A multi-spacecraft spherical path planning method based on improved redwood algorithm and application thereof

Abstract

This invention discloses a multi-spacecraft spherical path planning method based on an improved Sequoia algorithm, belonging to the field of spacecraft intelligent control and trajectory planning. Based on the Sequoia ecological algorithm, this invention introduces three enhancement mechanisms: an adaptive multi-parameter self-adjustment mechanism, an elite fire response strategy, and a directional local search with orthogonal exploration, to construct an improved Sequoia algorithm. The method establishes a spherical multi-spacecraft path planning model, comprehensively considering multi-objective fitness functions such as static no-fly zone avoidance, dynamic obstacle avoidance, safe distance between spacecraft, and spherical constraints. The improved Sequoia algorithm iteratively optimizes the cooperative flight trajectory of multiple spacecraft, ultimately outputting smooth, collision-free spherical flight trajectories for multiple spacecraft. This invention demonstrates superior convergence accuracy and robustness in multi-scenario spherical path planning simulations, and is suitable for aerospace applications such as planetary surface exploration and satellite orbit optimization.

Description

Technical Field

[0001] This invention belongs to the field of intelligent control and trajectory planning for spacecraft, specifically involving a multi-spacecraft spherical path planning method and its application based on an improved Sequoia algorithm. Background Technology

[0002] Path planning is a core challenge for autonomous systems, widely applied in robotics, aerospace, transportation, logistics, and intelligent control. Its primary goal is to determine the optimal or near-optimal trajectory that guides a moving object from its starting position to its target position, while simultaneously satisfying multiple constraints such as obstacle avoidance, energy efficiency, and time optimization. Traditionally, most path planning research has focused on planar environments, but Euclidean geometry provides a natural and computationally tractable framework for problem modeling.

[0003] In the field of planar path planning, numerous methodologies have been proposed and extensively studied. Classical methods include the A* algorithm, Dijkstra's algorithm, Rapid Exploratory Random Tree (RRT), and Artificial Potential Field (APF), which have demonstrated effectiveness in structured environments. However, as problem complexity increases (especially with dynamic obstacles and real-time constraints), these traditional methods often encounter computational bottlenecks and limited scalability. Therefore, metaheuristic optimization algorithms have emerged as powerful alternatives. Swarm intelligence and evolutionary algorithms such as Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Genetic Algorithm (GA), and Differential Evolution (DE) have shown superior capabilities in handling nonlinear constraints, multi-objective optimization, and complex search spaces.

[0004] Despite significant progress in planar path planning, trajectory optimization on spheres has received far less attention, revealing a fundamental research gap. In practical applications such as planetary surface exploration and satellite navigation, motion is inherently constrained by planetary curvature, and planar approximations introduce non-negligible geometric distortions. Existing research on spherical path planning primarily focuses on combinatorial optimization problems, particularly variations of the Traveling Salesman Problem adapted to spherical geometry—the spherical Traveling Salesman Problem—finding the shortest closed path to a set of predetermined locations on a sphere. This type of research only addresses static, point-to-point discrete node selection and cannot handle complex constraints such as continuous trajectory generation, dynamic obstacles, and multi-spacecraft cooperation.

[0005] Dynamic spherical multi-spacecraft path planning is a more challenging and under-researched problem. Unlike the spherical traveling salesman problem, dynamic spherical multi-spacecraft path planning requires continuous trajectory generation on a sphere while satisfying the following tightly coupled constraints: (1) continuous control in the spherical coordinate system, rather than discrete node selection; (2) collision avoidance with static no-fly zones and time-varying dynamic obstacles; (3) maintaining safe distances between multiple spacecraft operating on the same sphere; and (4) computational efficiency requirements for adapting to dynamic or near-real-time replanning. In addition, practical operational constraints further increase the difficulty: the trajectory must be kept on or near the sphere while satisfying velocity limits, angle deflection constraints, and energy consumption considerations. Static obstacles (no-fly zones) must be strictly avoided, and dynamic obstacles (other autonomous spacecraft and moving entities) introduce strong time dependence, requiring predictive collision avoidance strategies. These factors together make SMAPP a high-dimensional, nonlinear, and strongly constrained optimization problem.

[0006] The Sequoia Ecosystem Algorithm is a metaheuristic optimization algorithm proposed in recent years, inspired by the collective growth dynamics, adaptive resilience, and reproductive diversity of the sequoia forest ecosystem in nature. As one of the oldest and most resilient organisms on Earth, the sequoia maintains its ecological stability through dense spatial aggregation, deep root networks, intrinsic self-regulation under environmental stress, and rapid recovery and regeneration after droughts or wildfires. The Sequoia Ecosystem Algorithm maps these ecological characteristics to the core optimization challenges: efficient global information exchange, adaptive population behavior, diversity preservation, and prevention of premature convergence. However, the original Sequoia Ecosystem Algorithm suffers from three key shortcomings when applied to high-dimensional, strongly constrained spherical path planning: fixed parameter decay lacks responsiveness to the actual search state, easily leading to early stagnation or late overexploration; the uniform perturbation strategy ignores information asymmetry between elite and non-elite individuals; and the unidirectional isotropic Gaussian random walk has limited efficiency near the high-dimensional constraint boundary. Summary of the Invention

