An unmanned aerial vehicle pursuit and evasion game prediction control method and system fusing isochronous line guidance

Abstract

The application discloses a kind of unmanned aerial vehicle pursuit and evasion game prediction control method and system of fusion isochrone guidance, the method includes: obtaining the current state information of pursuit and evasion party;And based on dynamic model, isochrone is solved to determine the geometric reference information for characterizing earliest capture opportunity;According to the current motion state of evader, its future trajectory and terminal capture point are predicted, and based on geometric reference information, model predictive control optimization problem containing long time domain guiding term is constructed;Solving and generating candidate control sequence;From candidate control sequence, current control amount is selected and executed to control pursuer.The application combines isochrone geometric guidance with model predictive control rolling horizon optimization, while retaining geometric interpretability, it enhances the local correction ability, avoids the response lag of pure geometric method and the shortsighted decision problem of pure model predictive control method, improves the capture efficiency, robustness and obstacle avoidance safety in complex pursuit and evasion scene.

Description

Technical Field

[0001] This invention relates to the fields of moving target pursuit and escape control, model predictive control, reachability set computation and intelligent decision-making for unmanned systems, and UAV pursuit and escape game theory, and more specifically to a UAV pursuit and escape game predictive control method and system that integrates isochronous guidance. Background Technology

[0002] With the development of robotics, artificial intelligence, and unmanned systems, drone pursuit technology has significant application value in mission scenarios such as airspace monitoring, illegal target disposal, and swarm warfare. The pursuit process is typically adversarial, dynamic, and real-time, requiring pursuers to adjust control strategies promptly based on the escape target's movement to achieve rapid, safe, and stable capture.

[0003] Existing pursuit control methods mainly include differential game theory, geometric guidance, optimization, and reinforcement learning. Differential game theory can theoretically describe the adversarial relationship between the pursuer and the escapee, but it is often difficult to solve in high-dimensional dynamic systems and under complex constraints. Geometric guidance methods, such as isochronous methods and pure pursuit methods, have the advantages of high computational efficiency and strong interpretability, but in complex scenarios, they are prone to problems such as insufficient local response or guidance lag.

[0004] Model predictive control (MMCC) methods can handle dynamic constraints, input constraints, and environmental constraints within the rolling time domain, exhibiting strong local optimization capabilities. However, due to the limited prediction time domain, relying solely on MMCC may be affected by short-sighted decision-making and local optima, especially in scenarios with dense obstacles or highly maneuverable escape targets, where capture efficiency and trajectory smoothness are difficult to guarantee simultaneously. Reinforcement learning methods can acquire complex policies through offline training, but typically require a large number of training samples and are highly dependent on the training scenario. When the task environment, obstacle layout, or target maneuvering method changes, retraining may be necessary, resulting in high engineering deployment costs and relatively insufficient interpretability.

[0005] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0006] (1) High computational complexity. The HJI equation is prone to the "curse of dimensionality" in high-dimensional state spaces, and the solution cost is high. For constrained systems such as UAV pursuit, it is difficult to apply it directly in real time.

[0007] (2) Model defects. Simple motion models are easy to analyze, but they are difficult to fully reflect the inertia, acceleration limitations and velocity changes of UAVs; higher-order nonlinear models are closer to the real system, but they will significantly increase the difficulty of deriving the optimal strategy and solving online.

[0008] (3) Geometric methods have weak local planning capabilities. Geometric methods have strong global interpretability, but often require idealized adversarial conditions. When the escapee makes a sudden turn, feint, or random maneuver, geometric methods can provide long-term reference directions, but they may not be able to continuously correct them according to the real-time state.

[0009] (4) Short-sighted decision-making in optimization control methods. Optimization control methods, such as model predictive control, can only see a limited prediction window. Therefore, they prioritize dealing with limited prediction time domains and local optimization problems, and are prone to choosing actions with lower short-term costs but lower long-term disadvantages. They may get stuck in local optima or experience terminal tracking lag.

[0010] (5) Reinforcement learning requires offline training. Reinforcement learning methods typically rely on extensive offline training, and their performance is greatly affected by the training environment. When the test scenario does not match the training scenario, the strategy may experience performance degradation or even failure. At the same time, this type of method has weak interpretability and high adaptation costs to changes in scenario, obstacle layout, dynamic parameters, and safety constraints.

[0011] Because UAV pursuit missions are simultaneously influenced by factors such as maneuvering targets, obstacle environments, and real-time decision-making requirements, existing methods struggle to balance geometric interpretability, local correction capabilities, and online computational efficiency. Therefore, there is an urgent need for a UAV pursuit game theory approach that integrates long-term temporal geometric guidance and rolling optimization control to improve capture efficiency, robustness, and obstacle avoidance safety in complex dynamic scenarios. Summary of the Invention

[0012] The technical problems to be solved by this invention include: (1) How to avoid the terminal lag problem of the set method when the escapee has strong mobility and feints; (2) How to reduce the risk of model predictive control methods getting trapped in local optima under limited prediction time domain and complex obstacle environment; (3) Reinforcement learning-based pursuit methods perform well within the training distribution, but have high adaptation costs for scene changes, obstacle layout changes, dynamic parameter changes and safety constraint interpretation.

[0013] (4) Existing technologies rarely handle closed-loop collaboration between real-time solution of isochronous reachable boundaries, model prediction control terminal guidance, unknown maneuver prediction, close-range capture correction and multi-index performance evaluation.

[0014] In view of the above problems, the present invention is proposed to provide a method and system for predictive control of UAV pursuit and escape game based on fusion isochronous guidance to overcome or at least partially solve the above problems.

