Spacecraft cooperative formation safety control method and system based on adjustable adaptive control barrier function

Abstract

The application relates to a spacecraft cooperative formation safety control method and system based on an adjustable adaptive control barrier function, and the method comprises the following steps: establishing a six-degree-of-freedom model for describing the relative motion of a spacecraft formation; establishing multiple safety key constraints required to be met by the spacecraft formation, and the constraints are formalized as zero super-level set functions of state variables; designing a disturbance observer to online estimate and compensate unknown lumped disturbances existing in the six-degree-of-freedom model; constructing a safety controller, the safety controller comprises an adjustable adaptive control barrier function for generating a safety constraint boundary changing with time, and the parameters of the adjustable adaptive control barrier function are adjusted online through an auxiliary dynamic system; and constructing a quadratic programming problem to obtain optimal safety control instructions minimizing the deviation between actual control input and nominal control input. Compared with the prior art, the application has the advantages of improving the task success rate and safety of the spacecraft formation in a complex, dynamic and uncertain environment.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and in particular to the cooperative control technology of spacecraft orbit and attitude. More specifically, it relates to a spacecraft cooperative formation safety control method and system based on an adjustable adaptive control barrier function for performing target rendezvous, fly-around and observation missions in complex constraint environments. Background Technology

[0002] On-Orbit Servicing (OOS) is a foundational technology for next-generation space activities, aiming to transform spacecraft from disposable assets into sustainable, maintainable platforms. Its missions are broad, including in-orbit refueling, repair, and active debris removal. A common fundamental requirement of these missions is that the servicing spacecraft can autonomously and safely approach, inspect, and characterize target objects. This challenge is significantly amplified when the target is in motion, constituting a complex six-degree-of-freedom (6-DOF) tracking problem with significant uncertainties in dynamics and environmental characteristics. Traditional single-servicing spacecraft approaches have inherent limitations, such as low data acquisition efficiency and poor mission robustness. These limitations have prompted research to shift towards using formations composed of small, agile satellites. This distributed architecture can simultaneously acquire data from multiple perspectives, enabling accurate real-time 3D reconstruction and state estimation, and enhancing mission robustness through inherent redundancy. However, existing cooperative formation control research largely simplifies spacecraft and targets as point masses, neglecting the requirements of attitude dynamics and precise payload pointing. Furthermore, the validation of existing algorithmic frameworks is typically conducted in idealized, less disturbed space environments. When faced with complex dynamic environments filled with space debris, restricted by attitude no-go zones, and subjected to various disturbances, the performance of these algorithms may degrade significantly, making it impossible to complete true cooperative tracking and observation tasks.

[0003] Specifically, existing technologies face the following core challenges: Challenge 1 - Physical Constraints: The physical limitations of spacecraft actuators can lead to control input saturation. This saturation can cause abrupt spikes in the control signal, posing a risk of damage to the actuator. Therefore, a control strategy capable of generating smooth control inputs is needed to mitigate the adverse effects of saturation.

[0004] Challenge 2 - External Disturbances: During translation and rotation, spacecraft formations are subject to external time-varying disturbances. These disturbances directly affect velocity dynamics, therefore it is essential to ensure that safety constraints remain feasible in the presence of disturbances.

[0005] Challenge 3 - Constraint Coupling and Conservatism: State and input constraints are treated as hard constraints, and these heterogeneous constraints are in a state of dynamic coupling. Traditional constraint optimization methods often require extensive hyperparameter tuning for different scenarios, which is infeasible for spacecraft formations with limited onboard computing resources. Furthermore, due to the coupled and changing constraints, it is necessary to reduce the conservatism of the optimization process by enhancing the adaptability of the control framework to enable automatic adjustments, thereby improving the overall algorithm's feasibility.

[0006] Therefore, designing a control framework that enables small satellite formations to collaboratively track targets while ensuring accurate payload pointing and safe operation under multiple constraints and disturbances is a pressing technical challenge in the aerospace field. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the existing technology, especially to address the problems of insufficient robustness, poor adaptability, and conservative solutions in existing control methods when spacecraft formations face multiple safety constraints such as external disturbances, actuator saturation, and dynamic coupling. This invention proposes a spacecraft cooperative formation safety control method and system based on an adjustable adaptive control barrier function, aiming to provide a unified, robust, and computationally efficient solution to significantly improve the mission success rate and safety of spacecraft formations in complex, dynamic, and uncertain environments.