[0007] In view of this, the present invention provides a multi-spacecraft spherical path planning method based on an improved sequoia algorithm, comprising the following steps:

[0008] Step 1: Establish a mathematical model for the spherical multi-spacecraft path planning problem: with radius as... Using the sphere as the primary navigation space, the spacecraft's state variables are defined and given... The initial and target positions of the spacecraft are used as boundary conditions; based on this, a spherical motion model is constructed to describe the motion of the spacecraft on the sphere, and control variables, including step size, are defined. Polar angle and azimuth And establish spacecraft position update equations and motion constraints;

[0009] Step 2: Construct the multi-objective fitness function for spherical multi-spacecraft path planning The fitness function comprehensively considers the target distance term. Static no-fly zone avoidance items Dynamic obstacle avoidance items Spacecraft inter-spacecraft safety distance item and spherical constraint terms The penalty function mechanism is used to quantitatively evaluate constraint violations;

[0010] Step 3: Constructing an improved Sequoia algorithm: Based on the original Sequoia ecological algorithm framework, three enhancement mechanisms are introduced, including an adaptive multi-parameter self-adjustment mechanism, a differentiated perturbation strategy based on elite individuals, and a directional local search with orthogonal exploration;

[0011] Step 4: Initialize the population size based on the established spherical motion model and the constructed multi-objective fitness function constraints. Maximum number of iterations and control variable boundaries; using the improved Sequoia algorithm to analyze candidate solutions. Iterative optimization is performed, with parameters dynamically adjusted based on population diversity and stagnation states during the iteration process, and trajectory planning is executed to find the optimal solution. Candidate solutions are included. Depend on Spacecraft step length Polar angle and azimuth Parameter assembly structure: The system generates corresponding trajectories using a spherical motion model, evaluates the trajectories based on a fitness function, and finally outputs the spherical flight trajectory of multiple spacecraft with the best fitness.

[0012] Furthermore, in step 1, the spherical motion model is specifically as follows:

[0013] No. The spacecraft in The position of the next iteration is The target location is The position update equation is:

[0014] ;

[0015] The control variables satisfy the following constraints: , , ;

[0016] Spherical constraints require all spacecraft positions to satisfy: This ensures that the spacecraft remains above the sphere and does not penetrate its interior.

[0017] Candidate solutions Depend on It is composed of the control variables of a spacecraft: ,form Dimensional optimization problem.

[0018] Furthermore, in step 2, the multi-objective fitness function The specific construction method is as follows:

[0019] ;

[0020] 1) Target distance item Calculate the sum of Euclidean distances between the current position and the target position of all spacecraft, and apply a large penalty coefficient to trajectories that violate spherical constraints. :

[0021] ;

[0022] in, Euclidean distance between current location and its target destination:

[0023] ;

[0024] Penalty items Enforce basic spherical constraints to prevent the aircraft from penetrating the interior of the sphere:

[0025] ;

[0026] 2) Static No-Fly Zone Avoidance Items When a spacecraft encounters a static obstacle The distance is less than its radius Spacecraft radius and safe distance When the sum is equal to the sum of the values, it is considered a collision with a static obstacle and a penalty is applied. :

[0027] ;

[0028] in Represents static obstacles Location;

[0029] 3) Dynamic obstacle avoidance items Predictive collision avoidance is used for dynamic obstacles. When the predicted distance between the spacecraft and the dynamic obstacle does not meet the safety clearance requirement, it is judged as a collision with the dynamic obstacle and a penalty is imposed. The position of dynamic obstacles is updated over time based on their kinematic model.

[0030] ;

[0031] The position of each dynamic obstacle changes according to its kinematic model:

[0032] ;

[0033] in, Represents dynamic obstacles In the The position of the next iteration; Indicates the first During the nth iteration The flight speed of a dynamic obstacle and These represent the polar angle and azimuth angle at the same iteration time, respectively; this formula can achieve active trajectory planning and predict the future position of obstacles.

[0034] 4) Spacecraft inter-spacecraft safety clearance item When any two spacecraft and The distance between them is less than 3 times the spacecraft radius. At that time, a collision between spacecraft is determined and a penalty is imposed. :

[0035] ;

[0036] 5) Spherical constraint terms Constraining spacecraft radial deviation using a quadratic penalty function In the permitted altitude zone Inside, The punishment is too lenient. and too high flight:

[0037] .

[0038] Furthermore, in step 3, the redwood ecological algorithm includes initialization and population updates performed during iteration. The population update sequentially executes resource sharing, adaptive fire disturbance, reproduction updates, and elite retention operations according to a preset strategy to achieve global search and local optimization of candidate solutions. The specific implementation is as follows:

[0039] 1) Initialization: In Dimensional feasible search space Inner uniform sampling candidate solutions Evaluate the objective function value Record the optimal solution ;

[0040] 2) Resource sharing: Calculate the mean position of the top 50% of individuals in the population. Update each individual as follows:

[0041] ;

[0042] in Using standard normally distributed random numbers, we simulate resource sharing in the root network of a redwood forest;

[0043] 3) Adaptive fire disturbance: The fire probability decreases dynamically according to the following formula:

[0044] ;

[0045] When random number At that time, perturbation is applied to individuals To prevent early premature contraction;

[0046] 4) Reproduction and renewal: For adjacent individuals ( Perform a crossover operation to generate two descendants. and :

[0047] ;

[0048] ;

[0049] in The random weighting coefficients are within the range [0,1]; the mutation probability decays over time according to the following formula: When mutation is triggered, the offspring execute... And perform boundary correction. ;

[0050] 5) Elite Retention: Before Identification elite individuals It is temporarily stored and replaced with the worst individual in the population at the end of the iteration: Simultaneously, for the global optimal solution Perform local refinement: ,like Then update .