[0015] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, embodiments of the present invention provide a UAV pursuit and escape game prediction and control method incorporating isochronous guidance, comprising: Obtain the current status information and environmental information of both the pursuer and the fugitive; the current status information includes: the position and speed of the pursuer and the fugitive; the environmental information includes: the distribution information of obstacles; Based on the current state information and the preset dynamic model, the isochrones are solved to determine the geometric reference information used to characterize the earliest capture opportunity; Predict the future trajectory and final capture point of the escapee based on their current movement status; Based on the geometric reference information, the future trajectory of the escapee in the prediction time domain, and the terminal capture point, a model predictive control optimization problem containing a long-term guidance term is constructed. Solve the model predictive control optimization problem to generate candidate control sequences; Select the current control variable from the candidate control sequence and execute it to control the pursuer.

[0016] In one embodiment, the geometric reference information includes isochronous tangency points, which are the points of internal tangency between the hunter's extended reachable set and the escapee's reachable set at the earliest capture time.

[0017] In one embodiment, predicting the future trajectory and terminal capture point of the escapee based on their current motion state includes: Step 1: Based on the current location and speed of the escapee and the current location of the pursuer, determine the candidate escape directions of the escapee in the prediction time domain; Step 2: Based on the candidate escape direction and the dynamic model of the escapee, recursively predict the position and velocity of the escapee in the prediction time domain to obtain the future trajectory of the escapee. Step 3: Estimate the terminal capture point based on the future trajectory, the reachability of the pursuer, and the capture radius.

[0018] In one embodiment, the cost function of the model predictive control optimization problem includes: process cost, terminal cost, and smoothing cost; The process cost is used to constrain the pursuer to move closer to the geometric interception reference point or the predicted trajectory of the escapee. The terminal cost is used to constrain pursuers to approach the terminal capture point; The smoothing cost is used to suppress abrupt changes between adjacent control variables.

[0019] In one embodiment, the candidate control sequence includes: an isochronous guided control quantity generated based on the geometric reference information and an optimized control quantity obtained by solving the model predictive control optimization problem.

[0020] In one embodiment, the candidate control sequence further includes at least one of the following: local prediction interception point candidate control quantity, terminal capture point candidate control quantity, isochronous tangent point candidate control quantity, mixed direction candidate control quantity, and angle disturbance candidate control quantity.

[0021] In one embodiment, selecting and executing the current control variable from the candidate control sequence includes: A short-time-domain rolling evaluation is performed on each candidate control quantity in the candidate control sequence to predict its pursuit performance within a preset evaluation time domain. Within the preset evaluation time domain, the motion state of the pursuer after the action of each candidate control variable in the candidate control set is simulated. Based on the simulated movement state of the pursuer and the predicted trajectory of the escapee, calculate the evaluation value corresponding to each candidate control variable; From the candidate control sequence, select the candidate control quantity whose evaluation value meets the preset conditions as the current execution control quantity.

[0022] In one embodiment, after solving the model predictive control optimization problem and generating candidate control sequences, the method further includes: When an obstacle is detected, the candidate control quantities in the candidate control sequence are evaluated for safety or corrected for direction to generate a safe candidate control sequence that meets the obstacle avoidance constraints. The security assessment or direction correction includes: Calculate the minimum safe distance between the predicted trajectory and the obstacle for each candidate control variable; If the minimum safe distance is less than a preset threshold, an alternative candidate direction is generated. The alternative candidate direction includes a repulsion direction away from the obstacle or a tangential direction along the edge of the obstacle.

[0023] In one embodiment, the preset dynamic model is a damped double integrator model.

[0024] In a second aspect, embodiments of the present invention provide a drone pursuit and escape game prediction and control system with integrated isochronous guidance, comprising: a processor, a memory, and a computer program stored in the memory and executable by the processor; when the processor executes the computer program, it implements the drone pursuit and escape game prediction and control method with integrated isochronous guidance as described in any of the first aspects.

[0025] As can be seen from the above technical solution, compared with the prior art, the present invention has the following technical advantages: First, this invention combines isochronous geometric guidance with rolling optimization control. The isochronous line provides a geometric reference over a longer time domain, while rolling optimization enables local corrections within a finite prediction time domain. This avoids the problems of insufficient local response in the simple isochronous line method and short-sighted decision-making in model predictive control, thereby improving the synergy and robustness of the pursuit control closed loop.

[0026] Secondly, this invention can improve capture efficiency and terminal capture stability. This is achieved by introducing a geometric interception reference point. Local prediction reference points and composite terminal reference point The controller can simultaneously utilize long-term time-domain geometric direction and short-term time-domain prediction information, enabling the pursuer to maintain good real-time response and trajectory smoothness when facing strong maneuverability or local disturbances of the escapee.

[0027] Third, this invention exhibits good adaptability in obstacle environments. By modeling obstacles as regions with safety expansion boundaries and performing short-time-domain trajectory and safety assessments before control input execution, it is possible to quickly and safely correct control variables without significantly increasing the complexity of the model predictive control optimization problem, thereby reducing collision risk and local optima risk.

[0028] Fourth, this invention reduces the reliance on large-scale training data and scene retraining. This method does not rely on offline training of the policy network, but instead makes online decisions based on dynamic models, isochronous reachability regions, prediction models, and rolling optimization mechanisms. When the escaper's policy, environment, or initial conditions change, adaptation can be achieved through parameter adjustment and control policy switching, thereby reducing model deployment and scene migration costs.

[0029] Fifth, this invention balances computational efficiency and control stability. By introducing isochronous geometric references, local prediction references, and composite terminal references, it reduces complex long-term path constraints; at the same time, it only performs short-term prediction evaluations on a limited number of candidate control inputs, thereby reducing the online computational burden and maintaining control stability.

[0030] Sixth, this invention has strong application value and expansion potential. It can be used in dynamic target interception scenarios such as unmanned systems, mobile robots, and virtual simulation training. It can also be extended to tasks such as multi-agent pursuit, three-dimensional motion, and online parameter adaptation, and has good real-time performance, interpretability, and engineering feasibility.

