A multi-unmanned vehicle fault-tolerant control method based on SBC formation

Abstract

The application discloses a kind of multi-unmanned vehicle fault-tolerant control methods based on SBC formation, it is related to multi-agent control technical field.By directly based on relative measurement parameter as state variable, compact formation model architecture is constructed;And by explicitly including external disturbance into system dynamics model, and based on Lyapunov stability theory and performance criteria, passive fault-tolerant control strategy that can simultaneously cope with actuator failure and external disturbance is designed.This design makes the system fundamentally eliminate the dependence on global coordinate system, still can maintain accurate formation control performance under GPS denial environment, by establishing a perfect fault model, clearly define fault uncertainty boundary, using uncertainty item upper bound estimation method, combined with Schur complement lemma and other mathematical tools, complex stability condition is converted into solvable LMI problem.This processing method guarantees effective inhibition to fault uncertainty, ensures that the system maintains reliable formation performance in complex dynamic environment.

Description

Technical Field

[0001] This application relates to the field of multi-agent control technology, and in particular to a fault-tolerant control method for multiple unmanned vehicles based on SBC formation. Background Technology

[0002] Unmanned vehicle (UAV) platooning cooperative control technology is shifting from traditional single-vehicle independent operation to distributed autonomous cooperative control. While providing equivalent platooning performance, the new distributed cooperative control architecture eliminates the complex centralized communication topology and does not rely on real-time support from a global positioning system. It acquires relative distance and azimuth information solely through lightweight onboard sensing and communication modules, effectively reducing system complexity and improving the reliability and environmental adaptability of the platooning system. Furthermore, compared to traditional position-based platooning control methods, the distance-azimuth (SBC) control method is more compact, computationally less burdensome, effectively handles GPS-denied environments, and possesses advantages such as simple measurement, high accuracy, fast response, and strong practicality, achieving superior platooning maintenance and formation change performance.

[0003] Currently, distributed platooning control has become the mainstream trend in the field of unmanned vehicles. JD Logistics delivery vehicles, Meituan takeout robots, and unmanned mining transport vehicles have all adopted platooning collaborative operation modes to replace the original single-vehicle operations, demonstrating significant advantages in transportation efficiency, cost control, and safety. In the design of intelligent logistics systems and unmanned mining transportation systems, my country is also gradually upgrading traditional manual operation to multi-vehicle platooning autonomous control. However, platooning systems face severe reliability challenges in practical applications, making fault-tolerant control an indispensable key technology, especially since the impact of actuator failures on the platooning system is crucial.

[0004] In the field of fault-tolerant control for autonomous vehicle platooning, existing technologies typically design fault-tolerant control laws based on generalized linear state-space models. Their core focus is on estimating and compensating for actuator failures, but they do not incorporate specific platooning geometry models (such as distance-angle relationships) and do not include external disturbances as independent factors in system stability analysis. Their control relies on global state information, requiring coordinate transformation to process relative measurements or the use of global positioning systems (such as GPS) to obtain absolute position coordinates, resulting in a relatively generalized model structure. Therefore, when facing fault-tolerant control requirements in complex environments, they suffer from the following key shortcomings:

[0005] 1. Defects in environmental adaptability and computational efficiency caused by global coordinate system dependence Existing technical solutions suffer from fundamental limitations in formation state construction: their control algorithms rely on state information in a global coordinate system for calculation. This dependence manifests in two possible technical paths: one is to directly use absolute positioning systems such as GPS to obtain global coordinates; the other is to obtain relative measurement information (such as distance and angle) through onboard sensors, and then perform complex transformations to map it to the global coordinate system for error calculation. Regardless of the path chosen, this technical solution cannot escape its essential dependence on the global coordinate system. In the first path, the system will be completely paralyzed in GPS-denied environments due to the failure of the absolute positioning source. In the second path, although GPS signals are not directly required, the process of transforming relative measurements to global coordinates introduces significant model redundancy and computational burden. This transformation not only requires complex coordinate transformation algorithms but also accumulates errors due to sensor noise and motion estimation errors, leading to global coordinate system drift and formation distortion. More importantly, the control law design of this solution requires that all vehicle states must be mathematically meaningful within a unified global coordinate system. This design choice means the system cannot operate reliably even in GPS-denied environments, even using relative measurement information, because accumulated errors gradually distort the global coordinate system, thus affecting the accuracy of formation control. Furthermore, the complex coordinate transformations and matrix operations further increase the computational burden, impacting the system's real-time performance.

[0006] 2. Insufficient consideration of external disturbances leads to poor robustness in dynamic environments. Existing technical solutions are based on ideal operating conditions, neglecting the impact of external disturbances on system dynamics. In formation fault-tolerant control design, only actuator fault compensation is considered, without incorporating disturbances (such as changes in ground adhesion, slope undulations, and wind interference) into the model, lacking a specific suppression mechanism for the coupling effect of disturbances and faults. In real-world applications, autonomous vehicles continuously experience external disturbances such as wind resistance, changes in ground adhesion, and slope undulations. These disturbances, coupled with actuator faults, generate complex dynamic effects, leading to the accumulation of formation errors and even system instability. Existing control laws do not incorporate such... Robustness metrics such as performance criteria cannot maintain stable control performance under disturbed environments. This deficiency limits its applicability to static or mildly disturbed environments, making it unsuitable for reliability requirements in complex dynamic scenarios. Especially during the recovery phase after a fault, the impact of disturbances further exacerbates formation instability, limiting the practical value of this technology in real-world scenarios.

