Aircraft robust pursuit method and system based on chance constraint and topology acceleration

Abstract

The invention discloses an aircraft robust pursuit method and system based on opportunity constraint and topology acceleration. The method comprises the following steps: constructing a safety area of a pursuer; acquiring the real-time position of an escaper; projecting an escaper to the safe area as a target point, and then pursuing the target point in the safe area by a pursuer; the control input of each pursuer is continuously adjusted, so that the motion state of the pursuer is changed, the pursuer motion trail equation and the motion constraint condition are met, the pursuer motion trail is generated, the escaper moves with the center of the safety area of the escaper as the target point, the control input of the escaper is continuously adjusted, and the motion state of the escaper is changed. The escaper motion trail equation and the motion constraint condition are met, so that the motion trail of the escaper is generated; the method has the advantages of low calculation cost and high operation efficiency.

Description

Technical Field

[0001] This invention relates to the field of robotics and autonomous system optimization and decision-making technology, specifically to a robust pursuit method and system for aircraft based on chance constraints and topology acceleration. Background Technology

[0002] Pursuit and escape strategies, which effectively chase and capture moving targets, have been widely applied in fields such as target surveillance, security tracking, and area surveillance, attracting significant research interest. Existing research often employs simplified assumptions in its analyses, facing the challenge of balancing self-safety and successful pursuit, especially in non-ideal environments. Therefore, such methods are difficult to directly apply to real-world scenarios—in some real-world scenarios, both the pursuer and the escapee frequently encounter challenges from sensor noise and need to navigate in more cluttered environments.

[0003] The classic multi-robot chase-and-escape problem is formulated as a differential game and solved using the Hamilton-Jacobi-Isaacs (HJI) equations, but its high computational cost limits its scalability in multiplayer scenarios. Therefore, a series of geometric methods have been developed as alternatives, but most ignore the impact of state measurement noise and primarily focus on greedy pursuit and collision avoidance.

[0004] In existing technologies, topology path planning is used as a preliminary step in trajectory planning, serving as an appropriate initial guess to facilitate subsequent optimization processes. For example, the paper "B. Zhou, F. Gao, J. Pan, and S. Shen, 'Robust real-time UAV replanning using guided gradient-based optimization and topological paths,'" in Proc. of the IEEE Intl. Conf. on Robot. and Autom., May 2020, pp. 1208-1214, discloses a topology path map similar to visibility PRM, but it is limited to static environments. The paper "C. McBeth, J. Motes, D. Uwacu, M. Morales, and N. MAmato, 'Scalable multi-robot motion planning for congested environments using topological guidance,' IEEE Robot. Autom. Lett., vol. 8, no. 11, pp. 6867-6874, Nov. 2023" discloses a scalable method that uses topology to guide the sampling space to achieve efficient multi-robot motion planning. However, the computational cost of this method increases with the size and complexity of the map.

[0005] In summary, existing technologies have the following shortcomings: 1. Idealized assumptions lead to poor practical adaptability; 2. Insufficient balance between safety and efficiency; 3. Imperfect uncertainty handling mechanism; 4. Low efficiency of multi-robot collaboration; 5. Limited scene adaptability; 6. The contradiction between algorithm complexity and real-time performance. Summary of the Invention

[0006] The technical problem to be solved by this invention is that the existing aircraft pursuit methods have high computational costs and low efficiency.

[0007] This invention solves the above-mentioned technical problems through the following technical means: a robust pursuit method for aircraft based on chance constraints and topology acceleration, comprising the following steps:

[0008] A. For multiple robots, one is designated as the escapee and the others as the pursuers. The kinematic equations and motion constraints of the pursuers and escapees are constructed. During the motion, a collision avoidance hyperplane between the pursuer and uncertain obstacles is constructed as the obstacle separation hyperplane. The mutual collision avoidance separation hyperplane is calculated, and probability buffer terms, safety buffer terms, and acceleration buffer terms are set. The obstacle separation hyperplane is backed back by the corresponding distances of the probability buffer terms, safety buffer terms, and acceleration buffer terms in the opposite direction of its normal plane, respectively, to obtain multiple new planes. The mutual collision avoidance separation hyperplane is also backed back by the corresponding distances of the probability buffer terms, safety buffer terms, and acceleration buffer terms in the opposite direction of its normal plane, respectively, to obtain multiple new planes. The convex hull formed by the intersection of the obstacle separation hyperplane, the mutual collision avoidance separation hyperplane, and the obtained new planes is used as the safe area of ​​the pursuer.

[0009] B. Obtain the real-time location of the escapee;

[0010] C. Project the escapee onto a safe area as the target point, and then the pursuer chases the target point within the safe area;

[0011] D. Continuously adjust the control input of each pursuer to change its motion state, so as to satisfy the pursuit trajectory equation and motion constraints, thereby generating the pursuit trajectory. The escapee moves with the center of its own safe zone as the target point. Continuously adjust the escapee's control input to change its motion state, so as to satisfy the escapee trajectory equation and motion constraints, thereby generating the escapee's trajectory.

[0012] This invention determines a safe zone by constructing a hyperplane and a buffer term, thereby projecting the escapee onto the safe zone as the target point. The pursuer then chases the target point within the safe zone, avoiding risks such as collisions during the operation. Furthermore, by locking the safe zone, the operating range is effectively reduced, the algorithm's computational cost is lowered, and the execution efficiency is improved.

[0013] Furthermore, the construction of the kinematic equations and kinematic constraints for the pursuer and the escapee includes:

[0014] The kinematic equations are in, This represents the state of the i-th robot at the k'-th time step. This represents the control input of the i-th robot at the k'-th time step. The symbols representing the kinematic equations indicate the evolution of the system state at the next moment as a result of the system state at the previous moment and the control input.

[0015] Motion constraints are

[0016] Where prob represents probability, dst represents distance, and R f W represents the robot's safe radius. l W represents the position of the pursuer l. e Indicates the location of the escapee, O k Describes the k-th obstacle and O k =O+U k , k∈K, K={1,2,...,m}, m represents the total number of obstacles, K represents the set of obstacle sequences; U k O k Positional uncertainty offset, Σ k Indicates obstacle O k The uncertainty shifts to the covariance of the Gaussian distribution. Indicates a Gaussian distribution; Let σ represent the set of pursuers, and let σ represent the allowed collision probability.