[0008] The objective of this invention can be achieved through the following technical solutions: A spacecraft cooperative formation safety control method based on an adjustable adaptive control barrier function includes the following steps: A six-degree-of-freedom model describing the relative motion of spacecraft formations is established. This six-degree-of-freedom model couples orbital dynamics with attitude dynamics, including relative position dynamics equations and relative attitude dynamics equations. Based on mission requirements and environmental information, multiple safety-critical constraints that the spacecraft formation needs to satisfy are established, and the constraints are formalized as zero hyperlevel set functions of state variables. Design a perturbation observer to estimate and compensate for unknown lumped perturbations in the six-degree-of-freedom model online based on the spacecraft's state information; A safety controller based on the disturbance observer and safety-critical constraints is constructed. The safety controller includes an adjustable adaptive control barrier function for generating time-varying safety constraint boundaries. The parameters of the adjustable adaptive control barrier function are adjusted online through an auxiliary dynamic system. Based on the safety controller, a quadratic programming problem is constructed. Under the condition of satisfying the safety constraint boundary, the optimal safety control command that minimizes the deviation between the actual control input and the nominal control input is obtained to drive the spacecraft motion.

[0009] Furthermore, in the orbital coordinate system, the relative position dynamics equation is expressed as: in, For spacecraft indexing, It is a relative position vector. , , Here are the inertia matrix, the Coriolis and centripetal force matrix, and the gravitational gradient matrix. It is a nonlinear gravitational term. For aggregated disturbances, For control.

[0010] Furthermore, the relative attitude dynamics equations are expressed as follows: in, Let be the quaternion representing the error from the desired pose to the current pose. Relative angular velocity, For rotational inertia, To control the torque, For the disturbance torque, This is the correlation matrix of the error quaternions.

[0011] Furthermore, the safety-critical constraints include at least several of the following: obstacle avoidance constraints, inter-spacecraft collision avoidance constraints, attitude exclusion zone constraints, and control input constraints. The obstacle avoidance constraint is expressed as follows: ,in, For the first The location of the obstacle and These are the radii of the envelope spheres for the spacecraft and the obstacle, respectively. The inter-spacecraft collision avoidance constraint is expressed as follows: ,in, For the first The location of the spacecraft It is a spacecraft The minimum radius of the envelope sphere; The attitude restricted area constraint is expressed as follows: ,in, Half of the camera's field of view For the first A restricted area direction vector, Let be the rotation matrix from the body coordinate system to the inertial system. The camera pointing vector; The control input constraint is expressed as follows: and ,in, and Control force and control torque The maximum amplitude.

[0012] Furthermore, an augmenting system is introduced to solve the smoothness problem of the control input constraints. The augmenting system is expressed as: in, and The actual control input is considered as the state variable of the augmented system. and This provides new virtual control inputs, thereby transforming input constraints into state constraints. All are time-varying parameters.

[0013] Furthermore, the disturbance observer is a disturbance observer based on robust error integral, and its dynamic form is as follows: in, For system status, It is the corresponding system matrix. and These are the estimated values ​​of the state and the disturbance, respectively. , , For the gain of a normal controller, the function dir(x) = sign(x)|x, It is the virtual control input to be solved.

[0014] Furthermore, the adjustable adaptive control barrier function defines the safety control set through the following inequality: in, Let be any security constraint function, Let the relative order of this constraint be... and For Li Daoshu, and For terms related to disturbance estimation, For coefficient terms that include auxiliary dynamic variables, To assist in the control input of the dynamic system, and To assist the residual derivative term of the dynamic system, It is the virtual control input to be solved. This is the bound for the disturbance estimation error.

[0015] Furthermore, the adjustable adaptive control barrier function Defined as a state variable , And design an auxiliary dynamic system for it. By designing control input Adjust parameters online This alters the form of the adjustable adaptive control barrier function constraint to adapt to dynamically changing environments and coupled multiple constraints. , These are system parameters.

[0016] Furthermore, the quadratic programming problem is expressed as: in, It is the virtual control input to be solved. For nominal input, It is an auxiliary parameter adjustment input. It is a regularization term used to penalize adjustments made to the safety boundary. The coefficient matrix, This is the disturbance estimate. This refers to the system status.

[0017] This invention also provides a spacecraft cooperative formation safety control system based on an adjustable adaptive control barrier function, comprising: The dynamics modeling unit is used to build and store a six-degree-of-freedom model that describes the relative motion of spacecraft formations. This six-degree-of-freedom model couples orbital dynamics with attitude dynamics, including relative position dynamics equations and relative attitude dynamics equations. The safety constraint definition unit is used to establish multiple safety-critical constraints that the spacecraft formation needs to satisfy based on mission requirements and environmental information, and the constraints are formalized as zero hyperlevel set functions of state variables. The perturbation observer unit is used to construct a perturbation observer to estimate and compensate for unknown lumped perturbations in the six-degree-of-freedom model online based on the spacecraft's state information. A safety control unit is constructed based on the disturbance observer and safety-critical constraints. The safety controller includes an adjustable adaptive control barrier function for generating time-varying safety constraint boundaries. The parameters of the adjustable adaptive control barrier function are adjusted online through an auxiliary dynamic system. The optimal control solving unit is used to construct a primary and secondary programming problem based on the safety controller, and solve for the optimal safety control command that minimizes the deviation between the actual control input and the nominal control input under the condition of satisfying the safety constraint boundary. The actuator unit is used to receive and execute the optimal safety control command to drive the spacecraft's movement.