[0007] In summary, existing fault-tolerant control technologies for unmanned vehicle platooning face challenges in environments such as GPS rejection and complex terrain. GPS rejection can lead to complete paralysis of the unmanned vehicles due to the failure of their absolute positioning source, or introduce significant model redundancy and computational burden. Furthermore, unmanned vehicles operating in complex terrain and dynamic environments are subject to multiple factors, including changes in ground adhesion, slope undulations, and wind interference. These factors result in vehicles continuously experiencing unknown external disturbances, and actuator failures are sudden and uncertain, further increasing the difficulty of controlling unmanned vehicle platoons and making it difficult for existing fault-tolerant control methods to meet accuracy requirements. Summary of the Invention

[0008] Therefore, it is necessary to provide a fault-tolerant control method for multiple unmanned vehicles based on SBC formation to address the aforementioned technical problems.

[0009] The following technical solution is adopted in this specification: This specification provides a fault-tolerant control method for multiple unmanned vehicles based on SBC formation, including: The SBC formation dynamics model of the unmanned vehicle formation system is determined; and external disturbances are introduced to perform Jacobi linearization on the SBC formation dynamics model to obtain a linearized dynamic model of formation error including external disturbances. Based on the failure types of actuators in unmanned vehicle platooning systems, an unmanned vehicle failure model is constructed. Based on the formation error state and control input error of the linearized dynamic model of the formation error, a state feedback fault-tolerant control law for the unmanned vehicle formation system is designed. Based on the linearized dynamic model of the formation error, combined with the unmanned vehicle fault model and the state feedback fault-tolerant control law, a closed-loop system is obtained; based on Lyapunov stability theory and The performance criteria are used to design the state feedback of the unmanned vehicle platooning system. By solving a set of convex optimization problems represented by linear matrix inequalities, the controller gain matrix of the closed-loop system is obtained, thereby realizing fault-tolerant control of multiple unmanned vehicle platoons.

[0010] Furthermore, the construction of the SBC formation dynamics model includes: Based on the poses of the navigating and following unmanned vehicles, the relative positional relationship between the navigating and following unmanned vehicles is obtained by introducing the SBC formation state vector. A kinematic model of a differential-driven unmanned vehicle is constructed based on the vehicle's linear velocity and angular velocity. Based on the relative positional relationships and kinematic equations, the time derivative of the SBC formation state is obtained to obtain the SBC formation dynamic model; The pose of the navigating unmanned vehicle is represented as follows: ; The pose of the following unmanned vehicle is represented as: ; in, The position of the navigating unmanned vehicle in the inertial coordinate system; The heading angle for navigating the autonomous vehicle; To determine the position of the autonomous vehicle in the inertial coordinate system; To follow the heading angle of the autonomous vehicle; The relative positional relationship is expressed as follows: ; in, The relative distance between the following driverless car and the lead driverless car; The angle between the speed direction of the navigating unmanned vehicle and the line connecting the two vehicles; This is the difference in heading angle between the two vehicles; The kinematic model of the differential-driven unmanned vehicle is expressed as follows: in, The linear velocity of the vehicle; Angular velocity; The SBC formation dynamics model is expressed as follows: in, For control inputs to follow the driverless vehicle; These are the speed and angular velocity of the pilot autonomous vehicle, respectively. This is the offset distance of the navigation reference point relative to the center of the vehicle.

[0011] Furthermore, the SBC formation dynamics model is Jacobi linearized, including: For a fixed formation, define the desired formation state. and the corresponding desired control input ; Based on the SBC formation dynamics model and the desired formation state, the formation error state is obtained; Based on the SBC formation dynamics model and the desired control input, the control input error is obtained; In the expected trajectory Jacobian linearization is performed at the point to obtain a linear dynamic model of the formation error; The formation error state is represented as follows: in, The relative distance between the following vehicle and the lead vehicle; The angle between the speed direction of the lead vehicle and the line connecting the two vehicles; The difference in heading angle between the two vehicles The expected relative distance between the following vehicle and the lead vehicle; The desired angle between the speed direction of the lead vehicle and the line connecting the two vehicles; This is the difference in the expected heading angles of the two vehicles; The control input error is expressed as: in, For control inputs to follow the driverless vehicle; For the desired control input; To control input error; The linear dynamic model of formation error is expressed as follows: in, A Represents the linearized system matrix; B Represents the input matrix; Represented as an interference distribution matrix; Indicates external interference; The linearized system matrix is ​​represented as follows: The input matrix is ​​represented as: .

[0012] Furthermore, the fault types of the unmanned vehicle actuator include: The drive motor, which provides forward / reverse power, exhibits a malfunction characterized by reduced output torque. Steering motor / servo motor is used to control the steering angle. Faults manifest as slow response speed and insufficient torque. The battery system, which provides power, exhibits a malfunction characterized by a drop in voltage, leading to a decrease in overall performance. The transmission system, used for power transmission, exhibits a malfunction characterized by reduced transmission efficiency due to wear.

