Robust fixed-time encirclement tracking control method for heterogeneous multi-robot system

Abstract

This invention discloses a robust fixed-time encirclement tracking control method for heterogeneous multi-robot systems, applied to the field of cooperative control technology for multi-robot systems. First, a heterogeneous multi-robot system composed of first-order followers and fractional-order leaders is constructed, and a fixed-time encirclement tracking control objective is determined. Second, a robust fixed-time encirclement tracking controller composed of a sign function term and a power exponent term is designed, introducing high-gain parameters to suppress the influence of external disturbances and uncertainties. Simultaneously, adaptive techniques are used to estimate actuator failure factors in real time, thereby improving the robustness of the closed-loop system. Further, a Lyapunov function is constructed, and the stability conditions of the closed-loop error system are analyzed to obtain the upper bound of the settling time and the control parameter conditions. Finally, the designed robust fixed-time encirclement tracking controller is applied to the heterogeneous multi-robot system, demonstrating that all followers can converge to the dynamic convex hull constructed by the leaders within a fixed time.

Description

Technical Field

[0001] This invention belongs to the field of collaborative control technology for multi-robot systems, and specifically relates to an encirclement and tracking control technology. Background Technology

[0002] With the continuous development of computer technology, communication technology, and intelligent control theory, multi-robot systems are increasingly widely used in fields such as UAV swarms, mobile robot collaboration, intelligent transportation, and distributed sensing. In multi-robot cooperative control problems, encirclement and tracking control, as an important extension of the consistency problem, aims to design reasonable control strategies to make multiple follower robots converge into the dynamic convex hull formed by the leader robot, thereby completing practical tasks such as area guidance, collaborative operations, and swarm escort. However, existing research on encirclement and tracking control mostly focuses on asymptotically stable or finite-time stable cases. Although system convergence can be achieved, there are still certain limitations in terms of convergence speed and time controllability. In contrast, fixed-time control, because its upper bound on convergence time does not depend on the initial state of the system, can provide stronger time performance guarantees and therefore has broad research value in practical engineering applications.

[0003] Meanwhile, in practical applications, multi-robot systems typically operate in open wireless communication networks and complex physical environments, facing challenges from multiple uncertainties. On the one hand, the system is inevitably affected by unknown disturbances from the external environment, such as environmental interference, execution errors, and communication uncertainties; on the other hand, with the increase in cyberspace security threats, the system is highly vulnerable to malicious actuator attacks. The superposition of these disturbances and attacks can significantly reduce the stability of the system, and even lead to formation collapse. Furthermore, with the continuous improvement of application requirements, multi-robot systems are gradually exhibiting heterogeneous characteristics. For example, leader robots and follower robots differ in their dynamic structures, which further increases the complexity of controller design. Most existing research often employs relatively complex multinomial nonlinear structures in controller design. Although theoretically, fixed-time convergence can be achieved, it presents certain difficulties in practical implementation.

[0004] To address the aforementioned issues, existing methods still have shortcomings in fixed-time encirclement tracking control under the combined effects of multiple factors such as directed topology, heterogeneous systems, unknown disturbances, and actuator attacks. On the one hand, there is a lack of robust control frameworks that can simultaneously suppress environmental disturbances and resist actuator attacks; on the other hand, the problem of ensuring fixed-time convergence of the system under unknown disturbance conditions has not been fully resolved. Therefore, it is necessary to study a fixed-time encirclement tracking control method that balances attack resistance and high robustness for heterogeneous multi-robot systems in directed communication topology, in order to improve the stability and engineering application value of swarm systems in complex environments. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a robust fixed-time encirclement and tracking control method for heterogeneous multi-robot systems. By designing a controller and rationally selecting control parameters, it effectively suppresses and compensates for external unknown disturbances, system uncertainties, and malicious actuator attacks, thereby ensuring that the multi-robot system completes the encirclement and tracking task within a fixed time, and improving the system's convergence performance and robustness.

