An obstacle avoidance flight trajectory optimization method, system, device and storage medium for the undulating terrain of the lunar south pole

Abstract

This invention discloses a method, system, device, and storage medium for optimizing obstacle avoidance flight trajectories in the undulating terrain of the lunar south pole. The method includes: constructing a convex optimization problem model for the flight trajectory; constructing a three-dimensional convex hull based on a digital elevation model of the mission area and extracting effective external normal vectors; performing weighted clustering on the effective external normal vectors to fit a convex plane, forming an initial convex no-fly zone; expanding the initial convex no-fly zone outward along its respective normal direction to determine the no-fly zone boundary plane, obtaining no-fly zone constraints; performing a first-step trajectory optimization based on the no-fly zone constraints and the convex optimization problem model for the flight trajectory, obtaining a reference trajectory; and constructing spherical safe zones centered on discrete points of the reference trajectory, ensuring that adjacent spheres overlap to form a safe flight corridor, performing a second-step trajectory optimization to obtain the optimal obstacle avoidance flight trajectory. This invention's two-step optimization strategy, combining no-fly zones and safe zones, enables safe and low-fuel-consumption flight trajectory optimization.

Description

Technical Field

[0001] This invention relates to the technical field of flyover trajectory optimization, and in particular to a method, system, device, and storage medium for obstacle avoidance flyover trajectory optimization for the undulating terrain of the lunar south pole. Background Technology

[0002] The lunar south pole, due to the possibility of water ice or volatile components, has become a key target area for deep space exploration. A flyby spacecraft can overcome the obstacles of the undulating terrain in the lunar south pole region, flying at low altitudes on the lunar surface for rapid movement. Because the flyby spacecraft remains close to the lunar surface throughout its flight, the flyby trajectory requires high obstacle avoidance safety, and the flyby process consumes a significant amount of fuel. Therefore, it is urgent to achieve optimal fuel consumption trajectory planning while ensuring safety.

[0003] Trajectory optimization methods often avoid terrain obstacles by setting safety zones or no-fly zones, typically using regular geometry to simplify complex terrain models. These simplified models struggle to accurately depict the true shape of large-scale undulating terrain, especially in the crater-strewn lunar south pole region, where they significantly exaggerate the extent of terrain obstacles, compress feasible flight space, reduce trajectory optimization flexibility, and waste fuel. Furthermore, the trajectory optimization process is affected by various error factors. Trajectory optimization methods usually approximate a continuous trajectory using discrete trajectory points, introducing trajectory discretization errors. Due to limitations in measurement accuracy, errors also exist in the flyby vehicle's position and terrain data. The combined effect of these multiple errors places higher demands on the safety and robustness of obstacle avoidance trajectories. Summary of the Invention

[0004] In view of the aforementioned existing problems, this invention is proposed. Therefore, this invention provides a method, system, device, and storage medium for optimizing obstacle avoidance flight trajectories for the undulating terrain of the lunar south pole, solving the problem that existing methods, when optimizing trajectories, easily cause terrain simplification distortion and error accumulation, failing to simultaneously achieve optimal safety and fuel consumption.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, embodiments of the present invention provide a method for optimizing obstacle avoidance flight trajectories for the undulating terrain of the lunar south pole, including: Based on the flight mission constraints of the flyover vehicle, and with the goal of minimizing the flyover vehicle's fuel consumption, a convex optimization problem model for the flight trajectory is constructed. A three-dimensional convex hull is constructed based on the digital elevation model of the mission area, and effective external normal vectors are extracted. The effective external normal vectors are then subjected to weighted clustering to fit the convex plane and form an initial convex no-fly zone. The initial convex no-fly zone is expanded outward along its respective normal direction to determine the no-fly zone boundary plane, thus obtaining the no-fly zone constraint. Based on the no-fly zone constraint and the convex optimization problem model of the leap trajectory, a trajectory optimization is performed to obtain the reference trajectory. Centered on each discrete point of the reference trajectory, spherical safety zones are constructed, wherein the radius of each sphere is equal to the shortest distance from that point to the original digital elevation model minus the translation amount, and adjacent spheres are ensured to overlap to form a safe flight corridor; Based on the aforementioned safe flight corridor, a safe zone constraint is constructed, and secondary trajectory optimization is performed to solve the fuel consumption minimization problem, thereby obtaining the optimal obstacle avoidance flight trajectory.