[0018] This invention adopts a set of progressive and tightly coupled technical solutions, the core of which lies in building a comprehensive control framework that integrates augmented system modeling, robust disturbance observation, adaptive safety boundary and optimal control decision-making.

[0019] First, establish a unified model for augmented affine systems.

[0020] This invention first establishes a six-degree-of-freedom model describing the relative motion of spacecraft formations, precisely coupling orbital dynamics and attitude dynamics. To fundamentally address actuator saturation (Challenge 1) and unify the handling of various constraints, this invention introduces an auxiliary dynamic system, transforming the original control inputs (forces and torques) into state variables of the augmented system. Through this transformation, the saturation constraints of the physical actuators are seamlessly converted into constraints on the augmented system state, allowing them to be handled within a unified control barrier function (CBF) framework along with other state constraints (such as obstacle avoidance and attitude exclusion zones). The new virtual control inputs are no longer limited by amplitude, which not only simplifies the design of subsequent controllers but also ensures, through dynamic filtering effects, that the physical commands ultimately applied to the actuators are smooth, effectively protecting the hardware system.

[0021] Second, design a perturbation observer based on Robust Error Integration (RISE).

[0022] To address model uncertainties and external time-varying disturbances in the space environment (Challenge 2), this invention designs a disturbance observer based on Robust Error Integral (RISE). This observer can estimate and compensate for the impact of these uncertainties on the system online and in real time. Its design ensures that the disturbance estimation error and its derivative are bounded, and provides accurate disturbance bound information for the subsequent safety controller. This feedforward compensation mechanism is a key prerequisite for the controller to maintain safety constraints in unknown disturbance environments, significantly enhancing the robustness of the system.

[0023] Third, a novel adjustable adaptive control barrier function (DOB-TunableACBF) based on a disturbance observer is constructed.

[0024] This is the core innovation of this invention, aiming to solve the problem of dynamic coupling of multiple constraints and the conservatism of solution (Challenge 3). Traditional CBF uses fixed K-like function parameters, resulting in a static safety boundary, which can easily lead to the non-existence of a control solution when multiple constraints conflict. This invention makes two key improvements to address this: a) Disturbance robustness: The estimates of the disturbance observer and the known upper bound of the error are explicitly integrated into the definition of the higher-order control barrier function (HOCBF), forming the disturbance observer-higher-order control barrier function (DOB-HOCBF). This guarantees that the defined safety set remains positive and invariant even under the worst-case disturbance conditions.

[0025] b) Adjustability and Adaptability: Crucially, this invention no longer treats the K-like function parameters in DOB-HOCBF as preset constants, but defines them as state variables controlled by an auxiliary dynamic system. By designing the control input of this auxiliary dynamic system, these parameters can be adjusted in real time and online, thereby dynamically "relaxing" or "tightening" the safety boundary. This adaptive adjustment capability enables the controller to create feasible space for a safe control solution by adjusting its own parameters under critical conditions where multiple constraints conflict, greatly enhancing the system's adaptability and robustness.

[0026] Fourth, construct an optimal control decision framework based on quadratic programming (QP).

[0027] Finally, this invention integrates the designed nominal controller (for target tracking) and DOB-Tunable ACBF (for safety assurance) into a quadratic programming (QP)-based optimal control framework. This framework solves an optimization problem in real time during each control cycle, with the objective function being to minimize modifications to the nominal control law. Simultaneously, all safety constraints processed by DOB-Tunable ACBF (including position, attitude, and input constraints) are treated as hard constraints in the optimization problem. The control commands output in real time by the QP solver maximize mission performance requirements while absolutely guaranteeing spacecraft safety. This hierarchical optimization strategy achieves an intelligent trade-off between safety and performance.

[0028] Compared with the prior art, the present invention achieves the following significant progress through the organic combination of the above-mentioned parts: 1) High security and robustness: Through the synergistic effect of the perturbation observer and the adaptive barrier function, this invention can effectively cope with unknown bounded perturbations and theoretically guarantee that the safety constraints still hold in the worst case. Compared with traditional methods, its safety margin is more accurate, avoiding unnecessary conservatism.

