A Nonlinear Model Predictive Control Method for NRHO (Normally Oriented Hierarchical) Obstacle Avoidance

Abstract

This invention discloses a nonlinear model predictive control method for obstacle avoidance during NRHO rendezvous, belonging to the field of spacecraft rendezvous control technology. Addressing the simultaneous needs of rendezvous mission and dynamic debris avoidance during NRHO rendezvous under a three-body or high-fidelity ephemeris dynamics environment, modeling and control design are conducted within this high-fidelity ephemeris dynamics environment. A three-dimensional mapping method suitable for non-convex obstacle avoidance domains with apertures in three-dimensional space is constructed, mapping the non-convex feasible domain induced by obstacles in the original space to a convex feasible domain in convex space. A nonlinear model predictive control problem with obstacle avoidance constraints is constructed within the mapped space, unifying rendezvous terminal accuracy, control cost, thrust constraints, and obstacle avoidance constraints into a single optimization framework. This achieves unified closed-loop control of rendezvous and docking and dynamic debris avoidance under a three-body or high-fidelity dynamics background.

Description

Technical Field

[0001] This invention belongs to the technical field of spacecraft rendezvous control, and in particular relates to a nonlinear model predictive control method for NRHO rendezvous and obstacle avoidance. Background Technology

[0002] Research on autonomous rendezvous and docking (RVD) under three-body dynamics (such as CRTBP or high-fidelity perturbation models) has developed rapidly in recent years, resulting in closed-loop guidance and control methods such as SDRE control, Pontryagin optimal control, NMPC, time shift manager, and meta-reinforcement learning. Existing technologies face the following shortcomings: Shortcoming 1: Existing three-body RVD methods generally lack dynamic obstacle avoidance constraints or only perform post-trajectory corrections, making it difficult to ensure safety in high-density lunar orbit traffic. This is because research focuses primarily on terminal accuracy and closed-loop stability, lacking solvability modeling and real-time optimization mechanisms for non-convex obstacle avoidance domains. Shortcoming 2: Existing three-body obstacle avoidance designs are mostly single-spacecraft evasion maneuvers, decoupled from the coupling constraints of rendezvous and docking missions such as LOS cones, thrust constraints, and terminal tolerances. This is because separating obstacle avoidance from rendezvous and docking leads to inconsistent constraints, and the strong nonlinearity of three-body systems makes it difficult to guarantee closed-loop feasibility through segmented splicing. Defect 3: Two-body obstacle avoidance methods are difficult to transfer to the NRHO three-body environment; the assumptions of linearized relative motion and convex safety region do not hold in the vicinity of NRHO. Reason: The NRHO region exhibits multi-body gravitational coupling and strong nonlinearity, and the debris obstacle avoidance domain naturally exhibits a non-convex structure with "holes" in three-dimensional space. Defect 4: Non-convex set mapping / homeomorphism convexification is mature in two-dimensional robot scenarios, but lacks construction and verification for three-dimensional, time-varying obstacles and three-body dynamic coupling. Reason: Three-dimensional topological cutting, mapping invertibility, and interface mechanisms with NMPC recursive solutions have not yet been established. Summary of the Invention

[0003] The purpose of this invention is to provide a nonlinear model predictive control method for NRHO (Non- ...

[0004] To achieve the above objectives, this invention provides a nonlinear model predictive control method for NRHO (Normally Oriented Hierarchical Organization) obstacle avoidance, comprising the following steps: Step 1: Establish a high-fidelity dynamic model and its corresponding baseline NRHO orbital family in the lunar center inertial frame; Step 2: Based on the high-fidelity dynamics model, a continuous dynamics model of the objects to be calculated during the rendezvous is given. The objects to be calculated include the tracking spacecraft, the target spacecraft, and the debris. The rendezvous and obstacle avoidance problem is established as follows: the target spacecraft moves along the NRHO trajectory under the influence of natural dynamics; the tracking spacecraft is initially located several kilometers away from the target spacecraft, equipped with a low-thrust propulsion system, and needs to rendezvous with the target spacecraft; the space debris evolves in the Earth-Moon space according to natural dynamics; based on the rendezvous and obstacle avoidance problem, the objective function, acceleration constraints, and obstacle avoidance constraints are obtained accordingly. Step 3: Establish discrete dynamic models for the tracking spacecraft, the target spacecraft, and the debris, and establish constraints on the terminal rendezvous accuracy; Step 4: Based on the discrete rendezvous and obstacle avoidance problem, and combining the discrete dynamics model and the constraints of terminal rendezvous accuracy, establish a conventional NMPC solution problem; Step 5: Construct local coordinates and split lines, convexize the geometric collision constraints, and construct an invertible mapping from the original space to the mapping space; Step Six: Based on the content of Steps Four and Five, construct and solve the non-convex NMPC optimization problem based on the mapping space to obtain the optimal control sequence for tracking the spacecraft, and use the optimal control sequence to control the tracking spacecraft.

[0005] Preferably, in step one, establishing a high-fidelity dynamic model requires considering perturbation factors, including solar perturbation, radiation pressure perturbation, lunar J2 gravitational perturbation, and Earth J2 gravitational perturbation. The specific perturbation factors are as follows: To consider the actual perturbations in the Earth-Moon space, in the lunar-centric inertial coordinate system... Modeling in the middle, obtaining the computational object in the coordinate system acceleration in The formula is as follows: ; In the above formula, Acceleration caused by the Moon's gravitational field Acceleration caused by Earth's gravitational field Due to the gravitational acceleration of the sun, Let SRP be the solar radiation pressure acceleration; then define the computational object in the coordinate system. The status in is as follows: ; In the above formula, and These respectively represent the coordinate system in which the computational object is located. The position and velocity of the object are used to calculate its dynamics under high-fidelity ephemeris dynamics. as follows: ; ; In the above formula, The dynamic formula representing the object of computation, This represents the acceleration of the object being calculated. Represents the velocity of the object being calculated; the Moon and Earth are in their respective fixed coordinate systems. The gravitational fields in all of them use spherical harmonic gravitational potential. It means that, among them, , and Representing the Moon and Earth respectively, we obtain the universal gravitational potential. The formula is as follows: ; In the above formula, They respectively represent the objects of calculation relative to celestial bodies. The radial distance, latitude and longitude, celestial bodies gravitational constant, celestial bodies The average radius, subscript and Let represent the order and degree of the spherical harmonic expansion, respectively. To normalize the Legendre polynomial, and celestial bodies Normalized spherical harmonic coefficients; definition This indicates that the vector is transferred from the inertial frame. Transformation to solid connection The direction cosine matrix, then the object being calculated in The coordinates in the image are as follows: ; definition For the calculation object in In spherical coordinates, then spherical coordinates and The relationship is as follows: ; gravitational potential The gradient of celestial bodies exist Gravitational acceleration caused by the middle as follows: ; , ; The above formula corresponds to the moon in Gravitational acceleration caused by the middle and Earth Gravitational acceleration caused by the middle This corresponds to the lunar gravitational acceleration. The formula is as follows: ; Earth's tidal gravitational acceleration The formula is: ; In the above formula, This is the position vector pointing from the Moon to the Earth; Solar gravitational acceleration for: ; In the above formula, Represents the solar gravitational constant. This represents the position vector pointing from the Moon to the Sun; Solar radiation pressure acceleration for: ; In the above formula, As the shadow factor, It is the product of the solar radiation pressure coefficient and the area-to-mass ratio. Solar luminosity It is the speed of light in a vacuum. The baseline NRHO orbital family was obtained, and the candidate orbital family was set to Earth-Moon. The near-straight halo orbit NRHO is generated using a high-fidelity ephemeris model. To characterize the suitable orbital range for rendezvous, the mean apogee angle of NRHO is introduced. : ; In the above formula, This is the duration since the lunar flyby from the perigee. For orbital period, perigee and apogee are defined as the points on NRHO with the smallest and largest distances from the lunar center, respectively. Amplitude is defined as from the near-month point to The perpendicular distance between planes corresponds to The amplitude is used as a criterion for selecting different NRHO operating conditions.