[0031] In summary, this invention improves the real-time performance, security, robustness, and interpretability of the UAV pursuit and escape game process by integrating isochronous geometry guidance, rolling optimization control, candidate input screening, and obstacle avoidance mechanisms. Attached Figure Description

[0032] 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, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0033] Figure 1 This is a flowchart of the UAV pursuit and escape game prediction and control method guided by fused isochronous lines provided in the embodiments of the present invention; Figure 2 This is a detailed flowchart of model predictive control based on isochronous guidance provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of a pursuit and escape game provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of isochrones provided in an embodiment of the present invention; Figure 5a This is a trajectory comparison diagram of a random maneuver scenario provided by the experimental example of this invention and the classical method; Figure 5b This is a comparison diagram of the trajectories of feint attacks and breakthroughs provided by the experimental examples of this invention and the classic methods; Figure 5c The damping coefficients provided in the experimental examples of this invention are compared with those of the classical method. A trajectory comparison diagram of obstacle scenarios (red shaded areas represent obstacles and their safe distances); Figure 5d The damping coefficients provided in the experimental examples of this invention are compared with those of the classical method. A trajectory comparison diagram of obstacle scenarios; Figure 5e This is a trajectory comparison diagram of a random maneuvering scenario provided by the experimental example of this invention and a learning-type method; Figure 5f This is a trajectory comparison diagram of the feint attack and penetration scenario provided by the experimental example of this invention and the learning-type method; Figure 5g The damping coefficient of the learning method provided in the experimental examples of this invention. A trajectory comparison diagram of obstacle scenarios; Figure 5h The damping coefficient of the learning method provided in the experimental examples of this invention. A trajectory comparison diagram of obstacle scenarios; Figure 6 This is a performance comparison chart of the experimental examples of this invention with the classical method in a random maneuver scenario; Figure 7 This is a performance comparison chart of the feint attack and penetration scenarios provided by the experimental examples of this invention and the classic method; Figure 8 The damping coefficients provided in the experimental examples of this invention are compared with those of the classical method. Performance comparison chart of obstacle scene graphs; Figure 9 The damping coefficients provided in the experimental examples of this invention are compared with those of the classical method. Performance comparison chart of obstacle scene graphs; Figure 10 This is a performance comparison chart of the experimental examples of this invention and the learning-based methods in random maneuvering scenarios; Figure 11 This is a performance comparison chart of the experimental examples of this invention and the learning-based method in a feint attack and penetration scenario; Figure 12 The experimental examples provided by this invention are related to the learning method in terms of damping coefficient. Performance comparison chart of obstacle scene graphs; Figure 13 The experimental examples provided by this invention are related to the learning method in terms of damping coefficient. Performance comparison chart of obstacle scene graphs; Figures 6-13 In the diagram, subgraph (a) shows the evolution of the Euclidean distance and time between the pursuer and the pursuer under different methods in the corresponding scenario, and subgraph (b) shows the performance of each method in the corresponding scenario in terms of capture time, total path length, and total turning angle. Figure 14 This is a simulation diagram of the Gazebo environment provided in the experimental example of this invention. The blue circle represents the escapee, and the red circle represents the pursuer. Subgraphs (a) to (f) show the simulation visual diagram of the pursuit and escape game process in chronological order. Figure 15 This is a trajectory diagram in the Gazebo environment provided in the experimental example of this invention, wherein the left figure is a three-dimensional spatial trajectory diagram and the right figure is the corresponding two-dimensional top view; Figure 16 This is a block diagram of the UAV pursuit and escape game prediction and control system provided in the experimental example of the present invention. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and 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.

[0035] Example 1: This invention discloses a predictive control method for UAV pursuit and escape game theory based on isochronous guidance. This method combines isochronous-based geometric guidance with model predictive control-based local rolling time-domain optimization. Figure 1 As shown, it includes: S100. Obtain the current status information and environmental information of both the pursuer and the fleeing party; the current status information includes: the position and speed of the pursuer and the fleeing party; the environmental information includes: the distribution information of obstacles; S200. Based on the current state information and the preset dynamic model, solve for the isochrones to determine the geometric reference information used to characterize the earliest capture opportunity; wherein, the preset dynamic model is a plane-damped double integrator model; the plane-damped double integrator model explicitly incorporates control input constraints, velocity constraints, and capture radius criteria. This modeling framework provides a dynamic foundation for isochrone calculation, target trajectory prediction, and rolling time-domain optimization.

[0036] S300: Predict the future trajectory and terminal capture point based on the current movement status of the escapee; S400. Based on the geometric reference information, the future trajectory of the escapee during the prediction period, and the terminal capture point, construct a model predictive control optimization (MPC) problem that includes a long-term guiding term. S500. Solve the model predictive control optimization problem to generate candidate control sequences; S600: Select the current control quantity from the candidate control sequence and execute it to control the pursuer.

[0037] The method provided in this invention, a novel hybrid pursuit method called IG-MPC, combines isochronous-based geometric guidance with rolling temporal optimization of model predictive control. In this method, isochronous lines are used to generate geometric references (such as capture points), while model predictive control performs local online correction within a rolling temporal loop. In this way, the proposed method achieves a balance between geometric interpretability and closed-loop adaptability. Furthermore, this invention designs a composite cost function guided by isochronous lines (see the detailed description of the embodiments below). Specifically, the proposed objective function integrates the pursuit distance, control input, input smoothness, and isochronous-based terminal guidance term into a unified optimization formula. This design introduces long-term temporal geometric guidance into local model predictive control optimization and improves the robustness of the pursuit strategy in constrained dynamic environments.