[0017] Furthermore, the construction of the collision avoidance hyperplane between the chaser and the uncertain obstacle, serving as the obstacle separation hyperplane, includes:

[0018] By performing an affine coordinate transformation, the maximum λ-shading can be represented as: And ε k ={U|U T U≤C -1 (1-λ)}, where, Indicates obstacle O k The space occupied at its desired location, U represents the satisfaction of U. T U≤C -1 Elements of (1-λ), ε k C represents the set of elements U. -1 Let λ represent the reciprocal of the cumulative distribution function, and λ represent an adjustable parameter; by designing a transformation The maximum λ-shadow of an obstacle is represented in the transformation space as: in, ξ ε k ={ ξ U| ξ U Tξ U≤C -1 (1-λ)}, ξ U k =ξU k For maximum λ-shading ξ D k Its vertices are taken and represented as a list of vertices. b o Represents the total number of vertices. Let the first vertex be represented by the following quadratic programming problem, and then use an inverse transformation to obtain the obstacle-separating hyperplane in the original computational space:

[0019]

[0020] in, β lk Let represent the normal vector and displacement of the obstacle-separating hyperplane, respectively. The average position of pursuer l is represented by α, which is constantly changing. lk and β lk The value of is taken until the calculation formula for the obstacle separation hyperplane reaches its minimum value, thus obtaining the corresponding value. and β lk The obstacle separation hyperplane is determined based on the normal vector and displacement.

[0021] Furthermore, the calculation of the mutual collision avoidance separating hyperplane includes:

[0022] The misclassification probability pb of the pursuer l l Expressed as:

[0023]

[0024] in, b ln Let Γ(·) represent the normal vector and displacement of the collision avoidance separating hyperplane, respectively, and let Γ(·) be the cumulative distribution function of the normal Gaussian distribution. l The covariance matrix representing the Gaussian distribution of the position of pursuer l;

[0025] The probability of misclassification of pursuer n is pb n Expressed as:

[0026]

[0027] Continuously adjust a ln ,b ln The value of pb l ,pb n It also keeps changing, through solving Get the corresponding a ln ,b ln Using the obtained a ln ,b ln Determine the collision avoidance separation hyperplane.

[0028] Furthermore, the setting of the probability buffer, the safety buffer, and the acceleration buffer includes:

[0029]

[0030] in, These are the probability buffer, safety buffer, and acceleration buffer for the pursuer l, respectively, α l Let v represent the normal vectors of all planes to which the pursuer l is located, σ represent the allowable collision probability, and v l Represents the velocity vector, erf is the standard error function, Δ max This indicates the maximum acceleration.

[0031] Furthermore, the equation of the pursuer's trajectory is as follows:

[0032]

[0033] Among them, J l Let N represent the objective function of the pursuer l, and let N represent the step size count. This indicates the position of the pursuer l at time step N. Q represents the projection of the escapee's position onto the pursuer's safe zone. f Q and R are all semidefinite matrices. This indicates the position of the pursuer l at time step k'. This indicates the safe zone (CCPVC) for the pursuer. This represents the state of the pursuer l at time step k'. This represents the first step in solving the problem for the pursuer l. This represents the state of the pursuer l when it starts solving the problem. This indicates the permissible control space.

[0034] Furthermore, the equation for the escapee's trajectory is as follows:

[0035]

[0036] Among them, J e The objective function represents the escapee. This indicates the position of the escapee at time step N. This indicates the midpoint of the area where the escapee can drive. This represents the position of the escapee at time step k'. Indicates the area where the escapee can drive. This represents the state of the escapee at time step k'. This represents the first step of the solution for the escapee. This represents the state when the escapee starts solving the problem. This indicates the permissible control space.

[0037] This invention also provides a robust aircraft pursuit system based on chance constraints and topology acceleration, comprising:

[0038] The safe zone division module is used to define one robot as the escapee and the others as the pursuers for multiple robots. It constructs the kinematic equations and motion constraints for the pursuers and escapees. During the motion, it constructs a collision avoidance hyperplane between the pursuer and uncertain obstacles as the obstacle separation hyperplane, and calculates the mutual collision avoidance separation hyperplane. It sets probability buffer terms, safety buffer terms, and acceleration buffer terms. It backs away the obstacle separation hyperplane along the opposite direction of its normal plane by the corresponding distances of the probability buffer terms, safety buffer terms, and acceleration buffer terms, respectively, to obtain multiple new planes. Similarly, it backs away the mutual collision avoidance separation hyperplane along the opposite direction of its normal plane by the corresponding distances of the probability buffer terms, safety buffer terms, and acceleration buffer terms, respectively, to obtain multiple new planes. The convex hull formed by the intersection of the obstacle separation hyperplane, the mutual collision avoidance separation hyperplane, and the obtained new planes serves as the safe zone for the pursuer.

[0039] The location acquisition module is used to obtain the real-time location of the escapee;

[0040] The target point determination module is used to project the escapee onto a safe area as a target point, and then the pursuer chases the target point within the safe area;

[0041] The trajectory planning module continuously adjusts the control input of each pursuer to change its motion state, thereby satisfying the pursuer's motion trajectory equation and motion constraints, thus generating the pursuer's motion trajectory. The escapee moves with the center of its safe zone as the target point. The escapee's control input is continuously adjusted to change its motion state, thereby satisfying the escapee's motion trajectory equation and motion constraints, thus generating the escapee's motion trajectory.

[0042] Furthermore, the construction of the kinematic equations and kinematic constraints for the pursuer and the escapee includes:

[0043] The kinematic equations are in, This represents the state of the i-th robot at the k'-th time step. This represents the control input of the i-th robot at the k'-th time step. The symbols representing the kinematic equations indicate the evolution of the system state at the next moment as a result of the system state at the previous moment and the control input.

[0044] Motion constraints are

[0045] Where prob represents probability, dst represents distance, and R f W represents the robot's safe radius. l W represents the position of the pursuer l. e Indicates the location of the escapee, O kDescribes the k-th obstacle and O k =O+U k , k∈K, K={1,2,...,m}, m represents the total number of obstacles, K represents the set of obstacle sequences; U k O k Positional uncertainty offset, Σ k Indicates obstacle O k The uncertainty shifts to the covariance of the Gaussian distribution. Indicates a Gaussian distribution; Let σ represent the set of pursuers, and let σ represent the allowed collision probability.

[0046] Furthermore, the construction of the collision avoidance hyperplane between the chaser and the uncertain obstacle, serving as the obstacle separation hyperplane, includes:

[0047] By performing an affine coordinate transformation, the maximum λ-shading can be represented as: And ε k ={U|U T U≤C -1 (1-λ)}, where, Indicates obstacle O k The space occupied at its desired location, U represents the satisfaction of U. T U≤C -1 Elements of (1-λ), ε k C represents the set of elements U. -1 Let λ represent the reciprocal of the cumulative distribution function, and λ represent an adjustable parameter; by designing a transformation The maximum λ-shadow of an obstacle is represented in the transformation space as: in, ξ ε k ={ ξ U| ξ U Tξ U≤C -1 (1-λ)}, ξ U k =ξU k For maximum λ-shading ξ D k Its vertices are taken and represented as a list of vertices. b o Represents the total number of vertices. Let the first vertex be represented by the following quadratic programming problem, and then use an inverse transformation to obtain the obstacle-separating hyperplane in the original computational space:

[0048]

[0049] in, βlk Let represent the normal vector and displacement of the obstacle-separating hyperplane, respectively. The average position of pursuer l is represented by α, which is constantly changing. lk and β lk The value of is taken until the calculation formula for the obstacle separation hyperplane reaches its minimum value, thus obtaining the corresponding value. and β lk The obstacle separation hyperplane is determined based on the normal vector and displacement.