[0006] As a preferred embodiment of the obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole described in this invention, the method further includes, before constructing the convex optimization problem model of the flight trajectory: Define the jump coordinate system O-XYZ; The leap coordinate system has its origin O at the target landing position of the leap mission, the Z-axis perpendicular to the lunar surface and pointing outward into space, the X-axis pointing to the starting position of the leap mission, and the Y-axis forming a right-handed rectangular coordinate system with the Z-axis and the X-axis.

[0007] As a preferred embodiment of the obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole described in this invention, the construction of the convex optimization problem model for the flight trajectory includes: dividing the flight time into... N part; Based on the initial state of the jumper, the state expression at each time step is recursively derived, in the th... The state of the jumper at each time step is denoted as: in, , 、 The leap vehicle is at the 1st The natural logarithm of position, velocity, and mass at each time step. N The number of discrete time intervals; The discretized leap trajectory convex optimization problem model is expressed as follows: in, This is the initial position of the flying vehicle. For the first The normalized thrust of the step, for In time The theoretical lower limit of time, For the first Net control acceleration of the step, This represents the initial state of the jump device.

[0008] As a preferred embodiment of the obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole described in this invention, the method includes: constructing a three-dimensional convex hull based on a digital elevation model of the mission area and extracting effective external normal vectors; performing weighted clustering on the effective external normal vectors to fit a convex plane and forming an initial convex no-fly zone, including: Generate a 3D convex hull for each point in the digital elevation model of the task area, and obtain the set of unit outward normal vectors of the convex hull surface. ;from Selected from Normal vectors with components greater than 0 are removed, along with normal vectors perpendicular to the XOZ plane, resulting in the cleaned set of normal vectors. ; right Perform weighted k-means clustering to obtain A representative direction constitutes the direction set. ; Will The direction in the middle is used as the normal vector of the no-fly zone boundary plane. And determine the plane offset of the no-fly zone boundary. The flight trajectory optimization space is divided into a safe space with terrain obstacles and a dangerous space without terrain obstacles.

[0009] As a preferred embodiment of the obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole described in this invention, wherein: the initial convex no-fly zone is expanded outward along its respective normal direction to determine the boundary plane of the no-fly zone, thereby obtaining the no-fly zone constraint, including: the translational amount of the initial convex no-fly zone expanding outward along its respective normal direction, expressed as: in, The maximum flight speed of the aircraft. Let the discrete time step size be , and These are the standard deviations of the flyover's position along the direction of maximum error and the standard deviations of the digital elevation model's elevation, respectively. The offset of the translated boundary plane is denoted as The no-fly zone boundary plane is determined based on the plane normal vector and offset. ,in, Represent any point in space; based on the expanded boundary plane equation of the no-fly zone, construct the no-fly zone constraint, expressed as: in, The number of pre-defined no-fly zone boundary planes, It is a large integer. For the corresponding number A binary variable representing the boundary plane of a no-fly zone.

[0010] As a preferred embodiment of the obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole described in this invention, the method includes: performing a first-order trajectory optimization based on the no-fly zone constraint and a convex optimization problem model for the flight trajectory, comprising: the first-order trajectory optimization problem being expressed as: As a preferred embodiment of the obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole described in this invention, the method includes: constructing obstacle avoidance constraints based on the safe flight corridor, performing secondary trajectory optimization, solving the fuel consumption minimization problem, and obtaining the optimal obstacle avoidance flight trajectory, including: discretizing the flight time of the secondary trajectory optimization into 2... N Segment, construct obstacle avoidance constraints, represented as: With the safety zone constraint in mind, the quadratic trajectory optimization problem can be expressed as: in, For the first The center of a spherical safety zone, For the first The radius of the spherical safety zone.

