A safe multi-robot cooperative control method and system for manifold tracking

Abstract

The application discloses a kind of safe multi-robot cooperative control method and system for manifold tracking, comprising the following steps: S1, the real physical position of the current robot is obtained, and virtual parameter is randomly generated;S2, construct guiding propagation term and error reduction term, obtain the manifold tracking field of robot by summing up guiding propagation term and error reduction term;S3, according to the deviation between the real physical position and virtual parameter between adjacent robots, obtain cooperation control term and inter-machine collision avoidance term, and combine obstacle description implicit function to build obstacle avoidance term;S4, fusion forms unified composite navigation field, and generates target operation manifold motion control instruction of robot navigation in real environment according to unified composite navigation field.The application constructs unified high-dimensional navigation field framework, dynamically allocates virtual coordinates and organically fuses physical space safety constraints, which eliminates the singularity of navigation field, and realizes the cooperative optimization of task orientation and safety protection.

Description

Technical Field

[0001] This invention relates to a safe multi-robot cooperative control method and system for manifold tracking, belonging to a rapid planning method for cooperative movement of multi-robot systems in dynamic position environments. Background Technology

[0002] In recent years, with the rapid development of autonomous navigation systems, robot manifold tracking technology has gradually evolved from a theoretical model into a core support for practical applications. The ability of mobile robots, drones, and underwater vehicles to accurately track dynamic and complex manifolds (such as complex 3D curves and manifolds) is a crucial prerequisite for missions such as exploration in unknown environments, large-scale collaborative operations, and high-precision patrols and rescues. Guidance-based navigation methods, with their mathematical rigor and control smoothness, have become an important technical path for achieving these goals.

[0003] Faced with obstacles prevalent in real-world environments, manifold tracking must be combined with obstacle avoidance capabilities. Early obstacle avoidance strategies often employed artificial potential fields, superimposing the repulsive field of the obstacle onto the target's attractive field. However, simple superposition often results in local minima at the equilibrium point of the attractive and repulsive fields. Therefore, in real-world scenarios involving complex high-dimensional manifolds, dynamically dense obstacles, and multi-machine collaborative safety constraints, the following problems arise:

[0004] I. Singularities in the navigation field lead to insufficient system stability.

[0005] In early research, manifold tracking largely relied on geometric projection or parametric trajectory tracking. These methods require precise knowledge of the manifold parameter equations and are highly sensitive to initial errors and external disturbances. For example, Chinese patent application CN118605144A discloses a multi-robot restraint and cooperative control method for marine monitoring. This method uses matrix factorization, cooperative Lyapunov functions, and linear programming to design a restraint and cooperative consistency among multiple robots. By constructing a dynamic system that converges to the target manifold, the robots can asymptotically converge to the desired manifold without requiring a globally parametric description. This type of method transforms the manifold convergence problem into a stability analysis of vector fields, theoretically guaranteeing global or semi-global convergence performance. However, existing navigation field methods commonly suffer from singularity problems when directly constructing the field in physical space; that is, the navigation field intensity disappears to zero at certain locations, causing the robot to stagnate. These singularities are closely related to the topological properties of the manifold and are difficult to avoid when tracking complex geometric structures. When the robot approaches a singularity, navigation commands become ambiguous, leading to instability phenomena such as stagnation, oscillation, or deviation from the predetermined manifold. Especially in multi-robot collaborative scenarios, the singular state of individual units may propagate through the collaborative network, causing cascading failures of the group.

[0006] Second, there is a compatibility conflict between the obstacle avoidance mechanism and the navigation field structure.

[0007] Existing methods typically employ a strategy of simply superimposing the navigation field and the obstacle avoidance field. This "patchwork" approach disrupts the original mathematical structure of the navigation field. Whether using weighted summation or smooth mixing, both introduce new local extrema in the physical space, causing the robot to fall into an undesirable equilibrium state. While switching logic-based methods can avoid local extrema, they introduce discontinuities and system complexity, affecting the smoothness and analyzability of control.

[0008] Third, multi-target cooperative navigation lacks a unified mathematical framework.