[0050] Furthermore, the calculation of the mutual collision avoidance separating hyperplane includes:

[0051] The misclassification probability pb of the pursuer l l Expressed as:

[0052]

[0053] in, b ln Let Γ(·) represent the normal vector and displacement of the collision avoidance separating hyperplane, respectively, and let Γ(·) be the cumulative distribution function of the normal Gaussian distribution. l The covariance matrix representing the Gaussian distribution of the position of pursuer l;

[0054] The probability of misclassification of pursuer n is pb n Expressed as:

[0055]

[0056] Continuously adjust a ln ,b ln The value of pb l ,pb n It also keeps changing, through solving Get the corresponding a ln ,b ln Using the obtained a ln ,b ln Determine the collision avoidance separation hyperplane.

[0057] Furthermore, the setting of the probability buffer, the safety buffer, and the acceleration buffer includes:

[0058]

[0059] in, These are the probability buffer, safety buffer, and acceleration buffer for the pursuer l, respectively, α l Let v represent the normal vectors of all planes to which the pursuer l is located, σ represent the allowable collision probability, and v l Represents the velocity vector, erf is the standard error function, Δ max This indicates the maximum acceleration.

[0060] Furthermore, the equation of the pursuer's trajectory is as follows:

[0061]

[0062] Among them, J l Let N represent the objective function of the pursuer l, and let N represent the step size count. This indicates the position of the pursuer l at time step N. Q represents the projection of the escapee's position onto the pursuer's safe zone. f Q and R are all semidefinite matrices. This indicates the position of the pursuer l at time step k'. This indicates the safe zone (CCPVC) for the pursuer. This represents the state of the pursuer l at time step k'. This represents the first step in solving the problem for the pursuer l. This represents the state of the pursuer l when it starts solving the problem. This indicates the permissible control space.

[0063] Furthermore, the equation for the escapee's trajectory is as follows:

[0064]

[0065] Among them, J e The objective function represents the escapee. This indicates the position of the escapee at time step N. This indicates the midpoint of the area where the escapee can drive. This represents the position of the escapee at time step k'. Indicates the area where the escapee can drive. This represents the state of the escapee at time step k'. This represents the first step of the solution for the escapee. This represents the state when the escapee starts solving the problem. This indicates the permissible control space.

[0066] The advantages of this invention are:

[0067] (1) This invention determines the safe area by constructing a hyperplane and a buffer term, thereby projecting the escapee onto the safe area as the target point. Then the pursuer chases the target point within the safe area, avoiding risks such as collisions during operation. Furthermore, by locking the safe area, the operating range is effectively reduced, the algorithm computation cost is lowered, and the execution efficiency is improved.

[0068] (2) Step S2 of this invention takes into account the noise present in the actual sensing results and divides the solution of CCPVC into three steps: mutual collision avoidance plane, obstacle collision avoidance plane, and buffer term solution. Each step explicitly considers the noise present in the sensing results. Among them, the solutions to the mutual collision avoidance plane and obstacle collision avoidance plane are low-dimensional optimization problems that can be solved linearly. Therefore, it can solve the four problems of poor practical adaptability caused by the idealized assumptions of the prior art, imperfect uncertainty handling mechanism, limited scene adaptability, and the contradiction between algorithm complexity and real-time performance.

[0069] (3) In step S4 of this invention, each pursuer acquires its own target point in a distributed manner based on the escapee's movement and position. Furthermore, this invention effectively calculates virtual target points based on the escapee's movement direction, thus implicitly utilizing the map structure to achieve early blocking of the escapee. Projecting the escapee's position or virtual target point onto their respective CCPVs also requires only linear computational complexity. Therefore, it can solve the problems of insufficient balance between safety and efficiency in existing technologies, low efficiency of multi-robot collaboration, and the contradiction between algorithm complexity and real-time performance. Attached Figure Description

[0070] Figure 1 This is a flowchart of the robust pursuit method for aircraft based on chance constraints and topology acceleration disclosed in Embodiment 1 of the present invention;

[0071] Figure 2 This is a system architecture diagram of the pursuit system in the robust pursuit method for aircraft based on chance constraints and topology acceleration disclosed in Embodiment 1 of the present invention.

[0072] Figure 3 This is a structural diagram of the topology acceleration pursuit system in the robust pursuit method for aircraft based on chance constraints and topology acceleration disclosed in Embodiment 2 of the present invention.

[0073] Figure 4 This is a schematic diagram of the separation hyperplane formation in the robust pursuit method for aircraft based on chance constraints and topology acceleration disclosed in Embodiment 1 of the present invention, wherein... Figure 4 (a) to Figure 4 (d) is a schematic diagram of the different stages of the hyperplane formation process;

[0074] Figure 5 This is a schematic diagram of the heuristic topology-guided virtual target point selection in the robust pursuit method for aircraft based on chance constraints and topology acceleration disclosed in Embodiment 2 of the present invention.

[0075] Figure 6 This is a schematic diagram of the simulation results of MPC in scenario 1 using the robust pursuit method for aircraft based on chance constraints and topology acceleration disclosed in Embodiment 1 of the present invention; wherein, Figure 6(a) represents the randomly generated environment and the initial positions of the pursuer and the escapee. Figure 6 (b)- Figure 6 (d) The pursuit process in an obstacle environment with uncertainty;

[0076] Figure 7 This is a schematic diagram of the virtual line length variation in the robust pursuit method for aircraft based on chance constraints and topology acceleration disclosed in Embodiment 2 of the present invention.

