Pre-set performance distributed control method and system for multi-uav formation obstacle avoidance

Abstract

The present application relates to the technical field of unmanned aerial vehicle cooperative control, and proposes a preset performance distributed control method and system for multi-unmanned aerial vehicle formation obstacle avoidance, which comprises constructing a double-integral dynamic model of the multi-unmanned aerial vehicle, and designing a distributed predetermined time observer to accurately estimate the state of the leader. By solving the gradient of the obstacle and inter-vehicle collision potential function, the total obstacle avoidance control input is generated in combination with the gain coefficient determined by the transformation error. Based on the observation value, the tracking error and the reference trajectory are defined to generate the formation shape. In view of the control singularity during obstacle avoidance, a preset performance function containing an obstacle avoidance relaxation amount is designed, the constraint error is mapped into an unconstrained transformation error by using a tangent transformation, and the desired control input is generated accordingly. Finally, a quadratic programming controller is constructed to fuse multiple targets and multiple constraints, and the optimal control input is solved under the constraints of the actuator amplitude and the safety distance. The present application effectively improves the safety and tracking performance of formation obstacle avoidance.

Description

Technical Field

[0001] This invention relates to the field of collaborative control technology for unmanned aerial vehicles (UAVs), and in particular to a pre-defined performance distributed control method and system for obstacle avoidance in multi-UAV formations. Background Technology

[0002] Multi-UAV collaborative systems have significant application value in fields such as search and rescue, and environmental monitoring. In the lead-follow mode, the following UAVs need to acquire the leader's status information to achieve formation tracking. However, most existing distributed observers can only guarantee asymptotic or finite-time convergence, and their convergence time is highly dependent on initial conditions, making it difficult to meet real-time requirements. Although pre-time observers can achieve fixed-time convergence, they often suffer from gain divergence, limiting their engineering practicality. In addition, the traditional artificial potential field method, due to its fixed gain and susceptibility to local minima, often leads to obstacle avoidance failures or conflicts with tracking control commands. While preset performance control methods can force tracking errors to meet transient performance indicators, errors may exceed nominal boundaries during obstacle avoidance, and existing symmetric relaxation strategies can lead to a decrease in tracking accuracy in the safe direction. At the same time, existing technologies lack an effective coordination mechanism for tracking and obstacle avoidance commands, making it difficult to maintain high-precision formation tracking while ensuring flight safety. Summary of the Invention

[0003] To address the aforementioned shortcomings, the present invention aims to propose a distributed control method and system for pre-defined performance obstacle avoidance in multi-UAV formations. The goal is to achieve coordinated and unified pre-defined time state estimation, singular obstacle avoidance control, and high-precision formation tracking for multi-UAV formations in complex environments by constructing a distributed pre-defined time observer and relaxing the pre-defined performance function, combined with a quadratic programming optimization mechanism.

[0004] To achieve this objective, the present invention adopts the following technical solution: A pre-defined performance-based distributed control method for obstacle avoidance in multi-UAV formations includes: A dual-integral dynamic model of a multi-UAV system is constructed to describe the dynamic relationship between the position, velocity and control input vector of each UAV. By utilizing local neighbor node information interaction and a predetermined time adjustment function, a distributed predetermined time observer is designed for accurate estimation of the predetermined time of the navigator's state. The total obstacle avoidance control input is generated by solving the potential field gradient of the obstacle avoidance potential energy function and the inter-machine collision avoidance potential energy function, and combining it with the obstacle avoidance gain adjustment coefficient determined by the transformation error. Based on the estimated values ​​of the distributed predetermined time observer, the tracking error and reference trajectory are defined, and a preset formation for describing the expected flight trajectory of the UAV is generated; By introducing an obstacle avoidance relaxation amount related to the distance to the obstacle through a smoothing function, a relaxation preset performance function is designed to solve the singularity problem of obstacle avoidance control. The tracking error constrained by the relaxed preset performance function is mapped to an unconstrained error using the tangent transform function, so as to design the transform error and generate the preset performance expectation control input. A quadratic programming controller is constructed with the objective of minimizing the deviation between the actual control input and the total obstacle avoidance control input and the preset performance expectation control input. The optimal control input is obtained by solving the problem under the constraints of actuator amplitude and safe distance.

[0005] Preferably, constructing a dual-integral dynamics model for a multi-UAV system includes: For the first in a multi-drone formation For a UAV, a double-integral dynamic model is constructed to describe the dynamic relationship between position, velocity, and control input. The position derivative and velocity derivative of the UAV satisfy the following relationship: ; ; in, Indicates the first The position vector of the drone, Indicates the first The velocity vector of the drone Indicates the first The control input vector of the drone.

[0006] Preferably, a distributed time observer designed for accurate estimation of the navigator's state time, utilizing local neighbor node information exchange and a predetermined time adjustment function, includes: A state observation model is constructed based on the information exchange between local neighbor nodes. Derivative of the position estimate of the navigator observed by the drone With velocity estimation derivative Satisfying the relation: ; ; in, Indicates the first The derivative of the position estimation of the navigator observed by the drone. Indicates the first The estimated speed of the lead aircraft as observed by the drone. , and These represent the preset design gain parameters. This represents the pre-set time adjustment function. This represents the derivative of the predetermined time adjustment function with respect to time. Represents the elements of the communication topology adjacency matrix. and They represent the first frame and the first The estimated position of the navigator observed by the drone. Represents a symbolic function. Indicates the first The estimated speed of the lead aircraft as observed by the drone. Indicates the total number of drones; The predetermined time adjustment function Satisfying the relation: ; in, This represents the pre-set time adjustment function. Indicates the preset convergence time. Indicates the current moment. This represents a preset constant used to avoid numerical singularities.

[0007] Preferably, the process of achieving state estimation convergence by the distributed predetermined time observer includes: An estimation error model is constructed based on the state estimates observed by each UAV and the actual state of the navigator aircraft. The derivative of the global position estimation error is calculated. Derivative of global velocity estimation error The following error derivative relationship must be satisfied: ; ; in, , and These represent the preset design gain parameters. This represents the pre-set time adjustment function. This represents the derivative of the predetermined time adjustment function with respect to time. Represents the Laplace matrix of the communication topology. Indicates the Kronecker product. Represents a 3D identity matrix. This represents the global position estimation error vector. Represents a symbolic function. express A dimensional vector of all 1s This represents the acceleration vector of the navigator. Construct a Lyapunov function to evaluate the convergence properties of the observer. The following relation is satisfied: ; in, Represents the Lyapunov function. This represents the transpose of the global position estimation error vector. This represents the transpose of the global velocity estimation error vector; Based on the convergence characteristics of the predetermined time adjustment function, within the preset convergence time... The derivative of the Lyapunov function. Lyapunov function at the current moment Satisfies the convergence relation: ; Integrating the convergence relation yields the time step. The convergence boundary of the Lyapunov function Satisfying the relation: ; in, Indicates the current time The Lyapunov function value, This represents the initial value of the Lyapunov function. Indicates the current time The predetermined time adjustment function value, This represents the predetermined time adjustment function value at the initial moment.

[0008] Preferably, the total obstacle avoidance control input is generated by solving for the potential field gradients of the obstacle avoidance potential energy function and the inter-machine collision avoidance potential energy function, and combining this with the obstacle avoidance gain adjustment coefficient determined by the transformation error. Regarding the first The drone and the first Given an obstacle, calculate the obstacle collision avoidance potential field gradient used to generate the obstacle avoidance repulsion force. The following relation is satisfied: ; in, This represents the gradient of the potential field for obstacle avoidance. Indicates the first The detection radius of the drone Indicates the first The drone and the first The distance between the obstacles Indicates the first The position vector of the drone, Indicates the first The position vectors of the obstacles; Regarding the first The drone and the adjacent To deploy a drone and calculate the collision avoidance potential field gradient for inter-drone collision avoidance. The following relation is satisfied: ; in, This represents the gradient of the potential field for collision avoidance between machines. Indicates the first The drone and the first The distance between the drones This indicates the safe distance threshold between machines. Indicates the first The position vector of the drone, This represents the preset speed influence coefficient. Indicates the first frame and the first The relative velocity vector between the drones; By weighted and fused together the obstacle avoidance potential field gradient and the inter-machine avoidance potential field gradient, the first... Total obstacle avoidance control input for the drone The following relation is satisfied: ; in, and These represent the preset nominal repulsive force gain. This represents the obstacle avoidance gain adjustment coefficient. Indicates the total number of obstacles. Indicates the relationship with the first A group of drones adjacent to each other; Wherein, the obstacle avoidance gain adjustment coefficient Satisfying the relation: ; in, This indicates the preset adjustment coefficient. Indicates the first The norm of the transformation error of the drone.

[0009] Preferably, the process of defining the tracking error and reference trajectory based on the estimated values ​​of the distributed predetermined time observer, and generating a pre-defined formation to describe the expected flight trajectory of the UAV includes: A reference trajectory is constructed based on the estimates from the distributed predetermined time observer and a preset offset. The following relation is satisfied: ; in, Indicates the reference trajectory. This indicates the output of the distributed predetermined time observer. The estimated position of the navigator observed by the drone. Indicates the first The preset offset of the drone relative to the lead drone; Calculate the first based on the reference trajectory Tracking error of drones The following relation is satisfied: ; in, Indicates tracking error. Indicates the first The actual position vector of the drone.