[0029] 2) Strong adaptability: The innovative adjustable mechanism of this invention makes the safety boundary no longer fixed, but can be intelligently adjusted according to the real-time environment and task status. This significantly reduces the infeasibility problem caused by overly conservative constraints or dynamic coupling of multiple constraints, thereby greatly improving the task success rate.

[0030] 3) Framework Unity: This invention successfully unifies various heterogeneous constraints of different relative orders, such as position constraints, attitude constraints, and input constraints, under a single ACBF framework. Furthermore, through augmented system technology, the complex input saturation problem is transformed into a standard state constraint problem, making the entire control system design more systematic and modular.

[0031] 4) Performance Optimization: Within the QP framework, this invention strives to make minimal modifications to the nominal control commands intended to accomplish the mission (soft target) while ensuring absolute safety (hard constraints). This optimization mechanism ensures that mission performance (such as tracking accuracy and fuel efficiency) is maximized while ensuring safe flight, achieving an effective balance between safety and performance. Attached Figure Description

[0032] Figure 1 This is a schematic flowchart of the method of the present invention; Figure 2 This is a schematic diagram of relative coordinates; Figure 3 This is a three-dimensional trajectory diagram of a spacecraft formation encircling and observing a dynamic target in an embodiment of the present invention, wherein (a)~(d) represent three-dimensional trajectory diagrams at different simulation times, and (e)~(f) represent two-dimensional trajectory diagrams at different simulation times; Figure 4 The graphs are curves showing the change of barrier function values ​​over time for each safety constraint in the embodiments of the present invention, where (a) is a graph of multiple obstacle avoidance constraints and (b) is a graph of multiple attitude restriction constraints. Figure 5 The diagram shows the trajectories of various spacecraft avoiding attitude restrictions in the embodiments of the present invention, where (a) to (c) represent different spacecraft. Detailed Implementation

[0033] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0034] Example 1 This embodiment provides a spacecraft cooperative formation safety control method based on an adjustable adaptive control barrier function, such as... Figure 1 As shown, it includes the following steps: Step S1: Establish a six-degree-of-freedom (6-DOF) model describing the relative motion of the spacecraft formation. This six-DOF model couples orbital dynamics with attitude dynamics, including relative position dynamics equations and relative attitude dynamics equations. Step S2: Based on mission requirements and environmental information, establish multiple safety-critical constraints that the spacecraft formation needs to meet, and formalize the constraints as zero hyperlevel set functions of state variables. Step S3: Design a disturbance observer to estimate and compensate for unknown lumped disturbances in the six-degree-of-freedom model online based on the spacecraft's state information. These lumped disturbances include external environmental disturbances and model uncertainties. Step S4: Construct a safety controller based on a disturbance observer and safety-critical constraints. The safety controller includes an adjustable adaptive control barrier function (DOB-Tunable ACBF) for generating time-varying safety constraint boundaries. The parameters of the adjustable adaptive control barrier function are adjusted online through an auxiliary dynamic system. Step S5: Based on the safety controller, construct a quadratic programming (QP) problem. Under the condition of satisfying the safety constraint boundary, solve for the optimal safety control command that minimizes the deviation between the actual control input and the nominal control input to drive the spacecraft motion.

[0035] The key processes of the above method are described in detail below.

[0036] 1. Six-degree-of-freedom relative kinematics and dynamics modeling of spacecraft This step aims to provide an accurate mathematical model for subsequent controller design. For close-range operations such as spacecraft flybys and target inspections, the coupling effect between attitude and orbit cannot be ignored; therefore, using an LVLH (Local Vertical-Local Horizontal) coordinate system is more advantageous than an inertial frame. For example... Figure 2 As shown, the origin of the LVLH coordinate system is defined at the center of mass of a virtual spacecraft without any external forces acting on it.

[0037] 1.1 Relative Position Dynamics In the ECI (Earth-centric Inertial) coordinate system In the middle, the first The relative position dynamics of a spacecraft with respect to a virtual spacecraft can be expressed as: in, and They represent the first individual spacecraft and virtual spacecraft in The position vector in a system, the relative position vector is defined as follows: . and They represent in The control forces and lumped disturbances described in the system. It is the mass of the spacecraft. It is the Earth's gravitational constant.

[0038] For ease of control, the dynamic model needs to be transformed to the LVLH coordinate system. By rotation matrix (from Tie (System), the relative position vector can be represented as: Taking its second derivative, and considering the effect of coordinate system rotation, we obtain the... A spacecraft in The dynamic equations of relative position in the system: in, It is a virtual spacecraft relative to The angular velocity of the system, and in In system representation. Symbol Represents the antisymmetric matrix of a vector.