[0011] Secondly, the present invention provides an obstacle avoidance flight trajectory optimization system for the undulating terrain of the lunar south pole, comprising: The initial trajectory generation module, based on the leap mission constraints of the leap vehicle, constructs a convex optimization problem model for the leap trajectory with the goal of minimizing the fuel consumption of the leap vehicle; The convex no-fly zone construction module is used to construct a three-dimensional convex hull based on the digital elevation model of the mission area and extract effective external normal vectors. The effective external normal vectors are then weighted and clustered to fit a convex plane to form an initial convex no-fly zone. The first optimization module is used to expand the initial convex no-fly zone outward along its respective normal direction, determine the no-fly zone boundary plane, obtain the no-fly zone constraint, and perform a first trajectory optimization based on the no-fly zone constraint and the convex optimization problem model of the leap trajectory to obtain the reference trajectory. The safe zone construction module is used to construct spherical safe zones centered on each discrete point of the reference trajectory. The radius of each sphere is equal to the shortest distance from that point to the original digital elevation model minus the translation amount, and adjacent spheres are ensured to overlap to form a safe flight corridor. The secondary optimization module is used to construct obstacle avoidance constraints based on the safe flight corridor, perform secondary trajectory optimization, solve the fuel consumption minimization problem, and obtain the optimal obstacle avoidance flight trajectory.

[0012] Thirdly, the present invention provides an electronic device, comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the obstacle avoidance and flight trajectory optimization method for the undulating terrain of the lunar south pole.

[0013] Fourthly, the present invention provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the obstacle avoidance and flight trajectory optimization method for the undulating terrain of the lunar south pole.

[0014] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention establishes a no-fly zone incorporating lunar surface topography, solves for a reference trajectory, and further constructs a safe flight corridor consisting of multiple spherical safe zones along the reference trajectory. Within this corridor, the trajectory is optimized to obtain a flyover trajectory with better fuel efficiency. During the construction of the safe zone constraints, the effects of flyover vehicle position error, trajectory discretization error, and terrain error are simultaneously introduced, improving the safety and robustness of the flyover trajectory under uncertain conditions. This invention, by combining a no-fly zone with a safe zone under the premise of considering flyover vehicle position error, trajectory discretization error, and terrain error, achieves safe and low-fuel-consumption flyover trajectory optimization. Attached Figure Description

[0015] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a schematic diagram of the process flow of an obstacle avoidance and flight trajectory optimization method for the undulating terrain of the lunar south pole, according to an embodiment of the present invention. Figure 2 This is a lunar surface topography and no-fly zone boundary map of an obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole, as described in an embodiment of the present invention. Figure 3 This is a schematic diagram of a secondary trajectory optimization method for obstacle avoidance and flight trajectory optimization for the undulating terrain of the lunar south pole, as described in an embodiment of the present invention, which determines the safe zone based on a reference trajectory. Figure 4 This is a schematic diagram of secondary trajectory optimization based on the safety zone, which is a method for optimizing obstacle avoidance and flight trajectory for the undulating terrain of the lunar south pole according to an embodiment of the present invention. Figure 5The image shows the flight trajectory obtained by different optimization methods of the obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole, as described in one embodiment of the present invention. Detailed Implementation

[0016] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0017] Example 1, referring to Figures 1-4 This is one embodiment of the present invention, which provides a method for optimizing obstacle avoidance flight trajectories for the undulating terrain of the lunar south pole, including: S100: Based on the leap mission constraints of the leap vehicle, and with the goal of minimizing the fuel consumption of the leap vehicle, a convex optimization problem model of the leap trajectory is constructed. S200: Based on the digital elevation model of the mission area, a three-dimensional convex hull is constructed and effective external normal vectors are extracted. The effective external normal vectors are weighted and clustered to fit the convex plane and form an initial convex no-fly zone. S300: Expand the initial convex no-fly zone outward along its respective normal direction to determine the no-fly zone boundary plane and obtain the no-fly zone constraint. Based on the no-fly zone constraint and the convex optimization problem model of the leap trajectory, perform a trajectory optimization to obtain the reference trajectory. S400: Construct spherical safety zones centered on discrete points of the reference trajectory. The radius of each sphere is equal to the shortest distance from that point to the original digital elevation model minus the translation amount. Ensure that adjacent spheres overlap to form a safe flight corridor. S500: Based on the safe flight corridor, a safe zone constraint is constructed, a secondary trajectory optimization is performed, and the fuel consumption minimization problem is solved to obtain the optimal obstacle avoidance flight trajectory.