[0010] Preferably, the relaxed preset performance function designed to address the singularity problem of obstacle avoidance control includes: Based on the initial performance boundary, steady-state performance boundary, and obstacle avoidance relaxation, the first... Relaxed preset performance function of drone The following relation is satisfied: ; in, Indicates the first A drone in The relaxation preset performance function of the dimension, Represents the dimensional coordinates of the drone and , Indicates the initial performance boundary. Represents the steady-state performance boundary. This indicates the preset transition time. This indicates the preset power index. This represents the attenuation rate adjustment coefficient. Indicates the current moment. Indicates the obstacle avoidance slack; The obstacle avoidance slack Satisfying the relation: ; in, Indicates the first control gain. Indicates the second control gain. This represents the Sigmoid smoothing function. Indicates the detection radius threshold. Represents the obstacle's position vector. Indicates the first The position vector of the drone, Indicates the smooth transition coefficient. Represents the hyperbolic tangent function. Represents the absolute value function. Indicates the drone and obstacles in the first... Distance component in direction, Indicates the first Safety distance threshold for direction.

[0011] Preferably, the tracking error constrained by the relaxed preset performance function is mapped to an unconstrained transformation error using a tangent transform function, and a preset performance expectation control input is generated accordingly, including: By using the tangent transform function to perform a nonlinear mapping on the tracking error, a transform error is obtained to eliminate boundary constraint limitations. The following relation is satisfied: ; in, Indicates the first A drone in Dimensional transformation error, Indicates the first A drone in Dimensional tracking error, This indicates that the relaxation preset performance function is in The function value of the dimension; Based on the transformation error, a PD-type control law is designed to obtain the preset performance expectation control input for achieving closed-loop regulation. The following relation is satisfied: ; in, This indicates the preset performance expectation control input. The derivative vector of the reference trajectory is in Dimensional components, This indicates the preset proportional gain. This represents the preset differential gain. This represents the derivative of the transformation error with respect to time.

[0012] Preferably, a quadratic programming controller integrating multiple objectives and multiple constraints is constructed, and the optimal control input is obtained by solving for the actuator amplitude and safety distance constraints, including: Optimal control input Satisfying the relation: ; in, Indicates the first The optimal control input to be solved for the unmanned aerial vehicle (UAV) This indicates the overall obstacle avoidance control input. This indicates the preset energy consumption penalty weight. This indicates the preset performance control weights. This indicates the preset performance expectation control input; Optimal control input The following set of constraints must be satisfied: ; ; ; in, and These represent the lower and upper limits of the control input amplitude constraints for the actuator, respectively. Indicates the first The position vector of the drone, Indicates the first The position vectors of the obstacles This indicates the preset safe distance between the drone and the obstacle. and These represent the preset lower and upper limits of the safe distance between machines, respectively. Indicates the first The position vector of the drone.

[0013] A pre-defined performance distributed control system for obstacle avoidance in multi-drone formations includes: The dynamic modeling module is used to build a dual-integral dynamic model of a multi-UAV system, which describes the dynamic relationship between the position, velocity and control input vector of each UAV. The state observation module is used to design a distributed predetermined time observer for accurate estimation of the navigator's state predetermined time by utilizing local neighbor node information interaction and a predetermined time adjustment function. The obstacle avoidance guidance module is used to generate the total obstacle avoidance control input by solving the potential field gradient between the obstacle avoidance potential energy function and the inter-machine avoidance potential energy function, and combining it with the obstacle avoidance gain adjustment coefficient determined by the transformation error. The formation generation module is used to define the tracking error and reference trajectory based on the estimated value of the distributed predetermined time observer, and generate a preset formation to describe the expected flight trajectory of the UAV. The performance relaxation module is used to introduce obstacle avoidance relaxation amount related to the distance to the obstacle through a smoothing function, and is designed to solve the problem of obstacle avoidance control singularity by using a relaxation preset performance function. The error transformation module is used to map the tracking error constrained by the relaxed preset performance function into an unconstrained error using the tangent transformation function, so as to design the transformation error and generate the preset performance expectation control input. The optimal control module is used to construct a quadratic programming controller with the objective of minimizing the deviation between the actual control input and the total obstacle avoidance control input and the preset performance expectation control input, and to solve for the optimal control input under the constraints of actuator amplitude and safety distance.

[0014] One of the above technical solutions has the following advantages or beneficial effects: This invention provides a foundation for subsequent control design by constructing a dual-integral dynamic model. A distributed, predetermined-time observer is then designed, utilizing local neighbor information interaction and a predetermined-time adjustment function to achieve rapid and accurate estimation of the navigator's state, overcoming the limitation of traditional observers where convergence time depends on initial conditions. By solving for the gradient of the obstacle and inter-aircraft collision avoidance potential energy functions and introducing a gain coefficient adjusted by the transformation error to generate the total obstacle avoidance control input, dual safety assurance of adaptive obstacle avoidance and collision prevention is achieved. Subsequently, tracking error and reference trajectory are defined to generate formation, and a relaxation preset performance function containing obstacle avoidance relaxation is designed. Combined with tangent transformation, constrained errors are mapped to unconstrained errors, effectively solving the singularity problem in obstacle avoidance control and ensuring a smooth transition of control input. Based on the transformation error, a preset performance expectation control input is designed, and finally, a quadratic programming controller integrating obstacle avoidance, tracking, and energy consumption optimization is constructed to solve for optimal control under multiple constraints such as actuator amplitude and safe distance. In summary, this invention achieves rapid convergence of state estimation, optimized coordination of obstacle avoidance and tracking commands, and comprehensive satisfaction of multi-objective constraints, significantly improving the control accuracy, safety, and engineering practicality of multi-UAV formations in complex environments. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0016] Figure 1 This is a flowchart of a pre-defined performance distributed control method for obstacle avoidance in multi-UAV formations provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the pre-defined performance distributed control system for obstacle avoidance in multi-UAV formations provided in an embodiment of the present invention. Detailed Implementation

[0017] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0018] In this invention, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0019] Pre-defined performance distributed control methods for obstacle avoidance in multi-UAV formations, such as... Figure 1 As shown, a preferred embodiment of the present invention includes the following steps: S1: Construct a dual-integral dynamic model for a multi-UAV system to describe the dynamic relationship between the position, velocity and control input vector of each UAV; It should be noted that a multi-UAV system refers to a collaborative flight swarm composed of multiple UAVs, each acting as an intelligent agent interconnected via a communication topology. The dual-integral dynamics model is a classic method for describing dynamics, decomposing the UAV's motion state into two integral components: a position vector and a velocity vector. The derivative of the position vector equals the velocity vector, and the derivative of the velocity vector equals the control input vector. This model is established in three-dimensional space and can accurately describe the UAV's translational motion characteristics in the X, Y, and Z dimensions. The control input vector can represent the acceleration or equivalent force input generated by the UAV. This model allows for the establishment of a complete mapping relationship from control commands to motion states, providing a mathematical foundation for subsequent state observation and controller design.

[0020] Understandably, in multi-UAV formation control, an accurate dynamic model is a prerequisite for achieving cooperative control. By constructing a dual-integral dynamic model, the complex UAV flight dynamics can be simplified into a chain relationship of position-velocity-acceleration. This simplification retains the key dynamic characteristics required for control design while reducing the complexity of observer and controller design. Step S1, by establishing a standardized mathematical description, enables the motion states of each UAV to be uniformly modeled and predicted, providing a consistent analytical framework for distributed control algorithms, thereby ensuring the reliability and feasibility of the formation control strategy.

[0021] S2: Utilizing local neighbor node information interaction and a predetermined time adjustment function, a distributed predetermined time observer is designed for accurate estimation of the navigator's state predetermined time. It should be noted that local neighbor node information interaction refers to the UAV exchanging state information only with neighboring UAVs within its communication range, without relying on global communication or a central node. This distributed architecture conforms to the communication constraints of large-scale formations. The predetermined time adjustment function is a special time function whose value changes over time and converges to a minimum constant according to a preset rule. It can be in piecewise form, decreasing quadratically in the initial stage and maintaining a constant small value after reaching the preset time. The distributed predetermined time observer is a state estimation device. Each following UAV uses the observation information from its neighbor nodes to estimate the position and velocity of the lead UAV in real time through a specific differential equation structure. The observer's design parameters include the design gain parameter and the predetermined time adjustment function. By properly configuring these parameters, it can be ensured that the estimation error converges to near zero within a preset convergence time.

[0022] Understandably, in the lead-follow formation mode, the following drone cannot directly obtain the true state of the lead drone and must reconstruct the lead information through estimation. Step S2, by designing a distributed pre-set time observer, can estimate the state of the lead drone using only local neighbor information, avoiding dependence on global communication infrastructure and significantly improving the system's scalability and fault tolerance. The introduction of the pre-set time adjustment function allows the observer's convergence time to be preset, independent of the magnitude of the initial estimation error, a characteristic crucial for the real-time performance of formation control. Simultaneously, through the adaptive variation of the adjustment function, the gain divergence problem common in traditional fixed-time observers can be effectively suppressed, ensuring that the observer maintains a stable and finite gain level throughout the entire operating period, enhancing engineering practicality.