[0051] Furthermore, in the aforementioned redwood ecological algorithm, the original fire probability and mutation probability are controlled using a preset linear decay mechanism. This mechanism is a fixed scheduling method and cannot be dynamically adjusted according to the population state during the search process. Therefore, in the adaptive fire disturbance and reproduction update execution process, a multi-parameter self-adjustment mechanism is introduced to dynamically regulate the fire probability and mutation probability, enabling them to adapt to changes based on population diversity and optimization stagnation, thereby avoiding the problems of early convergence stagnation or overexploration in the later stages of the algorithm. The specific implementation method is as follows:

[0052] 1) Calculate population diversity ,in For the first The first generation of the population A vector of all individual values ​​in dimension;

[0053] 2) When population diversity Poor or optimal solution stalls for a limited number of iterations If too many cases occur, the crisis response mode will be triggered.

[0054] ;

[0055] ;

[0056] 3) Adaptive Elite Individual Quantity Adjust dynamically based on diversity: In the early exploration phase, the number of elite individuals is kept small, while in the convergence phase, the number of elite individuals is increased to prevent the loss of high-quality solutions.

[0057] Furthermore, the original Sequoia algorithm uses a uniform perturbation strength, ignoring the information asymmetry between elite and inferior solutions. To address this issue, a differentiated perturbation strategy based on elite individuals is introduced into the adaptive fire perturbation. This strategy applies differentiated perturbations based on fitness ranking to the population individuals, thereby enhancing the search capability for the neighborhood of high-quality candidate solutions. The specific implementation is as follows:

[0058] When a fire event is triggered ( When this is the case, differentiated perturbations are applied to elite and non-elite individuals based on their ranking within the population:

[0059] ;

[0060] Elite individuals are subjected to smaller perturbations to preserve valuable search information, while non-elite individuals are subjected to larger perturbations to enhance their exploration capabilities; the number of elites The adaptive mechanism in claim 4 dynamically determines the elite protection strength, enabling a dynamic response to the convergence state.

[0061] Furthermore, the Sequoia Ecosystem Algorithm employs Gaussian random walks for local optimization. While this strategy is effective in unconstrained environments, its blind search approach is inefficient in high-dimensional constrained environments. Therefore, during the iterative optimization process of the Sequoia Ecosystem Algorithm, a directional local search strategy with orthogonal exploration is introduced to perform secondary optimization on the current optimal solution. This strategy consists of two independent stages: gradient-guided exploration and orthogonal subspace exploration. The specific implementation is as follows:

[0062] 1) Gradient-guided development: for each elite individual Calculate its relationship with the global optimal solution. Direction vector :

[0063] ;

[0064] Then, noise is added along the negative gradient direction to generate candidate solutions. :

[0065] ;

[0066] in =0.05, =0.05;

[0067] 2) Exploration of orthogonal subspaces: Let Represents direction vector The zero space, so for any vector in All conditions are met. ;from A specific orthogonal direction vector is randomly selected from the basis. and normalize it:

[0068] ;

[0069] Simultaneously, a second candidate solution is generated. :

[0070] ;

[0071] in =0.03, =0.03; This mechanism enables spacecraft to bypass obstacles such as no-fly zones, performing lateral evasion while maintaining their overall direction of travel;

[0072] 3) Greedy selection mechanism: Boundary constraint correction and fitness evaluation are performed on two candidate solutions. Update is only performed when the fitness of the candidate solution is better than that of the current elite individual, ensuring monotonic improvement of the elite layer.

[0073] 8. The method as described in claim 1, wherein the specific process of trajectory planning and optimization in step 4 is as follows:

[0074] Step 4.1: Initialization candidate solutions At the boundary of control variables Uniformly distributed within the region, calculate the initial fitness, and record the global optimal solution. ;

[0075] Step 4.2: Sort the populations in ascending order of fitness and calculate diversity. Dynamic determination Store elite solutions and adaptively adjust fire probability. and mutation probability ;

[0076] Step 4.3: Implement collective growth resource sharing, with each individual moving to the top 50% of the elite mean position; implement the elite fire response strategy; perform crossover and mutation reproduction operations to maintain population diversity;

[0077] Step 4.4: Perform a directional local search with orthogonal exploration on the elite individuals; replace the current worst solution with the stored elite solution. Individuals, implementing an elite retention mechanism;

[0078] Step 4.5: Calculate the fitness of the new population and update the global optimum. Update the stall count Determine if the maximum number of iterations has been reached. If the target is not reached, return to step 4.2; otherwise, output the globally optimal solution. The corresponding sequence of spherical trajectory coordinates of multiple spacecraft.