[0006] Preferably, step two includes the following specific details: During the tracking of a spacecraft approaching a target spacecraft, debris trajectories intersecting with the tracking spacecraft's intersection path pose a collision risk and need to be handled during guidance. (In the coordinate system...) In the process of tracking the status of spacecraft The status of the target spacecraft and the state of fragments They are as follows: ; ; ; definition These represent the tracking spacecraft, the target spacecraft, and the debris, respectively. and Let represent the corresponding position and velocity vectors, respectively. Based on a high-fidelity dynamics model, the motion of the tracked spacecraft satisfies the following controlled dynamics: ; In the above formula, To track the low thrust acceleration of the spacecraft, for The initial state of the spacecraft is constantly tracked, and the motion of the target spacecraft and debris follows natural dynamics as follows: ; ; In the above formula, and The target spacecraft and debris were respectively located in The initial state at a given moment; The objective function for the rendezvous and obstacle avoidance problem is set, and a quadratic objective function is used to penalize the relative position error. Relative speed error and control of energy The formulas for relative position error and relative velocity error are as follows: ; The corresponding objective function is as follows: ; In the above formula, , and All are symmetric positive semidefinite weighted matrices; Acceleration constraints are set, and since the tracking spacecraft's thrust capability is limited, each control component is subject to the maximum thrust value. The constraint is such that the acceleration constraint formula is: ; ; in, The infinite norm of the control vector is represented; Set debris obstacle avoidance constraints, set Let the equivalent safety radius be the sum of the radii of the tracking spacecraft and the debris. The formula for the obstacle avoidance constraint is as follows: ; The non-convexity of the debris obstacle avoidance constraint works in conjunction with the nonlinear high-fidelity ephemeris model.

[0007] Preferably, step three includes the following specific details: Set the sampling period to and define ,in The formula for tracking the discrete-time dynamics of spacecraft, target spacecraft, and debris, as a discrete-time index, is as follows: ; ; ; in, Indicates time The control acceleration of the tracking spacecraft, Indicates the interval The single-step propagation mapping obtained by numerical integration of continuous dynamics at each time step... The system is subject to the following constraints: ; { | ; ; S={ | ≤ }; In the above formula, This represents the defined allowed control set. Defined set of allowed states, By fragment location And it changes over time; the control objective is to keep the tracking spacecraft's state unchanged. The intersection condition is satisfied, that is, there exists a certain It satisfies the following: ; in, and >0 represents the relative position and relative speed tolerances of the rendezvous terminals.

[0008] Preferably, in step four, the conventional NMPC problem-solving process is given as follows: To address the online guidance issue in NRHO rendezvous and obstacle avoidance, at each sampling moment... A nonlinear model predictive control (NMPC) approach is used to solve a finite-time optimal control problem. This problem is constrained by a high-fidelity ephemeris dynamics model, as well as state and control constraints. Based on the given discrete propagation relationships and constraint set, the conventional NMPC formula is as follows: ; The constraints are as follows: ; ; ; ; ; ; ; In the above formula, This represents the control sequence to be optimized; and Let represent the control time domain and the prediction time domain, respectively. The corresponding objective functions are as follows: ; in, and The formula is as follows: ; The objective function described above penalizes relative position error, relative velocity error, and control energy simultaneously.

[0009] Preferably, in step five, the invertible mapping from the original space to the mapped space is constructed as follows: Invertible mappings are constructed in three steps: S1: Cross-sectional geometry: Characterization Annular region on the cross section; let For the center of the debris, given the location of the tracking spacecraft... Considering height place Cross section, and define along Axis height offset as follows: ; On this cross section, the intersection yes A disk in a plane, its boundary being a radius. The formula is as follows: ; The aforementioned disk is called The fragment boundary on the cross section, therefore, when When, the debris on the cross-section induces free space is in a ring shape; S2: Splitting operation, introducing a splitting line on the cross-section: Due to the existence of internal cavities, this annular region is non-convex. The splitting plane s intersects with the plane to form a splitting line. To distinguish which side of the splitting line the tracking spacecraft is located on and to characterize its angular position around the debris on the cross-section, an angular coordinate relative to the direction of the splitting line is introduced; Let be the relative position vector projected onto the plane, is the unit direction of the splitting line on the same cross-section. Calculate the unsigned angle between as follows: as follows: ; Take as the reference ray. To specify a consistent direction for the angular coordinate on the cross-section, use the signed area of the parallelogram spanned by and as follows: ; In the above formula, when , it means a counterclockwise rotation from to , which is equivalent to being on the right side of . When , it means a clockwise rotation, which is equivalent to being on the left side of . Then the signed angular coordinate is defined as: ; After the splitting operation, the entire annular region around the debris cavity on the cross-section is covered by the interval and , and they represent the same ray in the original space; After the splitting operation, a coordinate also needs to be introduced to measure the in-plane distance from the tracking spacecraft to the debris boundary on the cross-section and to be used for imposing obstacle avoidance constraints in the optimal control problem. For a given altitude , this in-plane distance is defined as follows: ; where The formula is as follows: ; exist When, it means Located at the boundary of the debris Above; at When, it means Located outside the fragment boundary and having a positive margin; When, it means Located inside the boundary of the fragment, that is, in The debris avoidance constraint was violated at the cross-section. S3: Mapped coordinates: Reparameterize the free space to give the allowable set a convex representation; homeomorphism A convex mapping state space is defined, denoted as . ; definition Using coordinate axes in the mapping space, we obtain the tracking spacecraft in convex space. The position in the middle is as follows: ; Definition: (1) Signed angular coordinates on the cross section (2) In-plane distance from spacecraft to debris boundary tracked on cross section (3) Height offset along the z-axis Then three-dimensional mapping The formula is as follows: ; Mapped allow set for: ; The above equation is the Cartesian product of a convex set, therefore it is a convex set. Geometrically, the splitting operation unfolds the ring-shaped region into a strip-shaped region; the splitting plane... The selection of this parameter affects the obstacle avoidance trajectory of the tracking spacecraft; its direction is determined based on relative geometry and is used to specify the tracking spacecraft's path. relative to the cross section The preferred bypass side is the side from which the target spacecraft and the tracking spacecraft are located. When the target spacecraft and the tracking spacecraft are on the same side of the debris center, it is usually more direct to bypass from that side. Therefore, the split plane is arranged on the opposite side. In the mapping space, the angular coordinates are discontinuous at this plane, so the optimization process will naturally suppress crossing the plane, and the final trajectory will also tend to bypass the debris from the expected side.

