints.

[0073] Simulation and experimental verification demonstrate that the designed control algorithm can achieve formation tracking of multiple agents in obstacle environments, while satisfying constraints such as performance, safety, and input, and can avoid control singularity problems.

[0074] Based on the above method, the present invention also provides a multi-agent formation control device based on performance and safety decoupling control, such as... Figure 10 As shown, the device includes a nominal controller, a safety controller, and a time-varying performance function update module.

[0075] The nominal controller is a nominal controller designed based on a preset performance control PPC to meet performance constraints. This nominal controller employs a time-varying performance function with auxiliary variables to limit the evolution of the agent's formation tracking error within predefined dynamic limits; the nominal output of the nominal controller... Provided to the safety controller and variable performance function update module; The safety controller uses the control barrier function CBF as a safety constraint and the agent's control input being less than a known scalar as an input saturation constraint to model a quadratic programming problem, solving for the closest approximation to the nominal control output of the nominal controller. Safety control quantity Safety control quantity The output is given to the agent for execution and also provided to the variable performance function update module; The variable performance function update module is used to update the nominal control quantity. and safety control quantity The differences are used to adjust the auxiliary variables of the time-varying performance function to alleviate the conflict between performance and safety and eliminate control singularity; the adjusted time-varying performance function is used to update the nominal controller.

[0076] Specifically, the variable performance function update module updates according to the intelligent agent. i nominal control quantity and safety control quantity The differences, and combined with intelligent agents i Number of neighbors , construct adjustment amount The adjustment amount is used as the input to the auxiliary variable dynamics to update the auxiliary variable in real time, thereby updating the time-varying performance function and thus alleviating the conflict between performance and safety.

[0077] Furthermore, the multi-agent formation control method based on performance and safety decoupling control in the embodiments of this application can all be implemented by a single computer device. Figure 11 This is a schematic diagram of the hardware structure of a computer device according to an embodiment of this application. Figure 11 As shown, the device may include a processor 201 and a memory 202 storing computer program instructions.

[0078] Specifically, the processor 201 may include a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0079] The memory 202 may include a large-capacity memory for data or instructions. For example, and not limitingly, the memory 202 may include a hard disk drive (HDD), a floppy disk drive, a solid-state drive (SSD), flash memory, an optical disk drive, a magneto-optical disk drive, magnetic tape, or a Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, the memory 202 may include removable or non-removable (or fixed) media. Where appropriate, the memory 202 may be internal or external to a data processing device. In a particular embodiment, the memory 202 is non-volatile memory. In a particular embodiment, the memory 202 includes read-only memory (ROM) and random access memory (RAM). Where appropriate, the ROM may be a mask-programmed ROM, a programmable read-only memory (PROM), an erasable read-only memory (EPROM), an electrically erasable read-only memory (EEPROM), an electrically alterable read-only memory (EAROM), or flash memory, or a combination of two or more of these. Where appropriate, the RAM can be Static Random-Access Memory (SRAM) or Dynamic Random-Access Memory (DRAM). DRAM can be Fast Page Mode Dynamic Random-Access Memory (FPMDRAM), Extended Data Out Dynamic Random-Access Memory (EDODRAM), Synchronous Dynamic Random-Access Memory (SDRAM), etc.

[0080] The memory 202 can be used to store or cache various data files that need to be processed and / or communicated, as well as possible computer program instructions executed by the processor 201.

[0081] The processor 201 reads and executes computer program instructions stored in the memory 202 to implement any of the multi-agent formation control methods based on performance and safety decoupling control in the above embodiments.

[0082] In some embodiments, the computer device may further include a communication interface 203 and a bus 200. For example, Figure 11 As shown, the processor 201, memory 202, and communication interface 203 are connected through bus 200 and complete communication with each other.

[0083] The communication interface 203 is used to enable communication between the various modules, devices, units, and / or equipment in the embodiments of this application. The communication interface 203 can also enable data communication with other components such as external devices, image / data acquisition devices, databases, external storage, and image / data processing workstations.

[0084] Bus 200 includes hardware, software, or both, that couples components of a computer device together. Bus 200 includes, but is not limited to, at least one of the following: data bus, address bus, control bus, expansion bus, and local bus. For example, and not as a limitation, bus 200 may include an Accelerated Graphics Port (AGP) or other graphics bus, an Extended Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), a Hyper Transport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an InfiniBand interconnect, a Low Pin Count (LPC) bus, a memory bus, a MicroChannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local Bus (VLB) bus, or other suitable buses, or a combination of two or more of these. Where appropriate, bus 200 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, any suitable bus or interconnection is contemplated herein.

[0085] The computer device can execute the multi-agent formation control method based on performance and security decoupling control in the embodiments of this application, thereby realizing the multi-agent formation control method based on performance and security decoupling control described in this application.

[0086] Furthermore, in conjunction with the multi-agent formation control method based on performance and security decoupling control in the above embodiments, this application embodiment can provide a computer-readable storage medium for implementation. This computer-readable storage medium stores computer program instructions; when executed by a processor, these computer program instructions implement any of the multi-agent formation control methods based on performance and security decoupling control in the above embodiments.