[0013] Furthermore, the construction of an unmanned vehicle fault model based on the fault types of the unmanned vehicle actuators includes: Based on the fault types of actuators in unmanned vehicles, an actuator fault matrix is ​​defined. Based on the defined actuator fault matrix, a fault model for autonomous vehicles is constructed. The actual control input of the unmanned vehicle fault model is expressed as: in, The fault matrix is ​​diagonal; For linear velocity actuator efficiency; For angular velocity actuator efficiency; This is the nominal fault matrix; This represents the boundary of the fault uncertainty. These are the upper and lower bounds of the fault determined based on the hardware specifications and historical data of the autonomous vehicle. To account for the uncertainty of actual faults, the constraints must be satisfied. .

[0014] Furthermore, the closed-loop system is represented as: in, A Represents the linearized system matrix; B Represents the input matrix; Represented as an interference distribution matrix; Indicates external interference; This represents a state feedback fault-tolerant control law; Represents the gain matrix of the fault-tolerant controller; Indicates the formation error status; Describe the closed-loop system matrix ,but: in, The term represents the impact of fault uncertainty on the system. This indicates the impact of external interference; The state feedback fault-tolerant control law is expressed as: .

[0015] Furthermore, the process of obtaining the controller gain matrix by solving a set of convex optimization problems represented by linear matrix inequalities includes: Construct a quadratic Lyapunov function, represented as: in, Let be the positive definite matrix to be found; The time derivative of the quadratic Lyapunov function, when substituted into the closed-loop system, is expressed as: To ensure the robustness of the formation system to external interference and measurement noise, the following is introduced: Performance metrics; Define performance output: in, For the performance output matrix, it is usually taken as This indicates that attention is being paid to errors in all states; Performance requirements for closed-loop systems from interference To performance output The energy gain is less than a given threshold. : Equivalent to the pointwise time inequality: Furthermore, the controller gain matrix is ​​expressed as: ; in, Represents the gain matrix; Represents the gain matrix K With matrix Q The product; Q Let represent the inverse of the positive definite matrix to be found.

[0016] Furthermore, the design of the state feedback device for the unmanned vehicle platooning system includes: Based on Lyapunov stability theory and The performance criteria yield a matrix inequality that enables the closed-loop system to remain asymptotically stable under a preset disturbance and satisfies a preset H∞ disturbance suppression level. The upper bound of the uncertainty term in the matrix inequality is obtained by using the uncertainty upper bound estimation method; and based on Young's inequality, the upper bound of the uncertainty term is obtained by applying the lemma. Based on the upper bound of the uncertainty term, the matrix inequalities are transformed into a set of linear matrix inequalities concerning the Lyapunov matrix and the state feedback controller gain matrix using Schur's complement lemma. By solving the linear matrix inequality, the gain matrix is ​​obtained, and the design of the state feedback controller is completed. The uncertainty term is expressed as: ; The upper bound of the uncertainty term is expressed as: in, Let be any scalar, and ; Let be the positive definite matrix to be found; B The input matrix; This represents the boundary of the fault uncertainty. Represents the gain matrix of the fault-tolerant controller; This indicates the formation error status.

[0017] Furthermore, the construction of the linear matrix inequalities concerning the Lyapunov matrix and the state feedback controller gain matrix specifically includes: Based on the upper bound of uncertainty and Given the conditions, we can obtain: in, Written in matrix form, it can be represented as: Applying Schur's complement lemma and variable substitution ， By left multiplication Right multiplication By repeatedly applying Schur's complement lemma to eliminate quadratic terms, the standard convex optimization LMI form was finally obtained: in, Q represents the inverse of the positive definite matrix to be found. Represents the gain matrix K With matrix Q product The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: In the multi-unmanned vehicle fault-tolerant control method based on SBC formation provided in this specification, the control is achieved by directly using relative measurement parameters (distance). Azimuth , heading angle difference Using state variables, a compact formation model architecture is constructed, and external disturbances are incorporated. Explicitly incorporated into the system dynamics model, and based on Lyapunov stability theory and The performance criteria dictate the design of a passive fault-tolerant control strategy capable of simultaneously addressing actuator failures and external disturbances. This design fundamentally eliminates the system's dependence on the global coordinate system, maintaining precise formation control performance even in GPS-denied environments, while significantly reducing computational complexity and improving real-time response capabilities. Furthermore, by establishing a robust fault model and clearly defining the boundaries of fault uncertainty, the complex stability conditions are transformed into a solvable LMI problem using upper bound estimation methods for uncertainty terms, combined with mathematical tools such as Schur's complement lemma. This approach effectively suppresses fault uncertainty, ensuring reliable formation performance in complex dynamic environments. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0019] Figure 1 This document provides a flowchart illustrating a fault-tolerant control method for multiple unmanned vehicles based on SBC formation. Figure 2This is a schematic diagram comparing the distance error between the fault-free following vehicle 1 and the following vehicle 2 before and after the fault occurred, as provided in this manual. Figure 3 This is a schematic diagram comparing the azimuth angle error of the fault-free following vehicle 1 and the following vehicle 2 before and after the fault occurred, as provided in this manual. Figure 4 This is a schematic diagram comparing the difference in heading angle between the fault-free following vehicle 1 and the following vehicle 2 before and after the fault occurred, as provided in this manual. Figure 5 This is a schematic diagram comparing the state error norms of the fault-free following vehicle 1 and the following vehicle 2 before and after the fault occurred, as provided in this manual. Figure 6 This is a schematic diagram comparing the actuator efficiency of the fault-free following vehicle 1 and the following vehicle 2 before and after the fault, as provided in this manual. Figure 7 This is a schematic diagram comparing the linear speed commands of the fault-free following vehicle 1 and the following vehicle 2 before and after the fault occurred, as provided in this manual. Figure 8 This is a schematic diagram comparing the angular velocity commands of the fault-free following vehicle 1 and the following vehicle 2 before and after the fault occurred, as provided in this manual. Figure 9 This is a schematic diagram of the three-vehicle formation trajectory provided in this manual; Figure 10 This is a three-dimensional spatiotemporal schematic diagram of the three-vehicle formation trajectory provided in this manual. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0021] Existing formation fault-tolerant control technologies face two critical technical challenges that urgently need to be addressed. First, existing technologies generally employ state-space models based on a global coordinate system, making their control algorithms heavily reliant on state information within this global coordinate system. This dependence leads to fundamental limitations in GPS-denied environments: on the one hand, solutions using absolute positioning systems like GPS fail completely when signals are missing; on the other hand, even solutions employing relative measurement information to global coordinates introduce significant model redundancy and computational burden due to the complex coordinate transformation process. Simultaneously, sensor noise and motion estimation errors accumulate, causing global coordinate system drift and formation distortion. This architectural flaw severely restricts the feasibility of system applications in GPS-denied environments such as indoor spaces, canyons, or urban canyons. Second, because autonomous vehicles often operate in complex terrain and dynamic environments, they are continuously subjected to unknown external disturbances due to factors such as changes in ground adhesion, slope undulations, and wind interference. Furthermore, actuator failures (such as motor performance degradation and battery voltage drops) are sudden and uncertain, further increasing the difficulty of control.