[0038] This invention is implemented as follows: First, based on the damped double-integral dynamics of both the pursuer and the pursuer, the isochrones and reachable regions are solved, and then the minimum isochrone in-tangent time is solved. This is also the earliest time that can be captured. Based on the internal tangent times of the pursuing and pursuing parties, the tangent point of the internal tangent time can be obtained. The escapee's future trajectory is then predicted, and the terminal capture point is estimated based on the predicted trajectory. Subsequently, a cost function considering smoothing cost, process cost, and terminal cost is constructed to optimize the escape problem. Finally, a short-term rolling evaluation is performed on the candidate control set, which includes the optimized control quantity generated by isochronous candidate control and model predictive control, and the current control is selected.

[0039] When obstacles are present, this invention abstracts the obstacles as circular safety regions with safety expansion boundaries, and evaluates the obstacle cost and minimum safe distance for the short-time-domain rolling paths of candidate controls. If there is a collision risk, other candidate directions are generated, and a safe control scheme is selected by combining the progress amount and the safe distance.

[0040] The method of the present invention will be described in further detail below: 1. Overall Method Flow: The main process of the method of this invention is as follows: Figure 2 As shown: Step S1: First, the controller obtains the current status and environmental information of both the pursuer and the fleeing party, including the position, speed, and obstacle distribution of the pursuer and the fleeing party.

[0041] Step S2: Construct a damped double-integral discrete model based on system dynamics to provide an updated basis for subsequent trajectory prediction and rolling optimization.

[0042] Step S3: Solve for the earliest capture time using the isochron method. Step S4: Generate isochron tangent points based on the geometric relationship between the isochrons of the pursuer and the escapee, or use the current or predicted position of the escapee as a reference target, thereby providing a guiding direction with global geometric significance for the pursuit process.

[0043] Steps S5 and S6: Next, predict the future trajectory and terminal capture point of the escapee based on its current motion state. Then, steps S7 and S8: Combining isochronous guidance reference, the escapee's predicted trajectory, and system constraints, construct and solve the IG-MPC optimization problem to obtain a set of candidate control inputs. Step S9: To ensure safety during actual execution, the system further considers obstacle avoidance capabilities for the candidate control inputs, eliminating control schemes with collision risks. Then, step S10: Evaluate the performance of the candidate controls through a rolling scoring mechanism and select the control input for the current moment. Finally, steps S11 and S12: The controller executes the selected control command and updates the system state, while simultaneously determining whether the capture conditions are met or the maximum task time has been reached. If capture fails or the task does not time out, the system returns to the next control cycle, reacquires state information, and repeats the above process. Through this closed-loop rolling optimization mechanism, the method of this invention can continuously correct the control strategy during dynamic pursuit, thereby improving the real-time performance, robustness, and obstacle avoidance safety of target interception.

[0044] 2. Damped double integrator model: This embodiment describes the pursuit-escape problem as a pursuit-escape game, involving a pursuer (P) and an escapee (E) moving in a two-dimensional space. Since this invention primarily focuses on the pursuit-escape game of drones in the horizontal plane, and the flight altitude can be kept stable by an independent altitude controller, the three-dimensional drone pursuit-escape process can be simplified into a two-dimensional planar dynamic problem. To characterize the inertia and damping effects in the horizontal motion of the drone, this embodiment uses a damped double integrator model to describe the planar motion of the pursuer and the escapee. For the participants... The motion state is described using a damped double integrator model:

[0045] in, For position vectors, and Participants exist and Velocity in the axial direction. For velocity vectors, and Participants exist and Acceleration in the axial direction. Let Indicates participants The control input, which is in time The value is represented as The allowed set of control inputs is: And control input for all All meet For simplicity, unless otherwise stated, time variables are omitted in the following content. In the formula, Let be the damping coefficient, when At this point, the model degenerates into an undamped double integrator model. For ease of analytical processing, this invention sets the damping coefficients of both the pursuer and the escapee to be the same. The acceleration amplitudes of both sides in the game are constrained, specifically... In addition, a cap is set on the speed of both the pursuer and the escapee, expressed as... .

[0046] For ease of representation, for participants Its state vector is defined as Accordingly, the position output vector can be represented as , .

[0047] This invention assumes that the system has a complete information structure, that is, the pursuer P and the escapee E at any time... Both can obtain accurate complete state vectors .

[0048] 3. Pursuit and Escape Game Model: like Figure 3 As shown, this embodiment sets a capture radius for the pursuer. When the distance between the pursuer and the escapee is less than or equal to the capture radius. When the time is right, the pursuer wins. That is, the end of the game is defined as... .

[0049] in, This represents the standard Euclidean distance between vectors. Initially, it is assumed that the distance between the pursuer and the escapee is greater than the capture radius. ,Right now .

[0050] Given the maximum game duration In the case that, if the following conditions are met If the capture is successful, the escape is considered a success; otherwise, the escape is considered a success. Therefore, the pursuer's goal is to minimize the capture time. The escapee, on the other hand, tries to maximize Or at the maximum game duration To avoid being captured.

[0051] 4. Isochrones and geometric reference points: Considering game participants The dynamic model. Under allowable control constraints. Below, in time The reachable position boundary is defined by time. Isochrones, denoted as

[0052] Under the damped double integrator model, the isochrones can be expressed as:

[0053] Among them, participants center of isochron ,radius . and Participants The initial position and initial velocity.

[0054] The forward reachable set contains participants In time All accessible locations within it correspond to the closed region enclosed by isochrones. It can be described as... Because the pursuer has a non-zero capture radius. The pursuer's extended radius is The isochrones of the pursuers -Isochrones can be represented as:

[0055] The corresponding extended forward reachable set can be written as .