[0023] S3: By solving the potential field gradient of the obstacle avoidance potential energy function and the inter-machine collision avoidance potential energy function, and combining it with the obstacle avoidance gain adjustment coefficient determined by the transformation error, the total obstacle avoidance control input is generated; It should be noted that the obstacle avoidance potential energy function is a mathematical function based on artificial potential field theory. It generates a virtual repulsive force field by defining the distance relationship between the UAV and the obstacle. Its function value increases as the distance decreases, guiding the UAV away from the obstacle. The inter-UAV collision avoidance potential energy function describes the interaction between multiple UAVs. Also based on potential field theory, it generates a repulsive force to avoid inter-UAV collisions by introducing relative distance and relative velocity information. The potential field gradient refers to the partial derivative of the potential energy function with respect to the position vector, representing the direction of the fastest change in the potential field. Moving along the negative gradient direction minimizes the potential energy, corresponding to the direction of obstacle avoidance force generation. The obstacle avoidance gain adjustment coefficient is a weighting factor that varies with the magnitude of the transformation error. It is constructed using a maximum value function and norm operations. When the transformation error is small, the gain is close to 1; when the error exceeds a threshold, the gain linearly decreases to 0, achieving a dynamic trade-off between obstacle avoidance and tracking commands.

[0024] Understandably, obstacle avoidance is the primary constraint during multi-UAV formation flight. Step S3 transforms the obstacle avoidance requirement into specific control input commands by separately solving the gradients of the obstacle and inter-UAV collision avoidance potential energy functions. The obstacle collision avoidance potential energy function generates a repulsive force against static or dynamic obstacles in the environment, ensuring that UAVs maintain a safe distance from obstacles; the inter-UAV collision avoidance potential energy function generates anti-collision forces against adjacent UAVs within the formation, while introducing a velocity influence coefficient to consider relative motion trends and improve the predictability of collision avoidance. By weighted fusion of the two potential field gradients and introducing a gain coefficient adjusted by the transformation error, the obstacle avoidance response can be enhanced when tracking accuracy is high, while the obstacle avoidance weight can be appropriately reduced when tracking error is large to avoid control conflicts. This achieves coordinated optimization of obstacle avoidance and target tracking, ensuring the overall safety of formation flight.

[0025] S4: Based on the estimated value of the distributed predetermined time observer, define the tracking error and reference trajectory, and generate a preset formation to describe the expected flight trajectory of the UAV; It should be noted that the estimated value of the distributed pre-set time observer refers to the navigator's position estimate output by the observer, which converges to the navigator's actual state within a preset time. The reference trajectory is the flight path that the UAV is expected to follow, composed of the navigator's position estimate superimposed with a preset offset. The offset defines the UAV's relative position in the formation, such as the lateral spacing in a wedge formation or the fore-and-aft distance in a longitudinal formation. The tracking error is defined as the difference vector between the UAV's actual position and the reference trajectory, representing the degree of deviation of the current position from the desired position. The preset formation refers to the overall configuration formed by multiple UAVs arranged in a specific geometric pattern, achieved by assigning different offsets to each UAV, such as standard formations like a line, triangle, or diamond.

[0026] Understandably, the core objective of formation control is to enable each following UAV to accurately track a reference trajectory defined by the navigator's state and a preset offset. Step S4 generates a personalized reference trajectory for each UAV by utilizing the navigator's state estimate provided by the observer and combining it with a pre-set formation geometry. The definition of tracking error establishes a quantitative relationship between the actual motion state and the desired state, providing feedback signals for subsequent control law design. By rationally designing the offset, a stable formation can be formed in space, allowing multiple UAVs to maintain a coordinated motion pattern, satisfying both the spatial coverage requirements of the mission and maintaining a safe distance between UAVs. This trajectory generation method based on estimation values ​​allows the following UAVs to complete formation tracking without directly measuring the navigator's state, reducing the requirements for sensor configuration and communication bandwidth.

[0027] S5: By introducing an obstacle avoidance relaxation amount related to the distance to the obstacle through a smoothing function, a relaxation preset performance function is designed to solve the singularity problem of obstacle avoidance control. It should be noted that a smoothing function refers to a transition function with continuous differentiability, commonly including the sigmoid function and the hyperbolic tangent function. Its output smoothly transitions with changes in input values, avoiding abrupt changes. Obstacle avoidance relaxation is a correction term related to the distance between the drone and the obstacle. When the drone approaches the obstacle, this quantity generates a positive value through the smoothing function, expanding the preset performance boundary and providing additional error tolerance for obstacle avoidance operations. The preset performance function is a time-varying boundary function that defines the allowable range of tracking error variation, and can include parameters such as initial boundary, steady-state boundary, and transition time. Control singularity refers to the situation in control law design where the denominator is zero or the function is undefined. In preset performance control, when the tracking error approaches the performance boundary, the transformed error may tend to infinity, causing control input divergence, which is called control singularity. Relaxing the preset performance function by superimposing an obstacle avoidance relaxation on top of the traditional preset performance function allows the performance boundary to be dynamically adjusted according to obstacle avoidance requirements.

[0028] Understandably, traditional preset performance control methods use fixed performance boundaries. When the UAV performs obstacle avoidance maneuvers, the tracking error may temporarily exceed the nominal boundary, leading to singularities in the control law and generating unreasonable control commands. Step S5 introduces an obstacle avoidance relaxation amount related to the obstacle distance and uses a smoothing function to continuously adjust the boundary. This allows the performance boundary to automatically widen in obstacle avoidance scenarios, providing the necessary error space for obstacle avoidance operations, while maintaining strict accuracy constraints in normal tracking scenarios. This relaxation mechanism is activated only when approaching an obstacle, achieving spatial orientation of boundary adjustment through distance perception. That is, the boundary is widened only in the direction close to the obstacle, while the original constraints are maintained in other directions. This ensures obstacle avoidance safety while maximizing formation tracking accuracy and avoiding the overall accuracy loss caused by symmetrical widening strategies.

[0029] S6: The tracking error constrained by the relaxed preset performance function is mapped to an unconstrained error using the tangent transform function, so as to design the transform error and generate the preset performance expectation control input. It should be noted that the tangent transform function is a nonlinear mapping function that uses the properties of the tangent function to map variables within a finite interval to the entire real number domain. Its input is the ratio of the tracking error to the performance boundary, and its output is an unbounded variable. The transform error is a new error variable obtained through the tangent transform. When the original tracking error approaches the performance boundary, the transform error tends to infinity. This characteristic makes the controller extremely sensitive to boundary approach behavior, thus forcing the tracking error to remain strictly within the boundary. The preset performance expectation control input is an ideal control command designed based on the transform error. It adopts a proportional-derivative control structure, calculates the required control action based on the transform error and its derivative, and drives the transform error to converge to zero, thereby ensuring that the original tracking error meets the preset performance constraints.

[0030] Understandably, directly applying constrained tracking error to controller design presents mathematical challenges because the error must always remain within time-varying boundaries. Step S6 establishes a mapping from bounded error to unbounded error using the tangent transform function, transforming the constrained control problem into an unconstrained control problem, thus enabling the application of traditional control design methods. The characteristics of the transformed error ensure that as long as the original tracking error does not touch the performance boundary, the transformed error remains finite. However, once it approaches the boundary, the rapid increase in the transformed error drives the controller to generate a strong correction effect, forming a natural barrier to the boundary. Based on the preset performance expectation control input designed using the transformed error, the proportional term provides error correction force, and the derivative term provides damping, achieving accurate tracking of the reference trajectory while strictly ensuring that transient and steady-state performance indicators are met.

[0031] S7: Construct a quadratic programming controller with the objective of minimizing the deviation between the actual control input and the total obstacle avoidance control input and the preset performance expectation control input, and solve for the optimal control input under the constraints of actuator amplitude and safe distance.

[0032] It should be noted that the quadratic programming controller is an optimization controller. It obtains the control input by solving a constrained quadratic objective function minimization problem. The objective function includes multiple weighted squared deviation terms, which respectively measure the difference between the actual control input and obstacle avoidance commands, tracking commands, and control energy consumption. Actuator amplitude constraints refer to the maximum and minimum control input limits that the UAV flight control system can generate, corresponding to the maximum thrust of the motor or the maximum deflection angle of the servo. Safety distance constraints include the minimum distance constraint between the UAV and obstacles, as well as the minimum and maximum distance constraints between UAVs, ensuring flight safety. The optimal control input is the solution to the quadratic programming problem, a control command that minimizes the objective function while satisfying all constraints, and is solved in real-time using a numerical optimization algorithm.

[0033] Understandably, in multi-UAV formation control, obstacle avoidance requirements, tracking accuracy, and energy consumption often conflict, and simple superposition of control commands is insufficient to simultaneously address multiple objectives. Step S7 constructs a quadratic programming optimization framework, incorporating the deviation between the actual control input and the total obstacle avoidance control input, as well as the preset performance expectation control input, into the objective function, and introducing an energy consumption penalty term to achieve coordinated optimization of multiple objectives. Simultaneously, actuator physical limitations and flight safety requirements are incorporated as hard constraints into the optimization problem, ensuring that the solved control input possesses both good tracking and obstacle avoidance performance while meeting engineering feasibility and safety requirements. This optimization-based control allocation method, compared to traditional control command switching or weighted summation methods, can handle constraint boundaries more precisely, finding the globally optimal solution within the feasible region and improving the overall performance of formation control.