[0079] This invention also provides an application of a multi-spacecraft spherical path planning method based on an improved Sequoia algorithm. The application scenarios of this method include multi-probe collaborative path planning in planetary surface exploration missions, low-Earth orbit satellite swarm orbit collaborative optimization, and any multi-agent trajectory planning problem with spherical or near-spherical surfaces as motion constraints.

[0080] The beneficial effects of this invention are as follows: This invention provides the first systematic modeling of the dynamic spherical multi-spacecraft path planning problem, filling a research gap in this field; the adaptive multi-parameter self-adjustment mechanism adjusts key parameters in real time based on population diversity and stagnation states, significantly improving the algorithm's search adaptability in complex dynamic environments; the differentiated perturbation strategy based on elite individuals enhances population exploration capabilities while protecting high-quality solutions through differentiated perturbation intensity, thereby improving the global optimality and stability of path planning results; the directional local search with orthogonal exploration combined with orthogonal subspace exploration effectively alleviates the local stagnation problem under high-dimensional constraints, improving the spacecraft's obstacle-avoidance maneuvering and fine path adjustment capabilities in spherical environments; furthermore, this invention can take into account multiple objective constraints such as path length, energy consumption, and safety distance, achieving efficient generation and conflict avoidance of multi-spacecraft cooperative paths, improving the overall system cooperative efficiency and mission execution reliability. In four progressively complex scenario simulations, the improved Sequoia algorithm demonstrated superior convergence accuracy, robustness, and scalability. Attached Figure Description

[0081] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0082] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0083] Figure 1 This is a flowchart illustrating the overall process of the improved Sequoia algorithm of this invention.

[0084] Figure 2 A schematic diagram of the basic layout for the spherical multi-spacecraft path planning problem;

[0085] Figure 3 Schematic diagram of spherical path planning environment configuration for four progressively complex scenarios (Scenes 1 to 4, front and back views).

[0086] Figure 4 A comparison chart of the path planning results of each algorithm in scenario 1;

[0087] Figure 5 This is a comparison chart of the path planning results of each algorithm in scenario 2;

[0088] Figure 6 A comparison chart of the path planning results of each algorithm in scenario 3;

[0089] Figure 7 A comparison chart of the path planning results of each algorithm in scenario 4;

[0090] Figure 8 To improve the fitness convergence curves of the Sequoia algorithm and the comparison algorithm in four scenarios.

[0091] Figure 9 A bar chart comparing the average fitness values ​​of 30 independent runs in each scenario. Detailed Implementation

[0092] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of systems consistent with some aspects of the invention as detailed in the appended claims.

[0093] refer to Figure 1-9 This invention provides a multi-spacecraft spherical path planning method based on an improved Sequoia algorithm, comprising the following steps:

[0094] Step 1: Modeling the Path Planning Problem for Multiple Spacecraft on a Spherical Surface

[0095] Consideration of the spherical multi-spacecraft path planning problem The spacecraft has a radius of Each spacecraft flies simultaneously on the surface of the sphere. Must start from the initial position Navigate to the target location Simultaneously satisfying multiple constraints. Based on the spherical kinematics model, the control variables for each spacecraft include step size. (Flight distance per unit time), polar angle and azimuth The spherical motion model is as follows:

[0096] Establish a mathematical model for the spherical multi-spacecraft path planning problem: with radius as Using the sphere as the primary navigation space, the spacecraft's state variables are defined and given... The starting position of the spacecraft With the target location As boundary conditions; based on this, a spherical motion model is constructed to describe the motion of the spacecraft on the sphere, and control variables including step size are defined. Polar angle and azimuth And establish the spacecraft position update equation and motion constraints; the spherical motion model is as follows: Figure 2 As shown, the details are as follows:

[0097] No. The spacecraft in The position of the next iteration is The target location is The position update equation is:

[0098] ;

[0099] The control variables satisfy the following constraints: , , ;

[0100] Spherical constraints require all spacecraft positions to satisfy: To ensure spaceflight

[0101] The device remains above the sphere and does not penetrate its interior; simultaneously, the system includes A static hemispherical no-fly zone (each with center coordinates and radius) (characterization) and A dynamic obstacle. Candidate solutions. for The concatenated vector of spacecraft control variables forms This is a dimensional optimization problem. In the embodiment, the experimental environment is configured with a spherical radius... = 100, speed range polar angle azimuth Minimum safe distance =5, lower bound of height =0.1, upper limit of height = 3, penalty coefficient =10 6 .

[0102] Step 2: Construction of Multi-Objective Fitness Function

[0103] Constructing a multi-objective fitness function for spherical multi-spacecraft path planning The fitness function comprehensively considers the target distance term. Static no-fly zone avoidance items Dynamic obstacle avoidance items Spacecraft inter-spacecraft safety distance item and spherical constraint terms The constraint violation is quantitatively evaluated through a penalty function mechanism; the multi-objective fitness function The specific construction method is as follows:

[0104] ;

[0105] 1) Target distance item Calculate the sum of Euclidean distances between the current position and the target position of all spacecraft, and apply a large penalty coefficient to trajectories that violate spherical constraints. :

[0106] ;

[0107] in, Euclidean distance between current location and its target destination:

[0108] ;

[0109] Penalty items Enforce basic spherical constraints to prevent the aircraft from penetrating the interior of the sphere:

[0110] ;

[0111] 2) Static No-Fly Zone Avoidance Items When a spacecraft encounters a static obstacle The distance is less than its radius Spacecraft radius and safe distance When the sum is equal to the sum of the values, it is considered a collision with a static obstacle and a penalty is applied. :

[0112] ;

[0113] in Represents static obstacles Location;

[0114] 3) Dynamic obstacle avoidance items Predictive collision avoidance is used for dynamic obstacles. When the predicted distance between the spacecraft and the dynamic obstacle does not meet the safety clearance requirement, it is judged as a collision with the dynamic obstacle and a penalty is imposed. The position of dynamic obstacles is updated over time based on their kinematic model.