[0056] When the pursuers - When an isochrone can encircle the isochrone of the escapee, the pursuer is considered to have a geometrical chance of capture. To determine this encirclement relationship, this embodiment defines the isochrone encirclement function as follows:

[0057] In this expression, The pursuers -The isochrones surrounded the isochrones of the escapee; and This indicates that the encirclement condition has not yet been met. To determine the maximum game duration... Whether capture can be achieved within the time frame is determined by introducing a minimum isochronous encirclement time in this embodiment. Its definition

[0058] It is important to note that Different from actual terminal capture time Specifically, This represents the earliest geometric capture reference time obtained based on the isochronous encirclement relationship; while This indicates the actual capture time. Figure 4 Showing the time enclosed by the smallest isochrones The original isochron of the pursuers and its -Isochrones The capture radius.

[0059] In this invention, this embodiment considers satisfying The initial condition, that is, at the initial moment, the capture condition is not met. If there exists a certain ,make Then by The continuity indicates that there exists a minimum isochronous line enclosing time. ,satisfy This equation represents the pursuers'... - The moment when the isochrones become internally tangent to the isochrones of the escapee.

[0060] This embodiment defines in At any given moment, the unit vector pointing from the center of the isochron of the pursuer to the center of the isochron of the escapee is:

[0061] Based on this direction vector, in the pursuer - Select a geometric interception reference point on the isochronous boundary, denoted as .

[0062] Geometrically speaking, lie in The Constant Chaser -On the boundary of the isochrones. Due to Corresponding to the pursuers -The moment when the isochrones and the escapee's isochrones first intersect. It also coincides with the point of tangency of the two isochrones. According to the property of internal tangency, the centers of the two isochrones are collinear with the point of tangency.

[0063] The geometric quantities obtained above , and All of these originate from the family of isochrones in the location space, providing guiding information for subsequent model predictive control design. In this sense, the proposed guiding strategy should be understood as an approximation of the time-optimal pursuit target driven by geometric motivation, rather than a rigorous solution to the optimal value function in the complete state space.

[0064] 5. Model predictive control optimization: To improve the local trajectory correction capability of the isochronous method, this embodiment introduces the concept of model predictive control (MPC), and constructs a finite-time rolling optimization problem based on the current state of the pursuer and the predicted state of the escapee at each sampling time.

[0065] The dynamic model of this invention can be written in standard linear state-space form:

[0066] in

[0067] make Represents the sampling time The corresponding discrete-time step index. Assume the control quantity remains constant within a sampling interval through zero-order hold (ZOH), i.e. exist The values ​​inside are constants. The discrete-time model can be expressed as:

[0068] in ,

[0069] and

[0070] At sampling time k, the hunter's optimization variable is the control sequence.

[0071] in, For predicting length. Indicates at time step For future time steps The predicted control input, The corresponding predicted state satisfies

[0072] Its initial conditions are In the formula Indicates at time step For future time steps The predicted state.

[0073] To describe the relative positional relationship between the pursuer and the escapee in the prediction time domain, this embodiment predicts the states of both parties based on a discrete dynamics model and outputs a position matrix. Predicted location:

[0074] To simplify the expression, let , Accordingly, sampling time The model predictive control problem under the following conditions can be expressed as: Its constraints include discrete-time dynamics, input constraints, and state constraints, where the cost function is...

[0075] in, To predict the weight of the pursuit distance penalty in the time domain, This represents the terminal distance penalty weight.

[0076]

[0077] And there are ,in, To control the input amplitude penalty weight, To control the penalty weight for changes in input, and It is a positive definite weight matrix. The control increment is...

[0078] For the first prediction step, let .in, This is the actual control input applied at the previous sampling time.

[0079] At each sampling time First, based on the current status of both parties and Construct an optimization problem and use a discrete model to predict the future. The state evolution is used for prediction. Subsequently, the optimal control sequence for the pursuer is obtained by solving a constrained optimization problem. However, in actual execution, only the first step of control input is applied. .

[0080] At the next sampling moment, the states of both parties are reacquired, the predicted trajectory is updated, and the optimization problem is solved again. The optimization problem is reconstructed, and the closed-loop process of prediction, optimization, execution, and updating is repeated. It is important to note that the above terminal guidance depends only on the predicted terminal position of the escapee, i.e. It does not introduce any additional geometric reference information. Therefore, it serves as the reference baseline for subsequent isochronous-guided extension methods.

[0081] 6. Optimization of model predictive control guided by isochrones: To combine the long-term geometric guidance capability of isochronous lines with the local correction capability of rolling optimization control, this embodiment introduces a geometric interception reference point during the rolling optimization process. At the sampling time Based on the current status of the pursuer and the fugitive , Calculate the minimum isochronous encirclement time. .like If it exists, then it depends on the isochronous center of the pursuer and the escapee, and the pursuer's -Isochronous radius, constructing geometric interception reference points ;like If the reference point does not exist, the current or predicted position of the escapee will be used as a backup reference point. To avoid control direction jitter caused by excessively frequent updates of the geometric reference point, and without increasing the computational load, this embodiment sets a reference point update cycle. Updated according to this cycle .

[0082] It is important to note that It is not the sole terminal target, but rather geometric reference information serving as a terminal guidance term. Compared to model predictive control methods that rely solely on short-term predictions of the escapee's terminal position, this approach introduces... A longer temporal geometric guidance reference consistent with the minimum guaranteed capture configuration is provided, thereby improving the stability, robustness and interpretability of the resulting pursuit strategy.

[0083] To balance longer temporal geometric guidance with local prediction interception information, this embodiment defines a local prediction interception reference point. :

[0084] in, This indicates the earliest prediction step when the predicted pursuit distance meets the capture conditions. It reflects the geometric approach direction over a longer time domain in the pursuit-escape game; This reflects the local interception information within the current prediction time domain. Subsequent rolling optimization will utilize this information. and Construct terminal guidance items to improve the adaptability of the pursuit process to changes in the maneuverability of the escapee.