[0034] Preferably, constructing a dual-integral dynamics model for a multi-UAV system includes: For the first in a multi-drone formation For a UAV, a double-integral dynamic model is constructed to describe the dynamic relationship between position, velocity, and control input. The position derivative and velocity derivative of the UAV satisfy the following relationship: ; ; in, Indicates the first The position vector of the drone, Indicates the first The velocity vector of the drone Indicates the first The control input vector of the drone.

[0035] It should be noted that the position vector It describes the first The mathematical vector representing the instantaneous coordinates of a UAV relative to a reference coordinate system in three-dimensional space can be expressed as: ,in , , These respectively represent the movement of the UAV in the Earth coordinate system or the local coordinate system. axis, axis, The coordinate components of the axis, this vector is obtained in real time through onboard GPS module or visual positioning system, and is used to determine the absolute position of the UAV in space; velocity vector. It is a mathematical vector describing the rate of change of the UAV's position with respect to time, defined as the first derivative of the position vector with respect to time, i.e. The instantaneous linear velocity of the UAV along each coordinate axis is obtained through differential calculation using an onboard inertial measurement unit (IMU) or GPS; the control input vector... It is a mathematical vector describing the net external force or equivalent acceleration command acting on the UAV, defined as the first derivative of the velocity vector with respect to time, i.e. The flight control system's control allocation algorithm converts the desired acceleration command into motor speed or servo deflection command, and this vector directly determines the UAV's acceleration response; position derivative. It is the instantaneous rate of change of the position vector with respect to time, mathematically related to the velocity vector. Equal, obtained through differential operations or direct measurement by sensors; velocity derivative It is the instantaneous rate of change of the velocity vector with respect to time, mathematically related to the control input vector. Equal values ​​are obtained through accelerometer sensors or control command outputs.

[0036] Understandably, by constructing a dual-integral dynamics model, the motion characteristics of each UAV in a multi-UAV formation can be precisely abstracted into a two-level integral relationship between position and velocity. This provides a solid mathematical foundation for subsequent distributed observer design, control law derivation, and stability analysis. The dual-integral dynamics model is based on a simplified kinematic expression of Newton's second law, treating the UAV as a point mass and ignoring attitude coupling effects. Through the mathematical relationship that the derivative of position equals velocity and the derivative of velocity equals control input, it accurately describes the translational motion of the UAV in three-dimensional space. The dual-integral dynamics model establishes a transmission path from control input to position output through a dual-integral structure, enabling the acceleration command output by the control algorithm to be integrated sequentially to obtain velocity and position changes, achieving a smooth conversion from abstract control quantities to physical motion. This constructs a concise and complete mathematical framework, allowing subsequent control design to be based on deterministic dynamic relationships, ensuring that the UAV can accurately respond to control commands and maintain the stability and accuracy of formation flight. At the same time, the linearity of the dual-integral dynamics model facilitates theoretical analysis and controller parameter tuning, reducing the complexity of multi-UAV cooperative control.

[0037] Preferably, a distributed time observer designed for accurate estimation of the navigator's state time, utilizing local neighbor node information exchange and a predetermined time adjustment function, includes: A state observation model is constructed based on the information exchange between local neighbor nodes. Derivative of the position estimate of the navigator observed by the drone With velocity estimation derivative Satisfying the relation: ; ; in, Indicates the first The derivative of the position estimation of the navigator observed by the drone. Indicates the first The estimated speed of the lead aircraft as observed by the drone. , and These represent the preset design gain parameters. This represents the pre-set time adjustment function. This represents the derivative of the predetermined time adjustment function with respect to time. Represents the elements of the communication topology adjacency matrix. and They represent the first frame and the first The estimated position of the navigator observed by the drone. Represents a symbolic function. Indicates the first The estimated speed of the lead aircraft as observed by the drone. Indicates the total number of drones; The predetermined time adjustment function Satisfying the relation: ; in, This represents the pre-set time adjustment function. Indicates the preset convergence time. Indicates the current moment. This represents a preset minimum constant used to avoid numerical singularities.

[0038] It should be noted that the derivative of the position estimation It is the first The mathematical description of the rate of change of the navigator's position estimate by the UAV over time represents the rate of change of the navigator's position estimate output by the observer. It is obtained through the observer's dynamic equations and includes a velocity estimation term and a neighbor correction term; the velocity estimate... It is the first The estimated vector of the navigator's velocity state from the UAV is obtained through observer integration or sensor fusion and used to predict the navigator's motion trend; gain parameters are designed. , This is a positive constant used to adjust the convergence speed of the observer. It is determined through theoretical analysis and simulation debugging, and its value can range from 1.0 to 5.0. The main factor affecting the convergence rate of location estimation is... The main influence on the convergence rate of velocity estimation; design gain parameters This is the sliding mode gain constant used to enhance the robustness of the observer. It suppresses disturbances by setting a value greater than the upper limit of the navigator's acceleration, and can range from 3.0 to 10.0; a predetermined time adjustment function. It is a time-varying function used to ensure that observation errors converge within a preset fixed time. It is defined in piecewise form. The interval decays according to a quadratic polynomial law. The time remains a minimum constant. This function calculates the current time in real time using a timer. And substitute it into the function expression to obtain; It is the derivative of the predetermined time adjustment function with respect to time, obtained by... To obtain the time derivative, in The interval is negative, providing a time-varying gain adjustment mechanism; communication topology adjacency matrix elements It describes the first frame and the first The constant for the communication connection between the two UAVs is determined by a pre-configured communication topology; it is set to 1 when the two can communicate directly, and 0 otherwise; position estimate. , This is the estimated vector of each UAV's position relative to the navigator, obtained through integration of the observer's dynamic equations. The initial value can be set to zero or a rough estimate; sign function. It is a nonlinear function used to implement sliding mode control, defined as follows: when , when , when The speed estimate is obtained through comparison calculations. This is the estimated speed vector of the navigator from neighboring drones, obtained from neighboring nodes via the communication link; the total number of drones. The number of drones following in the formation is predetermined through mission configuration; the convergence time is preset. It is a fixed time constant for the observer to complete state estimation, which is preset according to the real-time requirements of the task, and its value can range from 3 to 10 seconds; the current time It is a real-time time variable of the system operation, obtained through an onboard clock or synchronization system; constant. It is used to avoid extremely small positive numbers with singular values. Through numerical stability analysis, its range of values ​​can be set to [value range missing]. to .

[0039] It is understandable that by utilizing local neighbor node information interaction and designing a distributed pre-set time observer, the technical problem of the convergence time of traditional distributed observers depending on initial conditions and being impossible to pre-set can be effectively solved. Introducing observer gain design, utilizing time-varying gain coefficients The regulating effect ensures that the observation error is within a preset fixed time. It achieves internal convergence unaffected by the magnitude of the initial estimation error, while utilizing a sign function term to provide sliding mode control characteristics to enhance robustness against navigator acceleration disturbances. The local neighbor information interaction mechanism ensures that each UAV only needs to communicate with neighboring UAVs to collaboratively estimate the navigator's state, eliminating the need for centralized data aggregation. This enables rapid and accurate estimation of UAV states, meeting the stringent real-time requirements of formation control, overcoming the excessive dependence of centralized observers on communication bandwidth and computing resources, and improving the scalability and fault tolerance of large-scale formations. Furthermore, the predetermined time convergence characteristic allows the system convergence time to be preset, facilitating mission planning and real-time scheduling.

[0040] Preferably, the process of achieving state estimation convergence by the distributed predetermined time observer includes: An estimation error model is constructed based on the state estimates observed by each UAV and the actual state of the navigator aircraft. The derivative of the global position estimation error is calculated. Derivative of global velocity estimation error The following error derivative relationship must be satisfied: ; ; in, , and These represent the preset design gain parameters. This represents the pre-set time adjustment function. This represents the derivative of the predetermined time adjustment function with respect to time. Represents the Laplace matrix of the communication topology. Indicates the Kronecker product. Represents a 3D identity matrix. This represents the global position estimation error vector. Represents a symbolic function. express A dimensional vector of all 1s This represents the acceleration vector of the navigator. Construct a Lyapunov function to evaluate the convergence properties of the observer. The following relation is satisfied: ; in, Represents the Lyapunov function. This represents the transpose of the global position estimation error vector. This represents the transpose of the global velocity estimation error vector; Based on the convergence characteristics of the predetermined time adjustment function, within the preset convergence time... The derivative of the Lyapunov function. Lyapunov function at the current moment Satisfies the convergence relation: ; Integrating the convergence relation yields the time step. The convergence boundary of the Lyapunov function Satisfying the relation: ; in, Indicates the current time The Lyapunov function value, This represents the initial value of the Lyapunov function. Indicates the current time The predetermined time adjustment function value, This represents the predetermined time adjustment function value at the initial moment.