[0010] Preferably, in step six, the specific content of constructing and solving the mapping-based NMPC solution is as follows: 3D mapping Each allowed set Transformed into the allowed set after mapping Such a convex representation makes NMPC subproblems easier to solve and improves feasibility and numerical convergence. To integrate 3D mapping into the conventional NMPC scheme, at each sampling time... Construct the following non-convex NMPC problem: ; Its constraints are: ; ; ; ; ; ; ; In the above formula, , To efficiently solve the non-convex NMPC problem within the rolling time domain framework, AL-iLQR is used as the internal solver for the defined convex map allowable set. At each sampling time, the current states of the tracking spacecraft, the target spacecraft, and the debris are used as initial values ​​to solve the finite-time optimal control problem. An augmented Lagrangian layer is used to handle the mapping state constraints, while the iterative LQR process is used to efficiently update the control sequence. The control sequence obtained at the previous sampling time is used as the hot start of the current optimization, thereby improving the numerical efficiency in the rolling time domain implementation.

[0011] The preferred implementation process for a non-convex NMPC solution is as follows: Given an initial state and and mapping Intersection tolerance and safety threshold Then, set the time index. Then, the splitting plane is selected based on the relative geometric relationship. And construct the corresponding mapping. Before the intersection condition is met, the control sequence is... Initialize the sequence and update the control sequence using the AL-iLQR solution, setting the first control variable of the control sequence as... Control measures are applied to the tracking spacecraft to monitor the system status. and mapped coordinates Update the time index to... Repeat the above process until the rendezvous conditions are met.

[0012] Therefore, the present invention employs the above-mentioned nonlinear model predictive control method for NRHO intersection obstacle avoidance, which has the following advantages: (1) Non-convex obstacle avoidance domain convexification solution: 3D mapping reconstructs the 3D non-convex free space into a convex feasible domain, enabling NMPC to handle obstacle avoidance constraints in the convex space, thus improving feasibility and real-time performance.

[0013] (2) Rendezvous and obstacle avoidance integrated closed loop: Within the same NMPC framework, track error, control energy, thrust limit and obstacle avoidance constraints are jointly processed to avoid the inconsistency and infeasibility risks caused by segmented planning-tracking.

[0014] (3) Adapted to three-body / high-fidelity dynamics: It does not depend on the two-body linearization model and the convex safety region assumption, and is suitable for strong nonlinearity, multi-body perturbation and three-dimensional obstacle avoidance scenarios near NRHO.

[0015] (4) Engineering scalability: It can be extended to multi-fragment scenarios. By simply activating obstacle avoidance constraints for the nearest fragment at each sampling time, the resulting subproblem can still be reduced to a single-fragment form. The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0016] Figure 1 This is a flowchart of a nonlinear model predictive control method for NRHO (Normally Oriented Hierarchical Organization) obstacle avoidance according to the present invention. Figure 2 This is a schematic diagram of dynamic debris obstacle avoidance during NRHO intersection in a nonlinear model predictive control method for NRHO intersection obstacle avoidance according to the present invention. Figure 3 This invention relates to a nonlinear model predictive control method for NRHO rendezvous and obstacle avoidance, specifically a lunar-centered rotating coordinate system based on a high-fidelity ephemeris model. Reference Earth-Moon Southbound NRHO; Figure 4 This is a schematic diagram in three dimensions and two dimensions of the split plane used in the nonlinear model predictive control method for NRHO intersection obstacle avoidance according to the present invention. Figure 5 This invention relates to a nonlinear model predictive control method for NRHO rendezvous and obstacle avoidance, which tracks the relative rendezvous trajectories of a spacecraft and a target spacecraft. Figure 6 This is a comparison diagram of the relative distance and relative velocity between the tracking spacecraft and the target spacecraft in a nonlinear model predictive control method for NRHO rendezvous and obstacle avoidance according to the present invention. Figure 7 This is a control comparison diagram showing the tracking spacecraft with obstacle avoidance enabled and disabled in a nonlinear model predictive control method for NRHO rendezvous and obstacle avoidance according to the present invention. Figure 8 The closest moment in the nonlinear model predictive control method for NRHO rendezvous and obstacle avoidance of this invention. A diagram illustrating the local obstacle avoidance process of the tracking spacecraft and debris in a fixed debris center coordinate system; Figure 9 This is a graph showing the evolution of the relative distance between the tracking spacecraft and debris over time in a nonlinear model predictive control method for NRHO rendezvous and obstacle avoidance according to the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Specific model specifications need to be selected and determined according to the actual specifications of the device, etc. The specific selection calculation method adopts existing technology in the art, and therefore will not be described in detail.

[0018] Example like Figure 1 As shown, this invention provides a nonlinear model predictive control method for NRHO (Normally Oriented Hierarchical) obstacle avoidance, comprising the following steps: Step 1: In the lunar-centric inertial frame, establish a high-fidelity dynamic model and its corresponding reference NRHO orbital family. Establishing the high-fidelity dynamic model requires considering perturbation factors, including solar perturbation, radiation pressure perturbation, lunar J2 gravitational perturbation, and Earth J2 gravitational perturbation. The specific perturbation factors are as follows: To account for actual perturbations in Earth-Moon space, in the lunar-centric inertial coordinate system... Modeling in the middle, obtaining the computational object in the coordinate system acceleration in The formula is as follows: ; in, a_Earth represents the acceleration caused by the Moon's gravitational field, and a_Earth represents the acceleration caused by the Earth's gravitational field. Due to the gravitational acceleration of the sun, Let solar radiation pressure (SRP) be the acceleration, and then the object to be calculated in the coordinate system be defined. The status in is as follows: ; in, and Let represent the position and velocity of the object in [I], respectively. Then, the dynamics of the object under high-fidelity ephemeris dynamics can be written as: ; ; In the above formula, The dynamic formula representing the object of computation, This represents the acceleration of the object being calculated. Indicates the speed of the object being calculated; The gravitational fields of the Moon and Earth: Both the Moon and Earth's gravitational fields exhibit significant non-spherical effects. To characterize these effects, the Moon and Earth are positioned in their respective fixed coordinate systems. The gravitational fields in all of them use spherical harmonic gravitational potential. Indicates, subscript and Representing the Moon and Earth respectively, the universal gravitational potential. The formula is: ; variable These represent the spacecraft's position relative to the celestial body. The radial distance, latitude and longitude, celestial bodies gravitational constant, celestial bodies The average radius, and Let represent the order and degree of the spherical harmonic expansion, respectively. To normalize the Legendre polynomial, and celestial bodies The normalized spherical harmonic coefficients.