[0077] Figure 8 This is a schematic diagram illustrating the simulation results of nine UAVs in the robust pursuit method for aircraft based on chance constraints and topology acceleration disclosed in Embodiment 1 of the present invention; wherein, Figure 8 (a) shows the environment and the initial positions of the pursuers and escapees, which were randomly generated during the simulation of nine drones. Figure 8 (b)- Figure 8 (d) is the pursuit process in an obstacle environment with uncertainty during the simulation of nine UAVs;

[0078] Figure 9 This is a schematic diagram of the obstacle avoidance and separation hyperplane used in the robust pursuit method for aircraft based on chance constraints and topology acceleration disclosed in Embodiment 2 of the present invention; wherein Figure 9 (a) and Figure 9 (b) demonstrates the two stages of obstacle avoidance hyperplane generation in CCOVC;

[0079] Figure 10 This is a schematic diagram comparing the pursuit efficiency under different target selection strategies in the robust pursuit method for aircraft based on chance constraints and topology acceleration disclosed in Embodiment 2 of the present invention. Figure 10 (a) shows the comparison results across multiple maps. Figure 10 (b) presents a specific map example. Figure 10 (c)- Figure 10 (e) represents the motion process and trajectory of each pursuer using the proposed method. Figure 10 Each line in (f) represents the distance from each pursuer to the escapee. Figure 10 (g)- Figure 10 (i) represents the movement process and trajectory of each pursuer in the comparison method. Figure 10 Each line in (j) represents the distance from each pursuer to the escapee. Detailed Implementation

[0080] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0081] Example 1

[0082] like Figure 1 As shown, Embodiment 1 of the present invention provides a robust pursuit method for aircraft based on chance constraints and topology acceleration, comprising the following steps:

[0083] S1. Addressing uncertainties such as information uncertainty and state measurement noise during the sensing and localization process. In this invention, a distributed tracking framework is constructed as follows: Figure 2 As shown.

[0084] During system initialization, the perception and localization modules begin operation. The perception module acquires environmental information, including the location and shape of obstacles, while the localization module determines the pursuer's own position and posture. Due to sensor accuracy limitations and environmental interference, uncertainties exist in the perception and localization processes. The system quantifies these uncertainties and represents them as probability distributions, specifically Gaussian distributions.

[0085] S2. Construct the relevant hyperplane and buffer terms for the safe area CCPVC.

[0086] In this embodiment, consider the following scenario:

[0087] Consider a bounded three-dimensional environment. There are S robots and S-1 chasers pursuing one escapee. The set of chasers is defined as P. Furthermore, each robot has a safety radius, denoted as R. f In this embodiment, it is assumed that both the pursuer and the escapee have the same mobility, and their dynamics are described as follows:

[0088]

[0089] in, This represents the state of the i-th robot (pursuer or escaper) at the k'-th time step, typically including parameters such as position, velocity, and acceleration. This represents the control input of the i-th robot at the k'-th time step.

[0090] In order to distinguish between pursuers and escapees, and Let x represent the positions of the pursuer l and the escapee l, respectively. l ,y l ,z l These are the x-coordinate, y-coordinate, and vertical coordinate of the pursuer l, respectively.

[0091] Furthermore, consider that the environment E contains m convex polyhedral obstacles O. k k∈K, K={1,2,...,m}, the shape and location of the obstacle are known, and its characteristic is a Gaussian distribution. The obstacle O k The potential space occupancy in the environment can be represented as:

[0092] O k =O+U k (2)

[0093] in Indicates obstacle O k Space occupied at its desired location, U k O k Positional uncertainty offset, Σ k Indicates obstacle O k The uncertainty shifts the covariance of the Gaussian distribution.

[0094] Similarly, considering the uncertainty in each robot's localization, we assume it follows a Gaussian distribution, i.e. and in and Let l represent the average positions of the pursuer and the escapee, respectively.

[0095] To ensure probabilistic obstacle avoidance and probabilistic collision avoidance, the following requirements must be met:

[0096]

[0097] Here, prob represents probability.

[0098] Based on the following derivation, construct the CCPV-related hyperplane and buffer terms:

[0099] 1) such as Figure 4 As shown, the concept of obstacle expansion is used to generate the collision avoidance hyperplane between the chaser and uncertain obstacles. Figure 4 (a) to Figure 4 (d) is a schematic diagram of different stages in the hyperplane formation process. By performing an affine coordinate transformation, the maximum λ-shading is represented as:

[0100]

[0101] Where, ε k={U|U T U≤C -1 (1-λ)}(5)

[0102] Through design transformation The maximum λ-shadow of an obstacle in the transformation space can be represented as: in ξ ε k ={ ξ U| ξ U Tξ U≤C -1 (1-λ)}, ξ U k =ξU k Meanwhile, the uncertainty of the obstacle can be expressed in the transformation space as: ξ Σ k =ξΣ k ξ T =I2, therefore ξ ε k It can be considered as a unit sphere. After processing with Minkowski's algorithm, the maximum λ-shading... ξ D k Represented as a list of vertices The obstacle-separating hyperplane in the original computational space is obtained by solving the following quadratic programming problem and performing an inverse transformation according to the following rules:

[0103]

[0104] This involves continuously changing α while satisfying the constraints of the above formula. lk and β lk The value of is taken until the formula reaches its minimum value, and the corresponding value is obtained. and β lk , β lk Let represent the normal vector and displacement of the obstacle-separating hyperplane, respectively. The relationship between the normal vector and displacement and the obstacle hyperplane is similar to that of a linear equation in one variable, for example... The obstacle separation hyperplane can be determined based on the normal vector and displacement.

[0105] 2) The collision avoidance separating hyperplane is calculated by solving the following minimax problem:

[0106] The misclassification probability of chaser l is expressed as:

[0107]

[0108] in, b lnLet represent the normal vector and displacement of the collision avoidance separating hyperplane, respectively. The relationship between the normal vector and displacement and the collision avoidance separating hyperplane is similar to a linear equation in one variable, for example... Therefore, the collision avoidance separating hyperplane can be determined based on the normal vector and displacement. Γ(·) is the cumulative distribution function (CDF) of the normal Gaussian distribution.

[0109] The misclassification probability of chaser n is expressed as:

[0110]

[0111] Continuously adjust a ln ,b ln The value of pb l ,pb n It also changes continuously. The parameters of the collision avoidance separating hyperplanes are calculated by solving the following minima problem:

[0112]

[0113] After solving the problem in formula (8) above, the corresponding a is obtained. ln ,b ln Using a ln ,b ln Determine the collision avoidance separation hyperplane.

[0114] 3) Simultaneously consider probability buffer, safety buffer, and acceleration buffer:

[0115]

[0116] In velocity vector v l and plane α l When the angle formed between the normal vectors exceeds 90°, the acceleration buffer term is set to zero. Instead, it is defined as:

[0117]

[0118] Where erf(·) is the standard error function, α l It is the normal vector of the hyperplane, Δ max This indicates the maximum acceleration.

[0119] After the obstacle separation hyperplane, mutual collision avoidance separation hyperplane, probability buffer term, safety buffer term, and acceleration buffer term are determined, the obstacle separation hyperplane is backed back by the corresponding distances of the probability buffer term, safety buffer term, and acceleration buffer term in the opposite direction of its normal plane, respectively, to obtain multiple new planes. Similarly, the mutual collision avoidance separation hyperplane is backed back by the corresponding distances of the probability buffer term, safety buffer term, and acceleration buffer term in the opposite direction of its normal plane, to obtain multiple new planes. The convex hull formed by the intersection of all the planes constitutes the safety area, i.e., CCPVC.