[0039] Substituting equation (1) into equation (3), and rearranging, we obtain the equations of relative motion in Euler-Lagrange form: The matrices are defined as follows: Inertia matrix: Coriolis and the centripetal force matrix: Stiffness matrix: Nonlinear gravitational term: The orbital angular velocity of a virtual spacecraft is determined by its true angle of anomaly. Decide: ,in , , and These are the semi-major axis and eccentricity of the virtual orbit, respectively.

[0040] Considering actual control and disturbance Typically in the spacecraft body coordinate system As defined in [the text], the final relative position dynamics model is: in From Tie The rotation matrix of the system.

[0041] For ease of subsequent analysis, equation (5) is written in standard state-space affine form: in, , , .

[0042] 1.2 Attitude Dynamics This embodiment uses unit quaternions to describe the spacecraft's attitude. The spacecraft is in... System relative to The attitude dynamics of the system are: in, It is a posture quaternion. It is relative angular velocity. It is the rotational inertia matrix. and These are the control torque and the disturbance torque, respectively. The correlation matrix for the attitude quaternions is expressed as follows: .

[0043] Similarly, it can be written in state-space affine form: in, , .

[0044] 1.3 Relative Attitude Dynamics The objective of this invention is not attitude alignment, but rather to require the airborne camera to continuously point at the target. Therefore, a desired coordinate system is defined. The camera is in The direction under the system is the unit vector. The desired camera pointing direction is .from The unit vector pointing the spacecraft toward the target in the system is: in The goal is to The position vector of the system.

[0045] The mission requires the camera's line of sight to be aligned with the target, i.e., satisfy the following conditions: ,in From Tie The rotation matrix of the system. From this, the desired attitude quaternion can be derived. and its derivative.

[0046] Ultimately, the attitude error dynamics are derived from the error quaternion. and error angular velocity describe, Its complete dynamic equation is: The control objective is to drive convergence to , This is the correlation matrix of the error quaternions.

[0047] 2. Problem Statement and Definition of Multiple Safety Critical Constraints This invention aims to solve the following two core problems: Problem 1 (Mission Achieved): Under the influence of attitude-orbit coupling, enable the spacecraft formation to ultimately track a dynamic target, maintain a constant observation distance, and maximize the camera's field of view aligned with the target. Mathematically, this can be represented as: in It is a very small positive number. To track the relative position of the target, For tracking distance.

[0048] Question 2 (Process Safety): Under unknown time-varying environments and multiple constraints, the formation can operate safely and continuously, and the controller always meets all constraints, demonstrating excellent adaptability and robustness.

[0049] Therefore, the following categories of safety-critical constraints are defined and formalized as follows: In the form of.

[0050] 2.1 Obstacle Avoidance Constraints To avoid collisions with obstacles such as space debris, the following must be met: in It is the first An obstacle in The location of the system, and It is the minimum envelope radius of the spacecraft and obstacles.

[0051] 2.2 Inter-spacecraft collision avoidance constraints To avoid collisions between spacecraft within a formation, the following conditions must be met: This constraint applies only to spacecraft. and Activated when a communication link exists. , For spacecraft and The relative position vector, , It is a spacecraft and The minimum envelope radius. For spacecraft. Its complete set of anti-collision constraints is ,in It is a spacecraft The set of communication neighbors.

[0052] 2.3 Attitude Forbidden Zone Constraints To protect sensitive payloads such as cameras, they must be kept away from strong light sources such as the sun. Assume... For the first The restricted directions are in If the unit vector of the system is given, then the constraint is: in It is half the field of view of the camera. Let be the camera pointing vector. This constraint is originally non-convex. Through state transformation, it can be converted into a convex constraint: in , It is a constant, which ensures the convexity of the constraint.

[0053] 2.4 Control Input Constraints The physical limits of the actuator require that the control input be bounded: in, and Control force and control torque The maximum amplitude.

[0054] 3. Augmented system modeling and disturbance observer design 3.1 Auxiliary Dynamics for Smooth Control and Constraint Unification To address Challenge 1 (input saturation) and unify the handling of heterogeneous constraints, this invention introduces an auxiliary dynamic system. Traditional methods, such as anti-saturation compensators or simple boundary constraints, cannot guarantee the smoothness of the control signal. This invention uses the actual control input... and Treat them as state variables and design dynamic equations of the form of first-order filters for them: in and It is a new, unconstrained virtual control input. All are time-varying parameters.

[0055] Through this transformation, the original spacecraft dynamics system is converted into an augmented system. For example, the position dynamics (Equation (6)) is augmented as follows: Attitude dynamics (Equation (8)) are also extended: The advantages of this transformation are: 1) it transforms the input constraints (Equation (15)) into state constraints, realizing the unified processing of various constraints; 2) it solves the problem of control signal smoothness caused by input saturation; 3) it also introduces mismatched disturbance, i.e., disturbance term. With new control input items It acts on different channels of the system.