[0022] In practice, the unmanned vehicle platooning system organically combines the lead vehicle and the following vehicles through distributed communication. Each following vehicle uses sensors to acquire relative distance and azimuth information with the lead vehicle, transforming the platooning fault-tolerant control problem into a robust tracking control problem of relative pose. Based on SBC platooning modeling technology, nonlinear platooning dynamics can be linearized, and then a linear system control strategy can be adopted to effectively adjust the platooning error state, ensuring precise formation maintenance.

[0023] Autonomous vehicle platooning systems typically employ differential drive or Ackerman steering. Essentially, vehicle motion control is achieved by controlling the left and right wheel speeds or steering angles and drive speeds. Autonomous vehicle platooning control usually uses a lead-follow mode, where the lead vehicle tracks the desired global trajectory, and the follower vehicles maintain the platoon formation by maintaining their relative distance and azimuth angle from the lead vehicle.

[0024] Based on this, a fault-tolerant control algorithm combining SBC formation modeling is proposed. The fault-tolerant controller is designed directly on the SBC formation error state space, avoiding complex global coordinate system transformations. The algorithm pre-considers the uncertainty of actuator failures and the impact of external disturbances in the controller design, constructing a passive fault-tolerant mechanism that eliminates the need for fault detection and diagnosis, thereby improving formation accuracy. Furthermore, it introduces… Robust control theory ensures that the system still has deterministic anti-interference and fault-tolerant performance when the actuator fails, thereby maintaining the stability and reliability of the formation under various complex working conditions.

[0025] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0026] Figure 1 This is a flowchart illustrating a multi-unmanned vehicle fault-tolerant control method based on SBC formation as described in this specification, which specifically includes the following steps: S101: Establish the SBC formation model.

[0027] 1) Define the formation geometry Define the pilot vehicle The position is ,in Let this be the vehicle's position (in meters) in the inertial coordinate system. Heading angle (rad). Following vehicle The position is .

[0028] Introducing SBC formation state vectors to describe relative positional relationships: in: The relative distance (m) between the following vehicle and the lead vehicle. The angle (in rad) between the direction of the lead vehicle's speed and the line connecting the two vehicles. The difference in heading angle between the two vehicles （ ）， Given the pose of the lead vehicle and the formation state of the SBC, the pose of the following vehicle can be uniquely determined by the combined angle (rad).

[0029] 2) Establish the kinematic model of the unmanned vehicle For a differential-driven autonomous vehicle, the kinematic model is: in The linear velocity of the vehicle (m / s) ω is the angular velocity (rad / s).

[0030] For an Ackerman steering autonomous vehicle, the kinematic model is: in, Wheelbase (m) The value is the front wheel steering angle (rad). This invention uses differential drive as an example for explanation; Ackermann steering can be derived similarly.

[0031] 3) Deriving the SBC formation dynamics Based on geometric relationships and kinematic equations, the time derivative of the SBC formation state is calculated to obtain the formation dynamics model: in, For the control input of the following vehicle, For the speed and angular velocity of the lead car, The offset distance (m) of the navigation reference point relative to the center of the vehicle.

[0032] 4) Linearization model of formation error For a fixed formation, define the desired formation state. and the corresponding desired control input .