[0009] Existing methods often employ a separate design approach for different navigation objectives such as manifold tracking, formation coordination, and obstacle avoidance, leading to architectural contradictions within the system. For example, Chinese Patent CN119396139A discloses a multi-robot collaborative method, device, electronic device, and storage medium. Robot formation coordination is typically achieved through virtual coordinate synchronization, while obstacle avoidance is handled in physical coordinate space. This separate design creates irreconcilable conflicts between safety constraints and collaborative objectives. The physical displacement of robots to avoid obstacles disrupts the established formation, while constraints imposed to maintain formation may limit the robots' effective obstacle avoidance capabilities. Summary of the Invention

[0010] The technical problem solved by this invention is to address the shortcomings of existing multi-robot systems in terms of navigation and obstacle avoidance uniformity, scalability, and manifold tracking safety when realizing complex manifold tracking and multi-robot collaborative operations. This invention provides a safe multi-robot collaborative control method and system for manifold tracking.

[0011] This invention is achieved using the following technical solution:

[0012] This invention first discloses a safe multi-robot cooperative control method for manifold tracking, comprising the following steps:

[0013] S1. Obtain the robot's current real physical position and randomly generate virtual parameters. Construct an extended position variable by combining the robot's real physical position and the corresponding virtual parameters.

[0014] S2. Target operation manifold modeling: Construct the desired manifold based on the robot's target operation manifold. Based on the deviation between the robot's current real physical position and the target operation manifold, construct a guiding propagation direction orthogonal to the constraint gradient of the desired manifold as a guiding propagation term. Also, construct an error reduction term that is only used in the robot's physical space. Summing the guiding propagation term and the error reduction term yields the robot's manifold tracking field.

[0015] S3. Obtain the current real physical position and virtual parameters of neighboring robots, obtain cooperative control terms and inter-robot collision avoidance terms based on the deviation between the real physical positions and virtual parameters of neighboring robots, and construct obstacle avoidance terms by combining the obstacle description implicit function.

[0016] S4. The manifold tracking field, cooperative control terms, inter-machine collision avoidance terms, and obstacle avoidance terms are weighted and fused to form a unified composite navigation field. Based on the unified composite navigation field, target operation manifold motion control commands for robot navigation in the real environment are generated.

[0017] In a safe multi-robot cooperative control method for manifold tracking according to the present invention, further, in step S2, an implicit function is used to construct the common desired manifold for all robots. , where n represents the physical dimension. An extended position variable representing the robot's actual physical position and the corresponding virtual parameters. , This is a set-based representation of the robot's current real physical location. , For the robot's actual physical coordinates, It is a set of virtual parameters. , To generate virtual coordinates for virtual parameters, The robot's true physical position in the current j-dimensional dimension. With the target operation manifold manifold deviation function between , Let be a known differentiable function of the target operation manifold.

[0018] In a safe multi-robot cooperative control method for manifold tracking according to the present invention, the guiding propagation term is a guiding propagation direction orthogonal to the desired manifold constraint gradient constructed based on the gradient information of the manifold deviation function, expressed as: ;

[0019] in This indicates the calculation of the wedge product. As an auxiliary vector, , , This represents the expected velocity of the virtual coordinates. This represents the set of partial derivatives of the manifold deviation function of robot i with respect to the current extended position variable in the j-th dimension. , , Let be the manifold deviation function of robot i in the current j-th dimension.

[0020] In a safe multi-robot cooperative control method for manifold tracking according to the present invention, the error reduction term is further expressed as: ,

[0021] in, Let represent the set of partial derivatives of the manifold deviation function of robot i with respect to its current real physical position in the j-th dimension. , It is the convergence coefficient of the j-th dimension.

[0022] In a safe multi-robot cooperative control method for manifold tracking according to the present invention, further, the manifold tracking field of robot i obtained in step S2 is... It is expressed as follows:

[0023] .

[0024] In a safe multi-robot cooperative control method for manifold tracking according to the present invention, further, in step S3, the cooperative control term of robot i and its neighboring robot k... It is expressed as follows:

[0025] ,

[0026] in, , These are the virtual parameters currently corresponding to robot i. For the virtual parameters currently corresponding to neighboring robot k, The expected deviation between adjacent robots i and k Let i be the set of all neighboring robots of robot i.