[0085] Therefore, this embodiment predicts the terminal location of the escapee. Local prediction interception reference point and geometric interception reference point Together they are used to construct a composite terminal reference point, denoted as

[0086] in, To predict the proximity weights of terminals, and The terminal weights in the formula remain consistent. As a reference point for prediction The guiding weight; Reference point for geometric interception The guiding weight. Let .

[0087] Therefore, the sampling time The IG-MPC method can be described as follows: The cost function is:

[0088] The proposed IG-MPC method incorporates not only the predicted terminal closure target into the terminal reference point, but also the geometric interception references in the local short-term and longer-term domains, thereby constructing an improved guidance mechanism that achieves a balance between local response capability and isochronous guidance geometric consistency.

[0089] 7. Candidate Control Selection: At each sampling time, the proposed method updates the isochronous geometric reference points online. Prediction reference points And predict the escaper trajectory, solve the rolling optimization problem, and obtain candidate optimal control inputs. Simultaneously, geometrically guided input is constructed based on the isochronous direction. And choose between the two to determine the actual control input applied.

[0090] For each candidate input, system dynamics and escaper trajectories are used for... This embodiment takes the short-time domain rolling prediction step. The predicted proximity performance is jointly evaluated by the predicted capture step and the cumulative distance in the short time domain, and is expressed as follows:

[0091] Among them, the weighting coefficient Adjust the capture time, and Adjustment The relative distance between prediction times is important. If a candidate input can bring an earlier prediction capture step, then that candidate input is preferred; otherwise, the candidate input with a smaller cumulative distance in the short time domain is selected. Therefore, the actual applied control can be written as...

[0092] in, This represents the online selection rule based on short-time domain prediction proximity performance. At the next sampling time, the system reacquires the states of the pursuer and the escapee, updates the isochronous geometric reference, the local prediction reference, and the escapee's predicted trajectory, and repeats the above optimization and candidate control selection process.

[0093] 8. Experimental Example: Experimental Evaluation; Experiment Example 1: Parameter Settings; In this embodiment, the damping coefficients of both the pursuer and the escapee are uniformly set to... The maximum game time is set to The sampling period was set to 0.05 s. For obstacle-free scenarios, the initial position of the pursuer was set to... The initial velocity is set to The maximum acceleration is set to The capture radius is set to The escapee's initial position is set to... The initial velocity is set to The maximum acceleration is set to .

[0094] This experimental example sets up scenarios including random escape by the escapee and feint attack / breakthrough scenarios. obstacle scenes, The proposed method is used in obstacle scenarios. To verify its effectiveness, this chapter compares it with isochronous-guided strategies, MPC, NMPC, and PP methods, and uses capture time, pursuit path length, and cumulative steering angle as evaluation metrics.

[0095] Experimental Example 2: Comparison with Classical Methods; Trajectories of various methods in different scenarios, such as Figures 5a-5h As shown, blue dots and red squares mark the initial positions of the pursuer and the escapee, respectively. The end marker indicates the final position, and a magnified view shows the details of the final phase.

[0096] in Figure 5a For trajectories obtained using non-learning methods in random maneuvering scenarios, all five methods achieved finite-time capture. Specific performance details for each method are as follows: Figure 6 As shown, IG-MPC achieved the best overall performance in the random maneuver scenario. Subgraph (a) shows the evolution of the Euclidean distance and time between the pursuer and pursuer, while subgraph (b) shows the performance of each method in this scenario in terms of capture time, total path length, and total turning angle. In subgraph (b), IG-MPC's capture time is 4.59 s, shorter than NMPC's 4.79 s, the isochronous method's 4.84 s, MPC's 4.86 s, and PP's 4.90 s. Meanwhile, IG-MPC's pursuit path length is... The cumulative steering angle is All of these methods are superior to other comparative methods. Figure 6 Subgraphs (a) and (b) show that IG-MPC achieves capture of the escapee earliest, while the capture times of the other four methods are relatively similar. This indicates that in random escape scenarios, IG-MPC achieves a more effective balance between capture efficiency, path economy, and motion smoothness.

[0097] In scenarios where the escapee feigns an attack to break through the defenses, such as Figure 5b As shown, the sudden strategy switching clearly distinguishes the responsiveness of the five methods; the isochronous method failed to respond within the maximum game duration. The escapee was captured internally. (Example) Figure 7 As shown, IG-MPC has the shortest acquisition time of 5.07s, which is better than MPC's 5.41s, PP's 5.78s, and NMPC's 7.73s. Meanwhile, IG-MPC's path length and cumulative steering angle are 18.67m and 1.17rad, respectively, both superior to other successfully acquired methods. This indicates that the IG-MPC method has better response capability and trajectory smoothness in sudden maneuver scenarios.

[0098] In the third and fourth scenarios, this experimental example introduces obstacles. Considering the actual physical volume of the game participants, this experimental example models the obstacles as circular regions and uses an expansion algorithm to handle their safe boundaries, such as... Figure 5c and Figure 5d As shown, the damping coefficients are obtained using the classical method, respectively. A comparison diagram of obstacle scene trajectories. The expansion radius is set to 0.1 m. The U-shaped obstacle area consists of 14 circular obstacles, each with a radius of 0.42 m. The initial states of the pursuer and the escapee are set as follows: , , , .

[0099] For the The effective safety radius of each obstacle is

[0100] in, The physical radius of the obstacle. The expansion radius is given by the short-time domain prediction path generated from a candidate control input. The minimum safe distance is defined as

[0101] in, Indicates the first The center of the obstacle. If If the distance exceeds the safety threshold, the original control input is applied directly. Otherwise, alternative candidate directions are generated and evaluated based on the minimum distance to the expanding obstacle, the deviation from the original control direction, and the forward propulsion along the original direction. The actual control input that satisfies the safety constraints and is beneficial for pursuit is selected. This obstacle avoidance module acts as an execution-layer safety filter for all methods, rather than as an explicit term in the objective function of the model predictive control optimization problem. Therefore, performance differences in obstacle-constrained scenarios primarily stem from different pursuit decision mechanisms.