[0018] It should be noted that existing trajectory optimization methods mostly avoid terrain obstacles by setting safety zones or no-fly zones, typically using regular geometry to simplify complex terrain models. This simplified modeling method struggles to accurately depict the true shape of large-scale undulating terrain, especially in the crater-strewn lunar south pole region, significantly exaggerating the extent of terrain obstacles, compressing feasible flight space, reducing trajectory optimization flexibility, and wasting fuel. Furthermore, the trajectory optimization process is affected by various error factors. Trajectory optimization methods usually approximate continuous trajectories using discrete trajectory points, thus introducing trajectory discretization errors. Due to limitations in measurement accuracy, errors also exist in the flyby vehicle's position and terrain data. The combined effect of multiple types of errors places higher demands on the safety and robustness of obstacle avoidance trajectories. This invention addresses the large-scale undulating terrain of the lunar south pole and the high safety requirements of multiple types of errors on flyby trajectories, providing a flyby trajectory optimization method that balances safety and fuel efficiency. To capture the overall characteristics of the terrain in the flyby mission area, a no-fly zone incorporating lunar surface terrain is established to solve for a reference trajectory. Subsequently, a safe flight corridor consisting of multiple spherical safety zones is constructed along the reference trajectory. The trajectory is optimized within this corridor to obtain a more fuel-efficient jump trajectory. During the obstacle avoidance constraint construction process, the effects of jump vehicle position error, trajectory discretization error, and terrain error are simultaneously introduced to improve the safety and robustness of the jump trajectory under uncertain conditions.

[0019] Furthermore, before constructing the convex optimization problem model of the leap trajectory, the embodiments of the present invention also include: Define the jump coordinate system O-XYZ; The flyover coordinate system takes the target landing position of the flyover mission as the origin O, the Z-axis is perpendicular to the lunar surface and points to outer space, the X-axis points to the starting position of the flyover mission, and the Y-axis, Z-axis and X-axis form a right-handed rectangular coordinate system.

[0020] Furthermore, the objective of trajectory optimization is to minimize fuel consumption. The leap process of the spacecraft is subject to dynamic constraints, initial and final state constraints, and thrust constraints. Ignoring the influence of Earth's rotation, a convex optimization problem model for the original fuel-optimal leap trajectory is established in the leap coordinate system, expressed as: in, This indicates the time taken for the entire flight process. , , These are the position, speed, and mass of the flying vehicle. and These represent the initial position and mass of the flying vehicle. Is the leap vehicle in position? The gravitational acceleration experienced by the Moon at that location, T It is the thrust applied by the thrusters on the flying vehicle. For quality normalization slack variables, It is a thrust relaxation variable. It is the net control acceleration of the thruster. It is the natural logarithm of mass. T max , T min These are the maximum and minimum thrust values, respectively. yes In time The lower limit of time, It is the fuel consumption rate.

[0021] It should be noted that the original optimal fuel consumption leap trajectory convex optimization problem model is a continuous trajectory optimization problem. The embodiments of the present invention discretize this continuous trajectory optimization problem to construct a leap trajectory convex optimization problem model, which can generate an initial optimal fuel consumption leap trajectory without obstacle avoidance.

[0022] In this embodiment of the invention, step S100, which involves constructing a convex optimization problem model for a leap trajectory, includes: Divide the leap time into N part; Based on the initial state of the jumper, the state expression at each time step is recursively derived, in the th... The state of the jumper at each time step is denoted as: in, , 、 The leap vehicle is at the 1st The natural logarithm of position, velocity, and mass at each time step. N The number of discrete time intervals; The discretized leap trajectory convex optimization problem model is expressed as follows: in, This is the initial position of the flying vehicle. For the first The normalized thrust of the step, for In time The theoretical lower limit of time, For the first Net control acceleration of the step, This represents the initial state of the jump device.

[0023] In one feasible embodiment, step S100 of this invention discretizes the continuous trajectory optimization problem, that is, divides the complete leap duration into... NAfter that, the state expression at each time step can be recursively derived based on the initial state of the jumper using the Runge-Kutta method.

[0024] Furthermore, after modeling the discretized trajectory convex optimization problem in a scientific computing platform (such as MATLAB or Python), mature commercial mathematical optimization solvers (such as Gurobi or CPLEX) can be called to solve it efficiently, obtaining the optimal jump trajectory with initial fuel consumption without considering obstacle avoidance.