[0027] In a safe multi-robot cooperative control method for manifold tracking according to the present invention, further, the collision avoidance term between robot i and its neighboring robot k is... It is expressed as follows:

[0028]

[0029] in, This represents the distance between robot i and its neighbor robot k. , , Let i and k be the actual physical positions of robots i and k, respectively. , To control the fusion rate parameter, This indicates the minimum distance set. This indicates the maximum distance that can be set. Let be the total number of neighboring robots of robot i.

[0030] In a safe multi-robot cooperative control method for manifold tracking according to the present invention, further, when the robot detects an obstacle... Then, the obstacle description implicit function is represented by a differentiable spherical closed manifold:

[0031] ,

[0032] in Represents the coordinates of the sphere's center. Represents the radius of the sphere. This represents the current physical location of robot i;

[0033] The obstacle avoidance of robot i It is expressed as follows:

[0034] ,

[0035] in, This represents the implicit function describing the obstacle. Find the partial derivative. Indicates will Rotate the matrix 90° clockwise. For coefficients, , , , The desired motion speed is represented by virtual coordinates.

[0036] In a safe multi-robot cooperative control method for manifold tracking according to the present invention, the unified composite navigation field of robot i is further represented as:

[0037] ,

[0038] in, Let i be the manifold tracking field of robot i. Let i be the control term for the collaboration between robot i and its neighboring robots. For the collision avoidance terms between robot i and its neighboring robots, For the obstacle avoidance term of robot i, This is a function of the obstacle balance coefficient. , This is the fusion rate control coefficient. To deal with obstacles The response distance, where M is the total number of obstacles. For the weighting coefficients of the collaborative control terms, This represents the weighting coefficient for obstacle items. This represents the weighting coefficient for inter-machine collision avoidance projects.

[0039] The present invention also discloses a multi-robot system, wherein the multi-robot system uses the method described above for manifold motion control.

[0040] The present invention, by adopting the above technical solution, has the following beneficial effects:

[0041] (1) This invention embeds the desired manifold of the robot's physical space into a higher-dimensional Euclidean space by introducing virtual coordinates. By introducing two virtual coordinates, the n-dimensional manifold tracking problem is elevated to an n+2-dimensional extended space. A manifold tracking field consisting of orthogonal guiding terms and truncated convergence terms that act only on the physical coordinates is constructed, achieving stable convergence to the desired working manifold and continuous motion along the manifold. The manifold tracking field consists of guiding propagation terms and error reduction terms, ensuring that there is a clear and non-zero guiding direction at any point in the field. This achieves the construction of a high-dimensional singularity-free navigation field, thereby eliminating the singularity problem inherent in the prior art from the root and laying a mathematical foundation for globally stable manifold tracking.

[0042] (2) This invention adopts an obstacle avoidance navigation field compatible with the guidance navigation field structure, and also introduces it into the high-dimensional space of virtual coordinates. The manifold tracking field and the obstacle avoidance field are dynamically fused according to the distance between the robot and the obstacle through the obstacle balance coefficient function. Since both fields maintain non-zero virtual coordinate dynamics, the fusion result is still continuous, smooth and without singularities in the entire high-dimensional space, thus realizing seamless coordination between manifold tracking and obstacle avoidance.

[0043] (3) This invention proposes a virtual-physical space decoupled cooperative control architecture for manifold tracking control of multi-robot systems. The execution domains of manifold tracking and formation coordination in the task-layer objectives are set in the virtual coordinate space generated by virtual parameters. The virtual coordinates of each robot are synchronized, and manifold tracking of multiple robots is achieved by constructing a manifold tracking field. Formation coordination between robots is achieved through cooperative control terms. Simultaneously, the execution domains of obstacle avoidance and inter-robot collision avoidance in the safety-layer objectives, including obstacle avoidance and inter-robot collision avoidance, are confined to the physical coordinate space, generating real-time obstacle avoidance actions. Based on the relative relationship between the robot and obstacles, the manifold tracking, cooperative, obstacle avoidance, and collision avoidance navigation fields are continuously weighted and fused to achieve simultaneous execution of task execution and safe obstacle avoidance. This spatial separation design allows the safety mechanism to temporarily adjust the robot's physical position without interfering with the global task logic, ensuring the parallelism of objectives and safety.