[0087] It should be noted that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. In addition, depending on the implementation needs, the various steps / components described in this application can be broken down into more steps / components, or two or more steps / components or parts of steps / components can be combined into new steps / components to achieve the purpose of this invention.

[0088] The specific embodiments described above only illustrate the design principles of the present invention. The shapes and names of the components in this description may differ and are not limited. Therefore, those skilled in the art can modify or make equivalent substitutions to the technical solutions described in the foregoing embodiments; and these modifications and substitutions do not depart from the inventive spirit and technical solutions of the present invention, and should all fall within the protection scope of the present invention.

Claims

1. A multi-agent formation control method based on performance and safety decoupling control, characterized in that, include: Design a nominal controller that meets performance constraints based on a pre-defined performance control PPC. The nominal controller employs a time-varying performance function with auxiliary variables to limit the evolution of the agent's formation tracking error within a predefined dynamic limit; We design a control barrier function (CBF) as a safety constraint, and use the agent's control input being less than a known scalar as an input saturation constraint. We then model a quadratic programming problem to find the control quantity that most closely approximates the nominal controller output. Safety control quantity ; According to the nominal control quantity and safety control quantity To mitigate the conflict between performance and safety and eliminate control singularity, the auxiliary variables of the time-varying performance function are adjusted to address the differences.

2. The method as described in claim 1, characterized in that, According to the nominal control quantity and safety control quantity The difference is used to adjust the auxiliary variable of the time-varying performance function as follows: According to the intelligent agent i nominal control quantity and safety control quantity The differences, and combined with intelligent agents i Number of neighbors , construct adjustment amount ; This adjustment is used to update the auxiliary variables, and then the time-varying performance function, avoiding issues caused by the nominal control quantity. and safety control quantity The different control singularities caused by these differences.

3. The method as described in claim 2, characterized in that, The time-varying performance function used by the nominal controller is constructed in the following way: Formation error for each agent Transform into unconstrained variables : in Represents dimensions; and It is a time-varying performance function that satisfies the following equation: in, It is an exponentially decreasing time-varying performance function; The auxiliary variable is represented as: in, ; It is an intermediate variable. It is the control gain matrix; Representing variables Initial value; Represents the zero vector; Auxiliary variables to be designed: in, Represents the retained vector Non-negative elements remain unchanged, and the rest are 0; ; and To be based on the nominal control quantity and safety control quantity The difference is used to construct the part of the time-varying performance function to adjust the time-varying performance function.

4. The method as described in claim 1, characterized in that, The design control barrier function CBF serves as a safety constraint as follows: Based on the relative positions and relative velocities between agents, construct CBFs between agents and between agents and obstacles, as safety constraints for solving the quadratic programming problem of safety control quantities.

5. The method according to any one of claims 1-4, characterized in that, When the quadratic programming problem becomes unsolvable, the control strategy is switched, and the agent decelerates to 0 with maximum acceleration in the current velocity direction.

6. A multi-agent formation control device based on performance and safety decoupling control, characterized in that, The device includes a nominal controller, a safety controller, and a time-varying performance function update module; The nominal controller is a nominal controller designed based on a preset performance control PPC to meet performance constraints. The nominal controller uses a time-varying performance function with auxiliary variables to limit the formation tracking error of the agent within a predefined dynamic limit. The nominal output of the nominal controller Provided to the safety controller and variable performance function update module; The safety controller uses the control barrier function CBF as a safety constraint and the agent's control input being less than a known scalar as an input saturation constraint to model a quadratic programming problem, solving for the closest approximation to the nominal control output of the nominal controller. Safety control quantity Safety control quantity The output is given to the agent for execution and also provided to the variable performance function update module; The variable performance function update module is used to update the nominal control quantity. and safety control quantity The differences are used to adjust the auxiliary variables of the time-varying performance function to alleviate the conflict between performance and safety and eliminate control singularity; the adjusted time-varying performance function is used to update the nominal controller.

7. The apparatus as described in claim 6, characterized in that, The variable performance function update module updates according to the nominal control quantity. and safety control quantity The difference is addressed by adjusting the auxiliary variables of the time-varying performance function as follows: According to the intelligent agent i nominal control quantity and safety control quantity The differences, and combined with intelligent agents i Number of neighbors , construct adjustment amount The adjustment amount is used as the input to the auxiliary variable dynamics to update the auxiliary variable in real time, thereby updating the time-varying performance function and thus alleviating the conflict between performance and safety.

8. The apparatus as claimed in claim 6, characterized in that, The safety controller uses a collision avoidance and obstacle avoidance (CBF) mechanism based on the relative position and relative velocity between agents, which is constructed for collision avoidance between agents and between agents and obstacles.

9. An electronic device, characterized in that, include: A processor and a memory, wherein the memory stores a program or instructions that can run on the processor, and when the program or instructions are executed by the processor, implement the steps of the multi-agent formation control method based on performance and safety decoupling control as described in any one of claims 1 to 5.

10. A readable storage medium, characterized in that, It stores programs or instructions, which, when executed by a processor, implement the steps of the multi-agent formation control method based on performance and safety decoupling control as described in any one of claims 1 to 5.

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