[0025] In this embodiment of the invention, step S200, which involves constructing a three-dimensional convex hull based on the digital elevation model of the task area and extracting effective external normal vectors, then performing weighted clustering on the effective external normal vectors to fit a convex plane and form an initial convex no-fly zone, includes: Generate a 3D convex hull for each point in the digital elevation model of the task area, and obtain the set of unit outward normal vectors of the convex hull surface. ;from Selected from Normal vectors with components greater than 0 are removed, along with normal vectors perpendicular to the XOZ plane, resulting in the cleaned set of normal vectors. ; right Perform weighted k-means clustering to obtain A representative direction constitutes the direction set. ; Specifically, for Perform weighted k-means clustering to obtain A representative direction constitutes the direction set. , including: Each unit normal vector in Set weights This weight is related to the area of ​​its corresponding convex hull. Correlation, through weight function Calculated, i.e. After testing, it was found that the weight function was... The modeling effect is best at this time. Each unit normal vector... With weight Multiplying them together yields a weighted vector. The standard k-means clustering algorithm is performed on the weighted vector set, using Euclidean distance as the distance metric for clustering, to obtain... The cluster centers are obtained from the weighted vectors. Each cluster center is then normalized to obtain... Each unit vector constitutes a representative direction set. .

[0026] Will The direction in the middle is used as the normal vector of the no-fly zone boundary plane. And determine the plane offset of the no-fly zone boundary. The flight trajectory optimization space is divided into a safe space with terrain obstacles and a dangerous space without terrain obstacles.

[0027] Specifically, determine the plane offset of the no-fly zone boundary. The principle is that the no-fly zone boundary plane is tangent to the terrain, and the terrain lies on the plane's normal vector. The other side of the direction it points to. Specifically, for each normal vector... Calculate the projection and offset of all 3D points corresponding to the digital elevation model of the terrain modeling area in this direction. It is the opposite of the maximum value among all projected values.

[0028] It should be noted that in step S200 of the present invention, the task area is the area between the starting points of the leap, i.e. the terrain modeling area. A set of planes is used to divide the leap trajectory optimization space into a safe space and a dangerous space, ensuring that the dangerous space is convex.

[0029] It should be noted that, in order to overcome the threats to trajectory safety posed by trajectory discretization errors, vehicle position errors, and terrain errors, and to expand the obstacle area (i.e., to translate the no-fly zone boundary plane along the normal direction), this embodiment of the invention assumes that both the vehicle position and the digital elevation model elevation conform to a Gaussian distribution, with their true values ​​located within three standard deviations of the expected values. The effect of constructing a no-fly zone based on the terrain is as follows: Figure 2 As shown.

[0030] In this embodiment of the invention, step S300, which involves expanding the initial convex no-fly zone outward along its respective normal direction to determine the no-fly zone boundary plane and obtain the no-fly zone constraint, includes: the translational amount of the initial convex no-fly zone expanding outward along its respective normal direction, expressed as: in, The maximum flight speed of the aircraft. Let the discrete time step size be , and These are the standard deviations of the flyover's position along the direction of maximum error and the standard deviations of the digital elevation model's elevation, respectively. The offset of the translated boundary plane is denoted as The no-fly zone boundary plane is determined based on the plane normal vector and offset. ,in, Represents any point in space; It should be noted that, in order to prevent the spacecraft from colliding with the lunar surface, it should be constrained to always be located within the safe zone, that is, on the side pointed to by the normal direction of any boundary plane.

[0031] Furthermore, based on the expanded no-fly zone boundary plane equation, the no-fly zone constraint is constructed, expressed as: in, The number of pre-defined no-fly zone boundary planes, It is a large integer. For the corresponding number A binary variable representing the boundary plane of a no-fly zone.

[0032] In this embodiment of the invention, step S300 involves performing a trajectory optimization based on the no-fly zone constraint and a convex optimization problem model for the flight trajectory, including: the trajectory optimization problem is expressed as: It should be noted that after modeling the above optimization problem in a scientific computing platform (such as MATLAB or Python), mature commercial mathematical optimization solvers (such as Gurobi or CPLEX) can be called to solve it efficiently, thereby obtaining the optimal control sequence and flight trajectory that satisfy all constraints.