[0006] The technical solution adopted in this invention is: a robust fixed-time encirclement tracking control method for heterogeneous multi-robot systems, the multi-robot system on which is based includes: One follower and A leader, with individuals interacting through a directed network; the encirclement and tracking control includes:

[0007] S1. Construct a multi-leader dynamics model and a follower dynamics model with unknown external interference and actuator attacks respectively; determine the target for encirclement and tracking control at a fixed time.

[0008] S2. Construct a global position error vector containing the relative position information of all followers and leaders; establish error dynamic equations based on the global position error vector, multi-leader dynamics model and follower dynamics model, and determine the error convergence criterion, thereby transforming the encirclement and tracking control problem into an error system stabilization problem.

[0009] S3. Design a robust fixed-time encirclement tracking controller composed of a sign function term and a power exponent term. Introduce a high-gain parameter to suppress the influence of external disturbances and uncertainties. At the same time, use adaptive technology to estimate the actuator failure factor in real time.

[0010] S4. Substitute the robust fixed-time encirclement tracking controller described in step S3 into the error dynamics equation constructed in step S2, analyze the stability conditions of the closed-loop error system, obtain the upper bound of the adjustment time, and the control parameter conditions.

[0011] S5. Apply the robust fixed-time encirclement tracking controller processed in step S4 to the heterogeneous multi-robot system to achieve fixed-time encirclement control.

[0012] The beneficial effects of this invention are as follows: In view of the multiple uncertainties in complex environments, this invention designs a robust fixed-time encirclement tracking control method for heterogeneous multi-robot systems. By introducing an online adaptive update law based on the reciprocal of actuator efficiency, it realizes real-time estimation and dynamic compensation for malicious attacks or performance degradation. At the same time, combined with a gain adjustment mechanism, it effectively suppresses the influence of external disturbances and significantly enhances the robustness of the closed-loop system under network security threats.

[0013] For heterogeneous systems composed of fractional-order and first-order dynamics, a deterministic encirclement deployment with time guarantees is achieved. A novel fixed-time control framework is proposed to ensure that the follower swarm accurately enters the dynamic convex hull formed by the leader within a preset time limit. This convergence time limit depends only on the controller parameters and topological properties, and is completely independent of the robot's initial state, greatly improving the predictability of heterogeneous swarms in time-sensitive tasks. Attached Figure Description

[0014] Figure 1 This is a flowchart of the fixed-time robust encirclement and tracking method for multi-robot systems against actuator attacks according to the present invention;

[0015] Figure 2 This is the directed communication topology of the robot in this embodiment;

[0016] Figure 3 This is a trajectory diagram of the multi-robot fixed-time encirclement tracking state under unknown external disturbances in this embodiment. Detailed Implementation

[0017] To facilitate understanding of the technical content of this invention by those skilled in the art, the following description, in conjunction with the accompanying drawings, further illustrates the invention.

[0018] like Figure 1 As shown, the method of the present invention includes the following steps:

[0019] S1. Establish a dynamic model of a heterogeneous multi-robot system, namely, construct a multi-leader model described by fractional differential equations and a first-order follower dynamic model with unknown external disturbances; explain the relevant definition of encirclement control and set the control objective as the follower entering the dynamic convex hull formed by the leaders within a fixed time.

[0020] S11. Construct a multi-leader dynamics model and a follower dynamics model with unknown external interference and actuator attacks, respectively, and define the system composition;

[0021] The multi-robot system is composed of One follower and The group consists of several leaders, who interact with each other through a directed network. The set of individual follower robots is represented as follows: The set of individual leader robots is represented as .