[0019] set up This indicates that the vector is transferred from the inertial frame. Transformation to solid connection The direction cosine matrix is ​​used to realize the inertial frame. and fixed coordinate system Coordinate transformation, computational object in fixed connection The position in the middle is as follows: ; definition For the calculation object in In spherical coordinates, then spherical coordinates and The relationship is as follows: ; gravitational potential The gradient of celestial bodies exist Gravitational acceleration caused by the middle as follows: ; , , ; The above formula corresponds to the moon in Gravitational acceleration caused by the middle and Earth Gravitational acceleration caused by the middle This corresponds to the lunar gravitational acceleration. The formula is as follows: Earth's tidal gravitational acceleration The formula is: in, This is the position vector pointing from the Moon to the Earth. Solar gravitational acceleration for: ; in, Represents the solar gravitational constant. This represents the position vector pointing from the Moon to the Sun.

[0020] Solar radiation pressure acceleration for: ; In the above formula, As the shadow factor, It is the product of the solar radiation pressure coefficient and the area-to-mass ratio. Solar luminosity For the NRHO rendezvous mission, since the spacecraft is typically far from the host object, the shadowing effect is negligible in most cases. Therefore, the shadow is set to a constant value. .

[0021] The baseline NRHO orbital family is obtained, and the candidate orbital family considered in this invention is the Earth-Moon orbital family. The near-straight halo orbit (NRHO) is generated using a high-fidelity ephemeris model. To characterize the orbital range suitable for rendezvous, the mean apogee angle of the NRHO is introduced. ; In the above formula, This is the duration since the lunar flyby from the perigee. The orbital period is defined as the perigee and apogee, respectively, as the points with the smallest and largest lunar center distances on the NRHO. In this embodiment, the recommended rendezvous interval is... In addition, NRHO's Amplitude is defined as from the near-month point to The perpendicular distance between the planes. The amplitude will be used as a criterion for selecting different NRHO operating conditions in subsequent analyses, such as... Figure 3 As shown, the lunar-centered rotating coordinate system in the high-fidelity ephemeris model. Reference Earth-Moon Southbound NRHO, the track starts from The spread begins, and the intersection area... Highlighted in red, the moon is represented by a solid circle, while the perigee and apogee are represented by hollow squares and hollow triangles, respectively. Figure 3 (a) represents the 3D view. Figure 3 (b), (c), and (d) represent projections of the 3D view in different directions.

[0022] Step Two: Based on a high-fidelity dynamics model, a continuous dynamics model of the objects to be calculated during the rendezvous is given. The objects to be calculated include the tracking spacecraft, the target spacecraft, and debris. The rendezvous and obstacle avoidance problem is established as follows: the target spacecraft moves along the NRHO trajectory under natural dynamics; the tracking spacecraft is initially located at a distance of kilometers from the target spacecraft, equipped with a low-thrust propulsion system, and needs to rendezvous with the target spacecraft; the space debris is assumed to evolve according to natural dynamics in the Earth-Moon space. The objective function, acceleration constraints, and obstacle avoidance constraints for the rendezvous and obstacle avoidance problem are obtained accordingly. Figure 2 The diagram shown illustrates dynamic debris obstacle avoidance during the NRHO rendezvous process. The lunar center J2000 inertial coordinate system is denoted as... The lunar rotating coordinate system is denoted as The baseline trajectory represents the nominal intersection path without considering debris obstacle avoidance.

[0023] Regarding the rendezvous and obstacle avoidance problem, during the approach of the tracking spacecraft to the target spacecraft, any debris whose trajectory intersects with the rendezvous path of the tracking spacecraft may pose a direct collision risk. Therefore, this risk must be addressed during the guidance process. The specific process for establishing the rendezvous and obstacle avoidance problem is as follows: In coordinate system In the process of tracking the status of spacecraft The status of the target spacecraft and the state of fragments They are as follows: ; ; ; In the above formula, here is defined Representing the tracking spacecraft, the target spacecraft, and debris respectively, the corresponding... and Let the position and velocity vectors of different computational objects be represented respectively. Then, the motion of the tracked spacecraft satisfies controlled dynamics: ; In the above formula, To track the low thrust acceleration of the spacecraft, for If we continuously track the initial state of the spacecraft, the motion of the target spacecraft and debris satisfies the following natural dynamics: ; ; in, and The target and the fragments are respectively in The initial state at a given moment.

[0024] The objective function for the rendezvous and obstacle avoidance problem is set, and a quadratic objective function is used to penalize the relative position error. Relative speed error and control of energy The corresponding formula is as follows: ; Combined with energy control The objective function is obtained. as follows: ; In the above formula, , and It is a symmetric positive semi-definite weighted matrix.

[0025] Acceleration constraints are set, and due to the limited thrust capability of the tracking spacecraft, each control component is subject to a maximum value. The constraints, therefore, the control saturation constraint is defined as ; ; In the above formula, The infinite norm of the control vector is represented; Debris obstacle avoidance constraints, set The equivalent safety radius is defined as the sum of the radii of the tracking spacecraft and the debris. To avoid collisions between the tracking spacecraft and the debris, the following obstacle avoidance constraints are applied: ; The non-convexity of debris obstacle avoidance constraints, combined with the nonlinear high-fidelity ephemeris model, poses a significant challenge to subsequent optimal guidance design.

[0026] Step 3: Establish discrete dynamic models for the tracking spacecraft, the target spacecraft, and the debris, and establish constraints on the terminal rendezvous accuracy; the process of establishing the corresponding discrete dynamic models is as follows: The states of the tracking spacecraft, target spacecraft, and debris in the lunar inertial coordinate system, as described in step two, are as follows: and ; set up These represent the tracking spacecraft, the target spacecraft, and the debris, respectively. and Let represent the position and velocity vectors of the corresponding computational object, respectively. Then, the motion of the tracked spacecraft satisfies controlled dynamics. in, For low thrust acceleration, for Constantly track the initial state of the spacecraft. The motion of the target spacecraft and debris follows natural dynamics. ; ; in, and The target spacecraft and debris were respectively located in The initial state at a given moment.

[0027] Set the sampling period to and define ,in The formula for tracking the discrete-time dynamics of spacecraft, target spacecraft, and debris, as a discrete-time index, is as follows: in, Indicates time The control acceleration of the tracking spacecraft, Indicates the interval The single-step propagation mapping obtained by numerical integration of continuous dynamics at each time step... The system is subject to the following constraints: ; { | ; ; S={ | ≤ }; In the above formula, This represents the defined allowed control set. Defined set of allowed states, By fragment location And it changes over time; the control objective is to keep the tracking spacecraft's state unchanged. The intersection condition is satisfied, that is, there exists a certain It satisfies the following: ; in, and >0 represents the relative position and relative speed tolerances of the rendezvous terminals.