[0120] S3. Obtain the real-time location of the escapee. In this embodiment, the location is assumed to be a known quantity, that is, the real-time location of the escapee is obtained through existing technical methods, or the real-time location of the escapee is given in advance.

[0121] S4. A distributed framework is used to find the target point for each pursuer. The escapee is projected onto a safe area as the target point, and then the pursuers chase the target point within the safe area. That is, for each pursuer, the closest point to the escapee in their respective safe area is calculated based on the escapee's position and taken as the target point. The calculation method for this target point can be equivalent to the following formula process:

[0122] Assuming that CCPVC is conceptualized as a convex hull consisting of a set of three-dimensional planes, the task of finding the nearest point is appropriately represented as a quadratic programming problem of least squares W:

[0123]

[0124] Step 5: Under the condition that the pursuer and the escapee have equal mobility, the method was tested and verified by simulating the complex and ever-changing environment to generate trajectories, executing path control and completing the pursuit task.

[0125] This invention uses MPC to solve for the control input of each chaser and generate the motion trajectory of each chaser:

[0126]

[0127] Continuously adjust the control input for each pursuer This changes its motion state, causing it to move closer to the target point and satisfy the above formulas (13) and (3), thus generating a motion trajectory. Here, N represents the count of these step lengths. Qf, Q, and R are semi-definite matrices, and U represents the permissible control space. For convenience, Qf remains a positive definite matrix, while zero matrices are assigned to Q and R.

[0128] The strategy of "moving to the center of mass" is used to generate the trajectory of the escapee.

[0129]

[0130] The escapee moves with the center of their safe zone as the target point, constantly adjusting their control inputs. This alters its motion state, causing it to move closer to its target point and satisfy the aforementioned formulas (14) and (3), thus generating the escapee's trajectory. It is the probabilistic safe zone CCEVC for escapees, constructed in the same way as CCPVC. This represents the center of CCEVC. Ensure Q... f Keep the positive definite matrices, while assigning the zero matrix to Q and R.

[0131] like Figure 6 The simulation results of MPC are used in Scenario 1. Among them, Figure 6 (a) The randomly generated environment and the initial positions of the pursuers and the escapees. Figure 6 (b)- Figure 6 (d) The chase process in an obstacle environment with uncertainty. Blue represents the chaser's CCPV (Collectible Capacity Limit), and red represents the escapee's CCEVC (Collectible Capacity Limit). Ultimately, the chaser successfully captures the escapee, achieving mutual collision avoidance and obstacle avoidance during the chase. For example... Figure 8 The scalability of the proposed method was verified by increasing the number of robots in the same environment to nine, including eight chasers and one escaper, while keeping other settings unchanged. The results showed that the proposed algorithm is still effective for system scaling.

[0132] Through the above technical solutions, this invention utilizes MPC for trajectory optimization. Simulation results show that in a noisy environment with clutter and obstacles, when the escapee adopts a "moving towards the center of mass" strategy and both the pursuer and the escapee use MPC to generate trajectories, the pursuer can effectively track the escapee, confirming the effectiveness of the proposed framework.

[0133] Example 2

[0134] The difference between this embodiment and Embodiment 1 is that this embodiment introduces a topology-accelerated robust tracing framework, such as... Figure 3 As shown, the framework consists of three main parts: selection of virtual target points, calculation of the probability-safe region CCPV, and solution of the path controller based on the control barrier function. The framework first utilizes a topological heuristic to obtain the topological structure of the environment, providing guidance for target point selection for each pursuer; then, it constructs the CCPV for each pursuer by calculating the separating hyperplane and buffer terms; finally, it establishes the opportunity-constrained barrier function (CBF) and opportunity-constrained control Lyapunov function (CLF) constraints based on the CCPV, and then obtains an adaptive robust path controller by solving a quadratic constrained quadratic programming (QCQP) to achieve accurate and robust escapee pursuit.

[0135] In a scenario similar to Example 1, the dynamic equations for the pursuer and the escapee are:

[0136]

[0137] Where x represents the state of the pursuer and the escapee, typically including parameters such as position, velocity, and acceleration. and It is the matrix that defines the linear dynamics, and u represents the control input.

[0138] It is also assumed that the state self-measurement of each robot is affected by Gaussian noise Θ, with a mean E of zero and a variance of θ.

[0139] like Figure 5 As shown, in the step of "finding the nearest point and virtual target point using a distributed-topology-accelerated robust tracking framework", this embodiment uses the local topology of the map to generate virtual target points, guiding the pursuer to preemptively prevent the escapee from moving further.

[0140] The direction of the virtual line generation is determined by the direction of the escapee's motion. The direction of the escapee's motion at time t can be expressed as:

[0141]

[0142] in, It represents the position of the escapee at time t.

[0143] like Figure 5 As shown in (a), the direction of virtual line generation Through t, and perpendicular to The direction of can be expressed by the formula:

[0144]

[0145] in It is a relative position vector. It is the position of the pursuer l at time t.

[0146] like Figure 7 To balance flexibility and accuracy, the virtual line length was designed to be... Functions:

[0147]

[0148] Wherein, τ1, τ2, and l1 are all preset constants.

[0149] The expression for the chaser's search for a virtual target point, with angle as an influencing factor, is as follows:

[0150]

[0151] in, Let θ be the virtual target point location. and The angle between them, where, Let ε be the direction of motion of the escapee at time t. i >0 is the scale parameter, i∈{1,2,3,4}. θ i-1 and θ i They are RI i The lower limit and upper limit of the angle, 0 < θ1 < θ2 < θ3 < θ4 = π, θ0 = 0.

[0152] In the step of "constructing CCPVC-related hyperplanes and buffer terms", this embodiment uses the method of minimizing the maximum misclassification probability to obtain the mutual avoidance hyperplane. The construction process is the same as the hyperplane construction process in Embodiment 1, as detailed below:

[0153] The misclassification probability of chaser l is expressed as:

[0154]

[0155] Where Γ(·) is the cumulative distribution function (CDF) of the normal Gaussian distribution.

[0156] The misclassification probability of chaser n is expressed as:

[0157]

[0158] The parameters of the mutually avoiding separating hyperplanes are calculated by solving the following minima problem:

[0159]

[0160] like Figure 9 The obstacle avoidance hyperplane of CCOVC is shown. Figure 9 (a) and Figure 9 (b) demonstrates the process of generating the obstacle-avoiding hyperplane in CCOVC, which is solved using the following quadratic programming:

[0161]

[0162] By translating the hyperplane along its normal vector and making it exactly tangent to the obstacle, the pursuer l relative to the obstacle O is finally obtained. k The obstacle avoidance hyperplane.

[0163] Simultaneously consider probability buffer, safety buffer, and acceleration buffer:

[0164]

[0165] Where erf(·) is the standard error function.