[0022] The dynamic model of the follower robot, i.e. the follower dynamic model with unknown external disturbances and actuator attacks, is expressed as Equation (1):

[0023] (1)

[0024] The dynamic model of the individual leader robot, namely the time-varying multi-leader dynamic model described by the Caputo fractional differential equation, is shown in equation (2):

[0025] (2)

[0026] in, Indicates time, Indicates the first The positional status of each follower Indicates the control input of the follower. This represents the unknown external environmental interference experienced by the follower, and the actuator efficiency factor of the follower. Indicates actuator health indicators, when When, it indicates the first The actuators of each follower are functioning normally; when When, it indicates the first The executor of one follower has partially lost its ability to execute, but it continues to operate. Indicates the first The position status of each leader, among which represent 3D space Indicates the order is Caputo fractional derivative, The time-varying nonlinear function representing the leader, in this embodiment .

[0027] S12. Based on the dynamic modeling in step S11, define the relevant geometric concepts in the encirclement control.

[0028] set up Let be a non-empty set in the real vector space. If for any two points in the set , ... and any scalar All have Then the set This is called a convex set. For sets composed of... A set of points consisting of leaders Its convex hull is the minimal convex set containing all points in the set, denoted as . The mathematical definition is:

[0029] (3)

[0030] in, The corresponding coefficient represents the convex combination weight coefficient acting on the j-th leader state (or position), when the follower's position state... When the target is located within the convex hull, it means that the geometrically encircled target is initially satisfied. This reflects the relative positional distribution or degree of interaction between specific followers and leaders. Through analysis of... We sum the weighted states of each leader to construct a dynamic geometric constraint space, namely the convex hull. As a non-negative scalar, it aims to ensure that followers are always controlled within the leader's point set, avoiding control divergence or exceeding the preset operating area. By setting the sum of weights to a unit of 1, a centroid correspondence is established between the follower and leader groups, ensuring that the system has translation invariance during spatial transformations.

[0031] S13. Based on the convex hull concept proposed in step S12, the control objective of the fixed-time encirclement control problem is defined.

[0032] The system topology is set to satisfy the condition that there exists at least one leader from which every follower has a directed path.

[0033] The control objective of the encirclement control problem is to design robust control laws. This ensures that all followers, within a fixed timeframe, do not depend on the initial state of the system. Internal satisfaction formula (4):

[0034] (4)

[0035] in It is a vector The convex hull, and It is the set of leader states. If the point To convex hull If the distance is zero, it means that the point Located within the convex hull. Equation (3) indicates that all followers in the system will eventually be driven into the dynamic convex hull region surrounded by multiple leaders, and remain in motion within that region thereafter, achieving robust fixed-time encirclement tracking control under switching or fixed topologies.

[0036] S2. Define a compact expression for the encirclement tracking error and construct a global position error vector that includes the relative position information of all followers and the leader. Combine the topology to establish the error dynamics equation and transform the encirclement tracking control problem into an error system stabilization problem.

[0037] S21. Construct the global encirclement tracking error vector.

[0038] The information interaction of a multi-robot system is defined by a directed graph. It means that, among them For a set of nodes, Let be the set of edges. This is a weighted adjacency matrix. If the node... Able to direct nodes To transmit information, and ,otherwise .

[0039] Definition of the first The encirclement tracking error of the follower robots is Its mathematical expression is shown in equation (5):

[0040] (5)

[0041] in, The adjacency weights represent the adjacency values ​​in the communication topology. Indicates the first A robot at any moment Location status. All The errors of each follower are stacked to obtain the global error vector of the system, as shown in equation (6):

[0042] (6)

[0043] in, For the follower state vector, For the leader's state vector, and These are the follower sub-matrix and the leader associated sub-matrix of the topological Laplace matrix, respectively. For Kronecker product, It is an identity matrix.

[0044] Full graph topology The Laplace matrix is ​​defined as The full graph topology consists of a follower directed graph and a leader directed graph, where... diagonal elements are A diagonal matrix. Matrix express Interactions between follower agents, matrix The off-diagonal elements are determined by the adjacency weights among followers, while the diagonal elements are determined by the sum of the in-degrees of all followers; the matrix express A follower agent and Interactions between leader agents, matrix The elements are assigned values ​​based on the observability of the leader's state by the followers. The number of followers can obtain the first Information about each leader, then The element at the corresponding position takes the value of a negative weight constant; otherwise, it takes the value of zero.