[0041] It should be noted that the derivative of the global position estimation error The rate of change of the global position estimation error vector with respect to time is obtained by taking the derivatives of the position estimation errors of each UAV and stacking them into a vector, describing the dynamic evolution of the position estimation error of the entire formation; the derivative of the global velocity estimation error... The rate of change of the global velocity estimation error vector with respect to time is obtained by taking the derivative of the velocity estimation errors of each UAV and stacking them into a vector, describing the dynamic evolution of the velocity estimation error of the entire formation; the global position estimation error vector... It is a stacked vector of deviations between the estimated positions of each follower drone and the actual position of the navigator drone, defined as... ,in The Laplace matrix of the communication topology is obtained by each UAV calculating its own estimation error and summarizing the results through communication. It is a mathematical matrix describing the connectivity characteristics of a multi-UAV communication network, obtained by subtracting the adjacency matrix from the degree matrix. ,in This is a degree matrix, whose elements reflect the number of node connections. The eigenvalues ​​determine the convergence properties of the observer; Kronecker product It is a mathematical operator that performs a tensor product operation on two matrices, defined through matrix operations. Acquire, used to extend scalar topological relations to three-dimensional vector operations; 3D identity matrix It is a 3x3 square matrix with 1s on the main diagonal and 0s elsewhere, obtained through the standard matrix definition, used to maintain the dimensional consistency of vectors in three-dimensional space; sign function It is a non-linear function that extracts variable signs, obtained through piecewise definition; 1-dimensional vector It is a set where all elements are 1. Dimensional column vector, obtained through vector initialization; navigator acceleration vector. It is the derivative of the navigator's velocity with respect to time, obtained through measurements by the navigator's onboard IMU or by pre-planned trajectory, describing the navigator's maneuvering state; Lyapunov function. It is the energy function for evaluating the stability of a dynamic system, constructed using a quadratic form of the error vector. The value obtained reflects the magnitude of the energy deviating the system from its equilibrium state; transpose sign. , This represents the matrix operation that converts a column vector into a row vector, obtained through matrix transpose; Lyapunov function value. , The system energies at the current and initial times are respectively obtained by substituting the error vectors at the corresponding times into the Lyapunov function expression; the predetermined time adjustment function value. , These represent the adjustment function values ​​at the current time and the initial time, respectively, obtained by substituting the time values ​​into the piecewise function expression.

[0042] Understandably, by constructing an estimation error model and a Lyapunov function, a rigorous theoretical convergence guarantee can be provided for the distributed predetermined-time observer, ensuring that the observer can complete state estimation within a fixed time. By defining a global estimation error vector, the observer's dynamic equations are transformed into an error dynamic system. The coupling relationship between multiple UAVs is described using the Laplace matrix and the Kronecker product. A Lyapunov function containing position and velocity errors is constructed, and the function satisfies differential inequalities is proven through differentiation analysis. This inequality shows that the Lyapunov function value decays at a rate that adjusts to the function over a predetermined time interval. Integrating this differential inequality yields the exponential convergence boundary. ,when Due to Since it is a very small constant, therefore This proves that the observation error is within the preset time. It converges to a small neighborhood close to zero, thereby ensuring the timeliness and accuracy of state estimation, overcoming the problem of uncertain convergence time in traditional finite-time observers, and making multi-UAV formation control predictable and reliable.

[0043] Preferably, the total obstacle avoidance control input is generated by solving for the potential field gradients of the obstacle avoidance potential energy function and the inter-machine collision avoidance potential energy function, and combining this with the obstacle avoidance gain adjustment coefficient determined by the transformation error. Regarding the first The drone and the first Given an obstacle, calculate the obstacle collision avoidance potential field gradient used to generate the obstacle avoidance repulsion force. The following relation is satisfied: ; in, This represents the gradient of the potential field for obstacle avoidance. Indicates the first The detection radius of the drone Indicates the first The drone and the first The distance between the obstacles Indicates the first The position vector of the drone, Indicates the first The position vectors of the obstacles; Regarding the first The drone and the adjacent To deploy a drone and calculate the collision avoidance potential field gradient for inter-drone collision avoidance. The following relation is satisfied: ; in, This represents the gradient of the potential field for collision avoidance between machines. Indicates the first The drone and the first The distance between the drones This indicates the safe distance threshold between machines. Indicates the first The position vector of the drone, This represents the preset speed influence coefficient. Indicates the first frame and the first The relative velocity vector between the drones; By weighted and fused together the obstacle avoidance potential field gradient and the inter-machine avoidance potential field gradient, the first... Total obstacle avoidance control input for the drone The following relation is satisfied: ; in, and These represent the preset nominal repulsive force gain. This represents the obstacle avoidance gain adjustment coefficient. Indicates the total number of obstacles. Indicates the relationship with the first A group of drones adjacent to each other; Wherein, the obstacle avoidance gain adjustment coefficient Satisfying the relation: ; in, This indicates the preset adjustment coefficient. Indicates the first The norm of the transformation error of the drone.

[0044] It should be noted that the obstacle collision avoidance potential field gradient This is a mathematical vector describing the direction and intensity of the repulsive force exerted by an obstacle on the drone. It is obtained by differentiating the upper bound function of the integral and calculating the distance gradient formula. Its direction points away from the obstacle, and its magnitude is inversely proportional to the distance. Detection radius This is the maximum distance constant at which a drone can detect obstacles. It is preset through the performance parameters of onboard sensors such as lidar or the field of view of a camera, and the value can range from 10 to 20 meters. It is the first The drone and the first The Euclidean distance between obstacles is calculated by measuring the norm of the difference between their position vectors. Real-time acquisition; obstacle position vector It describes the first The mathematical vectors of the coordinates of each obstacle in the reference coordinate system are obtained in real time through airborne sensing sensors such as LiDAR point cloud processing or visual SLAM algorithms; the gradient of the potential field for inter-aircraft collision avoidance. It is a mathematical vector describing the direction and intensity of the repulsive force generated between adjacent UAVs, obtained by calculating the derivative of the potential function, and includes a distance repulsion term and a velocity damping term; the distance between the UAVs. It is the first frame and the first The Euclidean distance between two drones is calculated by determining the norm of the difference between their position vectors. Location information can be obtained in real time or calculated through inter-machine communication; inter-machine safe distance threshold. It is the minimum permissible distance constant to prevent collisions between drones, preset based on the drone's physical size and safety margin requirements, with a value ranging from 1 to 2 meters; UAV position vector Acquired via the airborne positioning system and transmitted to the [unclear - likely a specific location] via a communication link. Unmanned aerial vehicle (UAV); speed influence coefficient It is a positive constant used to adjust the influence of relative velocity on obstacle avoidance. It is preset through collision risk assessment and simulation debugging, and its value can range from 0.1 to 1.0; relative velocity vector. It is the first frame and the first The difference in the velocity vectors of the two drones is calculated. Real-time acquisition and description of the relative motion state of the two machines as they approach or move away; total obstacle avoidance control input. It is a comprehensive control vector that integrates obstacle avoidance and inter-machine collision avoidance commands, obtained through weighted summation calculation; nominal repulsion gain , It is a positive constant used to adjust the weights of obstacle avoidance and inter-machine collision avoidance. It is preset through obstacle avoidance priority and maneuverability analysis, and its value ranges from 0.1 to 1.0; obstacle avoidance gain adjustment coefficient. It is a coefficient that adaptively adjusts the obstacle avoidance intensity based on the tracking error, calculated by transforming the error norm; the total number of obstacles. This refers to the number of obstacles detected in the current environment, obtained in real time through the onboard perception system; adjacent drones... Is with the first The set of drone indexes directly connected to each other in the communication topology is predetermined through the communication topology configuration; adjustment coefficients. It is a positive constant that controls the rate of decline of obstacle avoidance gain. It is preset through obstacle avoidance and tracking balance analysis, and its value ranges from 0.5 to 2.0; the transformation error norm. It is the magnitude of the transformation error vector, calculated by... Real-time acquisition reflects tracking accuracy.

[0045] Understandably, by solving the potential field gradient of the obstacle and inter-drone collision avoidance potential energy function and combining it with an adaptive gain adjustment mechanism to generate the total obstacle avoidance control input, the technical problem of conflict between obstacle avoidance and tracking commands caused by the fixed gain of the traditional artificial potential field method can be effectively solved. Based on the artificial potential field method, obstacles and adjacent UAVs are regarded as sources of repulsive potential fields. The direction of the repulsive force is obtained by solving the potential field gradient. At the same time, an obstacle avoidance gain adjustment coefficient determined by the transformation error is introduced, so that the obstacle avoidance intensity is dynamically adjusted according to the tracking error. When the error is small, obstacle avoidance is enhanced to ensure safety, and obstacle avoidance is weakened when the error is large to avoid control input conflict. This achieves a smooth integration of obstacle avoidance behavior and tracking control. The superposition of dual potential energy functions provides comprehensive collision avoidance protection. At the same time, the adaptive gain mechanism prevents command conflicts between obstacle avoidance control and tracking control, ensuring that UAVs can fly safely and maintain high-precision formation in complex environments, significantly improving the safety and coordination of multi-UAV formation flight.

[0046] Preferably, the process of defining the tracking error and reference trajectory based on the estimated values ​​of the distributed predetermined time observer, and generating a pre-defined formation to describe the expected flight trajectory of the UAV includes: A reference trajectory is constructed based on the estimates from the distributed predetermined time observer and a preset offset. The following relation is satisfied: ; in, Indicates the reference trajectory. This indicates the output of the distributed predetermined time observer. The estimated position of the navigator observed by the drone. Indicates the first The preset offset of the drone relative to the lead drone; Calculate the first based on the reference trajectory Tracking error of drones The following relation is satisfied: ; in, Indicates tracking error. Indicates the first The actual position vector of the drone.