[0028] Step 4: Based on the discrete rendezvous and obstacle avoidance problem, and combining the discrete dynamics model and the constraints of terminal rendezvous accuracy, establish a conventional NMPC solution problem; To address the online guidance issue in NRHO rendezvous and obstacle avoidance, at each sampling moment... A nonlinear model predictive control (NMPC) approach is used to solve a finite-time optimal control problem. The finite-time optimal control problem is constrained by a high-fidelity ephemeris dynamics model, as well as state and control constraints. Based on the given discrete propagation relationships and constraint set, the conventional NMPC formula is as follows: ; Its constraints are: ; ; ; ; ; ; ; In the above formula, This represents the control sequence to be optimized; and Let represent the control time domain and the prediction time domain, respectively. The corresponding objective functions are as follows: ; in, and The formula is as follows: ; The objective function described above penalizes relative position error, relative velocity error, and control energy simultaneously, thus achieving a reasonable trade-off between rendezvous accuracy and propulsion consumption. It should be noted that the feasibility and convergence of this NMPC optimization problem, and its feasible region... The convexity of the object is closely related to the fact that debris obstacle avoidance constraints introduce a topological "hole" in the state space, thereby making the object avoidance more complex and less convex. This makes the set nonconvex. This nonconvexity makes it easier to encounter convergence difficulties when directly solving the problem; furthermore, if a convex approximation method is used... This would introduce additional conservatism. Therefore, how to effectively handle non-convex obstacle avoidance constraints while maintaining geometric feasibility is a key issue in the subsequent method design, hence step five is proposed accordingly. Step 5: Construct local coordinates and split lines, convexize the geometric collision constraints, and construct an invertible mapping from the original space to the mapped space. Addressing the problem in Step 4, to make the allowable set easier to handle in optimization while preserving geometric feasibility, this paper introduces an auxiliary splitting operation. An intuitive idea is to... Split into , where s is an infinite splitting plane used to cut through the free space induced by the debris. Since this splitting operation removes the topological barrier caused by the debris no-fly zone, it is possible to... Construct a homeomorphic mapping between the map and a given convex set. The mapping will then be constructed in three steps: S1: Cross-sectional geometry: Let The center of the debris. For a given tracking spacecraft location. Considering height place Cross section, and define along Axis height offset ; On this cross section, the intersection yes A disk in a plane, its boundary being a radius. ; The circle. This circle is called... The fragment boundary on the cross section. Therefore, when At that time, fragments on the cross-section induce free space It is ring-shaped.

[0029] S2: Splitting operation, introducing a splitting line on the cross-section: due to the presence of internal voids, this annular region is non-convex. The splitting plane s intersects with the plane... They intersect, forming a split line.

[0030] To distinguish which side of the split line the tracking spacecraft was located on, and to characterize its position... The angular position of the fragment on the cross-section is used to introduce angular coordinates relative to the direction of the splitting line. Let... Relative position vector exist Projection on a plane For the same The unit direction of the splitting line on the cross section. First, calculate the unit vector. and The unsigned angle between ; For convenience, take As a reference ray. In order to... On the cross section, a consistent direction is specified for the angular coordinates, using and The directed area of ​​the parallelogram spanned by the parallelogram ; Specifically, Indicates from arrive For counterclockwise rotation (equivalently, lie in (on the right side), and Indicates clockwise rotation (equivalently, lie in (to the left). Therefore, the signed angular coordinates are defined as... ; Therefore, after the splitting operation, The entire annular region surrounding the cavity in the cross-section can be divided into intervals. Coverage. The split line simultaneously corresponds to... and They represent the same ray in the original space.

[0031] After the splitting operation, a coordinate system needs to be introduced for measurement. The in-plane distance from the spacecraft to the debris boundary is tracked on the cross-section because this quantity can be directly used to apply obstacle avoidance constraints in optimal control problems. For a given altitude... The distance in this plane is defined as ; in ; In particular, express Located at the boundary of the debris superior; express Located outside the fragment boundary and having a positive margin of separation; express Located inside the boundary of the fragment, that is, in The cross-section violated the debris obstacle avoidance constraint.

[0032] S3: Mapped coordinates: Reparameterize the free space to give the allowable set a convex representation; homeomorphism A convex mapping state space is defined, denoted as . .set up Let be the coordinate axes in the mapping space. Let the tracking spacecraft be in convex space. The position in the middle is ; Definition: (i) Signed angular coordinates on the cross section (ii) In-plane distance from spacecraft to debris boundary tracked on cross section (iii) Height offset along the z-axis Then three-dimensional mapping Represented as ; Mapped allow set as follows: ; It is the Cartesian product of convex sets, therefore it is a convex set. Geometrically, the splitting operation unfolds the ring-shaped region into a strip region. The cutting and unfolding process is as follows: Figure 4 As shown, the splitting plane (Red) The free space induced by the fragments was cut open and the ring-shaped region was unfolded, making it topologically equivalent to a convex set. Among them, Indicates the center of the fragment. Indicates the safety radius. The star-shaped marker indicates the position of the tracking spacecraft. In the mapped space, Indicates the angular position around the split line. This represents the in-plane distance from the tracking spacecraft to the debris boundary. Indicates along Height offset in the axial direction.

[0033] Splitting plane The selection of this parameter affects the obstacle avoidance trajectory of the tracking spacecraft; its direction is determined based on relative geometry and is used to specify the tracking spacecraft's path. relative to the cross section The preferred bypass side. When the target and the tracking spacecraft are on the same side of the debris center, bypassing from that side is generally more direct, so the split plane can be positioned on its opposite side. In the mapped space, the angular coordinates are discontinuous at this plane, so the optimization process naturally discourages crossing this plane, and the final trajectory tends to bypass the debris from the expected side.

[0034] Step 6: Based on the content of Step 4, construct and solve the non-convex NMPC optimization problem based on the mapping space to obtain the optimal control sequence for tracking the spacecraft, and use the optimal control sequence to control the tracking spacecraft.

[0035] A mapping-based NMPC scheme, 3D mapping Each allowed set Transformed into the allowed set after mapping Such a convex representation makes NMPC subproblems easier to solve and improves feasibility and numerical convergence.

[0036] To integrate 3D mapping into the conventional NMPC scheme, at each sampling time... Construct the following non-convex NMPC problem: ; Its constraints are: ; ; ; ; ; ; ; in, , The set of allowed convex maps as defined.

[0037] To efficiently solve the non-convex NMPC problem within a rolling time-domain framework, this paper employs AL-iLQR as the internal solver. At each sampling time step, the current states of the tracking spacecraft, the target spacecraft, and the debris are used as initial values ​​to solve the finite-time optimal control problem. An augmented Lagrangian layer is used to handle the mapped state constraints, while an iterative LQR process is used to efficiently update the control sequence. The control sequence obtained at the previous sampling time step is used as a warm start for the current optimization, thereby improving the numerical efficiency in the rolling time-domain implementation.

[0038] The algorithm for step six is ​​explained, and the implementation flow of the proposed non-convex NMPC scheme is given. Given the initial state... and and mapping Intersection tolerance and safety threshold After that, first order Subsequently, the splitting plane is selected based on the relative geometric relationship. And construct the corresponding mapping. Then, before the intersection condition is met, the control sequence is... Initialize the control sequence and update it using the AL-iLQR solution. Then, only update the first control variable of the optimized control sequence. Applied to the tracking spacecraft. System status. and mapped coordinates Updated. Finally, the time index is updated to... Repeat the above process until the rendezvous conditions are met.

[0039] In practical applications, it is not necessary to explicitly establish a dynamic model in the mapping space. In each NMPC prediction step, the dynamic model is first obtained from high-fidelity ephemeris dynamics. Then through Map it to a mapping space and apply obstacle avoidance constraints accordingly.