[0115] ;

[0116] The position of each dynamic obstacle changes according to its kinematic model:

[0117] ;

[0118] in, Represents dynamic obstacles In the The position of the next iteration; Indicates the first During the nth iteration The flight speed of a dynamic obstacle and These represent the polar angle and azimuth angle at the same iteration time, respectively; this formula can achieve active trajectory planning and predict the future position of obstacles.

[0119] 4) Spacecraft inter-spacecraft safety clearance item When any two spacecraft and The distance between them is less than 3 times the spacecraft radius. At that time, a collision between spacecraft is determined and a penalty is imposed. :

[0120] ;

[0121] 5) Spherical constraint terms Constraining spacecraft radial deviation using a quadratic penalty function In the permitted altitude zone Inside, The punishment is too lenient. and too high flight:

[0122] .

[0123] Step 3: Improve the Sequoia Algorithm Construction

[0124] 3.1 Basic Framework of the Original Sequoia Ecosystem Algorithm

[0125] The Sequoia Ecosystem Algorithm, inspired by the sequoia forest ecosystem, achieves the following five ecological functions:

[0126] (1) Initialization: In Dimensional feasible search space Inner uniform sampling For each candidate solution, evaluate the objective function value and record the optimal solution. .

[0127] (2) Resource sharing: In nature, individual redwoods form dense communities through intertwined root networks, achieving resource exchange and collaborative support. In the algorithm, the mean position of the top 50% of individuals in the population is calculated. Each individual is updated using the following formula:

[0128] ;

[0129] This mechanism will pull the unwinding towards the high-performance region while maintaining exploration diversity through Gaussian perturbations.

[0130] (3) Adaptive Fire Disturbance: The redwood ecosystem exhibits remarkable resilience to wildfires. The redwood ecosystem algorithm dynamically decays the wildfire probability. Simulate this feature. When At that time, perturbation is applied to individuals In the early iterations, premature convergence is prevented, while in the later iterations, convergence tends to occur.

[0131] (4) Reproduction and Renewal: Redwood reproduction occurs through seed dispersal (generating genetic diversity) and vegetative germination (preserving successful genotypes). In the algorithm, crossover operations are performed on adjacent individuals to generate offspring. and Probability of mutation Decays over time, and is triggered by descendants. And perform boundary correction.

[0132] (5) Elite preservation: Before preservation Each generation assigns an elite individual to replace the worst individual at the end of each generation, ensuring that optimal information does not degenerate. Simultaneously, the global optimal solution is... Perform local refinement: If improvements are made, then updates will be made. .

[0133] 3.2 Improved Sequoia Algorithm with Three Enhancement Mechanisms

[0134] (1) Adaptive multi-parameter self-adjustment mechanism

[0135] The original Sequoia ecological algorithm, with its fixed parameter decay, lacks responsiveness to the search state. The improved Sequoia algorithm introduces a population diversity-based approach. Adaptive feedback. Diversity. This represents the mean of the standard deviations for each dimension. When... < 0.05 (diversity crisis) or number of consecutive periods of stagnation > 5 (Stagnation Crisis) triggers Crisis Response Mode, significantly improving... and Inject exploratory behavior; otherwise, maintain the exploration-development balance in proportion to diversity. Adaptive elite number. This is negatively correlated with diversity, causing the elitist protection strength to dynamically respond to the convergence rate: a small elitist set is maintained during the exploration phase, and the elitist set is expanded during the convergence phase to prevent the loss of high-quality solutions, with the number of elitists not exceeding 20% ​​of the total population. The specific implementation is as follows:

[0136] 1) Calculate population diversity ,in For the first The first generation of the population A vector of all individual values ​​in dimension;

[0137] 2) When population diversity Poor or optimal solution stalls for a limited number of iterations If too many cases occur, the crisis response mode will be triggered.

[0138] ;

[0139] ;

[0140] 3) Adaptive Elite Individual Quantity Adjust dynamically based on diversity: In the early exploration phase, the number of elite individuals is kept small, while in the convergence phase, the number of elite individuals is increased to prevent the loss of high-quality solutions.

