A method and system for generating a maneuvering target interception trajectory considering a passing point constraint
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF SCI & TECH
- Filing Date
- 2026-03-11
- Publication Date
- 2026-05-12
Smart Images
Figure CN121806981B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of interception and control technology, specifically relating to a method and system for generating interception trajectories for maneuvering targets that takes into account waypoint constraints. Background Technology
[0002] Due to sea clutter and weather interference at sea, and the influence of complex airspace and electromagnetic environments in the air, the detection and tracking of maneuvering targets are becoming increasingly difficult, necessitating improvements in interception capabilities against medium- and long-range maneuvering targets. Existing target interception technologies primarily address trajectory planning from two aspects: control and optimization. Control-based target interception mostly relies on theories such as PID control, sliding mode control, adaptive control, or model predictive control to generate target interception trajectories to ensure tracking accuracy. Optimization-based target interception often uses the shortest interception time and lowest energy consumption as indicators, constructing constrained optimization models to generate the optimal interception trajectory. Considering the complexity of target maneuvering and the uncertainties of medium- and long-range interception processes, the limitations of existing target interception trajectory generation methods are mainly reflected in the following two aspects:
[0003] First, at medium to long ranges, it is difficult to fully guarantee the safety of the interception process. Most current research on target interception planning focuses on short-range operations. At medium to long ranges, the environmental characteristics are complex, and the interceptor's safe operational airspace / sea area is often irregular, unstructured, and sometimes dynamically changing. In such cases, it is necessary to consider allowing the interceptor to pass through dynamically updated waypoints. If waypoint constraints are not considered during interception planning, the safety of the interception process cannot be fully guaranteed.
[0004] Secondly, it is difficult to meet the terminal interception accuracy requirements under target maneuvering conditions. During the interception process, the target's penetration maneuvering can easily cause the interceptor's trajectory prediction error to accumulate, and environmental disturbances at medium and long ranges will further amplify the target trajectory prediction deviation. Due to the narrow terminal interception window and short response time, traditional trajectory generation methods are unable to adapt to the target's maneuvering state in a timely manner and cannot quickly correct the interception path, resulting in insufficient spatial position matching between the interceptor and the target, ultimately making it difficult to achieve the terminal accuracy threshold for precise interception. Summary of the Invention
[0005] The purpose of this invention is to provide a method and system for generating interception trajectories for maneuvering targets that takes into account waypoint constraints, so as to ensure the safety, accuracy and dynamic responsiveness of the interception trajectory in medium and long-range maneuvering target interception scenarios.
[0006] The technical solution to achieve the purpose of this invention is as follows:
[0007] A method for generating interception trajectories for maneuvering targets considering waypoint constraints, comprising:
[0008] Step 1: Set the initial parameters for the interceptor's status, target motion model library, and waypoint locations;
[0009] Step 2: Predict the trajectory of the maneuvering target based on the interceptor's status, target motion model, and waypoint location;
[0010] Step 3: Using the last waypoint as the dividing point, the interception path is divided into a waypoint interception segment and a rolling optimization interception segment. A multi-stage interception planning model is constructed based on the maneuver target trajectory prediction results. The multi-stage interception planning model includes a waypoint interception segment planning model and a rolling optimization interception segment planning model.
[0011] Step 4: Generate the interception trajectory based on the multi-stage interception planning model, including: for the interception segment that passes through the waypoint, solve the planning model of the interception segment that passes through the waypoint to generate the interception trajectory of the segment that passes through the waypoint; for the rolling optimization interception segment, within each cycle, the interceptor solves the planning model of the rolling optimization interception segment based on the current target state to generate the interception trajectory for future time periods.
[0012] Step 5: The interceptor navigates and intercepts based on the interception trajectory of the interception segment passing through the waypoints. When the interceptor passes through each waypoint, it determines whether the interception is complete. If the interception is not complete, it determines whether a new waypoint has been added. If a new waypoint appears, steps 2-4 are re-executed to generate a new interception trajectory. If no new waypoint appears, and if the current waypoint is the last waypoint, the interceptor navigates according to the trajectory of the rolling optimized interception segment and dynamically intercepts the target in the last control cycle. If the current waypoint is not the last waypoint, the interception continues according to the interception trajectory generated by the interception segment passing through the waypoints.
[0013] Furthermore, the interceptor's state includes the interceptor's position and the interceptor's motion state, and the target motion model. The target motion model library includes uniform linear motion model, uniformly accelerated linear motion model, uniform circular motion model, and Singer maneuver model.