[0033] Define formation error state: Controlling input error: In the expected trajectory By performing Jacobi linearization, we obtain the linear dynamic model of the formation error: The linearized system matrix is: The input matrix is: The interference distribution matrix is... This indicates external interference (such as uneven ground, wind disturbance, measurement noise, etc.).

[0034] S102: Fault model of unmanned vehicle actuators.

[0035] This step involves mathematical modeling of the faults in the drive actuators of unmanned vehicles, providing a theoretical basis for the design of fault-tolerant controllers.

[0036] 1) Fault type analysis The drive system of an autonomous vehicle mainly includes: Drive motor: provides forward / reverse power; a fault manifests as reduced output torque. Steering motor / servo motor: controls the steering angle; malfunctions manifest as slow response speed and insufficient torque. Battery system: A drop in supply voltage leads to a decrease in overall performance; Transmission system: Wear leads to reduced transmission efficiency.

[0037] These faults share the common characteristic of causing the actual control output to be less than the expected control output, which can be uniformly modeled as a reduction in actuator efficiency.

[0038] 2) Mathematical model of actuator failure In autonomous vehicle platooning systems, drive actuators may experience reduced efficiency or partial failure. Define an actuator fault matrix. The actual control input is:

[0039] in The fault matrix is ​​diagonal. For linear velocity actuator efficiency, The efficiency of the angular velocity actuator. For the nominal fault matrix, For the boundary of fault uncertainty, These are the upper and lower bounds of the fault determined based on the hardware specifications and historical data of the autonomous vehicle. To account for the uncertainty of actual faults, the constraints must be satisfied. .

[0040] 3) Dynamics of closed-loop systems with faults Design state feedback fault-tolerant control law: in The gain matrix of the fault-tolerant controller needs to be solved using LMI.

[0041] Substituting the control law (11) and the fault model (10) into the system dynamics (7), we obtain the closed-loop system: Describe the closed-loop system matrix ,but: in The term represents the impact of fault uncertainty on the system. This indicates the impact of external interference.

[0042] S103: LMI-based Fault-tolerant controller design.

[0043] This step involves solving the linear matrix inequality (LMI) to design a robust controller that simultaneously satisfies stability, fault tolerance, and anti-interference requirements.

[0044] 1) Lyapunov stability analysis Define candidate quadratic Lyapunov functions: in Let be the positive definite matrix to be determined.

[0045] Substituting the time derivative of the Lyapunov function into the closed-loop system (12), we obtain: 2) Anti-interference performance criteria To ensure the robustness of the formation system to external interference and measurement noise, the following is introduced: Performance metrics. Define performance output:

[0046] in For the performance output matrix, it is usually taken as This indicates that attention is paid to all state errors.

[0047] Performance requirements for closed-loop systems from interference To performance output The energy gain is less than a given threshold. : Equivalent to pointwise time inequalities 3) Robust handling of fault uncertainty The key lies in handling uncertainties: Lemma (Young's Inequality): For any scalar ， because It can be decomposed into ,in For an unknown matrix to satisfy .

[0048] Applying the lemma, let , Thus, the upper bound of the uncertainty term is obtained: 4) Derivation of LMI and Schur's supplementary lemma Substituting the upper bound of uncertainty (21) into Condition (18), rearranged, yields: in: Written in matrix form: Applying Schur's complement lemma and variable substitution ， By left multiplication Right multiplication By repeatedly applying Schur's complement lemma to eliminate quadratic terms, the standard convex optimization LMI form was finally obtained: in: Additional constraints: 5) Controller gain calculation The optimal solution is obtained by solving LMI(25)-(27) using the LMI toolbox in MATLAB.

[0049] The gain matrix of the fault-tolerant controller is: To date, a fault-tolerant controller based on the SBC formation model has been designed that can overcome the limitations of global coordinate system dependence and effectively handle the coupling effect of disturbance and fault.

[0050] Theorem: For the fault-tolerant control system of unmanned vehicles based on the range-azimuth (SBC) formation model, its dynamics are described by formula (7), where the actuator fault model is defined by formula (10). A state feedback controller is designed (formula 11), and the performance output is defined (formula 16). If a symmetric positive definite matrix exists... and scalar If the linear matrix inequality (LMI) condition (Equation 25) holds, then the closed-loop fault-tolerant control system is asymptotically stable and satisfies the following conditions. Performance indicators This enables the stable maintenance of formation and provides a definite resistance to interference.

[0051] Proof: The proof consists of two steps. The first step uses the uncertainty upper bound lemma to perform a scaling estimate of the uncertainty of actuator faults, transforming the nonlinear fault terms into a tractable linear matrix inequality form. The second step proves that when the LMI condition is satisfied, the system possesses asymptotic stability and performance.

[0052] Step 1: Scaling estimation of uncertain faults System closed-loop dynamics: Among them, the uncertainty term Characterize the bias effect of actuator failure. Define candidate Lyapunov functions. Its time derivative is:

[0053] Let the uncertainty term Based on the constraints of the fault model It can be represented as ,in Applying Lemma 1: For any scalar ,have

[0054] make , Then the uncertainty term satisfies the upper bound: This scaling transforms the nonlinear fault uncertainty into a quadratic upper bound, laying the foundation for the derivation of LMI.