[0044] In summary, the safe multi-robot cooperative control method and system for manifold tracking provided by this invention organically integrates the dynamic allocation of virtual coordinates with physical space safety constraints by constructing a unified high-dimensional navigation field framework. This eliminates the singularity of the navigation field and achieves synergistic optimization of task orientation and safety protection. It solves the problem that existing multi-robot navigation methods cannot simultaneously guarantee the global convergence of manifold tracking, the real-time safety of dynamic obstacle avoidance, and the consistency of multi-robot cooperation in complex environments, thus providing a systematic solution for reliable navigation of multiple robots in dynamic and dense scenarios.

[0045] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating a safe multi-robot cooperative control method for manifold tracking according to the present invention.

[0047] Figure 2 This is a schematic diagram of the simulation results of a drone simulation experiment using the present invention in the embodiment.

[0048] Figure 3a and 3b This is a schematic diagram of the error analysis results of the UAV cooperative formation in the simulation experiment of the embodiment.

[0049] Figure 4a and 4b This is a schematic diagram of the manifold tracking error analysis results of the UAV simulation experiment in the embodiment. Detailed Implementation

[0050] Example

[0051] See Figure 1 The implementation process of a safe multi-robot cooperative control method for manifold tracking according to the present invention includes the following steps:

[0052] S1. Obtain the robot's current real physical position and randomly generate virtual parameters. Construct an extended variable by combining the robot's real physical position and the corresponding virtual parameters.

[0053] Taking robot i in a multi-robot system as an example, the control and processing unit of the multi-robot system first obtains the real-time operating status of robot i, including obtaining the robot's current real physical position through the localization and perception module. , , The virtual parameters are generated by randomly generating virtual parameters based on the current physical coordinates of robot i, such as robot coordinates obtained from a GNSS satellite system. , , To generate virtual coordinates for virtual parameters, the actual physical position of robot i and the virtual parameters are combined to construct an extended position variable. .

[0054] S2. Target operation manifold modeling: Construct the desired manifold based on the robot's target operation manifold. Based on the deviation between the robot's current real physical position and the target operation manifold, construct a guiding propagation direction orthogonal to the constraint gradient of the desired manifold as the guiding propagation term. Construct an error reduction term that is only used in the robot's physical space. Summing the guiding propagation term and the error reduction term yields the robot's manifold tracking field.

[0055] Specifically, this step, based on the robot's arrival task requirements, predefines a known differentiable function of the target work manifold that the robot system needs to track. Then, using implicit functions, the desired manifold for the same target task manifold for all robots is constructed as follows:

[0056] .

[0057] Where n represents the dimension of physical space, An extended position variable representing the robot's actual physical position and the corresponding virtual parameters. , This is a set-based representation of the robot's current real physical location. , For the robot's actual physical coordinates, It is a set of virtual parameters. , To generate virtual coordinates for virtual parameters, The robot's true physical position in the current j-dimensional dimension. With the target operation manifold manifold deviation function between , Let be a known differentiable function of the target operation manifold.

[0058] The guided propagation term is a guided propagation direction orthogonal to the desired manifold constraint gradient, constructed based on the gradient information of the manifold deviation function, and is expressed as: ,in This indicates the calculation of the wedge product. As an auxiliary vector, , , This represents the expected velocity of the virtual coordinates. This represents the set of partial derivatives of the manifold deviation function of robot i with respect to the current extended position variable in the j-th dimension. , , Let be the manifold deviation function of robot i in the current j-th dimension.

[0059] The error reduction term is a truncation correction term that only applies to the physical space, and its expression is: ,in, Let represent the set of partial derivatives of the manifold deviation function of robot i with respect to its current real physical position in the j-th dimension. , It is the convergence coefficient of the j-th dimension, taking values ​​between 0 and 1, which determines the convergence speed of the robot relative to the expected flow. The larger the value, the faster the convergence speed.

[0060] Summing the guidance propagation term and error reduction term obtained from the above calculations yields the manifold tracking field of robot i. , means as follows:

[0061] .

[0062] This invention no longer directly addresses the manifold tracking problem in the physical space of robot i, but instead introduces two virtual coordinates. The original robot's true physical information The problem of tracking 3D manifolds has been elevated to a The problem of high-dimensional navigation is addressed by constructing a truncated manifold convergent navigation field as the manifold tracking field in this high-dimensional space, which, after expansion, yields:

[0063] .