[0056] 3.2 Perturbation Observer Based on RISE (Robust Integral of the Sign of the Error) To address Challenge 2 (external disturbance) and provide disturbance information for the subsequent controller, this invention designs the following RISE (Robust Error Integration) disturbance observer: in, It is the state of the augmented system ( or ), It is the corresponding system matrix. It is a virtual control input ( or ), It is a lumped disturbance. and These are the estimated values ​​of the state and the disturbance, respectively. It is the state estimation error. These are positive definite design parameters, specifically the gain of the positive constant controller. This observer can guarantee the estimation error. Its derivative is bounded, and the function dir(x) = sign(x)|x, in equation (20), x is .

[0057] 4. Construction of the Adjustable Adaptive Control Barrier Function (DOB-TunableACBF) This step is the core of this invention, aiming to address Challenge 3 (constraint coupling and conservatism). This invention proposes a unified, robust, and adaptive framework for higher-order control barrier functions.

[0058] 4.1 Higher-order CBF and perturbation robustness For a safety-critical constraint Its safe set is defined as To ensure the positive invariance of this set, its derivatives must satisfy specific conditions. Let the control input be... The relative degree (IRD) is: Disturbance The relative order (Disturbance Relative Degree, DRD) is (i.e., mismatch perturbation). For Continuous differentiation This yields: in This represents the Li derivative.

[0059] Traditional HOCBF (Higher-Order CBF) definition When there is an unknown disturbance In this case, the inequality contains unknown terms and cannot be used directly. This invention utilizes the aforementioned perturbation observer to propose a perturbation observer-higher-order control barrier function (DOB-HOCBF). Substitute and use the known perturbation to estimate the error bound. and A robust CBF constraint can be derived: in and It is a known function containing the system state and its derivative, and the terms are... It is determined by the parameters of class K function. The polynomial formed is of the form of This formula ensures that the safety constraints still hold under the worst-case perturbation conditions.

[0060] 4.2 Adjustability and Adaptive Mechanism The fundamental limitation of traditional HOCBF lies in its parameters. It is fixed. This results in static safety boundaries, and in scenarios with multiple tightly coupled constraints, it may be impossible to find control inputs that satisfy all constraints. .

[0061] The core innovation of this invention lies in the parameter set Treat it as a controllable state variable Design an auxiliary dynamic system for it: in It is a new auxiliary control input used to adjust parameters. , These are system parameters. Control inputs are designed... Adjust parameters online This changes the shape of the adjustable adaptive control barrier function constraint to adapt to the dynamically changing environment and coupled multiple constraints.

[0062] This dynamic parameter Substituting into the recurrence relation of HOCBF In, it will produce containing Additional items. For example, for In this case, the new constraint becomes: The terms on the right introduce new decision variables. This effectively "relaxes" the CBF constraint, providing better control input. This creates a larger feasible domain.

[0063] Ultimately, the resulting DOB-Tunable-ACBF constraint is defined as follows: in It is an auxiliary input The coefficient term is derived from Derivatives and parameters of each order constitute; It is determined by parameters The remainder term is formed by the derivative of the derivative. This formula constitutes the core safety criterion of this invention.

[0064] 5. Optimal Security Control Framework Based on QP This invention minimizes deviations from the nominal controller while satisfying safety constraints.

[0065] 5.1 Nominal Controller Design Design a nominal controller based on sliding mode control. This is used to drive the system state to track the desired trajectory in order to achieve problem 1. For example, for position tracking, a sliding surface is defined. and design a nominal controller For attitude tracking, a sliding surface is similarly defined. and design . All are nominal inputs .

[0066] 5.2 Construction and Solution of QP Problems In each control cycle, construct and solve the following quadratic programming (QP) problem: in, It is the virtual control input to be solved. These are auxiliary parameters used to adjust the input. The first term of the objective function ensures that the control behavior serves the task objective as much as possible, and the second term... It is a regularization term used to penalize adjustments to the safety boundary, ensuring that it is only activated when necessary. The constraint condition is to apply equation (25) to each safety constraint. (Obstacle avoidance, collision avoidance, attitude restriction zones, input restrictions, etc.) are rewritten as linear inequalities.

[0067] 5.3 Implementation of specific constraints The specific form of constraints of different relative orders differs in QP. The following are the derivative terms of some key constraints, used to construct the coefficient matrix in QP. : Obstacle avoidance constraint (IRD=3): Attitude restricted area constraint (IRD=3): The partial derivatives for each term are calculated as follows: The optimal solution output by the QP solver and This is the optimal safety control instruction at the current moment. The smooth physical command applied to the actuator is finally obtained through the inverse transformation of auxiliary dynamics (i.e., equations (16) and (17)). and .