[0055] Step 2: LMI conditions are met Performance and stability Substituting the upper bound of uncertainty Performance Criteria: Organize into matrix form: in If LMI conditions If it is established, then it applies to all ,have under zero initial conditions Integral: This indicates that the system satisfies Performance indicators At the same time, by Derivable (Through Schur's supplementary lemma), combined with The system asymptotically stabilizes. Finally, the LMI transformation can convert the nonlinear problem into a convex optimization solvable form, ensuring the controller gain... The existence of.

[0056] Based on this, the embodiments in this specification rely on, for example Figure 9 and Figure 10 The three-vehicle triangular formation system shown is based on an SBC formation simulation model built according to the actual physical parameters of unmanned vehicles. The implementation process of the present invention is demonstrated in detail, and simulation results of system performance and fault tolerance performance are provided to better understand the actual effect of the algorithm of the present invention.

[0057] Step 1: Setting parameters for the unmanned vehicle platooning system.

[0058] The formation adopts a navigator-follower structure, with an equilateral triangle geometry and a base distance. Navigator vehicle baseline speed angular velocity The expected distance between following vehicle 1 and the lead vehicle. azimuth Heading angle difference The expected distance between follower vehicle 2 and the lead vehicle azimuth Heading angle difference Reference point offset distance Considering actuator saturation limitations, the maximum linear velocity is set. Maximum angular velocity .

[0059] Step 2: Selection of reference trajectory and initial values.

[0060] The reference trajectory equation is The trajectory is a circle with center at (10, 0) and radius 10m. (Initial position of the navigator vehicle) x=10m, y=0m ;like Figure 2 , Figure 3 , Figure 4 , Figure 5 The initial state errors of following vehicle 1 are: distance error 0.40m, azimuth error 0.15rad, and heading angle difference error 0.10rad; the initial state errors of following vehicle 2 are: distance error 0.40m, azimuth error 0.15rad, and heading angle difference error 0.035rad.

[0061] Step 3: Actuator fault model design and fault-tolerant controller.

[0062] The actuator of vehicle 1 is normal, therefore the fault matrix is ​​as follows: The following vehicle 2 later exhibited a serious actuator failure; the upper bound of the fault matrix was set to... The lower bound is Nominal Fault Matrix Upper bound of fault uncertainty Actual Fault Matrix This indicates that the linear velocity and angular velocity actuators have failed to achieve 30% and 25% efficiency, respectively. Figure 6 , Figure 7 and Figure 8 As shown. The fault injection time is... Simulates sudden actuator failure.

[0063] The fault-tolerant controller is designed using the LMI optimization method, and the following settings are made: Performance indicators To balance robustness and performance controller gain; by solving the LMI problem, the following is obtained: , .

[0064] Step 4: External disturbances and simulation settings.

[0065] The disturbance model is selected as Simulation of continuous external disturbances. Simulation parameter settings: sampling time. Total duration .

[0066] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: 1. Eliminate global coordinate system dependency to improve environmental adaptability and computational efficiency. This invention establishes a SBC (range-azimuth-heading angle difference) formation model, directly using relative measurement parameters as system state variables, fundamentally eliminating the dependence on a global coordinate system. This design brings three significant advantages:

[0067] (1) Reliable operation capability in GPS denied environment: In scenarios where GPS signals are limited, such as tunnels, indoors, and urban canyons, the system can complete formation control by directly acquiring relative measurement information from vehicle-mounted sensors (LiDAR, vision sensors), without the need for a global positioning source, thus solving the system failure problem in the case of positioning failure in existing technologies.

[0068] (2) Significantly improved computational efficiency: The transformation from relative measurement to global coordinates is eliminated, avoiding complex coordinate transformation matrix operations and multiple trigonometric function calculations. Compared with the existing technology that requires a two-step process of coordinate transformation before error calculation, the SBC model of this invention can directly calculate the formation error based on sensor measurements, reducing intermediate calculation steps, lowering computational complexity, improving real-time response capability, and making it more suitable for embedded control systems with limited computing power.

[0069] (3) Eliminating cumulative errors and coordinate drift: In the long-term operation of existing technologies, the transformation from relative to global coordinates will have a cumulative effect due to sensor noise and motion estimation errors, resulting in gradual drift of the global coordinate system and distortion of the formation. The present invention directly implements closed-loop control in the relative coordinate system. The formation state variables (distance, angle) are all directly measurable parameters. From the control structure, the cumulative error propagation path is avoided, which is conducive to maintaining the formation accuracy during long-term operation.

[0070] 2. Robust performance under disturbance and fault coupling This invention will external disturbance Explicit modeling is an independent input to the system dynamics, and through... The performance criteria establish energy gain constraints from disturbance to performance output, realizing a unified design framework for disturbance suppression and fault tolerance. This design produces the following key effects:

[0071] (1) Systematic treatment of disturbance-fault coupling effect: In real-world scenarios, when external disturbances such as changes in ground adhesion, slope undulations, and crosswind interference act simultaneously with actuator efficiency reduction (fault), complex coupled dynamic effects will occur. This invention considers both fault uncertainty and disturbance terms in Lyapunov stability analysis and solves the integrated design control gain using LMI. This ensures that the closed-loop system can simultaneously handle two types of disturbances, preventing performance trade-offs that arise when dealing with faults or disturbances individually.