[0047] It should be noted that the reference trajectory It is a mathematical vector describing the ideal flight path that the drone is expected to follow, obtained by taking the lead drone's position estimate from the output of a distributed, pre-defined time observer. With preset offset The trajectory, obtained through vector addition calculation, defines the expected spatial coordinates of the UAV within the formation, providing a target reference for tracking and control; the navigator's position estimate... It is the first The estimated vector of the navigator's true position is obtained by integrating the dynamic equations of the observers through distributed, pre-defined time observers, and converges to the navigator's true position within a predetermined time; a preset offset is also included. It describes the first The three-dimensional vector of the desired relative position of the drone with respect to the lead aircraft is pre-set by mission planners according to the formation geometry requirements, for example, set as follows in a wedge formation: This vector, representing 8 meters behind and 5 meters to the left, determines the relative geometric position of the UAV within the formation; tracking error. It is a mathematical vector describing the degree to which the actual position of the drone deviates from the reference trajectory, obtained through vector subtraction. Real-time calculation and acquisition, with each component representing the deviation in the longitudinal, lateral, and vertical directions, provides feedback signals for the control law; actual position vector It is the first The actual coordinate vector of the drone in the reference coordinate system is obtained in real time through airborne GPS or visual positioning system.

[0048] Understandably, defining the tracking error and reference trajectory based on the estimated values ​​from a distributed, pre-defined time observer can effectively solve the problems of unclear reference trajectories and difficulty in quantifying tracking accuracy in traditional formation control. By adopting a lead-follow mode, the estimated state of the lead aircraft provided by the observer is used as a benchmark, and a preset offset is superimposed to generate a reference trajectory for each UAV. This allows the UAV to maintain a specific geometric configuration relative to the lead aircraft. The tracking error is obtained by calculating the difference between the actual position and the reference trajectory, thereby achieving a precise description of the formation and a quantitative calculation of the tracking error. This ensures that the UAV can adjust its position according to the estimated state of the lead aircraft, maintaining the preset formation geometry. Simultaneously, the definition of the tracking error provides a constraint for subsequent preset performance control, enabling the control algorithm to force the error to converge within the preset boundaries, ensuring the stability and accuracy of formation flight.

[0049] Preferably, the relaxed preset performance function designed to address the singularity problem of obstacle avoidance control includes: Based on the initial performance boundary, steady-state performance boundary, and obstacle avoidance relaxation, the first... Relaxed preset performance function of drone The following relation is satisfied: ; in, Indicates the first A drone in The relaxation preset performance function of the dimension, Represents the dimensional coordinates of the drone and , Indicates the initial performance boundary. Represents the steady-state performance boundary. This indicates the preset transition time. This indicates the preset power index. This represents the attenuation rate adjustment coefficient. Indicates the current moment. Indicates the obstacle avoidance slack; The obstacle avoidance slack Satisfying the relation: ; in, Indicates the first control gain. Indicates the second control gain. This represents the Sigmoid smoothing function. Indicates the detection radius threshold. Represents the obstacle's position vector. Indicates the first The position vector of the drone, Indicates the smooth transition coefficient. Represents the hyperbolic tangent function. Represents the absolute value function. Indicates the drone and obstacles in the first... Distance component in direction, Indicates the first Safety distance threshold for direction.

[0050] It should be noted that the relaxation preset performance function It is a time function used to constrain the dynamic boundary of tracking error, defined in piecewise form, during the transition time. The performance decays exponentially from the initial performance boundary to the steady-state performance boundary, with the addition of obstacle avoidance relaxation. Maintaining steady-state boundaries and obstacle avoidance relaxation at the current moment Substitute into the function expression to calculate and obtain in real time; dimension coordinates. It is an index variable representing a direction in three-dimensional space, and its value is... , or The initial performance boundary is predetermined by defining a coordinate system. This is the maximum boundary constant for the allowable tracking error at the start of control, preset based on the initial positioning error analysis of the UAV and the mission accuracy requirements, with a value ranging from 0.5 to 2.0 meters; steady-state performance boundary. This is the maximum boundary constant for the allowable tracking error after control stabilizes. It is preset based on control accuracy requirements and sensor noise levels, and its value can range from 0.1 to 0.5 meters; preset transition time. It is the time constant required for the performance boundary to decay from its initial value to its steady-state value. It is preset according to the task response speed requirements and can range from 5 to 15 seconds; power exponent. It is a positive constant that adjusts the shape of the attenuation curve. It is preset based on the dynamic response characteristics and can be set to a value of 2; the attenuation rate adjustment coefficient. It is a positive constant that adjusts the rate of exponential decay, preset according to the convergence rate requirement, and its value can range from 0.05 to 0.2; obstacle avoidance slack. It is the performance boundary extension dynamically adjusted based on the distance between the UAV and obstacles, obtained through a composite calculation of the Sigmoid function and the hyperbolic tangent function; the first control gain It is a positive constant that adjusts the sensitivity of obstacle avoidance slack to distance difference, and is preset according to the obstacle avoidance response speed requirements. Its value can range from 1.0 to 5.0; the second control gain. It is a positive constant that adjusts the maximum amplitude of obstacle avoidance slack, preset according to obstacle avoidance strength requirements, and its value ranges from 0.1 to 0.5 meters; Sigmoid smoothing function. It maps the input to The S-shaped function over the interval, obtained through exponential operations, is used to achieve a smooth transition; detection radius threshold. It is the maximum distance constant that triggers the obstacle avoidance slack calculation, which is preset through the sensor detection range; obstacle position vector Acquired in real time via onboard sensing sensors; smooth transition coefficient It is a positive constant that controls the steepness of the transition of the Sigmoid function. It is preset according to smoothness requirements, and its value can range from 0.5 to 2.0; hyperbolic tangent function. It maps the input to Hyperbolic functions over intervals are obtained through exponential operations; absolute value functions. It is a mathematical function that extracts the non-negative values ​​of variables, obtained through sign determination; distance component. It is the projected distance between the drone and the obstacle along a specific coordinate axis, obtained by calculating the difference between the corresponding components of the position vector; safety distance threshold. It is the minimum distance constant to prevent collisions in a specific direction, which is preset by the obstacle size and safety margin.

[0051] It is understandable that by introducing an obstacle avoidance relaxation amount related to the distance to the obstacle through a smoothing function to design a relaxation preset performance function, the control singularity problem caused by the tracking error exceeding the preset performance boundary during obstacle avoidance can be effectively solved. The Sigmoid smoothing function is used to dynamically adjust the performance boundary according to the proximity of the UAV to the obstacle. When the UAV approaches the obstacle, the output value of the Sigmoid function increases, and after being scaled by the hyperbolic tangent function, an obstacle avoidance relaxation amount is generated. This relaxation amount is superimposed on the preset performance function to achieve a smooth widening of the boundary, so that the tracking error can temporarily exceed the nominal boundary during obstacle avoidance without triggering control singularity. When moving away from the obstacle, the relaxation amount gradually fades and restores the original boundary. This achieves adaptive and flexible adjustment of the performance boundary, avoiding the abrupt change in control input caused by the rigid constraints of traditional preset performance control during obstacle avoidance, ensuring a smooth transition of control input and system stability, and ensuring that the tracking accuracy can be restored to the preset level after obstacle avoidance, thus achieving a coordinated unity of safety and accuracy.

[0052] Preferably, the tracking error constrained by the relaxed preset performance function is mapped to an unconstrained transformation error using a tangent transform function, and a preset performance expectation control input is generated accordingly, including: By using the tangent transform function to perform a nonlinear mapping on the tracking error, a transform error is obtained to eliminate boundary constraint limitations. The following relation is satisfied: ; in, Indicates the first A drone in Dimensional transformation error, Indicates the first A drone in Dimensional tracking error, This indicates that the relaxation preset performance function is in The function value of the dimension; Based on the transformation error, a PD-type control law is designed to obtain the preset performance expectation control input for achieving closed-loop regulation. The following relation is satisfied: ; in, This indicates the preset performance expectation control input. The derivative vector of the reference trajectory is in Dimensional components, This indicates the preset proportional gain. This represents the preset differential gain. This represents the derivative of the transformation error with respect to time.

[0053] It should be noted that the transformation error It is the unconstrained error variable obtained by mapping the constrained tracking error through tangent transformation, and then calculating... This transformation will originally limit the scope to The tracking error within the interval is extended to the entire real number range, which facilitates control law design; tracking error components The tracking error vector is at the th... Scalar components of dimension, extracted from vectors The Each element is retrieved, representing the positional deviation in that direction; the preset performance function value is relaxed. It is the first The instantaneous value of the dimensional performance boundary is obtained by substituting the current moment into the relaxed preset performance function expression, representing the maximum allowable tracking error boundary at that moment; the preset performance expectation control input... It is an ideal control command scalar based on the transformation error design, obtained through PD control law calculation, used to drive the convergence of tracking error in this dimension; reference trajectory derivative components. The reference trajectory is at the 1st The rate of change of dimension with respect to time is obtained by differentiating the reference trajectory and extracting the first... Individual component acquisition, providing feedforward compensation; proportional gain It is a positive constant used to adjust the control action, which is proportional to the current error. It is preset based on response speed requirements and stability analysis, and its value can range from 1.0 to 5.0; differential gain. It is a positive constant used to adjust the control action, which is proportional to the rate of change of error. It is preset by damping requirements and overshoot limits, and its value can range from 0.5 to 2.0; transforming the error derivative... It is the rate of change of the transformation error with respect to time, which is obtained by taking the derivative of the tangent function and applying the chain rule. It includes the effects of the rate of change of the tracking error and the rate of change of the performance boundary.