[0068] This embodiment uses the following simulation experiment to verify the effectiveness and robustness of the above method.

[0069] Simulation settings: such as Figure 2 As shown, a formation of three spacecraft is tasked with encircling and continuously observing a target, and setting up a virtual reference spacecraft. The space environment contains four static obstacles and four attitude exclusion zones. The spacecraft's mass... Moment of inertia .

[0070] Simulation results: such as Figure 3The diagram shows the 3D trajectory at different simulation moments, with icons including Obstacle, Start Point: Spacecraft, Start Point: Target, Target, and Spacecraft 1-3. Figure 3 In the process, the formation started from its initial position, and the controller based on the aforementioned method successfully guided the spacecraft to avoid obstacles. Faced with the dual constraints of position and attitude, DOB-Tunable ACBF successfully calculated feasible safety control commands by adjusting internal parameters, avoiding failures caused by overly rigid constraints in traditional CBF methods. Figure 4 As shown, all barrier function values ​​remained non-negative throughout the mission, verifying the effectiveness and robustness of the method of this invention. The graphs for the Safety Region, Unsafe Region, and individual spacecraft are displayed. Furthermore, Figure 5 It shows the start point, end point, and the real trajectory and desired trajectory for avoiding attitude exclusion zones of the spacecraft. Figure 5 This indicates that the spacecraft formation successfully avoided all restricted areas and aimed the camera at the target.

[0071] If the above methods are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0072] Example 2 This embodiment provides a spacecraft cooperative formation safety control system, which includes: (a) Dynamics modeling unit, used to build and store six-degree-of-freedom relative kinematics and dynamics models of spacecraft formations; (b) Safety constraint definition unit, used to define safety constraint functions such as obstacle avoidance, collision prevention, attitude restriction zone and input limit according to task requirements and environmental information; (c) Disturbance observer unit, used to estimate the lumped disturbances to the system in real time based on the spacecraft's state information; (d) Safety control unit, the core of which is an adjustable adaptive control barrier function module. This module receives the disturbance estimate from the disturbance observer unit and, in conjunction with the auxiliary dynamic system, generates a time-varying safety constraint boundary. (e) Optimal control solving unit, used to construct and solve quadratic programming problems, calculate optimal control commands, including control force and torque commands, under the constraints of the safety control unit output; (f) Actuator unit, used to receive and execute optimal control commands to drive the spacecraft's movement.

[0073] Furthermore, the safety control unit works in conjunction with the optimal control solution unit. When the spacecraft approaches any constraint boundary, the constraints generated by the safety control unit will dominate the control output, enabling the spacecraft to fly safely along the boundary. When it is far from the constraint boundary, the control output is mainly determined by the nominal controller designed to complete the tracking mission, thereby achieving the optimization of mission performance while ensuring absolute safety.

[0074] The rest is the same as in Example 1.

[0075] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A spacecraft cooperative formation safety control method based on an adjustable adaptive control barrier function, characterized in that, Includes the following steps: A six-degree-of-freedom model describing the relative motion of spacecraft formations is established. This six-degree-of-freedom model couples orbital dynamics with attitude dynamics, including relative position dynamics equations and relative attitude dynamics equations. Based on mission requirements and environmental information, multiple safety-critical constraints that the spacecraft formation needs to satisfy are established, and the constraints are formalized as zero hyperlevel set functions of state variables. Design a perturbation observer to estimate and compensate for unknown lumped perturbations in the six-degree-of-freedom model online based on the spacecraft's state information; A safety controller based on the disturbance observer and safety-critical constraints is constructed. The safety controller includes an adjustable adaptive control barrier function for generating time-varying safety constraint boundaries. The parameters of the adjustable adaptive control barrier function are adjusted online through an auxiliary dynamic system. Based on the safety controller, a quadratic programming problem is constructed. Under the condition of satisfying the safety constraint boundary, the optimal safety control command that minimizes the deviation between the actual control input and the nominal control input is obtained to drive the spacecraft motion. The adjustable adaptive control barrier function Defined as a state variable , And design an auxiliary dynamic system for it. By designing control input Adjust parameters online This alters the form of the adjustable adaptive control barrier function constraint to adapt to dynamically changing environments and coupled multiple constraints. , For system parameters; The quadratic programming problem is expressed as: in, It is the virtual control input to be solved. For nominal input, It is an auxiliary parameter adjustment input. It is a regularization term used to penalize adjustments made to the safety boundary. The coefficient matrix, This is the disturbance estimate. This refers to the system status.