[0040] Here is a simulation process: In a typical NRHO rendezvous simulation, with collision avoidance constraints enabled, the system undergoes local trajectory adjustments during potential close encounters while maintaining rendezvous accuracy and control input boundaries. Compared to the "close-range crossing" trajectory without collision avoidance, this significantly increases the minimum tracking spacecraft-debris distance and meets the probability threshold. This part can serve as supplementary experimental data to demonstrate feasibility and engineering feasibility.

[0041] The simulation aims to verify the feasibility and effectiveness of the "NRHO rendezvous and collision avoidance method based on three-dimensional mapping and nonlinear model predictive control (NMPC)" under high-fidelity dynamic conditions. A comparison without collision avoidance constraints is used, and the following aspects are examined: (1) Whether the intersection trajectory can produce necessary and controlled local deviations when there is a debris threat, and maintain an overall convergence trend after the threat disappears; (2) Whether the minimum distance from the debris can be continuously greater than the safety threshold, and whether the collision risk is significantly reduced; (3) Whether the control input remains within the thrust limit and changes smoothly; (4) Whether the position / velocity accuracy at the end of the rendezvous is kept within an acceptable range.

[0042] The simulation scenario and basic settings are as follows: (1) Dynamics and coordinate system: The motion of the tracking spacecraft (Chaser), target spacecraft (Target), and debris (Debris) is uniformly described using a high-fidelity dynamic model of the Earth-Moon system in the lunar inertial frame; the tracking spacecraft is a low-thrust controlled object, the control quantity is a three-axis acceleration vector, and the thrust (acceleration) amplitude is limited. The target spacecraft and debris evolve according to natural dynamics.

[0043] (2) Mission definition: The target spacecraft operates along the nominal NRHO orbit, the tracking spacecraft is initially located at a relative position of "a few kilometers" from the target spacecraft, and needs to achieve the docking / capture accuracy requirements at the specified terminal time.

[0044] (3) Debris threat: Assuming that space debris evolves naturally in lunar-Earth space and its initial state is randomly generated. During the tracking of the spacecraft's approach, a debris trajectory may intersect or approach the planned rendezvous path, creating a potential collision risk.

[0045] To demonstrate the impact of the collision avoidance module on closed-loop rendezvous control, two sets of comparative operating conditions are set up: Condition A: Collision avoidance constraints (Baselinetrajectory) are turned off, and only regular NMPC closed-loop control is executed.

[0046] Condition B: Collision avoidance constraint (Debrisavoidancetrajectory) is enabled, and the non-convex NMPC closed-loop framework is used to perform rendezvous and dynamic collision avoidance.

[0047] Key parameters and constraints: (1) Terminal rendezvous accuracy: The rendezvous terminals must simultaneously meet the tolerance constraints of relative position error and relative velocity error.

[0048] (2) Control limit: Tracking spacecraft low-thrust control acceleration Must meet .

[0049] (4) Solution method: In the three-dimensional mapping space, the original three-dimensional non-convex collision avoidance constraint is transformed into a convex feasible region constraint, so as to solve the convex constraint in each control cycle, apply the first control variable in a rolling manner and update in a closed loop.

[0050] Simulation results are as follows Figure 5 and Figure 6 As shown, the relative trajectories of the tracking spacecraft and the target spacecraft during their rendezvous are as follows: Figure 5 As shown, compared to condition A (no collision avoidance constraints), condition B (collision avoidance enabled) exhibits a local trajectory deviation during the approach phase to avoid the debris hazard area; however, during the remaining time periods, the collision avoidance trajectory maintains an overall convergence trend consistent with the baseline intersection trajectory, without introducing unnecessary global path modifications. This represents the position vector of the tracking spacecraft relative to the target spacecraft.

[0051] like Figure 6As shown, under both scenarios, the relative distance and relative velocity between the tracking spacecraft and the target spacecraft exhibit a smooth convergence trend over time. The solid orange line represents scenario B, and the dashed blue line represents scenario A. Scenario B (orange), even with the introduction of additional maneuvers during the mid-flight maneuver, maintains continuous distance and velocity without sharp changes, indicating that the introduction of collision avoidance constraints does not disrupt the basic convergence of rendezvous control.

[0052] like Figure 7 As shown in the control chart, after activating the collision avoidance constraint, the control input exhibits a localized increase in amplitude during the time interval when the collision avoidance constraint is active, which supports short-term flyaround. In the remaining stages, the control input is similar to the baseline condition and gradually decays to near zero as the error decreases. Throughout the entire process, the three-axis control input remains within the preset limits without any high-frequency, severe oscillations, indicating good engineering feasibility.

[0053] To directly assess the effectiveness of collision risk mitigation, the relative geometric relationship between the tracked spacecraft and debris was further analyzed. Figure 8 Showing the closest moment The local obstacle avoidance process of the tracking spacecraft and debris in a fixed debris center coordinate system. Subfigures (a)–(c) illustrate the approach, fly-around, and departure phases, respectively. Orange dots, gray rhombuses, and purple squares represent the positions of the tracking spacecraft, the target spacecraft, and the debris, respectively. Black dashed circles represent radii of... The fragment safety boundary. The orange solid line, gray dashed line, and purple dotted line represent the corresponding trajectories up to the current moment. The location of the debris at any given moment. It can be seen that the tracking spacecraft first flew towards the debris's vicinity during the approach phase, and then at the closest approach moment... The area was partially detoured, and the group eventually left the risk zone from a safe side.

[0054] Tracking the evolution of the relative distance between spacecraft and debris over time, such as Figure 9 As shown in the figure. The black dashed line in the figure corresponds to the probability safety threshold. In scenario B (solid orange line), the distance remains above the safety threshold throughout the closest approach, significantly reducing the potential collision risk; while in scenario A (dashed blue line), the distance falls below the safety threshold at the closest approach. (See figure.) Considering the minimum relative distance between the spacecraft and debris during debris avoidance, Considering the minimum relative distance required for debris obstacle avoidance, a comparison shows that the proposed obstacle avoidance method can effectively increase the nearest contact distance and ensure that the tracking spacecraft passes through the debris neighborhood outside the safety boundary.

[0055] In summary, the comparative simulation results show that under the high-fidelity dynamics conditions of NRHO rendezvous, this invention, through "3D convex equivalent mapping + NMPC rolling optimization," can automatically introduce necessary and controlled local trajectory adjustments when debris threats exist, ensuring that the minimum distance between the tracker and debris is significantly greater than the safety threshold, thereby effectively reducing the collision risk. Simultaneously, it keeps the control input within limits and ensures smooth changes, resulting in only a limited impact on the accuracy at the rendezvous end, which remains within an acceptable range. Therefore, the method of this invention is suitable for NRHO rendezvous missions in lunar-Earth space under complex non-convex obstacle environments, achieving a comprehensive balance between safety and performance.