[0054] It is understandable that by using the tangent transform function to map the tracking error constrained by the relaxed preset performance function into an unconstrained error and generating a preset performance expectation control input, the boundary limitations of the preset performance constraint on the control design can be effectively eliminated, and the error constraint and control law design can be decoupled. By utilizing the bounded input and unbounded output characteristics of the tangent function, the tracking error strictly limited within the performance boundary is nonlinearly mapped into an unconstrained transform error, transforming the original tracking problem constrained by inequalities into an unconstrained adjustment problem. The PD-type preset performance expectation control input designed based on the transform error suppresses the current error through the proportional term, improves the dynamic response through the differential term, and compensates for the change of the reference trajectory through the feedforward term, thereby achieving a quantitative guarantee of the transient and steady-state performance of the tracking error. The saturation characteristics of the tangent transform prevent the control input from being too large. At the same time, the dynamic boundary adaptive adjustment mechanism of the relaxed preset performance function ensures the smooth transition of the control input during obstacle avoidance, achieving a coordinated unity of high-precision tracking and obstacle avoidance safety.

[0055] Preferably, a quadratic programming controller integrating multiple objectives and multiple constraints is constructed, and the optimal control input is obtained by solving for the actuator amplitude and safety distance constraints, including: Optimal control input Satisfying the relation: ; in, Indicates the first The optimal control input to be solved for the unmanned aerial vehicle (UAV) This indicates the overall obstacle avoidance control input. This indicates the preset energy consumption penalty weight. This indicates the preset performance control weights. This indicates the preset performance expectation control input; Optimal control input The following set of constraints must be satisfied: ; ; ; in, and These represent the lower and upper limits of the control input amplitude constraints for the actuator, respectively. Indicates the first The position vector of the drone, Indicates the first The position vectors of the obstacles This indicates the preset safe distance between the drone and the obstacle. and These represent the preset lower and upper limits of the safe distance between machines, respectively. Indicates the first The position vector of the drone.

[0056] It should be noted that the optimal control input The actual control command vector is obtained by solving a quadratic programming optimization problem. It is calculated by minimizing the objective function and satisfying the constraints, so that the actual control takes into account obstacle avoidance, tracking, and energy consumption requirements; the total obstacle avoidance control input is... The obstacle avoidance command vector is generated through weighted fusion of potential field gradients and is calculated in step S3 to guide the UAV away from obstacles and avoid inter-UAV collisions; energy consumption penalty weights. This is a positive constant used to adjust the intensity of the penalty for the control input amplitude. It is preset based on energy consumption optimization requirements and task endurance needs, and its value ranges from 0.01 to 0.5. A larger value indicates a greater focus on reducing energy consumption. Preset performance control weights are also included. This is a positive constant used to adjust the priority of tracking accuracy. It is preset based on tracking accuracy requirements and obstacle avoidance priority, and its value ranges from 1.0 to 10.0. A larger value indicates a greater emphasis on tracking accuracy. (Preset performance expectation control input) The tracking command vector, generated by the transformation error PD control, is calculated in step S6 to guide the UAV in tracking the reference trajectory; and controls the lower limit constraint of the input amplitude. It is the minimum control force or torque constant vector that the actuator can generate, which is predetermined by the physical limitations of the minimum motor speed or the minimum deflection angle of the servo motor; upper limit constraint of control input amplitude. It is the vector of the maximum control force or torque constant that the actuator can generate, which is predetermined by the physical limitations of the motor's maximum speed or the servo motor's maximum deflection angle; obstacle position vector. Real-time detection and acquisition via onboard sensing sensors; safe distance It is the minimum distance constant to prevent drones from colliding with obstacles. It is preset by the obstacle size and safety margin, and the value can range from 2 to 5 meters; the lower limit of the safe distance between drones. It is the minimum distance constant to prevent collisions between drones, which is preset based on the physical size of the drones and collision avoidance requirements, and can range from 1 to 2 meters; the upper limit of the safe distance between drones. This is the maximum distance constant for maintaining communication and coordination between UAVs. It is preset based on communication range and coordination accuracy requirements, and its value can range from 10 to 20 meters. UAV position vector It is obtained through an airborne positioning system and transmitted via a communication link.

[0057] It is understandable that by constructing a quadratic programming controller with the objective of minimizing the deviation between the actual control input and the total obstacle avoidance control input and the preset performance expectation control input, it is possible to effectively achieve optimal coordination of multiple objectives such as obstacle avoidance, tracking, and energy consumption, and strictly satisfy multiple constraints. The multi-UAV formation control problem can be formulated as a constrained quadratic optimization problem. The three weighted squared deviations in the objective function measure the degree of deviation between the actual control and obstacle avoidance commands, the magnitude of control energy consumption, and the degree of deviation from the tracking command, respectively. Under the hard constraints of ensuring that the actuators are not saturated, that the UAVs maintain a safe distance from obstacles, and that the distance between UAVs is maintained within a reasonable range, the convex optimization characteristics of quadratic programming are used to solve for the globally optimal control input, thereby achieving balanced optimization of multiple control objectives. By adjusting the weights, different task priorities can be flexibly adapted. By constraining, flight safety is ensured. By optimizing the solution, smooth and executable control commands are obtained, significantly improving the comprehensive control performance and engineering practicality of multi-UAV formations in complex environments.

[0058] A pre-defined performance distributed control system for obstacle avoidance in multi-drone formations, such as... Figure 2 As shown, it includes: The dynamic modeling module is used to build a dual-integral dynamic model of a multi-UAV system, which describes the dynamic relationship between the position, velocity and control input vector of each UAV. The state observation module is used to design a distributed predetermined time observer for accurate estimation of the navigator's state predetermined time by utilizing local neighbor node information interaction and a predetermined time adjustment function. The obstacle avoidance guidance module is used to generate the total obstacle avoidance control input by solving the potential field gradient between the obstacle avoidance potential energy function and the inter-machine avoidance potential energy function, and combining it with the obstacle avoidance gain adjustment coefficient determined by the transformation error. The formation generation module is used to define the tracking error and reference trajectory based on the estimated value of the distributed predetermined time observer, and generate a preset formation to describe the expected flight trajectory of the UAV. The performance relaxation module is used to introduce obstacle avoidance relaxation amount related to the distance to the obstacle through a smoothing function, and is designed to solve the problem of obstacle avoidance control singularity by using a relaxation preset performance function. The error transformation module is used to map the tracking error constrained by the relaxed preset performance function into an unconstrained error using the tangent transformation function, so as to design the transformation error and generate the preset performance expectation control input. The optimal control module is used to construct a quadratic programming controller with the objective of minimizing the deviation between the actual control input and the total obstacle avoidance control input and the preset performance expectation control input, and to solve for the optimal control input under the constraints of actuator amplitude and safety distance.

[0059] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0060] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A pre-defined performance distributed control method for obstacle avoidance in multi-UAV formations, characterized in that, include: A dual-integral dynamic model of a multi-UAV system is constructed to describe the dynamic relationship between the position, velocity and control input vector of each UAV. By utilizing local neighbor node information interaction and a predetermined time adjustment function, a distributed predetermined time observer is designed for accurate estimation of the predetermined time of the navigator's state. The total obstacle avoidance control input is generated by solving the potential field gradient of the obstacle avoidance potential energy function and the inter-machine collision avoidance potential energy function, and combining it with the obstacle avoidance gain adjustment coefficient determined by the transformation error. Based on the estimated values ​​of the distributed predetermined time observer, the tracking error and reference trajectory are defined, and a preset formation for describing the expected flight trajectory of the UAV is generated; By introducing an obstacle avoidance relaxation amount related to the distance to the obstacle through a smoothing function, a relaxation preset performance function is designed to solve the singularity problem of obstacle avoidance control. The tracking error constrained by the relaxed preset performance function is mapped to an unconstrained error using the tangent transform function, so as to design the transform error and generate the preset performance expectation control input. A quadratic programming controller is constructed with the objective of minimizing the deviation between the actual control input and the total obstacle avoidance control input and the preset performance expectation control input. The optimal control input is obtained by solving the problem under the constraints of actuator amplitude and safe distance.

2. The pre-defined performance distributed control method for obstacle avoidance in multi-UAV formations according to claim 1, characterized in that, The construction of a dual-integral dynamic model for a multi-UAV system includes: For the first in a multi-drone formation For a UAV, a double-integral dynamic model is constructed to describe the dynamic relationship between position, velocity, and control input. The position derivative and velocity derivative of the UAV satisfy the following relationship: ； ； in, Indicates the first The position vector of the drone, Indicates the first The velocity vector of the drone Indicates the first The control input vector of the drone.