[0045] Furthermore, the above error expression can be equivalently transformed into:

[0046] (7)

[0047] in, This represents a dynamic convex combination of leader states. Therefore, the error vector... Used to characterize the geometric deviation of the overall state of followers relative to the dynamic convex hull of the leader.

[0048] S22. Establish a dynamic model of the error system.

[0049] For the error vector described in step S21 Regarding time By taking the derivative and combining it with the follower dynamics model and the leader dynamics model in step S11, the dynamic equation of the error system is constructed as shown in equation (8):

[0050] (8)

[0051] in, Indicates the actuator failure factor. The input vector is used to control the followers. Let be an unknown bounded external perturbation vector. This represents the rate of change of the leader's state. The error dynamics model fully reflects the combined influence of control input, external disturbances, and leader dynamics on the evolution of the system's encirclement error, providing a controlled object model for the subsequent design of the controller.

[0052] S23. Determine the encirclement and tracking control target and its convergence criterion.

[0053] Under the premise that the directed communication topology satisfies the reachability condition, due to the matrix For a non-singular matrix, when the error vector satisfies Then, according to equation (7), we can derive:

[0054] (9)

[0055] That is, the states of all follower robots converge to the dynamic convex hull formed by the states of the leader robot. Furthermore, to achieve fixed-time encirclement tracking control, the convergence criterion of the error system is set as shown in equation (10):

[0056] (10)

[0057] in, The upper limit of the fixed-time adjustment, independent of the initial state of the system, is determined by formula (18). Therefore, the encirclement control problem of a multi-robot system is transformed into: by designing a reasonable controller... This allows the error dynamics system to converge globally to zero within a fixed time, thereby enabling robust tracking of the leader's convex hull by the follower.

[0058] S3. Based on the convergence requirements of the error system in step S2, quantitatively analyze the upper bound of the disturbance and the threshold of the nonlinear term, and design an anti-attack adaptive law to compensate for the performance loss of the actuator in real time; accordingly, design a fixed-time robust encirclement controller based on a single power term, that is, the controller structure contains only one power term greater than 1, and set the robust compensation gain according to the upper bound of the disturbance.

[0059] S31. Construct an ideal encirclement control law based on a single power term structure.

[0060] To address the complex uncertainties of the multi-robot system in step S1, we first assume that the external disturbances to the followers are bounded, i.e., satisfying... The nonlinear term of the leader also satisfies the bounded condition after fractional transformation, that is... ,in and All are positive numbers. The upper bound of the amplitude of the unknown external disturbance experienced by the follower robot; The upper bound of the residual nonlinear term after fractional transformation represents the leader's nonlinear term.

[0061] To reduce computational complexity while ensuring convergence in a fixed time, a robust encirclement controller as shown in equation (11) is designed:

[0062] (11)

[0063] in, For the first An estimate of the inverse of the attack factor of each follower. Ideal control inputs that exclude terms related to uncertainty. For the first The actual control input of a follower The local encirclement error defined in step S21, For symbolic functions, It is the output intensity factor of the controller. In practical applications The value is determined based on the interference intensity and encirclement speed requirements. The value is usually determined by experimental calibration based on the theoretical lower bound, so that the system is both fast and does not jitter. It is generally between 1 and 20. In this example, α=1.5 is selected. The controller gain coefficient is defined in step S33, and its constraints are shown in step S33.

[0064] The controller of this invention consists of two parts: the first part Used to suppress external disturbances and cancel nonlinear terms; Part Two Used to accelerate the convergence speed of the system when it is far from the equilibrium point.

[0065] S32, Regarding actuator health indicators To address the unknown nature of attacks, an adaptive law for attack resistance is designed.