[0056] Therefore, this invention employs a nonlinear model predictive control method for NRHO rendezvous and obstacle avoidance. First, a high-precision dynamic model and rendezvous and obstacle avoidance problem are constructed. Second, a three-dimensional mapping suitable for obstacle avoidance domains with "holes" in three-dimensional space is constructed, reconstructing the original non-convex feasible region into a convex set. Furthermore, an energy-weighted NMPC is established in the mapping space, unifying orbital error, control energy, thrust constraints, and obstacle avoidance constraints into the same optimization problem, and employing rolling time-domain closed-loop execution.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A nonlinear model predictive control method for NRHO (Normally Oriented Hierarchical) obstacle avoidance, characterized in that, Includes the following steps: Step 1: Establish a high-fidelity dynamic model and its corresponding baseline NRHO orbital family in the lunar center inertial frame; Step 2: Based on the high-fidelity dynamics model, a continuous dynamics model of the objects to be calculated during the rendezvous is given. The objects to be calculated include the tracking spacecraft, the target spacecraft, and the debris. The rendezvous and obstacle avoidance problem is established as follows: the target spacecraft moves along the NRHO trajectory under the influence of natural dynamics; the tracking spacecraft is initially located several kilometers away from the target spacecraft, equipped with a low-thrust propulsion system, and needs to rendezvous with the target spacecraft; the space debris evolves in the Earth-Moon space according to natural dynamics; based on the rendezvous and obstacle avoidance problem, the objective function, acceleration constraints, and obstacle avoidance constraints are obtained accordingly. Step 3: Establish discrete dynamic models for the tracking spacecraft, the target spacecraft, and the debris, and establish constraints on the terminal rendezvous accuracy; Step 4: Based on the discrete rendezvous and obstacle avoidance problem, a conventional NMPC solution problem is established by combining the discrete dynamics model and the constraints of terminal rendezvous accuracy. Step 5: Construct local coordinates and split lines, convexize the geometric collision constraints, and construct an invertible mapping from the original space to the mapping space; Step Six: Based on the content of Steps Four and Five, construct and solve the non-convex NMPC optimization problem based on the mapping space to obtain the optimal control sequence for tracking the spacecraft, and use the optimal control sequence to control the tracking spacecraft.

2. The nonlinear model predictive control method for NRHO (Normally Oriented Hierarchical Organization) obstacle avoidance as described in claim 1, characterized in that: In step one, establishing a high-fidelity dynamic model requires considering perturbation factors, including solar perturbation, radiation pressure perturbation, lunar J2 gravitational perturbation, and Earth J2 gravitational perturbation. The specific perturbation factors are as follows: To account for actual perturbations in the Earth-Moon space, in the lunar-centric inertial coordinate system... Modeling in the middle, obtaining the computational object in the coordinate system acceleration in The formula is as follows: ； In the above formula, Acceleration caused by the Moon's gravitational field Acceleration caused by Earth's gravitational field Due to the gravitational acceleration of the sun, Let SRP be the solar radiation pressure acceleration; then define the computational object in the coordinate system. The status in is as follows: ； In the above formula, and These respectively represent the coordinate system in which the computational object is located. The position and velocity of the object are used to calculate its dynamics under high-fidelity ephemeris dynamics. as follows: ； ； In the above formula, The dynamic formula representing the object of computation, This represents the acceleration of the object being calculated. Represents the velocity of the object being calculated; the Moon and Earth are in their respective fixed coordinate systems. The gravitational fields in all of them adopt spherical harmonic gravitational potential. It means that, among them, , and Representing the Moon and Earth respectively, we obtain the universal gravitational potential. The formula is as follows: ； In the above formula, These respectively represent the objects of calculation relative to celestial bodies. The radial distance, latitude and longitude, celestial bodies gravitational constant, celestial bodies The average radius, subscript and Let represent the order and degree of the spherical harmonic expansion, respectively. To normalize the Legendre polynomial, and celestial bodies Normalized spherical harmonic coefficients; definition This indicates that the vector is transferred from the inertial frame. Transformation to solid connection The direction cosine matrix, then the object being calculated in The coordinates in the image are as follows: ； definition For the calculation object in In spherical coordinates, then spherical coordinates and The relationship is as follows: ； gravitational potential The gradient of celestial bodies exist Gravitational acceleration caused by the middle as follows: ； ， ； The above formula corresponds to the moon in Gravitational acceleration caused by the middle and Earth Gravitational acceleration caused by the middle This corresponds to the lunar gravitational acceleration. The formula is as follows: ； Earth's tidal gravitational acceleration The formula is: ； In the above formula, This is the position vector pointing from the Moon to the Earth; Solar gravitational acceleration for: ； In the above formula, Represents the solar gravitational constant. This represents the position vector pointing from the Moon to the Sun; Solar radiation pressure acceleration for: ； In the above formula, As the shadow factor, It is the product of the solar radiation pressure coefficient and the area-to-mass ratio. Solar luminosity It is the speed of light in a vacuum. The baseline NRHO orbital family was obtained, and the candidate orbital family was set to Earth-Moon. The near-straight halo orbit NRHO is generated using a high-fidelity ephemeris model. To characterize the suitable orbital range for rendezvous, the mean apogee angle of NRHO is introduced. : ； In the above formula, This is the duration since the lunar flyby from the perigee. For orbital period, perigee and apogee are defined as the points on NRHO with the smallest and largest distances from the lunar center, respectively. Amplitude is defined as from the nearest point to the end of the month. The perpendicular distance between planes corresponds to The amplitude is used as a criterion for selecting different NRHO operating conditions.

3. The nonlinear model predictive control method for NRHO (Normally Oriented Hierarchical Organization) obstacle avoidance as described in claim 2, characterized in that: The specific details of step two are as follows: During the tracking of a spacecraft approaching a target spacecraft, debris trajectories intersecting with the tracking spacecraft's intersection path pose a collision risk and need to be handled during guidance. (In the coordinate system...) In the process of tracking the status of spacecraft The status of the target spacecraft and the state of fragments They are as follows: ； ； ； definition These represent the tracking spacecraft, the target spacecraft, and the debris, respectively. and Let represent the corresponding position and velocity vectors, respectively. Based on a high-fidelity dynamics model, the motion of the tracked spacecraft satisfies the following controlled dynamics: ； In the above formula, To track the low thrust acceleration of the spacecraft, for The initial state of the spacecraft is constantly tracked, and the motion of the target spacecraft and debris follows natural dynamics as follows: ； ； In the above formula, and The target spacecraft and debris were respectively located in The initial state at a given moment; The objective function for the rendezvous and obstacle avoidance problem is set, and a quadratic objective function is used to penalize the relative position error. Relative speed error and control of energy The formulas for relative position error and relative velocity error are as follows: ； The corresponding objective function is as follows: ； In the above formula, , and All are symmetric positive semidefinite weighted matrices; Acceleration constraints are set, and since the tracking spacecraft's thrust capability is limited, each control component is subject to the maximum thrust value. The constraint is such that the acceleration constraint formula is: ； ； in, The infinite norm of the control vector is represented; Set debris obstacle avoidance constraints, set Let the equivalent safety radius be the sum of the radii of the tracking spacecraft and the debris. The formula for the obstacle avoidance constraint is as follows: ； The non-convexity of the debris obstacle avoidance constraint works in conjunction with the nonlinear high-fidelity ephemeris model.