[0033] Furthermore, such as Figure 3 As shown, the trajectory obtained in step S300 is used as the reference trajectory, and the discrete trajectory points of the reference trajectory are... The shortest distance from the center of the spherical safe zone to the lunar surface is calculated. The minimum distance from the trajectory point to all grid points of the DEM is used as the radius of the spherical safety zone. This is because the no-fly zone model was expanded by translation in step S300. Then any The distance to the lunar surface is greater than the translation. The radius of the safety zone must be greater than half the distance between adjacent trajectory points. Adjacent safety zones overlap, and all safety zones merge together to form a safe flight corridor from the start point to the target point. To avoid collision risks introduced by the positional errors of the flyover vehicle and terrain errors, the radius of the safety zone is reduced to... .

[0034] In this embodiment of the invention, step S400 involves constructing a safe zone constraint based on a safe flight corridor, performing secondary trajectory optimization, solving the fuel consumption minimization problem, and obtaining the optimal obstacle avoidance flight trajectory. This includes discretizing the flight time of the secondary trajectory optimization into 2... N The segment constructs a safe zone constraint, represented as: Furthermore, such as Figure 4As shown, the obstacle avoidance constraint requires that adjacent trajectory points in the secondary trajectory optimization be located in the same safe zone. Thus, the line connecting these two trajectory points must also be located in the same safe zone, avoiding the threat to trajectory safety posed by trajectory discretization error.

[0035] In this embodiment of the invention, step S400, combined with the safety zone constraint, represents the quadratic trajectory optimization problem as follows: in, For the first The center of a spherical safety zone, For the first The radius of the spherical safety zone.

[0036] It should be noted that after modeling the above optimization problem in a scientific computing platform (such as MATLAB or Python), mature commercial mathematical optimization solvers (such as Gurobi or CPLEX) can be called to solve it efficiently, thereby obtaining the optimal control sequence and flight trajectory that satisfy all constraints.

[0037] It should also be noted that the trajectory obtained in step S400 of the present invention has lower fuel consumption than the trajectory obtained in step S300. The method of the present invention achieves safe and low-fuel-consumption flight trajectory optimization by combining a no-fly zone and a safe zone, taking into account the position error of the flying vehicle, the trajectory discretization error and the terrain error.

[0038] The above is a schematic scheme of an obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole according to this embodiment. It should be noted that the technical solution of this obstacle avoidance flight trajectory optimization system for the undulating terrain of the lunar south pole belongs to the same concept as the technical solution of the obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole described above. For details not described in detail in the technical solution of the obstacle avoidance flight trajectory optimization system for the undulating terrain of the lunar south pole in this embodiment, please refer to the description of the technical solution of the obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole described above.

[0039] This embodiment presents an obstacle avoidance and flight trajectory optimization system for the undulating terrain of the lunar south pole, comprising: The initial trajectory generation module, based on the leap mission constraints of the leap vehicle, constructs a convex optimization problem model for the leap trajectory with the goal of minimizing the fuel consumption of the leap vehicle; The convex no-fly zone construction module is used to construct a three-dimensional convex hull based on the digital elevation model of the task area and extract the effective external normal vectors. The effective external normal vectors are then weighted and clustered to fit the convex plane, forming the initial convex no-fly zone. The first optimization module is used to expand the initial convex no-fly zone outward along its respective normal direction, determine the boundary plane of the no-fly zone, obtain the no-fly zone constraint, and perform a first trajectory optimization based on the no-fly zone constraint and the convex optimization problem model of the leap trajectory to obtain the reference trajectory; The safe zone construction module is used to construct spherical safe zones centered on each discrete point of the reference trajectory. The radius of each sphere is equal to the shortest distance from that point to the original digital elevation model minus the translation amount, and adjacent spheres are ensured to overlap to form a safe flight corridor. The secondary optimization module is used to construct a safe zone constraint based on the safe flight corridor, perform secondary trajectory optimization, solve the fuel consumption minimization problem, and obtain the optimal obstacle avoidance flight trajectory.

[0040] This embodiment also provides an electronic device applicable to the optimization method of obstacle avoidance flight trajectory for the undulating terrain of the lunar south pole, including: The system includes a memory and a processor. The memory stores computer-executable instructions, and the processor executes these instructions to implement the obstacle avoidance and trajectory optimization method for the undulating terrain of the lunar south pole, as proposed in the above embodiments.

[0041] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the obstacle avoidance and flight trajectory optimization method for the undulating terrain of the lunar south pole as proposed in the above embodiments.