[0066] Regarding the actuator efficiency factor in the follower dynamics model described in step S11 To address the unknown issue and achieve online compensation for executor attacks, an inverse executor efficiency parameter is introduced. Here, we define... and The estimated value is Therefore, the following identity relation holds:

[0067] (12)

[0068] in It is the estimation error.

[0069] When designing control inputs, terms related to uncertainty should be excluded, and feedback should be incorporated into the feedback state based on the new state.

[0070] (13)

[0071] in, For the first An ideal control input for a follower The local encirclement error defined in step S21, For symbolic functions, , The controller gain coefficient is defined in step S33, and its constraints are shown in step S33.

[0072] Furthermore, to achieve real-time estimation of the executor attack factor, the following adaptive update law is designed:

[0073] (14)

[0074] in, For adaptive gain, It is a positive definite parameter used to adjust the convergence speed of actuator fault estimation. Its value is usually obtained through experimental testing based on the system's sampling frequency and the frequency of actuator attacks, and is usually selected between 0.1 and 10. In this patent example, the value is 1. For the first An ideal control input for a follower This refers to the local encirclement error defined in step S21.

[0075] S33. Based on the topology parameters and limit characteristics, establish the selection criteria for controller gain.

[0076] First, using matrices Calculate the positive vector corresponding to its minimum eigenvalue. Subsequently, using the positive vector Each component generates a diagonal matrix. In this diagonal matrix, the diagonal elements are respectively equal to the vectors The reciprocal of the corresponding component. Through the aforementioned diagonal matrix. For topological matrix After transformation, a symmetric positive definite matrix is ​​obtained. .

[0077] Based on this, the controller gain coefficient is determined. The robustness constraints that must be met are shown in equation (15):

[0078] (15)

[0079] Among them, matrix It will be introduced in step S41. Representation matrix The smallest eigenvalue, , The infinity norm is used in this invention to refer to the upper bound of the global norm of the perturbation, i.e., the worst case of the system perturbation.

[0080] S4. Substitute the robust encirclement controller described in step S3 into the error dynamics equation constructed in step S2 to construct a closed-loop error system and prove its stability, and determine the fixed time upper limit. .

[0081] S41. Construct the state equations of the controlled closed-loop error dynamic system. Then, use the robust controller from step S31... Substituting into the error dynamics equation of step S22, the dynamic evolution expression of the global closed-loop error system is obtained as shown in equation (16):

[0082] (16)

[0083] in, Represents a vector Take each component Power of 1 This formula characterizes how the system error changes under external disturbances when a single power-term controller is applied. Leader Score Dynamics Under the combined influence of various factors, they tend to reach an equilibrium point.

[0084] S42. Construct a weighted Lyapunov stability analysis function using the left eigenvector. To analyze the convergence of the above nonlinear system, the function derived in step S33 is used... The generated diagonal matrix and its associated vector Construct the Lyapunov function as shown below. :

[0085] (17)

[0086] The construction of this function combines linear terms with higher-order power terms, using vectors. The weighting effect of the directional topology cancels out the asymmetry of the Laplace matrix caused by the directional topology, providing an energy function basis for proving fixed-time convergence.

[0087] S43. Analyze the fixed-time reachability of the encirclement error based on the stability criterion. Differentiate equation (17) and combine it with the gain constraint in step S33 to derive the inequality form that satisfies fixed-time convergence. Analysis shows that due to the gain... It is sufficient to compensate for all nonlinear uncertainties inside and outside the system, and the encirclement error will converge to zero within a fixed time.

[0088] To ensure that the encirclement error converges within a finite and fixed time under the directed topology, a fixed-time stability criterion is introduced: if the differential inequality is satisfied... ,in The system state will then converge to an equilibrium point within a fixed time, and the adjustment time has an upper limit. The formula is shown in equation (18):

[0089] (18)

[0090] in, , These are positive constants determined by both the controller parameters and the system topology. These are the nonlinear exponential parameters in the controller. To ensure the convergence condition holds, the controller parameters must satisfy... and By appropriately selecting the gain, the influence of unknown external disturbances can be offset. The specific value is determined based on the interference intensity and the algebraic connectivity of the communication topology. In this embodiment, the value is 1.5.