[0141] (2) Differentiated perturbation strategy based on elite individuals

[0142] The original Sequoia Ecosystem Algorithm applied a uniform perturbation to all individuals, failing to fully utilize information asymmetry between population levels. The improved Sequoia Algorithm differentiates individuals based on fitness ranking: elite individuals (top...) Small perturbations (0.1 times the standard normal distribution) preserve valuable search patterns; large perturbations (0.5 times the standard normal distribution) enhance global exploration in non-elite individuals. This mechanism, in conjunction with the adaptive elite number, ensures that both the number of elite protected individuals and the intensity of perturbations dynamically respond to the search status, fully simulating the differentiated response mechanism between mature trees and young vegetation in the redwood forest fire ecosystem. The specific implementation is as follows:

[0143] When a fire event is triggered ( When this is the case, differentiated perturbations are applied to elite and non-elite individuals based on their ranking within the population:

[0144] ;

[0145] Elite individuals are subjected to smaller perturbations to preserve valuable search information, while non-elite individuals are subjected to larger perturbations to enhance their exploration capabilities; the number of elites The adaptive mechanism in claim 4 dynamically determines the elite protection strength, enabling a dynamic response to the convergence state.

[0146] (3) Directional local search with orthogonal exploration

[0147] The original Sequoia Ecosystem Algorithm uses isotropic Gaussian random walks for local refinement, frequently exploring directions that violate constraints or deviate from the optimal basin in high-dimensional constrained environments, resulting in low computational efficiency. The improved Sequoia Algorithm introduces a two-stage directional local search for elite individuals: a gradient-guided development stage accelerates convergence to the optimal region by moving along the negative gradient direction between the elite individual and the global optimum; the orthogonal subspace exploration stage searches within the subspace perpendicular to the principal gradient, allowing solutions to laterally bypass obstacles without deviating from the Euclidean distance of the global optimum when the global optimum direction is hindered by local extrema or no-fly zones. This is particularly valuable in spherical path planning scenarios—spacecraft need to maneuver laterally around no-fly zones while maintaining their overall direction of travel. Greedy selection ensures monotonic improvement of the elite layer, accepting only candidate solutions with better fitness. The specific implementation is as follows:

[0148] 1) Gradient-guided development: for each elite individual Calculate its relationship with the global optimal solution. Direction vector :

[0149] ;

[0150] Then, noise is added along the negative gradient direction to generate candidate solutions. :

[0151] ;

[0152] in =0.05, =0.05;

[0153] 2) Exploration of orthogonal subspaces: Let Represents direction vector The zero space, so for any vector in All conditions are met. ;from A specific orthogonal direction vector is randomly selected from the basis. and normalize it:

[0154] ;

[0155] Simultaneously, a second candidate solution is generated. :

[0156] ;

[0157] in =0.03, =0.03; This mechanism enables spacecraft to bypass obstacles such as no-fly zones, performing lateral evasion while maintaining their overall direction of travel;

[0158] 3) Greedy selection mechanism: Boundary constraint correction and fitness evaluation are performed on two candidate solutions. Update is only performed when the fitness of the candidate solution is better than that of the current elite individual, ensuring monotonic improvement of the elite layer.

[0159] Step 4: Perform trajectory planning and optimization

[0160] Initialize the population size under the constraints of the spherical motion model and fitness function. =50, maximum number of iterations =100. The specific process of trajectory planning and optimization in the improved Sequoia algorithm is as follows:

[0161] Step 4.1: Initialization candidate solutions At the boundary of control variables Uniformly distributed within the region, calculate the initial fitness, and record the global optimal solution. ;

[0162] Step 4.2: Sort the populations in ascending order of fitness and calculate diversity. Dynamic determination Store elite solutions and adaptively adjust fire probability. and mutation probability ;

[0163] Step 4.3: Implement collective growth resource sharing, with each individual moving to the top 50% of the elite mean position; implement the elite fire response strategy; perform crossover and mutation reproduction operations to maintain population diversity;

[0164] Step 4.4: Perform a directional local search with orthogonal exploration on the elite individuals; replace the current worst solution with the stored elite solution. Individuals, implementing an elite retention mechanism;

[0165] Step 4.5: Calculate the fitness of the new population and update the global optimum. Update the stall count Determine if the maximum number of iterations has been reached. If the target is not reached, return to step 4.2; otherwise, output the globally optimal solution. The corresponding sequence of spherical trajectory coordinates of multiple spacecraft.

[0166] Figure 1 A flowchart of the overall algorithm is provided, clearly demonstrating the integration of the original five ecosystem operations and three enhancement mechanisms.

[0167] Example: Simulation Verification

[0168] This invention has a spherical radius Design four progressively complex simulation scenarios in an environment with a resolution of 100, such as... Figure 3 As shown. Specific scenario configuration parameters are as follows:

[0169] Scenario 1 (Basic Complexity): 3 spacecraft, 2 static no-fly zones, 2 dynamic obstacles. Establish a benchmark assessment environment for multi-spacecraft coordination.

[0170] Scenario 2 (Medium Complexity): 5 spacecraft, 2 static obstacles, and 2 dynamic obstacles, introducing higher requirements for collision avoidance between spacecraft.

[0171] Scenario 3 (High Complexity): 8 spacecraft, 2 static no-fly zones, and 2 dynamic obstacles pose a significant challenge to the coordination of multiple spacecraft at high density.

[0172] Scenario 4 (Extreme Complexity): 12 spacecraft, 7 static obstacles, and 6 dynamic obstacles, closely resembling a real high-density airspace management scenario.