[0042] The storage medium proposed in this embodiment and the method for optimizing obstacle avoidance flight trajectory for the undulating terrain of the lunar south pole proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0043] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0044] Example 2, refer to Figure 5This is one embodiment of the present invention. Unlike the first embodiment, this embodiment verifies the feasibility of the leap trajectory planning of the present invention through simulation experiments.

[0045] In this embodiment, the Shackleton Crater area is selected as the mission area to simulate the scenario of the spacecraft flying from outside the Shackleton Crater to inside the crater. The simulation is carried out in the Antarctic stereoscopic projection coordinate system.

[0046] The standard deviations of the flyover position and terrain data elevation were set to 10m and 0.5m, respectively. The parameter settings for trajectory optimization are shown in Table 1.

[0047] Table 1 Parameter Settings

[0048] A two-step optimization method combining no-fly zones and safe zones is compared with a piecewise optimization method based on altitude constraints, and the resulting trajectory is as follows: Figure 5 As shown. From Figure 5 As can be seen, the segmented leap method divides the leap process into three parts: ascent, leap, and descent. This allows the vehicle to ascend to a certain height before making a horizontal leap, and it remains above that height throughout the leap, descending only after reaching the landing point.

[0049] Neither of the two trajectory optimization methods resulted in a lunar trajectories that collided with the lunar surface, ensuring trajectory safety. Compared to the trajectory obtained using the segmented leap method, the trajectory obtained using the two-step optimization method was closer to the lunar surface and had a lower overall flight altitude. Based on the trajectories obtained using the segmented leap method and the two-step optimization method, the fuel consumption during the leap was 29.87 kg and 23.51 kg, respectively, with the two-step optimization method showing better fuel efficiency. This invention, through a two-step optimization strategy combining no-fly zones and safe zones, achieves safe and low-fuel-consumption leap trajectory optimization while considering the leap vehicle's position error, trajectory discretization error, and terrain error.

[0050] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. 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 be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for optimizing obstacle avoidance flight trajectories for the undulating terrain of the lunar south pole, characterized in that, include: Based on the flight mission constraints of the flyover vehicle, and with the goal of minimizing the flyover vehicle's fuel consumption, a convex optimization problem model for the flight trajectory is constructed. A three-dimensional convex hull is constructed based on the digital elevation model of the mission area, and effective external normal vectors are extracted. The effective external normal vectors are then subjected to weighted clustering to fit the convex plane and form an initial convex no-fly zone. The initial convex no-fly zone is expanded outward along its respective normal direction to determine the no-fly zone boundary plane, thus obtaining the no-fly zone constraint. Based on the no-fly zone constraint and the convex optimization problem model of the leap trajectory, a trajectory optimization is performed to obtain the reference trajectory. Centered on each discrete point of the reference trajectory, spherical safety zones are constructed, wherein the radius of each sphere is equal to the shortest distance from that point to the original digital elevation model minus the translation amount, and adjacent spheres are ensured to overlap to form a safe flight corridor; Based on the aforementioned safe flight corridor, a safe zone constraint is constructed, and secondary trajectory optimization is performed to solve the fuel consumption minimization problem, thereby obtaining the optimal obstacle avoidance flight trajectory.

2. The obstacle avoidance and flight trajectory optimization method for the undulating terrain of the lunar south pole as described in claim 1, characterized in that, Before constructing the convex optimization problem model for the leap trajectory, the following steps are also included: Define a flyover coordinate system O-XYZ; the flyover coordinate system takes the target landing position of the flyover mission as the origin O, the Z-axis is perpendicular to the lunar surface and points to outer space, the X-axis points to the starting position of the flyover mission, and the Y-axis, Z-axis and X-axis form a right-handed rectangular coordinate system.

3. The obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole as described in claim 2, characterized in that, Constructing a convex optimization problem model for the leap trajectory includes: dividing the leap duration into... N part; Based on the initial state of the jumper, the state expression at each time step is recursively derived, in the th... The state of the jumper at each time step is denoted as: in, , 、 The leap vehicle is at the 1st The natural logarithm of position, velocity, and mass at each time step. N The number of discrete time intervals; The discretized leap trajectory convex optimization problem model is expressed as follows: in, This is the initial position of the flying vehicle. For the first The normalized thrust of the step, for In time The theoretical lower limit of time, For the first Net control acceleration of the step, This represents the initial state of the jump device.