[0091] S5. Apply the robust encirclement tracking controller described in step S4 to a multi-robot system to achieve fixed-time encirclement control, enabling the followers in the system to effectively track the dynamic convex hull of multiple leaders within a fixed time limit under the condition of unknown external interference and actuator attacks.

[0092] S51. Apply the control protocol from S4 to the individual dynamic equations of each follower robot; in an environment with directed communication topology and unknown external interference and actuator attacks, control the gain... Real-time robust compensation is provided for external disturbances and leader dynamics, so that followers in any initial state can enter the dynamic convex hull formed by the leader under fixed time constraints.

[0093] S52. Based on the above steps, a robust fixed-time encirclement tracking control method for heterogeneous multi-robot systems has been designed.

[0094] This embodiment considers a multi-robot system consisting of 4 fractional-order leaders and 6 first-order followers, with the following communication topology: Figure 2 As shown. The leader's dynamic settings are as follows. External interference for each follower is set to The superscript T indicates transpose. The interference limit is determined according to the estimation method in step S3. Select the following controller parameters: Calculations show that the topological association vector components satisfy... Set the initial position state of the 6 followers to Set the initial position state of the four leaders to... .

[0095] visible, Figure 3 This is a trajectory diagram of the multi-robot encirclement tracking in this embodiment, where the dashed trajectory represents the state of the four leaders and the solid trajectory represents the state of the followers. Simulation results show that the final embodiment achieves robust, fixed-time encirclement tracking of a multi-robot system resistant to actuator attacks.

[0096] Those skilled in the art will recognize that the embodiments described herein are for the purpose of helping to understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A robust fixed-time encirclement and tracking control method for a heterogeneous multi-robot system, characterized in that, The multi-robot system on which it is based includes: One follower and A leader, with individuals interacting through a directed network; the encirclement and tracking control includes: S1. Construct a multi-leader dynamics model and a follower dynamics model with unknown external interference and actuator attacks respectively; determine the target for encirclement and tracking control at a fixed time. S2. Construct a global position error vector containing the relative position information of all followers and leaders; establish error dynamic equations based on the global position error vector, multi-leader dynamics model and follower dynamics model, and determine the error convergence criterion, thereby transforming the encirclement and tracking control problem into an error system stabilization problem. S3. Design a robust fixed-time encirclement tracking controller composed of a sign function term and a power exponent term. Introduce a high-gain parameter to suppress the influence of external disturbances and uncertainties. At the same time, use adaptive technology to estimate the actuator failure factor in real time. S4. Substitute the robust fixed-time encirclement tracking controller described in step S3 into the error dynamics equation constructed in step S2, analyze the stability conditions of the closed-loop error system, obtain the upper bound of the adjustment time, and the control parameter conditions. S5. Apply the robust fixed-time encirclement tracking controller processed in step S4 to the heterogeneous multi-robot system to achieve fixed-time encirclement control.

2. The robust fixed-time encirclement and tracking control method for a heterogeneous multi-robot system according to claim 1, characterized in that, The multi-leader dynamics model in step S1 is described by Caputo fractional differential equations, expressed as follows: ； in, Indicates time, Indicates the first The position and status of a leader ,in represent 3D space Indicates the order is Caputo fractional derivative, , The time-varying nonlinear function representing the leader, Represents a set of leaders; The follower dynamics model expression with unknown external disturbances and actuator attacks is as follows: ； in, Indicates the first The positional status of each follower , Indicates the control input of the follower. , This represents the actuator efficiency factor of the follower. , Indicates actuator health indicators, It represents the set of followers.