[0072] (2) Quantitative guarantee of anti-interference performance: index It provides a clear measure of the system's disturbance rejection performance—the amplification factor of formation error from any energy-bounded disturbance does not exceed [a certain value]. This makes control performance predictable and verifiable. Compared to existing technologies that lack quantifiable disturbance rejection metrics, this invention allows for adjustments during the design phase. The value clearly defines the performance boundary of the system under the expected disturbance intensity, providing a theoretical basis for engineering applications.

[0073] (3) Enhanced adaptability to dynamic environments: Under complex working conditions such as slopes, slippery roads, and strong winds, The control law can adaptively adjust the control response according to the spectral characteristics of the disturbance, suppressing the impact of the disturbance on the formation accuracy while ensuring stability. Especially under the harsh conditions of simultaneous actuator failure and environmental disturbance, the system can still maintain the basic stability of the formation, while existing technologies, due to the lack of consideration for disturbance-fault coupling, are prone to rapid performance degradation or even instability under such combined conditions.

[0074] 3. Reduce hardware costs Eliminating global coordinate system dependency eliminates the need for high-precision GPS / RTK equipment, allowing the use of low-cost vehicle-mounted sensors (LiDAR, vision sensors, ultrasonic sensors, etc.) for formation control, which is expected to reduce the hardware configuration cost per vehicle.

[0075] 4. Improve operational reliability The fault-tolerant design enables the system to maintain platoon operation even in the event of partial actuator failure (reduced efficiency), avoiding the immediate shutdown of the entire platoon due to minor faults in a single vehicle, reducing the frequency of emergency maintenance and unplanned downtime, and improving the overall operational continuity of the fleet.

[0076] 5. Expand application scenarios GPS rejection capability enables the system to be applied to scenarios that are difficult to cover with traditional solutions, such as mines, underground warehouses, long tunnels, and indoor parks, thus expanding the boundaries of technology applications and market space.

[0077] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A fault-tolerant control method for multiple unmanned vehicles based on SBC formation, characterized in that, include: Determine the SBC formation dynamics model for the unmanned vehicle formation system; Furthermore, external disturbances are introduced, and the SBC formation dynamics model is Jacobi linearized to obtain a formation error linearized dynamic model that includes external disturbances. Based on the failure types of actuators in unmanned vehicle platooning systems, an unmanned vehicle failure model is constructed. Based on the formation error state and control input error of the linearized dynamic model of the formation error, a state feedback fault-tolerant control law for the unmanned vehicle formation system is designed. Based on the linearized dynamic model of the formation error, combined with the unmanned vehicle fault model and the state feedback fault-tolerant control law, a closed-loop system is obtained; based on Lyapunov stability theory and The performance criteria are used to design the state feedback of the unmanned vehicle platooning system. By solving a set of convex optimization problems represented by linear matrix inequalities, the controller gain matrix of the closed-loop system is obtained, thereby realizing fault-tolerant control of multiple unmanned vehicle platoons.

2. The fault-tolerant control method for multiple unmanned vehicles based on SBC formation as described in claim 1, characterized in that, The construction of the SBC formation dynamics model includes: Based on the poses of the navigating and following unmanned vehicles, the relative positional relationship between the navigating and following unmanned vehicles is obtained by introducing the SBC formation state vector. A kinematic model of a differential-driven unmanned vehicle is constructed based on the vehicle's linear velocity and angular velocity. Based on the relative positional relationships and kinematic equations, the time derivative of the SBC formation state is obtained to obtain the SBC formation dynamic model; The pose of the navigating unmanned vehicle is represented as follows: ; The pose of the following unmanned vehicle is represented as: ; in, The position of the navigating unmanned vehicle in the inertial coordinate system; The heading angle for navigating the autonomous vehicle; To determine the position of the autonomous vehicle in the inertial coordinate system; To follow the heading angle of the autonomous vehicle; The relative positional relationship is expressed as follows: ; in, The relative distance between the following driverless car and the lead driverless car; The angle between the speed direction of the navigating unmanned vehicle and the line connecting the two vehicles; This is the difference in heading angle between the two vehicles; The kinematic model of the differential-driven unmanned vehicle is expressed as follows: in, The linear velocity of the vehicle; Angular velocity; The SBC formation dynamics model is expressed as follows: in, For control inputs to follow the driverless vehicle; These are the speed and angular velocity of the pilot autonomous vehicle, respectively. This is the offset distance of the navigation reference point relative to the center of the vehicle.