[0064] It can be seen that the virtual part of the manifold tracking field is a constant, indicating that the target point located on the desired manifold will move at a constant value. It moves at a certain speed.

[0065] S3. Obtain the current real physical position and virtual parameters of neighboring robots. Based on the deviation between the real physical position and virtual parameters of neighboring robots, obtain cooperative control terms and inter-robot collision avoidance terms. Combine these with the obstacle description implicit function to construct obstacle avoidance terms.

[0066] The multi-robot system obtains the physical coordinates and virtual parameters of robot i's neighboring robots through communication. The cooperative control terms are represented using the virtual parameters of robot i itself and its neighboring robot k. as follows:

[0067] .

[0068] in, , represents the set of zero vectors with n elements. These are the virtual parameters currently corresponding to robot i. For the virtual parameters currently corresponding to neighboring robot k, The expected deviation between adjacent robots i and k Let i be the set of all neighboring robots of robot i.

[0069] This invention, building upon single-robot manifold tracking, further introduces a virtual coordinate-based cooperative control mechanism through cooperative control terms. This enables multiple robots to achieve cooperative movement and formation maintenance within the desired operational manifold without deviating from it. Furthermore, it gradually corrects deviations between virtual coordinates by incorporating collision avoidance terms between adjacent robots. Unlike conventional methods that operate on the robots' physical coordinates, this invention operates on virtual coordinates, adjusting the positions of desired points on the manifold to ensure the multi-robot system can achieve cooperative formation.

[0070] When the robot's environmental perception module detects an obstacle Then, the implicit function describing the obstacle is represented by a differentiable closed manifold:

[0071] ,

[0072] in Represents the coordinates of the sphere's center. Represents the radius of the sphere. This represents the current physical location of robot i.

[0073] The obstacle avoidance of robot i It is expressed as follows:

[0074] .

[0075] in, This represents the implicit function describing the obstacle. Find the partial derivative, where E is the matrix of a 90° clockwise rotation. Indicates will Rotate according to E. For coefficients, , , , The desired motion speed is represented by virtual coordinates.

[0076] In practical applications of multi-robot manifold tracking and cooperative formation, when an obstacle avoidance mechanism is introduced, this invention does not simply construct an obstacle avoidance term in physical space. Instead, it introduces an obstacle avoidance navigation field with a non-zero virtual propulsion component as an obstacle avoidance term in a high-dimensional extended space constructed from the robot's real physical position and virtual parameters. By introducing virtual coordinate components, the overall situation where the obstacle avoidance field and the cooperative manifold tracking field become zero after fusion is structurally avoided.

[0077] When multiple robots operate densely within a local space, the control processing unit of the multi-robot system constructs an inter-robot collision avoidance term based on the relative physical distances between robot i and its neighboring robots. The inter-robot collision avoidance term between robot i and its neighboring robot k. It is expressed as follows:

[0078] .

[0079] in, This represents the set of zero vectors with n elements. This represents the distance between robot i and its neighbor robot k. , , Let i and k be the actual physical locations of robot i and its neighbor robot k, respectively. , To control the fusion rate parameter, a value between 0.3 and 0.5 is selected. This indicates the minimum distance set. This indicates the maximum distance that can be set. Let be the total number of neighboring robots of robot i.

[0080] S4. The manifold tracking field, cooperative control terms, inter-machine collision avoidance terms, and obstacle avoidance terms are weighted and fused to form a unified composite navigation field. Based on the unified composite navigation field, target operation manifold motion control commands for robot navigation in the real environment are generated.

[0081] Based on the above, various navigation fields are weighted and fused to form a unified composite navigation field for the robot i in a scenario with multiple obstacles. Represented as:

[0082] ,

[0083] in, Let i be the manifold tracking field of robot i. Let i be the control term for the collaboration between robot i and its neighboring robots. For the collision avoidance terms between robot i and its neighboring robots, For the obstacle avoidance term of robot i, This is a function of the obstacle balance coefficient. , This is the fusion rate control coefficient. To deal with obstacles The response distance is used to balance the impact of obstacles and manifold tracking, as well as the cooperative component, where M is the total number of obstacles. For the weighting coefficients of the collaborative control terms, This represents the weighting coefficient for obstacle items. This is the weighting coefficient for inter-machine collision avoidance, with a value ranging from 0.3 to 0.5.