3. The pre-defined performance distributed control method for obstacle avoidance in multi-UAV formations according to claim 1, characterized in that, A distributed time-based observer for accurately estimating the navigator's state time is designed by utilizing local neighbor node information exchange and a pre-defined time adjustment function. A state observation model is constructed based on the information exchange between local neighbor nodes. Derivative of the position estimate of the navigator observed by the drone With velocity estimation derivative Satisfying the relation: ； ； in, Indicates the first The derivative of the position estimation of the navigator observed by the drone. Indicates the first The estimated speed of the lead aircraft as observed by the drone. , and These represent the preset design gain parameters. This represents the pre-set time adjustment function. This represents the derivative of the predetermined time adjustment function with respect to time. Represents the elements of the communication topology adjacency matrix. and They represent the first frame and the first The estimated position of the navigator observed by the drone. Represents a symbolic function. Indicates the first The estimated speed of the lead aircraft as observed by the drone. Indicates the total number of drones; The predetermined time adjustment function Satisfying the relation: ； in, This represents the pre-set time adjustment function. Indicates the preset convergence time. Indicates the current moment. This represents a preset constant used to avoid numerical singularities.

4. The pre-defined performance distributed control method for obstacle avoidance in multi-UAV formations according to claim 3, characterized in that, The process by which the distributed, predetermined-time observer achieves state estimation convergence includes: An estimation error model is constructed based on the state estimates observed by each UAV and the actual state of the navigator aircraft. The derivative of the global position estimation error is calculated. Derivative of global velocity estimation error The following error derivative relationship must be satisfied: ； ； in, , and These represent the preset design gain parameters. This represents the pre-set time adjustment function. This represents the derivative of the predetermined time adjustment function with respect to time. Represents the Laplace matrix of the communication topology. Indicates the Kronecker product. Represents a 3D identity matrix. This represents the global position estimation error vector. Represents a symbolic function. express A dimensional vector of all 1s This represents the acceleration vector of the navigator. Construct a Lyapunov function to evaluate the convergence properties of the observer. The following relation is satisfied: ； in, Represents the Lyapunov function. This represents the transpose of the global position estimation error vector. This represents the transpose of the global velocity estimation error vector; Based on the convergence characteristics of the predetermined time adjustment function, within the preset convergence time... The derivative of the Lyapunov function. Lyapunov function at the current moment Satisfies the convergence relation: ; Integrating the convergence relation yields the time step. The convergence boundary of the Lyapunov function Satisfying the relation: ； in, Indicates the current time The Lyapunov function value, This represents the initial value of the Lyapunov function. Indicates the current time The predetermined time adjustment function value, This represents the predetermined time adjustment function value at the initial moment.

5. The pre-defined performance distributed control method for obstacle avoidance in multi-UAV formations according to claim 1, characterized in that, By solving for the potential field gradients of the obstacle avoidance potential energy function and the inter-machine collision avoidance potential energy function, and combining this with the obstacle avoidance gain adjustment coefficient determined by the transformation error, the total obstacle avoidance control input is generated, including: Regarding the first The drone and the first Given an obstacle, calculate the obstacle collision avoidance potential field gradient used to generate the obstacle avoidance repulsion force. The following relation is satisfied: ； in, This represents the gradient of the potential field for obstacle avoidance. Indicates the first The detection radius of the drone Indicates the first The drone and the first The distance between the obstacles Indicates the first The position vector of the drone, Indicates the first The position vectors of the obstacles; Regarding the first The drone and the adjacent To deploy a drone and calculate the collision avoidance potential field gradient for inter-drone collision avoidance. The following relation is satisfied: ； in, This represents the gradient of the potential field for collision avoidance between machines. Indicates the first The drone and the first The distance between the drones This indicates the safe distance threshold between machines. Indicates the first The position vector of the drone, This represents the preset speed influence coefficient. Indicates the first frame and the first The relative velocity vector between the drones; By weighted and fused together the obstacle avoidance potential field gradient and the inter-machine avoidance potential field gradient, the first... Total obstacle avoidance control input for the drone The following relation is satisfied: ； in, and These represent the preset nominal repulsive force gain. This represents the obstacle avoidance gain adjustment coefficient. Indicates the total number of obstacles. Indicates the relationship with the first A group of drones adjacent to each other; Wherein, the obstacle avoidance gain adjustment coefficient Satisfying the relation: ； in, This indicates the preset adjustment coefficient. Indicates the first The norm of the transformation error of the drone.

6. The pre-set performance distributed control method for obstacle avoidance in multi-UAV formations according to claim 1, characterized in that, Based on the estimated values ​​from the distributed predetermined time observer, the tracking error and reference trajectory are defined, and a preset formation for describing the expected flight trajectory of the UAV is generated, including: A reference trajectory is constructed based on the estimates from the distributed predetermined time observer and a preset offset. The following relation is satisfied: ； in, Indicates the reference trajectory. This indicates the output of the distributed predetermined time observer. The estimated position of the navigator observed by the drone. Indicates the first The preset offset of the drone relative to the lead drone; Calculate the first based on the reference trajectory Tracking error of drones The following relation is satisfied: ； in, Indicates tracking error. Indicates the first The actual position vector of the drone.

7. The pre-defined performance distributed control method for obstacle avoidance in multi-UAV formations according to claim 1, characterized in that, The relaxation preset performance functions designed to address the singularity problem in obstacle avoidance control include: Based on the initial performance boundary, steady-state performance boundary, and obstacle avoidance relaxation, the first... Relaxed preset performance function of drone The following relation is satisfied: ； in, Indicates the first A drone in The relaxation preset performance function of the dimension, Represents the dimensional coordinates of the drone and , Indicates the initial performance boundary. Represents the steady-state performance boundary. This indicates the preset transition time. This indicates the preset power index. This represents the attenuation rate adjustment coefficient. Indicates the current moment. Indicates the obstacle avoidance slack; The obstacle avoidance slack Satisfying the relation: ； in, Indicates the first control gain. Indicates the second control gain. This represents the Sigmoid smoothing function. Indicates the detection radius threshold. Represents the obstacle's position vector. Indicates the first The position vector of the drone, Indicates the smooth transition coefficient. Represents the hyperbolic tangent function. Represents the absolute value function. Indicates the drone and obstacles in the first... Distance component in direction, Indicates the first Safety distance threshold for direction.

8. The pre-defined performance distributed control method for obstacle avoidance in multi-UAV formations according to claim 1, characterized in that, The tracking error constrained by the relaxed preset performance function is mapped to an unconstrained transformation error using the tangent transform function, and a preset performance expectation control input is generated accordingly, including: By using the tangent transform function to perform a nonlinear mapping on the tracking error, a transform error is obtained to eliminate boundary constraint limitations. The following relation is satisfied: ； in, Indicates the first A drone in Dimensional transformation error, Indicates the first A drone in Dimensional tracking error, This indicates that the relaxation preset performance function is in The function value of the dimension; Based on the transformation error, a PD-type control law is designed to obtain the preset performance expectation control input for achieving closed-loop regulation. The following relation is satisfied: ； in, This indicates the preset performance expectation control input. The derivative vector of the reference trajectory is in Dimensional components, This indicates the preset proportional gain. This represents the preset differential gain. This represents the derivative of the transformation error with respect to time.

9. The pre-defined performance distributed control method for obstacle avoidance in multi-UAV formations according to claim 1, characterized in that, A quadratic programming controller integrating multiple objectives and constraints is constructed, and the optimal control inputs are obtained by solving the problem under the constraints of actuator amplitude and safety distance: Optimal control input Satisfying the relation: ； in, Indicates the first The optimal control input to be solved for the unmanned aerial vehicle (UAV) This indicates the overall obstacle avoidance control input. This indicates the preset energy consumption penalty weight. This indicates the preset performance control weights. This indicates the preset performance expectation control input; Optimal control input The following set of constraints must be satisfied: ； ； ； in, and These represent the lower and upper limits of the control input amplitude constraints for the actuator, respectively. Indicates the first The position vector of the drone, Indicates the first The position vectors of the obstacles This indicates the preset safe distance between the drone and the obstacle. and These represent the preset lower and upper limits of the safe distance between machines, respectively. Indicates the first The position vector of the drone.

10. A pre-defined performance distributed control system for obstacle avoidance in multi-UAV formations, characterized in that, include: The dynamic modeling module is used to build a dual-integral dynamic model of a multi-UAV system, which describes the dynamic relationship between the position, velocity and control input vector of each UAV. The state observation module is used to design a distributed predetermined time observer for accurate estimation of the navigator's state predetermined time by utilizing local neighbor node information interaction and a predetermined time adjustment function. The obstacle avoidance guidance module is used to generate the total obstacle avoidance control input by solving the potential field gradient between the obstacle avoidance potential energy function and the inter-machine avoidance potential energy function, and combining it with the obstacle avoidance gain adjustment coefficient determined by the transformation error. The formation generation module is used to define the tracking error and reference trajectory based on the estimated value of the distributed predetermined time observer, and generate a preset formation to describe the expected flight trajectory of the UAV. The performance relaxation module is used to introduce obstacle avoidance relaxation amount related to the distance to the obstacle through a smoothing function, and is designed to solve the problem of obstacle avoidance control singularity by using a relaxation preset performance function. The error transformation module is used to map the tracking error constrained by the relaxed preset performance function into an unconstrained error using the tangent transformation function, so as to design the transformation error and generate the preset performance expectation control input. The optimal control module is used to construct a quadratic programming controller with the objective of minimizing the deviation between the actual control input and the total obstacle avoidance control input and the preset performance expectation control input, and to solve for the optimal control input under the constraints of actuator amplitude and safety distance.

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