[0166] λ l p =R p ||a lq ||. (25)

[0167] Similar to Example 1, after solving for the hyperplane and buffer terms, the hyperplane is backed up by the distances corresponding to the probability buffer term, safety buffer term, and acceleration buffer term in the opposite direction of the normal plane, thereby forming a new plane. The intersection of all hyperplanes and the new plane forms the convex hull, which is also the safety region.

[0168] In this embodiment, the adaptive robust path controller for each chaser is solved by the following optimization problem:

[0169]

[0170] in, It is α hi The (n+1)th element, It is β V The (n+1)th element, W = G xi A r-1 B,Y=e T A r-1 B, i = 1, 2, ..., n h-1 j = 1, 2, ..., n u .

[0171] For the convex approximation of this problem, the following expression is derived:

[0172]

[0173] in, α i =α hi,0 f xi .

[0174]

[0175] Among them, κ u =Kx,κ uj =G uj K.

[0176]

[0177] in, β e =β V,0 f e .

[0178] The adaptive robust controller is solved using expressions (27)(28)(29) through the following QCQP:

[0179]

[0180] The control input u = K(x + Θ) is used to adjust the control gain K of the pursuer under the constraints of formulas (27) to (29), thereby adjusting its control input to satisfy formula (30) and obtaining the corresponding motion state under the control input at each moment, thus forming its motion trajectory.

[0181] Finally, simulation results validated the effectiveness of the proposed algorithm framework. Figure 10 As shown, the chasing efficiency is compared with the strategy of directly using the nearest point as the target point instead of using virtual target points generated by map topology.

[0182] Figure 10 (a) shows the comparison results across multiple maps. Figure 10 (b) presents a specific map example. Figure 10 (c)- Figure 10 (e) represents the movement process and trajectory of each pursuer using the proposed method, with each line of a different color representing the trajectory of a different pursuer. Figure 10 Each line in (f) represents the distance from each pursuer to the escapee. Figure 10 (g)- Figure 10 (i) represents the movement process and trajectory of each pursuer in the comparison method, with each line of different color representing the trajectory of a different pursuer. Figure 10 Each line in (j) represents the distance from each pursuer to the escapee. Using the proposed strategy, the escapee is captured at t = 28.8 s, while the strategy disclosed in the literature "B. Tian, ​​P. Li, H. Lu, Q. Zong, and L. He, "Distributed pursuit of an evader with collision and obstacle avoidance," IEEE Trans. Cybern., vol. 52, no. 12, pp. 13512-13520, Dec. 2022." directly sets the escapee's position as the target point, and even fails at t = 80.0 s.

[0183] By addressing the dependence of traditional methods on ideal sensor models, this invention proposes a communication-free convex polyhedral obstacle environment pursuit strategy (CCPVC). This strategy constructs a pre-built geometric collision region between the pursuer and obstacles, explicitly quantifies the impact of positioning and perception uncertainties on the safe distance, and generates a probabilistically safe and feasible capture region, effectively adapting to complex 3D obstacle scenarios. Furthermore, a chance-constrained distributed MPC optimization framework is constructed, incorporating high-order dynamic models of the pursuer and escapee into a unified control law design. To further reduce the collision probability, a quadratic constrained quadratic programming problem (QCQP) is constructed and solved using convex approximations, achieving real-time trajectory planning and collision avoidance in complex systems, overcoming the limitations of traditional single-integrator models. Simultaneously, a heuristic virtual target point selection method combining environmental topology is proposed. By analyzing map connectivity and the escapee's potential movement paths, the redundancy of the pursuer's path overlap is optimized, and key movement directions of the escapee are blocked in advance, significantly improving the initiative of the strategy in dynamic environments. Specific initial conditions are provided, and the effectiveness of the method is verified through simulation. This invention provides some theoretical support and algorithmic framework for improving the success rate of pursuit and dynamic environment adaptability in diverse and complex scenarios.

[0184] Example 3

[0185] Based on Embodiment 1, Embodiment 3 of the present invention also provides a robust aircraft pursuit system based on chance constraints and topology acceleration, including:

[0186] The safe zone division module is used to define one robot as the escapee and the others as the pursuers for multiple robots. It constructs the kinematic equations and motion constraints for the pursuers and escapees. During the motion, it constructs a collision avoidance hyperplane between the pursuer and uncertain obstacles as the obstacle separation hyperplane, and calculates the mutual collision avoidance separation hyperplane. It sets probability buffer terms, safety buffer terms, and acceleration buffer terms. It backs away the obstacle separation hyperplane along the opposite direction of its normal plane by the corresponding distances of the probability buffer terms, safety buffer terms, and acceleration buffer terms, respectively, to obtain multiple new planes. Similarly, it backs away the mutual collision avoidance separation hyperplane along the opposite direction of its normal plane by the corresponding distances of the probability buffer terms, safety buffer terms, and acceleration buffer terms, respectively, to obtain multiple new planes. The convex hull formed by the intersection of the obstacle separation hyperplane, the mutual collision avoidance separation hyperplane, and the obtained new planes serves as the safe zone for the pursuer.

[0187] The location acquisition module is used to obtain the real-time location of the escapee;

[0188] The target point determination module is used to project the escapee onto a safe area as a target point, and then the pursuer chases the target point within the safe area;

[0189] The trajectory planning module continuously adjusts the control input of each pursuer to change its motion state, thereby satisfying the pursuer's motion trajectory equation and motion constraints, thus generating the pursuer's motion trajectory. The escapee moves with the center of its safe zone as the target point. The escapee's control input is continuously adjusted to change its motion state, thereby satisfying the escapee's motion trajectory equation and motion constraints, thus generating the escapee's motion trajectory.

[0190] Specifically, the construction of the kinematic equations and motion constraints for the pursuer and the escapee includes:

[0191] The kinematic equations are in, This represents the state of the i-th robot at the k'-th time step. This represents the control input of the i-th robot at the k'-th time step. The symbols representing the kinematic equations indicate the evolution of the system state at the next moment as a result of the system state at the previous moment and the control input.

[0192] Motion constraints are

[0193] Where prob represents probability, dst represents distance, and R f W represents the robot's safe radius. l W represents the position of the pursuer l. e Indicates the location of the escapee, O k Describes the k-th obstacle and O k =O+U k , k∈K, K={1,2,...,m}, m represents the total number of obstacles, K represents the set of obstacle sequences; U k O k Positional uncertainty offset, Σ k Indicates obstacle O k The uncertainty shifts to the covariance of the Gaussian distribution. Indicates a Gaussian distribution; Let σ represent the set of pursuers, and let σ represent the allowed collision probability.