4. The obstacle avoidance and flight trajectory optimization method for the undulating terrain of the lunar south pole as described in claim 3, characterized in that, A three-dimensional convex hull is constructed based on the digital elevation model of the mission area, and effective external normal vectors are extracted. Weighted clustering of these effective external normal vectors is then performed to fit a convex plane, forming an initial convex no-fly zone, including: Generate a 3D convex hull for each point in the digital elevation model of the task area, and obtain the set of unit outward normal vectors of the convex hull surface. ;from Selected from Normal vectors with components greater than 0 are removed, along with normal vectors perpendicular to the XOZ plane, resulting in the cleaned set of normal vectors. ; right Perform weighted k-means clustering to obtain A representative direction constitutes the direction set. ; Will The direction in the middle is used as the normal vector of the no-fly zone boundary plane. And determine the plane offset of the no-fly zone boundary. The flight trajectory optimization space is divided into a safe space with terrain obstacles and a dangerous space without terrain obstacles.

5. The obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole as described in claim 4, characterized in that, Expanding the initial convex no-fly zone outward along its respective normal direction to determine the no-fly zone boundary plane, thus obtaining the no-fly zone constraint, includes: the translational amount of the initial convex no-fly zone outward along its respective normal direction, expressed as: in, The maximum flight speed of the aircraft. Let the discrete time step size be , and These are the standard deviations of the flyover's position along the direction of maximum error and the standard deviations of the digital elevation model's elevation, respectively. The offset of the translated boundary plane is denoted as The no-fly zone boundary plane is determined based on the plane normal vector and offset. ,in, Represent any point in space; based on the expanded boundary plane equation of the no-fly zone, construct the no-fly zone constraint, expressed as: in, The number of pre-defined no-fly zone boundary planes, It is a large integer. For the corresponding number A binary variable representing the boundary plane of a no-fly zone.

6. The obstacle avoidance and flight trajectory optimization method for the undulating terrain of the lunar south pole as described in claim 5, characterized in that, Based on the aforementioned no-fly zone constraints and the flyover trajectory optimization problem model, a primary trajectory optimization is performed, including: The primary trajectory optimization problem is expressed as:

7. The obstacle avoidance and flight trajectory optimization method for the undulating terrain of the lunar south pole as described in claim 6, characterized in that, Based on the aforementioned safe flight corridor, a safe zone constraint is constructed, and a secondary trajectory optimization is performed to solve the fuel consumption minimization problem, thereby obtaining the optimal obstacle avoidance flight trajectory. This includes discretizing the flight time of the secondary trajectory optimization into 2... N The segment constructs a safe zone constraint, represented as: With the safety zone constraint in mind, the quadratic trajectory optimization problem can be expressed as: in, For the first The center of a spherical safety zone, For the first The radius of the spherical safety zone.

8. A trajectory optimization system for obstacle avoidance over undulating terrain at the lunar south pole, applied to the method described in any one of claims 1-7, characterized in that, include: The initial trajectory generation module, based on the leap mission constraints of the leap vehicle, constructs a convex optimization problem model for the leap trajectory with the goal of minimizing the fuel consumption of the leap vehicle; The convex no-fly zone construction module is used to construct a three-dimensional convex hull based on the digital elevation model of the mission area and extract effective external normal vectors. The effective external normal vectors are then weighted and clustered to fit a convex plane to form an initial convex no-fly zone. The first optimization module is used to expand the initial convex no-fly zone outward along its respective normal direction, determine the no-fly zone boundary plane, obtain the no-fly zone constraint, and perform a first trajectory optimization based on the no-fly zone constraint and the convex optimization problem model of the leap trajectory to obtain the reference trajectory. The safe zone construction module is used to construct spherical safe zones centered on each discrete point of the reference trajectory. The radius of each sphere is equal to the shortest distance from that point to the original digital elevation model minus the translation amount, and adjacent spheres are ensured to overlap to form a safe flight corridor. The secondary optimization module is used to construct a safety zone constraint based on the safe flight corridor, perform secondary trajectory optimization, solve the fuel consumption minimization problem, and obtain the optimal obstacle avoidance flight trajectory.

9. An electronic device, comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the obstacle avoidance and flight trajectory optimization method for the undulating terrain of the lunar south pole as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the obstacle avoidance flight trajectory optimization method for the undulating terrain of the lunar south pole as described in any one of claims 1 to 7.

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