[0173] like Figure 8 and Figure 9 As shown, the improved Sequoia algorithm achieved an average fitness of 0.23 in scenario 1, 0.67 in scenario 2, 2.61 in scenario 3, and 4.03 in scenario 4 across all scenarios, outperforming the comparison algorithms (HBO, ASMO, MSO, ETO, and the original Sequoia ecosystem algorithm) in all scenarios. The performance advantage increased with scenario complexity: compared to the original Sequoia ecosystem algorithm, it improved by 84.5% in scenario 1 and by 26.2% in scenario 4, fully validating the necessity and effectiveness of multi-layered enhancement strategies in high-dimensional, strongly constrained scenarios.

[0174] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these changes and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-spacecraft spherical path planning method based on an improved Sequoia algorithm, characterized in that, Includes the following steps: Step 1: Establish a mathematical model for the spherical multi-spacecraft path planning problem: with radius as... Using the sphere as the primary navigation space, the spacecraft's state variables are defined and given... The initial and target positions of the spacecraft are used as boundary conditions; based on this, a spherical motion model is constructed to describe the motion of the spacecraft on the sphere, and control variables, including step size, are defined. Polar angle and azimuth And establish spacecraft position update equations and motion constraints; Step 2: Construct the multi-objective fitness function for spherical multi-spacecraft path planning The fitness function comprehensively considers the target distance term. Static no-fly zone avoidance items Dynamic obstacle avoidance items Spacecraft inter-spacecraft safety distance item and spherical constraint terms The penalty function mechanism is used to quantitatively evaluate constraint violations; Step 3: Constructing an improved Sequoia algorithm: Based on the original Sequoia ecological algorithm framework, three enhancement mechanisms are introduced, including an adaptive multi-parameter self-adjustment mechanism, a differentiated perturbation strategy based on elite individuals, and a directional local search with orthogonal exploration; Step 4: Initialize the population size based on the established spherical motion model and the constructed multi-objective fitness function constraints. Maximum number of iterations and control variable boundaries; using the improved Sequoia algorithm to analyze candidate solutions. Iterative optimization is performed, and parameters are dynamically adjusted based on population diversity and stagnation during the iteration process to perform trajectory planning optimization.

2. The method as described in claim 1, characterized in that, In step 1, the spherical motion model is as follows: No. The spacecraft in The position of the next iteration is The target location is The position update equation is: ； The control variables satisfy the following constraints: , , ; Spherical constraints require all spacecraft positions to satisfy: This ensures that the spacecraft remains above the sphere and does not penetrate its interior; the system also includes A static hemispherical no-fly zone (each with center coordinates and radius) (characterization) and A dynamic obstacle.

3. The method as described in claim 1, characterized in that, In step 2, the multi-objective fitness function The specific construction method is as follows: ； 1) Target distance item Calculate the sum of Euclidean distances between the current position and the target position of all spacecraft, and apply a large penalty coefficient to trajectories that violate spherical constraints. : ； in, Euclidean distance between current location and its target destination: ； Penalty items Enforce basic spherical constraints to prevent the aircraft from penetrating the interior of the sphere: ； 2) Static No-Fly Zone Avoidance Items When a spacecraft encounters a static obstacle The distance is less than its radius Spacecraft radius and safe distance When the sum is equal to the sum of the values, it is considered a collision with a static obstacle and a penalty is applied. : ； in Represents static obstacles Location; 3) Dynamic obstacle avoidance items Predictive collision avoidance is used for dynamic obstacles. When the predicted distance between the spacecraft and the dynamic obstacle does not meet the safety clearance requirement, it is judged as a collision with the dynamic obstacle and a penalty is imposed. The position of dynamic obstacles is updated over time based on their kinematic model. ； The position of each dynamic obstacle changes according to its kinematic model: ； in, Represents dynamic obstacles In the The position of the next iteration; Indicates the first During the nth iteration The flight speed of a dynamic obstacle and These represent the polar angle and azimuth angle at the same iteration time, respectively; this formula can achieve active trajectory planning and predict the future position of obstacles. 4) Spacecraft inter-spacecraft safety clearance item When any two spacecraft and The distance between them is less than 3 times the spacecraft radius. At that time, a collision between spacecraft is determined and a penalty is imposed. : ； 5) Spherical constraint terms Constraining spacecraft radial deviation using a quadratic penalty function In the permitted altitude zone Inside, The punishment is too lenient. and too high flight: 。 4. The method as described in claim 1, characterized in that, In step 3, the redwood ecological algorithm includes initialization and population update performed during iteration. The population update sequentially executes resource sharing, adaptive fire disturbance, reproduction update, and elite retention operations according to a preset strategy to achieve global search and local optimization of candidate solutions. The specific implementation is as follows: 1) Initialization: In Dimensional feasible search space Inner uniform sampling candidate solutions Evaluate the objective function value Record the optimal solution ; 2) Resource sharing: Calculate the mean position of the top 50% of individuals in the population. Update each individual as follows: ； in Using standard normally distributed random numbers, we simulate resource sharing in the root network of a redwood forest; 3) Adaptive fire disturbance: The fire probability decreases dynamically according to the following formula: ； When random number At that time, perturbation is applied to individuals To prevent early premature contraction; 4) Reproduction and renewal: For adjacent individuals ( Perform a crossover operation to generate two descendants. and : ； ； in The random weighting coefficients are within the range [0,1]; the mutation probability decays over time according to the following formula: ; When mutation is triggered, the descendants execute... ; And perform boundary correction. ; 5) Elite Retention: Before Identification elite individuals It is temporarily stored and replaced with the worst individual in the population at the end of the iteration: Simultaneously, for the global optimal solution Perform local refinement: ,like Then update .