[0194] More specifically, the construction of the collision avoidance hyperplane between the chaser and the uncertain obstacle as the obstacle separation hyperplane includes:

[0195] By performing an affine coordinate transformation, the maximum λ-shading can be represented as: And ε k ={U|U T U≤C -1 (1-λ)}, where, Indicates obstacle Ok The space occupied at its desired location, U represents the satisfaction of U. T U≤C -1 Elements of (1-λ), ε k C represents the set of elements U. -1 Let λ represent the reciprocal of the cumulative distribution function, and λ represent an adjustable parameter; by designing a transformation The maximum λ-shadow of an obstacle is represented in the transformation space as: in, ξ ε k ={ ξ U| ξ U Tξ U≤C -1 (1-λ)}, ξ U k =ξU k For maximum λ-shading ξ D k Its vertices are taken and represented as a list of vertices. b o Represents the total number of vertices. Let the first vertex be represented by the following quadratic programming problem, and then use an inverse transformation to obtain the obstacle-separating hyperplane in the original computational space:

[0196]

[0197] in, β lk Let represent the normal vector and displacement of the obstacle-separating hyperplane, respectively. The average position of pursuer l is represented by α, which is constantly changing. lk and β lk The value of is taken until the calculation formula for the obstacle separation hyperplane reaches its minimum value, thus obtaining the corresponding value. and β lk The obstacle separation hyperplane is determined based on the normal vector and displacement.

[0198] More specifically, the calculation of the mutual collision avoidance separating hyperplane includes:

[0199] The misclassification probability pb of the pursuer l l Expressed as:

[0200]

[0201] in, b ln Let Γ(·) represent the normal vector and displacement of the collision avoidance separating hyperplane, respectively, and let Γ(·) be the cumulative distribution function of the normal Gaussian distribution. l The covariance matrix representing the Gaussian distribution of the position of pursuer l;

[0202] The probability of misclassification of pursuer n is pb n Expressed as:

[0203]

[0204] Continuously adjust a ln ,b ln The value of pb l ,pb n It also keeps changing, through solving Get the corresponding a ln ,b ln Using the obtained a ln ,b ln Determine the collision avoidance separation hyperplane.

[0205] More specifically, the setting of the probability buffer, the safety buffer, and the acceleration buffer includes:

[0206]

[0207] in, These are the probability buffer, safety buffer, and acceleration buffer for the pursuer l, respectively, α l Let v represent the normal vectors of all planes to which the pursuer l is located, σ represent the allowable collision probability, and v l Represents the velocity vector, erf is the standard error function, Δ max This indicates the maximum acceleration.

[0208] More specifically, the equation of the pursuer's trajectory is as follows:

[0209]

[0210] Among them, J l Let N represent the objective function of the pursuer l, and let N represent the step size count. This indicates the position of the pursuer l at time step N. Q represents the projection of the escapee's position onto the pursuer's safe zone. f Q and R are all semidefinite matrices. This indicates the position of the pursuer l at time step k'. This indicates the safe zone (CCPVC) for the pursuer. This represents the state of the pursuer l at time step k'. This represents the first step in solving the problem for the pursuer l. This represents the state of the pursuer l when it starts solving the problem. This indicates the permissible control space.

[0211] More specifically, the equation for the escapee's trajectory is:

[0212]

[0213] Among them, J e The objective function represents the escapee. This indicates the position of the escapee at time step N. This indicates the midpoint of the area where the escapee can drive. This represents the position of the escapee at time step k'. Indicates the area where the escapee can drive. This represents the state of the escapee at time step k'. This represents the first step of the solution for the escapee. This represents the state when the escapee starts solving the problem. This indicates the permissible control space.

[0214] 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 the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A robust pursuit method for aircraft based on chance constraints and topology acceleration, characterized in that, Includes the following steps: A. For multiple robots, designate one as the escapee and the others as the pursuers, and construct the kinematic equations and motion constraints for the pursuers and escapees. During the movement, a collision avoidance hyperplane is constructed between the pursuer and uncertain obstacles as the obstacle separation hyperplane. The mutual collision avoidance separation hyperplane is calculated, and probability buffer, safety buffer, and acceleration buffer are set. The obstacle separation hyperplane is backed back by the corresponding distances of probability buffer, safety buffer, and acceleration buffer in the opposite direction of its normal plane, respectively, to obtain multiple new planes. The mutual collision avoidance separation hyperplane is also backed back by the corresponding distances of probability buffer, safety buffer, and acceleration buffer in the opposite direction of its normal plane, respectively, to obtain multiple new planes. The convex hull formed by the intersection of the obstacle separation hyperplane, the mutual collision avoidance separation hyperplane, and the obtained new planes is used as the safe area for the pursuer. B. Obtain the real-time location of the escapee; C. Project the escapee onto a safe area as the target point, and then the pursuer chases the target point within the safe area; D. Continuously adjust the control input of each pursuer to change its motion state, so as to satisfy the pursuit trajectory equation and motion constraints, thereby generating the pursuit trajectory. The escapee moves with the center of its own safe zone as the target point. Continuously adjust the escapee's control input to change its motion state, so as to satisfy the escapee trajectory equation and motion constraints, thereby generating the escapee's trajectory.

2. The robust pursuit method for aircraft based on chance constraints and topology acceleration according to claim 1, characterized in that, The kinematic equations and kinematic constraints for constructing the pursuer and the escapee include: The kinematic equations are in, This represents the state of the i-th robot at the k'-th time step. This represents the control input of the i-th robot at the k'-th time step. Symbols representing kinematic equations; Motion constraints are Where prob represents probability, dst represents distance, and R f W represents the robot's safe radius. l W represents the position of the pursuer l. e Indicates the location of the escapee, O k Describes the k-th obstacle and O k =O+U k , k∈K, K={1,2,...,m}, m represents the total number of obstacles, K represents the set of obstacle sequences; U k O k Positional uncertainty offset, Σ k Indicates obstacle O k The uncertainty shifts to the covariance of the Gaussian distribution. Indicates a Gaussian distribution; Let σ represent the set of pursuers, and let σ represent the allowed collision probability.

3. The robust pursuit method for aircraft based on chance constraints and topology acceleration according to claim 2, characterized in that, The construction of the collision avoidance hyperplane between the chaser and the uncertain obstacle, serving as the obstacle separation hyperplane, includes: By performing an affine coordinate transformation, the maximum λ-shading can be represented as: And ε k ={U|U T U≤C -1 (1-λ)}, where, Indicates obstacle O k The space occupied at its desired location, U represents the satisfaction of U. T U≤C -1 Elements of (1-λ), ε k C represents the set of elements U. -1 Let λ represent the reciprocal of the cumulative distribution function, and λ represent an adjustable parameter; by designing a transformation The maximum λ-shadow of an obstacle is represented in the transformation space as: in, ξ ε k ={ ξ U| ξ U Tξ U≤C -1 (1-λ)}, ξ U k =ξU k For maximum λ-shading ξ D k Its vertices are taken and represented as a list of vertices. b o Represents the total number of vertices. Let the first vertex be represented by the following quadratic programming problem, and then use an inverse transformation to obtain the obstacle-separating hyperplane in the original computational space: in, β lk Let represent the normal vector and displacement of the obstacle-separating hyperplane, respectively. The average position of pursuer l is represented by α, which is constantly changing. lk and β lk The value of is taken until the calculation formula for the obstacle separation hyperplane reaches its minimum value, thus obtaining the corresponding value. and β lk The obstacle separation hyperplane is determined based on the normal vector and displacement.