[0084] The generation and execution of motion control commands require normalization of the unified composite navigation field and extraction of its physical components to generate motion control commands that drive the robot to perform navigation tasks in the real environment.

[0085] This embodiment also includes a multi-robot system that uses the above method for manifold motion control. The multi-robot system can be a platform such as a mobile robot, a drone, or an underwater vehicle that has the ability to accurately track dynamic and complex manifolds.

[0086] To verify the feasibility and effectiveness of the proposed safe multi-robot cooperative manifold tracking control method in practical engineering scenarios, a software-in-the-loop (SIL) simulation was employed. The experimental system was built upon a high-fidelity fixed-wing UAV simulation environment, running a PX4 fixed-wing virtual autopilot on an Intel NUC computing platform to simulate the operation of a real flight control system. The UAV's aerodynamic model, sensor feedback, and flight environment were simulated using the Gazebo simulation platform, thus reproducing actual flight conditions without relying on a real aircraft. The proposed cooperative manifold tracking and obstacle avoidance control algorithm runs in the host computer control program. The generated navigation and guidance commands are sent to the PX4 virtual flight control system at a frequency of 100Hz via the ROS communication mechanism, forming a complete closed-loop control structure, enabling the simulation process to accurately reflect the airborne execution effect. Specific parameter settings are... .

[0087] In the simulation scenario, multiple fixed-wing UAVs simultaneously perform a task, requiring them to track the desired manifold in a complex spatial environment containing multiple spherical obstacles while maintaining a pre-defined cooperative formation. To verify the system's safety under high-risk conditions, some UAVs initially overlap with the target formation, theoretically posing a risk of collision. Simultaneously, multiple obstacles are placed along the flight path, creating locally narrow passages to examine the UAVs' ability to simultaneously perform manifold tracking, cooperative formation, and obstacle avoidance maneuvers in complex environments. During the simulation, the UAVs' flight trajectories, manifold tracking errors, formation errors, and changes in relative distances between UAVs are continuously recorded to evaluate system performance.

[0088] When multiple drones simultaneously pass through a narrow passage formed by multiple spherical obstacles, the simulation results are as follows: Figure 2As shown, the drones were able to autonomously maintain a safe distance and successfully navigate obstacle areas through path adjustments and altitude maneuvers. Throughout this process, the minimum safe distance between the drones was consistently maintained, and no collisions or stalling occurred. The analysis results of the cooperative formation performance are as follows: Figure 3a and 3b As shown, the formation error of multiple UAVs generally shows a downward trend. Although it temporarily increases when encountering obstacles, it can quickly drop back to near zero after leaving the obstacle area, which verifies that the present invention can maintain stable and continuous cooperative formation capability in complex environments.

[0089] like Figure 4a and 4b As shown, simulation results indicate that after the mission begins, the manifold tracking error of each UAV gradually decreases and eventually converges to a stable range close to zero. During obstacle avoidance maneuvers, the manifold tracking error briefly increases, but quickly recovers and reconverges after obstacle avoidance, demonstrating the good stability and robustness of the manifold tracking field under the proposed high-dimensional truncated manifold navigation mechanism. Since some UAVs initially intersect with the target formation structure, the constructed obstacle and collision avoidance navigation field effectively guides different UAVs to perform evasive maneuvers in different directions, as observed from their flight trajectories. For example, some UAVs primarily adjust their tracks horizontally, while others avoid collisions by changing their altitude, thus successfully avoiding the risk of mid-course collisions.

[0090] Furthermore, no system stagnation due to mutual cancellation of control inputs was observed during the entire simulation process, indicating that the obstacle avoidance design with non-zero virtual propulsion components introduced in this invention can effectively avoid the singularity problem of overall zero after the superposition of multiple navigation fields, ensuring that the system always maintains a continuous and safe operating state. The simulation results show that the safe multi-robot cooperative control method proposed in this invention can operate stably in a high-fidelity flight environment, simultaneously achieving manifold tracking, cooperative formation, and safe obstacle avoidance under complex obstacle conditions, fully demonstrating the effectiveness and reliability of this technical solution in practical engineering applications.