[0102] like Figure 5c and Figure 8 As shown, in In obstacle-constrained scenarios, IG-MPC can shorten the pursuit distance more quickly and complete the capture earliest; Figure 5c In the image, the red shaded area represents obstacles and their safe distance. The capture time is... It outperforms NMPC, PP, MPC, and isochronous methods; the path length is It is slightly higher than other methods, but the cumulative steering angle is the smallest, at [value missing]. The results show that the proposed method can balance capture efficiency, path cost, and trajectory smoothness in obstacle environments.

[0103] like Figure 5d and Figure 9 As shown, in In high-damped obstacle scenarios, neither MPC nor PP could achieve [the desired result]. The capture is completed within [timeframe]. Among the successful capture methods, IG-MPC has the shortest capture time, [timeframe value missing]. Superior to NMPC and the isochronous method Meanwhile, the path length of IG-MPC is... The cumulative steering angle is The proposed method outperforms other successful capture methods. The results show that the proposed method still exhibits good capture efficiency, path economy, and motion smoothness under high damping and obstacle constraints.

[0104] Simulation results across four scenarios demonstrate that the proposed IG-MPC method exhibits superior overall performance under various escape strategies and environmental constraints. This method effectively combines geometric guidance with MPC prediction optimization, maintaining high pursuit efficiency in conventional scenarios while demonstrating stronger robustness and overall advantages in scenarios involving sudden maneuvers and obstacles.

[0105] Experiment Example 3: Comparison with reinforcement learning methods; like Figures 5e-5h as well as Figures 10-13 As shown, this experimental example compares the proposed IG-MPC method with the TD3 reinforcement learning strategy. The TD3 strategy was trained offline in obstacle-free, simple obstacle, and complex obstacle scenarios, denoted as TD3-NoObs, TD3-Simple, and TD3-Complex, respectively. Experimental results show that IG-MPC can achieve successful capture in all four types of pursuit scenarios without offline training; while the performance of the TD3 strategy is greatly affected by the coverage of the training environment, and performance tends to degrade when the test scenario is inconsistent with the training scenario. This indicates that the proposed method maintains online decision-making ability and interpretability while exhibiting good scenario adaptability and capture stability.

[0106] Experiment Example 4: Gazebo Simulation; To verify the effectiveness of the proposed method, this embodiment uses an obstacle constraint scenario in the Gazebo simulation, such as... Figure 14 As shown, the sub-graphs, from top left to bottom right, are divided into (a) to (f) in chronological order, sequentially displaying the simulated visual landscape of the pursuit-escape game process. Since this invention focuses on two-dimensional pursuit-escape games, this embodiment reduces the dimensionality of the three-dimensional simulation environment by fixing the flight altitude. Specifically, the planar control input is mapped to the horizontal component of the MAVROS speed setpoint, while the vertical direction is independently controlled by the altitude controller, ensuring that both drones maintain a constant altitude. The height.

[0107] The initial positions of the pursuers and the escapees are set as follows: and The pursuit begins once both aircraft reach the target altitude and their speeds have decreased to near zero. The damping coefficient is set to... The maximum control inputs for the pursuer and the escapee are respectively and .

[0108] like Figure 14 and Figure 15 As shown, the pursuer successfully avoided the cylindrical obstacle while continuously closing the distance to the escapee. Its overall flight trajectory remained smooth without any collisions. Near the end of its trajectory, the escapee made a partial turn, and the pursuer adjusted its course in real time based on the escapee's movement, ultimately achieving a successful escape. The capture was completed nearby. The entire process, from takeoff and reaching the designated altitude to final capture, took 5.10 seconds. This result fully demonstrates that the control strategy designed in the numerical simulation can be smoothly transferred to the Gazebo physics engine and maintain efficient pursuit and obstacle avoidance performance under conditions close to actual UAV flight dynamics.

[0109] Example 2: This embodiment provides a drone pursuit and escape game prediction and control system based on integrated isochronous line guidance, comprising a processor, a memory, and a computer program stored in the memory and executable by the processor; when the processor executes the computer program, it implements the drone pursuit and escape game prediction and control method based on integrated isochronous line guidance described in Embodiment 1.

[0110] 1. System structure; like Figure 16 As shown, the UAV pursuit-escape game prediction and control system guided by isochrones includes the following modules: state acquisition module, isochrone solving module, global interception reference generation module, escape trajectory prediction module, terminal capture point estimation module, IG-MPC module, candidate control set generation module, obstacle avoidance module, rolling optimization and selection module, control and state update module, and simulation evaluation module. These modules can be deployed in the same controller, or in a simulation platform, robot control platform, or unmanned system task computing unit.

[0111] 2. Functional description of each module; Status acquisition module: used to acquire the current status information of the pursuer and the escapee in real time, including position, speed, acceleration, and obstacle distribution information in the environment.

[0112] Isochrone Solving Module: Based on the acquired state and the preset dynamic model, calculate the reachable regions (isochrones) of the pursuer and the escapee at different times, and solve for the minimum isochrone in-tangent time.

[0113] Global interception reference generation module: Generates geometric interception reference points based on the isochrone solution results. , serving as a long-term guiding direction.

[0114] Escape trajectory prediction module: Based on the escapee's current state and dynamic model, predict its future trajectory in the prediction time domain.

[0115] Terminal capture point estimation module: Estimates the terminal capture point based on the predicted escapee trajectory and the pursuer's capabilities.

[0116] The IG-MPC module constructs and solves the isochronous-guided model predictive control optimization problem, generating candidate control inputs.