4. The robust pursuit method for aircraft based on chance constraints and topology acceleration according to claim 3, characterized in that, The calculation of the mutual collision avoidance separation hyperplane includes: The misclassification probability pb of the pursuer l l Expressed as: in, b ln Let Γ(·) represent the normal vector and displacement of the collision avoidance separating hyperplane, respectively, and let Γ(·) be the cumulative distribution function of the normal Gaussian distribution. l The covariance matrix representing the Gaussian distribution of the position of pursuer l; The probability of misclassification of pursuer n is pb n Expressed as: Continuously adjust a ln ,b ln The value of pb l ,pb n It also keeps changing, through solving Get the corresponding a ln ,b ln Using the obtained a ln ,b ln Determine the collision avoidance separation hyperplane.

5. The robust pursuit method for aircraft based on chance constraints and topology acceleration according to claim 4, characterized in that, The setting of probability buffer, safety buffer, and acceleration buffer includes: in, These are the probability buffer, safety buffer, and acceleration buffer for the pursuer l, respectively, α l Let v represent the normal vectors of all planes to which the pursuer l is located, σ represent the allowable collision probability, and v l Represents the velocity vector, erf is the standard error function, Δ max This indicates the maximum acceleration.

6. The robust pursuit method for aircraft based on chance constraints and topology acceleration according to claim 5, characterized in that, The equation of the pursuer's trajectory is: Among them, J l Let N represent the objective function of the pursuer l, and let N represent the step size count. This indicates the position of the pursuer l at time step N. Q represents the projection of the escapee's position onto the pursuer's safe zone. f Q and R are all semidefinite matrices. This indicates the position of the pursuer l at time step k'. This indicates the safe zone for the pursuer l. This represents the state of the pursuer l at time step k'. This represents the first step in solving the problem for the pursuer l. This represents the state of the pursuer l when it starts solving the problem. This indicates the permissible control space.

7. The robust pursuit method for aircraft based on chance constraints and topology acceleration according to claim 6, characterized in that, The equation for the escapee's trajectory is: Among them, J e The objective function represents the escapee. This indicates the position of the escapee at time step N. This indicates the midpoint of the area where the escapee can drive. This represents the position of the escapee at time step k'. Indicates the area where the escapee can drive. This represents the state of the escapee at time step k'. This represents the first step of the solution for the escapee. This represents the state when the escapee starts solving the problem. This indicates the permissible control space.

8. A robust pursuit system for aircraft based on chance constraints and topology acceleration, characterized in that, include: The safe zone division module is used to designate one robot as the escapee and the others as the pursuers for multiple robots, and to construct the kinematic equations and motion constraints for the pursuers and escapees. During the movement, a collision avoidance hyperplane is constructed between the pursuer and uncertain obstacles as the obstacle separation hyperplane. The mutual collision avoidance separation hyperplane is calculated, and probability buffer, safety buffer, and acceleration buffer are set. The obstacle separation hyperplane is backed back by the corresponding distances of probability buffer, safety buffer, and acceleration buffer in the opposite direction of its normal plane, respectively, to obtain multiple new planes. The mutual collision avoidance separation hyperplane is also backed back by the corresponding distances of probability buffer, safety buffer, and acceleration buffer in the opposite direction of its normal plane, respectively, to obtain multiple new planes. The convex hull formed by the intersection of the obstacle separation hyperplane, the mutual collision avoidance separation hyperplane, and the obtained new planes is used as the safe area for the pursuer. The location acquisition module is used to obtain the real-time location of the escapee; The target point determination module is used to project the escapee onto a safe area as a target point, and then the pursuer chases the target point within the safe area; The trajectory planning module continuously adjusts the control input of each pursuer to change its motion state, thereby satisfying the pursuer's motion trajectory equation and motion constraints, thus generating the pursuer's motion trajectory. The escapee moves with the center of its safe zone as the target point. The escapee's control input is continuously adjusted to change its motion state, thereby satisfying the escapee's motion trajectory equation and motion constraints, thus generating the escapee's motion trajectory.

9. The robust pursuit system for aircraft based on chance constraints and topology acceleration according to claim 8, characterized in that, The kinematic equations and kinematic constraints for constructing the pursuer and the escapee include: The kinematic equations are in, This represents the state of the i-th robot at the k'-th time step. This represents the control input of the i-th robot at the k'-th time step. Symbols representing kinematic equations; Motion constraints are Where prob represents probability, dst represents distance, and R f W represents the robot's safe radius. l W represents the position of the pursuer l. e Indicates the location of the escapee, O k Describes the k-th obstacle and O k =O+U k , k∈K, K={1,2,...,m}, m represents the total number of obstacles, K represents the set of obstacle sequences; U k O k Positional uncertainty offset, Σ k Indicates obstacle O k The uncertainty shifts to the covariance of the Gaussian distribution. Indicates a Gaussian distribution; Let σ represent the set of pursuers, and let σ represent the allowed collision probability.

10. The robust pursuit system for aircraft based on chance constraints and topology acceleration according to claim 9, characterized in that, The construction of the collision avoidance hyperplane between the chaser and the uncertain obstacle, serving as the obstacle separation hyperplane, includes: By performing an affine coordinate transformation, the maximum λ-shading can be represented as: And ε k ={U|U T U≤C -1 (1-λ)}, where, Indicates obstacle O k The space occupied at its desired location, U represents the satisfaction of U. T U≤C -1 Elements of (1-λ), ε k C represents the set of elements U. -1 Let λ represent the reciprocal of the cumulative distribution function, and λ represent an adjustable parameter; by designing a transformation The maximum λ-shadow of an obstacle is represented in the transformation space as: in, ξ ε k ={ ξ U| ξ U Tξ U≤C -1 (1-λ)}, ξ U k =ξU k For maximum λ-shading ξ D k Its vertices are taken and represented as a list of vertices. b o Represents the total number of vertices. Let the first vertex be represented by the following quadratic programming problem, and then use an inverse transformation to obtain the obstacle-separating hyperplane in the original computational space: in, β lk Let represent the normal vector and displacement of the obstacle-separating hyperplane, respectively. The average position of pursuer l is represented by α, which is constantly changing. lk and β lk The value of is taken until the calculation formula for the obstacle separation hyperplane reaches its minimum value, thus obtaining the corresponding value. and β lk The obstacle separation hyperplane is determined based on the normal vector and displacement.

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