3. The robust fixed-time encirclement and tracking control method for a heterogeneous multi-robot system according to claim 2, characterized in that, The process of determining the target for encirclement and tracking at a fixed time is as follows: The topology of the multi-robot system satisfies the following condition: there exists at least one leader from each follower, and there is a directed path from the leader to each follower. The fixed-time encirclement and tracking control target is defined as: through design... This ensures that all followers, regardless of the initial state of the multi-robot system, remain within a fixed time. The following equation is satisfied: ； in, It is a set of leader states. It is a vector convex hull, .

4. The robust fixed-time encirclement and tracking control method for a heterogeneous multi-robot system according to claim 3, characterized in that, The expression is: ； in, Indicates action on The convex combination weight coefficients.

5. A robust fixed-time encirclement and tracking control method for a heterogeneous multi-robot system according to claim 4, characterized in that, The process of constructing a global position error vector containing the relative position information of all followers and the leader in step S2 is as follows: The information interaction of a multi-robot system is represented as a directed graph. ,in For a set of nodes, , Let be the set of edges. , For a weighted adjacency matrix, , Represents the adjacency weights of the communication topology; Definition of the first The encirclement tracking error of the follower robots is Its mathematical expression is: ； All The errors of the individual followers are stacked to obtain the global error vector expression of the multi-robot system: ； in, For the follower state vector, For the leader's state vector, and These are the follower sub-matrix and the leader associated sub-matrix of the topological Laplace matrix, respectively. For Kronecker product, It is the identity matrix; Will The equivalent transformation is: ； in, This represents a dynamic convex assemblage of leader states. .

6. A robust fixed-time encirclement and tracking control method for a heterogeneous multi-robot system according to claim 5, characterized in that, The error dynamics equation is expressed as: ； in, Indicates the actuator failure factor. Let be an unknown bounded external perturbation vector. This indicates the rate of change in the leader's state.

7. A robust fixed-time encirclement and tracking control method for a heterogeneous multi-robot system according to claim 6, characterized in that, The error convergence criterion is: 。 8. A robust fixed-time encirclement and tracking control method for a heterogeneous multi-robot system according to claim 7, characterized in that, Step S3 specifically includes the following sub-steps: S31. Construct an ideal encirclement control law based on a single power term structure, with the following expression: ； in, For the first An ideal control input for a follower For symbolic functions, It is the output intensity factor of the controller. This is the controller gain coefficient. For the first An estimate of the inverse of the attack factor of each follower; S32, Definition , The estimated value is Therefore, the following identity relation holds: ； in It is an estimation error; Design the following adaptive update law: ； in, For adaptive gain, It is a positive definite parameter used to adjust the convergence speed of actuator fault estimation; S33, Using matrices Calculate the positive vector corresponding to its smallest eigenvalue: ； Using the positive vector Each component generates a diagonal matrix: ； Wherein, the diagonal matrix The diagonal elements of the vector are respectively equal to the positive vectors. The reciprocal of the corresponding component; Through the diagonal matrix For topological matrix After transformation, a symmetric positive definite matrix is ​​obtained: ； Build The robustness constraints that must be satisfied are: ； in, Representation matrix The smallest eigenvalue, , It represents an infinite range.

9. A robust fixed-time encirclement and tracking control method for a heterogeneous multi-robot system according to claim 8, characterized in that, Step S4 specifically includes the following sub-steps: S41, The robust controller in step S31 Substituting into the error dynamics equation of step S22, the dynamic evolution expression of the global closed-loop error system is obtained as follows: ； in, Represents a vector Take each component Power; S42, using the method from step S33 The generated diagonal matrix and its associated vector Construct the Lyapunov function as shown below. : ； S43. The Lyapunov function constructed in step S42 By taking the derivative and combining it with the gain constraint in step S33, we can derive the inequality form that satisfies fixed-time convergence: ； in, ; S44. When the inequality in step S43 is satisfied, the system state will converge to the equilibrium point within a fixed time, and the upper limit of the adjustment time will be set. The formula is: ； in, , , This refers to the nonlinear exponential parameter in the controller.

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