[0091] The above embodiments are merely illustrative examples to clearly illustrate the present invention and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all embodiments here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A safe multi-robot cooperative control method for manifold tracking, characterized in that... Includes the following steps: S1. Obtain the robot's current real physical position and randomly generate virtual parameters. Construct an extended position variable by combining the robot's real physical position and the corresponding virtual parameters. S2. Target Operation Manifold Modeling: Construct the desired manifold based on the robot's target operation manifold. Based on the deviation between the robot's current real physical position and the target operation manifold, construct a guiding propagation direction orthogonal to the constraint gradient of the desired manifold as a guiding propagation term. This guiding propagation term is a guiding propagation direction orthogonal to the constraint gradient of the desired manifold, constructed based on the gradient information of the manifold deviation function, and is expressed as: ;in This indicates the calculation of the wedge product. As an auxiliary vector, , , This represents the expected velocity of the virtual coordinates. This represents the set of partial derivatives of the manifold deviation function of robot i with respect to the current extended position variable in the j-th dimension. , , Let be the manifold deviation function of robot i in the current j-th dimension; And construct an error reduction term for use only in the robot's physical space, the error reduction term being expressed as: ,in, Let represent the set of partial derivatives of the manifold deviation function of robot i with respect to its current real physical position in the j-th dimension. , It is the convergence coefficient of the j-th dimension; The manifold tracking field of robot i is obtained by summing the guidance propagation term and the error reduction term in step S2. It is expressed as follows: ; S3. Obtain the current real physical position and virtual parameters of neighboring robots, and obtain cooperative control terms and inter-robot collision avoidance terms based on the deviation between the real physical positions and virtual parameters of neighboring robots. Collaborative control terms between robot i and its neighbor robot k It is expressed as follows: ,in, , These are the virtual parameters currently corresponding to robot i. For the virtual parameters currently corresponding to neighboring robot k, The expected deviation between adjacent robots i and k Let i be the set of all neighboring robots; The collision avoidance terms between robot i and its neighboring robot k It is expressed as follows: ,in, This represents the distance between robot i and its neighbor robot k. , , Let i and k be the actual physical positions of robots i and k, respectively. , To control the fusion rate parameter, This indicates the minimum distance set. This indicates the maximum distance that can be set. Let be the total number of neighboring robots of robot i; An obstacle avoidance term is constructed by combining the implicit function describing the obstacle; the obstacle avoidance term of robot i is... It is expressed as follows: , in, This represents the implicit function describing the obstacle. Find the partial derivative. Indicates will Rotate the matrix 90° clockwise. For coefficients, , , , The desired motion velocity for virtual coordinates; S4. The manifold tracking field, cooperative control term, inter-machine collision avoidance term, and obstacle avoidance term are weighted and fused to form a unified composite navigation field. The unified composite navigation field of robot i is represented as follows: ,in, Let i be the manifold tracking field of robot i. Let i be the control term for the collaboration between robot i and its neighboring robots. For the collision avoidance terms between robot i and its neighboring robots, For the obstacle avoidance term of robot i, This is a function of the obstacle balance coefficient. , This is the fusion rate control coefficient. To deal with obstacles The response distance, where M is the total number of obstacles. For the weighting coefficients of the collaborative control terms, This represents the weighting coefficient for obstacle items. The weighting coefficients for inter-machine collision avoidance are used to generate target operation manifold motion control commands for robot navigation in the real environment based on a unified composite navigation field.

2. The safe multi-robot cooperative control method for manifold tracking according to claim 1, characterized in that: In step S2, implicit functions are used to construct the common desired manifold for all robots. , where n represents the physical dimension. An extended position variable representing the robot's actual physical position and the corresponding virtual parameters. , This is a set-based representation of the robot's current real physical location. , For the robot's actual physical coordinates, It is a set of virtual parameters. , To generate virtual coordinates for virtual parameters, The robot's true physical position in the current j-dimensional dimension. With the target operation manifold manifold deviation function between , Let be a known differentiable function of the target operation manifold.

3. A safe multi-robot cooperative control method for manifold tracking according to claim 1, characterized in that: When the robot detects an obstacle Then, the obstacle description implicit function is represented by a differentiable spherical closed manifold: ， in Represents the coordinates of the sphere's center. Represents the radius of the sphere. This represents the current physical location of robot i.

4. A multi-robot system, characterized in that: The multi-robot system uses the method described in any one of claims 1-3 for manifold motion control.

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