4. The nonlinear model predictive control method for NRHO (Normally Oriented Hierarchical Organization) obstacle avoidance as described in claim 3, characterized in that: The specific details of step three are as follows: Set the sampling period to and define ,in The formula for tracking the discrete-time dynamics of spacecraft, target spacecraft, and debris, as a discrete-time index, is as follows: ； ； ； in, Indicates time The control acceleration of the tracking spacecraft, Indicates the interval The single-step propagation mapping obtained by numerical integration of continuous dynamics at each time step... The system is subject to the following constraints: ； { | ； ； S={ | ≤ }； In the above formula, This represents the defined allowed control set. Defined set of allowed states, By fragment location And it changes over time; the control objective is to keep the tracking spacecraft's state unchanged. The intersection condition is satisfied, that is, there exists a certain It satisfies the following: ； in, and >0 represents the relative position and relative speed tolerances of the rendezvous terminals.

5. A nonlinear model predictive control method for NRHO (Normally Oriented Hierarchical Organization) obstacle avoidance as described in claim 4, characterized in that: In step four, the process of solving a conventional NMPC problem is given as follows: To address the online guidance issue in NRHO rendezvous and obstacle avoidance, at each sampling moment... A nonlinear model predictive control (NMPC) approach is used to solve a finite-time optimal control problem. This problem is constrained by a high-fidelity ephemeris dynamics model, as well as state and control constraints. Based on the given discrete propagation relationships and constraint set, the conventional NMPC formula is as follows: ； The constraints are as follows: ； ； ； ； ； ； ； In the above formula, This represents the control sequence to be optimized; and Let represent the control time domain and the prediction time domain, respectively. The corresponding objective functions are as follows: ； in, and The formula is as follows: ； The objective function described above penalizes relative position error, relative velocity error, and control energy simultaneously.

6. A nonlinear model predictive control method for NRHO (Normally Oriented Hierarchical Organization) obstacle avoidance as described in claim 5, characterized in that: In step five, the invertible mapping from the original space to the mapped space is constructed as follows: Invertible mappings are constructed in three steps: S1: Cross-sectional geometry: Characterization Annular region on the cross section; let For the center of the debris, given the location of the tracking spacecraft... Considering height place Cross section, and define along Axis height offset as follows: ； On this cross section, the intersection yes A disk in a plane, its boundary being a radius. The formula is as follows: ； The aforementioned disk is called The fragment boundary on the cross section, therefore, when At that time, fragments on the cross-section induce free space It is ring-shaped; S2: Splitting operation, introducing a splitting line on the cross-section: Due to the presence of internal voids, the annular region is non-convex, and the splitting plane s intersects with the plane. The two lines intersect, forming a split line. This is used to distinguish which side of the split line the tracking spacecraft is on and to characterize its position. The angular position of the fragment on the cross section is used to introduce angular coordinates relative to the direction of the splitting line; set up Relative position vector exist Projection on a plane For the same Calculate the unit vector along the unit direction of the splitting line on the cross section. and The unsigned angle between as follows: ； Pick As a reference ray, in order to On the cross section, a consistent direction is specified for the angular coordinates, using and The directed area of ​​the parallelogram spanned by the parallelogram is given by the following formula: ； In the above formula, when it means from to is counterclockwise rotation, equivalent to being located at on the right side of), when it means clockwise rotation, equivalent to being located at on the left side of, then the signed angular coordinate is defined as: ； After the splitting operation The entire annular region surrounding the cavity in the cross-section is composed of intervals. Coverage, splitting line simultaneously correspond and They represent the same ray in the original space; After the splitting operation, a coordinate system needs to be introduced to measure the result. On the cross-section, the in-plane distance from the spacecraft to the debris boundary is tracked and used for obstacle avoidance constraint application in the optimal control problem, for a given altitude. The distance within this plane is defined as follows: ； in The formula is as follows: ； exist When, it means Located at the boundary of the debris Above; at When, it means Located outside the fragment boundary and having a positive margin; When, it means Located inside the boundary of the fragment, that is, in The debris avoidance constraint was violated at the cross-section. S3: Mapped coordinates: Reparameterize the free space to give the allowable set a convex representation; homeomorphism A convex mapping state space is defined, denoted as . ; definition Using coordinate axes in the mapping space, we obtain the tracking spacecraft in convex space. The position in the middle is as follows: ； Definition: (1) Signed angular coordinates on the cross section (2) In-plane distance from spacecraft to debris boundary tracked on cross section (3) Height offset along the z-axis Then three-dimensional mapping The formula is as follows: ； Mapped allow set for: ； The above equation is the Cartesian product of a convex set, therefore it is a convex set. Geometrically, the splitting operation unfolds the ring-shaped region into a strip-shaped region; the splitting plane... The selection of this parameter affects the obstacle avoidance trajectory of the tracking spacecraft; its direction is determined based on relative geometry and is used to specify the tracking spacecraft's path. relative to the cross section The preferred bypass side is the side from which the target spacecraft and the tracking spacecraft are located. When the target spacecraft and the tracking spacecraft are on the same side of the debris center, it is usually more direct to bypass from that side. Therefore, the split plane is arranged on the opposite side. In the mapping space, the angular coordinates are discontinuous at this plane, so the optimization process will naturally suppress crossing the plane, and the final trajectory will also tend to bypass the debris from the expected side.

7. A nonlinear model predictive control method for NRHO (Normally Oriented Hierarchical Organization) obstacle avoidance as described in claim 6, characterized in that: In step six, the specific details of constructing and solving the mapping-based NMPC solution are as follows: 3D mapping Each allowed set Transformed into the allowed set after mapping Such a convex representation makes NMPC subproblems easier to solve and improves feasibility and numerical convergence. To integrate 3D mapping into the conventional NMPC scheme, at each sampling time... Construct the following non-convex NMPC problem: ； Its constraints are: ； ； ； ； ； ； ； In the above formula, , To efficiently solve the non-convex NMPC problem within the rolling time domain framework, AL-iLQR is used as the internal solver for the defined convex map allowable set. At each sampling time, the current states of the tracking spacecraft, the target spacecraft, and the debris are used as initial values ​​to solve the finite-time optimal control problem. An augmented Lagrangian layer is used to handle the mapping state constraints, while the iterative LQR process is used to efficiently update the control sequence. The control sequence obtained at the previous sampling time is used as the hot start of the current optimization, thereby improving the numerical efficiency in the rolling time domain implementation.

8. A nonlinear model predictive control method for NRHO (Normally Oriented Hierarchical Organization) obstacle avoidance as described in claim 7, characterized in that: The implementation process for the non-convex NMPC solution is as follows: Given an initial state and and mapping Intersection tolerance and safety threshold Then, set the time index. Then, the splitting plane is selected based on the relative geometric relationship. And construct the corresponding mapping. ; Before the intersection condition is met, the control sequence Initialize the sequence and update the control sequence using the AL-iLQR solution, setting the first control variable of the control sequence as... Control measures are applied to the tracking spacecraft to monitor the system status. and mapped coordinates Update the time index to... Repeat the above process until the rendezvous conditions are met.

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