[0117] Candidate control set generation module: Generates candidate control sets based at least on the isochronous guided control quantity and the optimized control quantity generated by model predictive control, and may also include other candidate directions, such as prediction leading point, terminal capture point, mixed direction, etc.

[0118] Obstacle avoidance module: When an obstacle is detected, the module performs safety screening or direction correction on the candidate control inputs and generates a safety control scheme that meets the obstacle avoidance constraints.

[0119] Rolling optimization and selection module: Performs short-time rolling evaluation on each candidate variable in the candidate control set, and selects the candidate variable with the best evaluation value as the current execution control variable.

[0120] Control and Status Update Module: Executes the selected control command, updates the pursuer's status, and determines whether the capture conditions are met or the maximum mission time has been reached.

[0121] Simulation evaluation module: used to record data of the pursuit process and evaluate control performance based on indicators such as capture time, path length and cumulative steering angle.

[0122] 3. System workflow; The system's workflow corresponds entirely to the method described in Example 1. After system startup, the state acquisition module obtains the current state information, while the isochronous line solving module and the escape trajectory prediction module work in parallel to generate geometric references and predicted trajectories, respectively. The IG-MPC module combines these two modules to construct and solve an optimization problem. The candidate control set generation module gathers various candidate control variables, the obstacle avoidance module performs safety filtering on them, and the rolling optimization and selection module selects the optimal control variable and submits it to the control and state update module for execution. The system repeats the above process until capture or the task ends.

[0123] 4. Hardware and software implementation; The system can be implemented on the following platforms: embedded controllers, such as STM32, NVIDIA Jetson series, etc.; ground station computers or cloud servers, etc.; the system software can be written in languages ​​such as C++ and Python, and integrated with middleware such as ROS and MAVROS to support UAV communication and control.

[0124] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A predictive control method for UAV pursuit and escape game theory based on isochronous line guidance, characterized in that, include: Obtain the current status and environmental information of both parties involved in the pursuit; The current status information includes: the position and speed of the pursuer and the escapee; the environmental information includes: the distribution information of obstacles; Based on the current state information and the preset dynamic model, the isochrones are solved to determine the geometric reference information used to characterize the earliest capture opportunity; Predict the future trajectory and final capture point of the escapee based on their current movement status; Based on the geometric reference information, the future trajectory of the escapee in the prediction time domain, and the terminal capture point, a model predictive control optimization problem containing a long-term guidance term is constructed. Solve the model predictive control optimization problem to generate candidate control sequences; Select the current control variable from the candidate control sequence and execute it to control the pursuer.

2. The method according to claim 1, characterized in that, The geometric reference information includes isochronous tangency points, which are the points of internal tangency between the hunter's extended isochronous line and the escapee's isochronous line at the earliest capture time.

3. The method according to claim 1, characterized in that, Predict the future trajectory and final capture point of the escapee based on their current movement state, including: Step 1: Based on the current location and speed of the escapee and the current location of the pursuer, determine the candidate escape directions of the escapee in the prediction time domain; Step 2: Based on the candidate escape direction and the dynamic model of the escapee, recursively predict the position and velocity of the escapee in the prediction time domain to obtain the future trajectory of the escapee. Step 3: Estimate the terminal capture point based on the future trajectory, the reachability of the pursuer, and the capture radius.

4. The method according to claim 1, characterized in that, The cost function of the model predictive control optimization problem includes: process cost, terminal cost, and smoothing cost; The process cost is used to constrain the pursuer to move closer to the geometric interception reference point or the predicted trajectory of the escapee. The terminal cost is used to constrain pursuers to approach the terminal capture point; The smoothing cost is used to suppress abrupt changes between adjacent control variables.

5. The method according to claim 1, characterized in that, The candidate control sequence includes: isochronous guided control quantity generated based on the geometric reference information and optimized control quantity obtained by solving the model predictive control optimization problem.

6. The method according to claim 5, characterized in that, The candidate control sequence further includes at least one of the following: a predicted leading point candidate control quantity, a terminal capture point candidate control quantity, an isochronous tangent point candidate control quantity, a mixed direction candidate control quantity, and an angle disturbance candidate control quantity.

7. The method according to claim 5, characterized in that, The step of selecting and executing the current control variable from the candidate control sequence includes: A short-time-domain rolling evaluation is performed on each candidate control quantity in the candidate control sequence to predict its pursuit performance within a preset evaluation time domain. Within the preset evaluation time domain, the motion state of the pursuer after the action of each candidate control variable in the candidate control set is simulated. Based on the simulated movement state of the pursuer and the predicted trajectory of the escapee, calculate the evaluation value corresponding to each candidate control variable; From the candidate control sequence, select the candidate control quantity whose evaluation value meets the preset conditions as the current execution control quantity.

8. The method according to claim 1, characterized in that, After solving the model predictive control optimization problem and generating candidate control sequences, the method further includes: When an obstacle is detected, the candidate control variables in the candidate control sequence are subjected to safety screening or direction correction to generate a safe candidate control sequence that satisfies the obstacle avoidance constraint. The security screening or direction correction includes: Calculate the minimum safe distance between the predicted trajectory and the obstacle for each candidate control variable; If the minimum safe distance is less than a preset threshold, an alternative candidate direction is generated. The alternative candidate direction includes a repulsion direction away from the obstacle or a tangential direction along the edge of the obstacle.

9. The method according to claim 1, characterized in that, The preset dynamic model is a damped double integrator model.

10. A game-theoretic prediction and control system for unmanned aerial vehicle (UAV) pursuit and escape, guided by isochronous lines, characterized in that: include: A processor, a memory, and a computer program stored in the memory and executable by the processor; When the processor executes the computer program, it implements the UAV pursuit and escape game prediction and control method according to any one of claims 1 to 9.

Images