2. The spacecraft cooperative formation safety control method based on an adjustable adaptive control barrier function according to claim 1, characterized in that, In the orbital coordinate system, the relative position dynamic equation is expressed as: in, For spacecraft indexing, It is a relative position vector. , , Here are the inertia matrix, the Coriolis and centripetal force matrix, and the gravitational gradient matrix. It is a nonlinear gravitational term. For aggregated disturbances, For control.

3. The spacecraft cooperative formation safety control method based on an adjustable adaptive control barrier function according to claim 1, characterized in that, The relative attitude dynamics equation is expressed as: in, Let be the quaternion representing the error from the desired pose to the current pose. Relative angular velocity, For rotational inertia, To control the torque, For the disturbance torque, This is the correlation matrix of the error quaternions.

4. The spacecraft cooperative formation safety control method based on an adjustable adaptive control barrier function according to claim 1, characterized in that, The safety-critical constraints include at least several of the following: obstacle avoidance constraints, inter-spacecraft collision avoidance constraints, attitude exclusion zone constraints, and control input constraints. The obstacle avoidance constraint is expressed as follows: ,in, For the first The location of the spacecraft For the first The location of the obstacle and These are the radii of the envelope spheres for the spacecraft and the obstacle, respectively. The inter-spacecraft collision avoidance constraint is expressed as follows: ,in, For the first The location of the spacecraft It is a spacecraft The minimum radius of the envelope sphere; The attitude restricted area constraint is expressed as follows: ,in, Half of the camera's field of view For the first A restricted area direction vector, Let be the rotation matrix from the body coordinate system to the inertial system. The camera pointing vector; The control input constraint is expressed as follows: and ,in, and Control force and control torque The maximum amplitude.

5. The spacecraft cooperative formation safety control method based on an adjustable adaptive control barrier function according to claim 4, characterized in that, An augmenting system is introduced to solve the smoothness problem of the control input constraints. The augmenting system is expressed as follows: in, and The actual control input is considered as the state variable of the augmented system. and This provides new virtual control inputs, thereby transforming input constraints into state constraints. All are time-varying parameters.

6. The spacecraft cooperative formation safety control method based on an adjustable adaptive control barrier function according to claim 1, characterized in that, The disturbance observer is a robust error integral-based disturbance observer, and its dynamic form is as follows: in, For system status, It is the corresponding system matrix. and These are the estimated values ​​of the state and the disturbance, respectively. , , For the gain of a normal controller, the function dir(x) = sign(x)|x, It is the virtual control input to be solved.

7. The spacecraft cooperative formation safety control method based on an adjustable adaptive control barrier function according to claim 1, characterized in that, The adjustable adaptive control barrier function defines the safety control set through the following inequality: in, Let be any security constraint function, Let the relative order of this constraint be... and For Li Daoshu, and For terms related to disturbance estimation, For coefficient terms that include auxiliary dynamic variables, To assist in the control input of the dynamic system, and To assist the residual derivative term of the dynamic system, It is the virtual control input to be solved. For the perturbation estimation error bound, It is an estimate of the disturbance.

8. A spacecraft cooperative formation safety control system based on an adjustable adaptive control barrier function, characterized in that, include: The dynamics modeling unit is used to build and store a six-degree-of-freedom model that describes the relative motion of spacecraft formations. This six-degree-of-freedom model couples orbital dynamics with attitude dynamics, including relative position dynamics equations and relative attitude dynamics equations. The safety constraint definition unit is used to establish multiple safety-critical constraints that the spacecraft formation needs to satisfy based on mission requirements and environmental information, and the constraints are formalized as zero hyperlevel set functions of state variables. The perturbation observer unit is used to construct a perturbation observer, which estimates and compensates for unknown lumped perturbations in the six-degree-of-freedom model online based on the spacecraft's state information. A safety control unit is constructed based on the disturbance observer and safety-critical constraints. The safety controller includes an adjustable adaptive control barrier function for generating time-varying safety constraint boundaries. The parameters of the adjustable adaptive control barrier function are adjusted online through an auxiliary dynamic system. The optimal control solving unit is used to construct a primary and secondary programming problem based on the safety controller, and solve for the optimal safety control command that minimizes the deviation between the actual control input and the nominal control input under the condition of satisfying the safety constraint boundary. An actuator unit is used to receive and execute the optimal safety control command to drive the spacecraft's movement; The adjustable adaptive control barrier function Defined as a state variable , And design an auxiliary dynamic system for it. By designing control input Adjust parameters online This alters the form of the adjustable adaptive control barrier function constraint to adapt to dynamically changing environments and coupled multiple constraints. , For system parameters; The quadratic programming problem is expressed as: in, It is the virtual control input to be solved. For nominal input, It is an auxiliary parameter adjustment input. It is a regularization term used to penalize adjustments made to the safety boundary. The coefficient matrix, This is the disturbance estimate. This refers to the system status.

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