5. The method as described in claim 4, characterized in that: In the redwood ecological algorithm, the original fire probability and mutation probability are controlled by a preset linear decay mechanism. This mechanism is a fixed scheduling method and cannot be dynamically adjusted according to the population state during the search process. Therefore, a multi-parameter self-adjustment mechanism is introduced during the adaptive fire disturbance and reproduction update process to dynamically regulate the fire probability and mutation probability, enabling them to adapt to changes based on population diversity and optimization stagnation, thereby avoiding early convergence stagnation or overexploration in the later stages. The specific implementation is as follows: 1) Calculate population diversity ,in For the first The first generation of the population A vector of all individual values ​​in dimension; 2) When population diversity Poor or optimal solution stalls for a limited number of iterations If too many cases occur, the crisis response mode will be triggered. ； ； 3) Adaptive Elite Individual Quantity Adjust dynamically based on diversity: In the early exploration phase, the number of elite individuals is kept small, while in the convergence phase, the number of elite individuals is increased to prevent the loss of high-quality solutions.

6. The method as described in claim 4, characterized in that: The original Sequoia algorithm uses a uniform perturbation strength, ignoring the information asymmetry between elite and inferior solutions. To address this issue, a differentiated perturbation strategy based on elite individuals is introduced into the adaptive fire perturbation. This strategy applies differentiated perturbations based on fitness ranking to the population individuals, thereby enhancing the search capability for neighborhoods of high-quality candidate solutions. The specific implementation is as follows: When a fire event is triggered ( When this is the case, differentiated perturbations are applied to elite and non-elite individuals based on their ranking within the population: ； Elite individuals are subjected to smaller perturbations to preserve valuable search information, while non-elite individuals are subjected to larger perturbations to enhance their exploration capabilities; the number of elites The adaptive mechanism in claim 4 dynamically determines the elite protection strength, enabling a dynamic response to the convergence state.

7. The method as described in claim 4, characterized in that: The Sequoia Ecosystem Algorithm employs Gaussian random walks for local optimization. While effective in unconstrained environments, this blind search strategy is inefficient in high-dimensional constrained environments. In the iterative optimization process of the Sequoia Ecosystem Algorithm, a directional local search strategy with orthogonal exploration is introduced for secondary optimization of the current optimal solution. This strategy consists of two independent stages: gradient-guided exploration and orthogonal subspace exploration. The specific implementation is as follows: 1) Gradient-guided development: for each elite individual Calculate its relationship with the global optimal solution. Direction vector : ； Then, noise is added along the negative gradient direction to generate candidate solutions. : ； in =0.05, =0.05; 2) Exploration of orthogonal subspaces: Let Represents direction vector The zero space, so for any vector in All conditions are met. ;from A specific orthogonal direction vector is randomly selected from the basis. and normalize it: ； Simultaneously, a second candidate solution is generated. : ； in =0.03, =0.03; This mechanism enables spacecraft to bypass obstacles such as no-fly zones, performing lateral evasion while maintaining their overall direction of travel; 3) Greedy selection mechanism: Boundary constraint correction and fitness evaluation are performed on two candidate solutions. Update is only performed when the fitness of the candidate solution is better than that of the current elite individual, ensuring monotonic improvement of the elite layer.

8. The method as described in claim 1, characterized in that, In step 4, the specific process of trajectory planning and optimization is as follows: Step 4.1: Initialization candidate solutions At the boundary of control variables Uniformly distributed within the region, calculate the initial fitness, and record the global optimal solution. ; Step 4.2: Sort the populations in ascending order of fitness and calculate diversity. Dynamic determination Store elite solutions and adaptively adjust fire probability. and mutation probability ; Step 4.3: Implement a resource-sharing mechanism, with each individual moving to the mean position of the top 50% of elites; implement a differentiated perturbation strategy based on elite individuals; and perform crossover and mutation reproduction operations to maintain population diversity. Step 4.4: Perform a directional local search with orthogonal exploration on the elite individuals; replace the current worst solution with the stored elite solution. Individuals, implementing an elite retention mechanism; Step 4.5: Calculate the fitness of the new population and update the global optimum. Update the stall count Determine if the maximum number of iterations has been reached. If the target is not reached, return to step 4.2; otherwise, output the globally optimal solution. The corresponding sequence of spherical trajectory coordinates of multiple spacecraft.

9. The method as described in claim 1, characterized in that, The candidate solutions Depend on Spacecraft step length Polar angle and azimuth Parameter assembly structure: The system generates corresponding trajectories using a spherical motion model, evaluates the trajectories based on a fitness function, and finally outputs the spherical flight trajectory of multiple spacecraft with the best fitness.

10. An application of a multi-spacecraft spherical path planning method based on an improved Sequoia algorithm, characterized in that, The application scenarios of the method include multi-detector cooperative path planning in planetary surface exploration missions, low-Earth orbit satellite swarm orbit cooperative optimization, and any multi-agent trajectory planning problem with spherical or near-spherical surfaces as motion constraints.

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