3. The fault-tolerant control method for multiple unmanned vehicles based on SBC formation as described in claim 1, characterized in that, The SBC formation dynamics model is Jacobi linearized, including: For a fixed formation, define the desired formation state. and the corresponding desired control input ; Based on the SBC formation dynamics model and the desired formation state, the formation error state is obtained; Based on the SBC formation dynamics model and the desired control input, the control input error is obtained; In the expected trajectory Jacobian linearization is performed at the point to obtain a linear dynamic model of the formation error; The formation error state is represented as follows: in, The relative distance between the following vehicle and the lead vehicle; The angle between the speed direction of the lead vehicle and the line connecting the two vehicles; The difference in heading angle between the two vehicles The expected relative distance between the following vehicle and the lead vehicle; The desired angle between the speed direction of the lead vehicle and the line connecting the two vehicles; This is the difference in the expected heading angles of the two vehicles; The control input error is expressed as: in, For control inputs to follow the driverless vehicle; For the desired control input; To control input error; The linear dynamic model of formation error is expressed as follows: in, A Represents the linearized system matrix; B Represents the input matrix; Represented as an interference distribution matrix; Indicates external interference; The linearized system matrix is ​​represented as follows: The input matrix is ​​represented as: 。 4. The fault-tolerant control method for multiple unmanned vehicles based on SBC formation as described in claim 1, characterized in that, The failure types of the actuators in the unmanned vehicle platooning system include: The drive motor, which provides forward / reverse power, exhibits a malfunction characterized by reduced output torque. Steering motor / servo motor is used to control the steering angle. Faults manifest as slow response speed and insufficient torque. The battery system, which provides power, exhibits a malfunction characterized by a drop in voltage, leading to a decrease in overall performance. The transmission system, used for power transmission, exhibits a malfunction characterized by reduced transmission efficiency due to wear.

5. The fault-tolerant control method for multiple unmanned vehicles based on SBC formation as described in claim 1, characterized in that, The construction of the unmanned vehicle fault model includes: Based on the fault types of actuators in unmanned vehicles, an actuator fault matrix is ​​defined. Based on the defined actuator fault matrix, a fault model for autonomous vehicles is constructed. The actual control input of the unmanned vehicle fault model is expressed as: in, The fault matrix is ​​diagonal; For linear velocity actuator efficiency; For angular velocity actuator efficiency; This is the nominal fault matrix; This represents the boundary of the fault uncertainty. These are the upper and lower bounds of the fault determined based on the hardware specifications and historical data of the autonomous vehicle. To account for the uncertainty of actual faults, the constraints must be satisfied. .

6. The fault-tolerant control method for multiple unmanned vehicles based on SBC formation as described in claim 1, characterized in that, The closed-loop system is represented as follows: in, A Represents the linearized system matrix; B Represents the input matrix; Represented as an interference distribution matrix; Indicates external interference; This represents a state feedback fault-tolerant control law; Represents the gain matrix of the fault-tolerant controller; Indicates the formation error status; Describe the closed-loop system matrix ,but: in, The term represents the impact of fault uncertainty on the system. This indicates the impact of external interference; The state feedback fault-tolerant control law is expressed as: 。 7. The fault-tolerant control method for multiple unmanned vehicles based on SBC formation as described in claim 1, characterized in that, The process of obtaining the controller gain matrix of the closed-loop system by solving a set of convex optimization problems represented by linear matrix inequalities includes: Construct a quadratic Lyapunov function, represented as: in, Let be the positive definite matrix to be found; The time derivative of the quadratic Lyapunov function, when substituted into the closed-loop system, is expressed as: To ensure the robustness of the formation system to external interference and measurement noise, the following is introduced: Performance metrics; Define performance output: in, For the performance output matrix, it is usually taken as This indicates a focus on errors in all states; Performance requirements for closed-loop systems from interference To performance output The energy gain is less than a given threshold. : Equivalent to the pointwise time inequality: .

8. The fault-tolerant control method for multiple unmanned vehicles based on SBC formation as described in claim 1, characterized in that, The controller gain matrix is ​​expressed as: ； in, Represents the gain matrix; Represents the gain matrix K With matrix Q The product; Q Let represent the inverse of the positive definite matrix to be found.

9. The fault-tolerant control method for multiple unmanned vehicles based on SBC formation as described in claim 1, characterized in that, The design of the state feedback device for the unmanned vehicle platooning system includes: Based on Lyapunov stability theory and The performance criteria yield a matrix inequality that enables the closed-loop system to remain asymptotically stable under a preset disturbance and satisfies a preset H∞ disturbance suppression level. The upper bound of the uncertainty term in the matrix inequality is obtained by using the uncertainty upper bound estimation method; and based on Young's inequality, the upper bound of the uncertainty term is obtained by applying the lemma. Based on the upper bound of the uncertainty term, the matrix inequalities are transformed into a set of linear matrix inequalities concerning the Lyapunov matrix and the state feedback controller gain matrix using Schur's complement lemma. By solving the linear matrix inequality, the gain matrix is ​​obtained, and the design of the state feedback controller is completed. The uncertainty term is expressed as: ； The upper bound of the uncertainty term is expressed as: in, Let be any scalar, and ; Let be the positive definite matrix to be found; B The input matrix; This represents the boundary of the fault uncertainty. Represents the gain matrix of the fault-tolerant controller; This indicates the formation error status.

10. The fault-tolerant control method for multiple unmanned vehicles based on SBC formation as described in claim 9, characterized in that, The construction of the linear matrix inequalities concerning the Lyapunov matrix and the state feedback controller gain matrix specifically includes: Based on the upper bound of uncertainty and Given the conditions, we can obtain: in, Written in matrix form, it can be represented as: Applying Schur's complement lemma and variable substitution ， By left multiplication Right multiplication By repeatedly applying Schur's complement lemma to eliminate quadratic terms, the standard convex optimization LMI form is finally obtained: in, Q represents the inverse of the positive definite matrix to be found. Represents the gain matrix K With matrix Q product

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