[0014] Furthermore, the interceptor is an unmanned aerial vehicle, and the initial value of the interceptor's state is... ,in The initial position in the coordinate system. The initial heading angle, These represent the forward speed, drift speed, and bow roll rate in the ship's coordinate system, respectively. This represents the initial accumulated energy consumption.
[0015] Furthermore, step 2 specifically includes:
[0016] At the start of the interception, the initial target motion model is used to predict the trajectory of the initial maneuvering target.
[0017] As the interceptor passes each waypoint, the distance prediction error between the interceptor and the target is calculated and analyzed in real time. If the error is always lower than the preset threshold, the current target motion model is used to predict the trajectory of the maneuvering target. Otherwise, the target motion model that best matches the actual observation data of the target is selected from the target motion model library to predict the trajectory of the maneuvering target.
[0018] Furthermore, the planning model for the interception segment via the transit point is as follows:
[0019]
[0020] in, For the performance indicators of the route segments, These are adjustable weighting coefficients. For the first The start time of the phase, For the first The end time of the phase, For the intercepting party The position vector at time , For the goal The position vector at time , For the first The position vectors of the points along the way For the first Energy consumed by the interceptor in each phase.
[0021] The performance indicators The constraints include:
[0022] Dynamic constraints ;
[0023] State variable constraints ;
[0024] Control variable constraints ;
[0025] Terminal constraints ;
[0026] Phase transition constraints ;
[0027] in, For the first stage The derivative of the state vector at time t, For the first stage The state vector at time t, For the first stage The control input vector at time t, The state transition function is determined by the dynamic model of the vehicle pair. This refers to the upper and lower bounds of the state variables throughout the entire interception process. This refers to the upper and lower bounds of the control variables throughout the entire interception process. For the first The position vector of the interceptor at the end of the phase. For the first At the initial moment of the phase, For the first The end point of the phase, For the first The position vectors of the points along the way For the first The state of the interceptor at the initial moment of the phase. For the first The state of the interceptor at each stage terminal.
[0028] Furthermore, the rolling optimization interception segment planning model is as follows:
[0029]
[0030] in, It is a performance metric for the rolling optimization interception segment. This is the start time of the current control cycle. It predicts the length of the time domain. It predicts the terminal time in the time domain. Is the interceptor at any moment? The planar position vector, Is the interceptor at any moment? The planar position vector, The goal is at all times The predicted position vector, The goal is at all times The predicted position vector, For the energy consumption of the intercepting party, These are adjustable weighting coefficients;
[0031] The performance indicators The constraints include:
[0032] Dynamic constraints ;
[0033] State variable constraints ;
[0034] Control variable constraints ;
[0035] Prediction Time Domain Constraints ;
[0036] Target motion prediction constraints ;
[0037] Intercepting terminal constraints ;
[0038] in, To predict the minimum length in the time domain, in order to ensure sufficient information, To predict the maximum length in the time domain, and to control the computational load, The target motion prediction function is determined by the specific model in the model library. The current observed target state, For other parameters of the target model, such as the attenuation coefficient, The radius of successful interception. This is the terminal moment of the rolling interception process. Is the interceptor at any moment? The planar position vector, The goal is at all times The predicted position vector.
[0039] Furthermore, in step 4, the hp-adaptive Radau pseudospectral method is used to solve the planning model for the interception segment via the waypoint and the rolling optimization interception segment planning model.
[0040] Furthermore, for the rolling optimization interception segment, a Warm-Start strategy is adopted in each control cycle, using the optimization solution of the previous cycle as the initial guess for this optimization, and achieving dynamic interception of the target in the last control cycle.
[0041] Furthermore, if the real-time distance between the interceptor and the target is less than a set value, the interception is considered successful.
[0042] A system for generating interception trajectories for maneuvering targets considering waypoint constraints, employing the aforementioned method for generating interception trajectories for maneuvering targets, includes:
[0043] The parameter setting unit sets the initial parameters for the interceptor's status, target motion model library, and waypoint location;
[0044] The target trajectory prediction unit predicts the trajectory of the maneuvering target based on the interceptor's status, the target's motion model, and the location of the waypoints.
[0045] The multi-stage interception planning model construction unit divides the interception path into a passing-through interception segment and a rolling optimization interception segment, with the last waypoint as the dividing point. Based on the trajectory prediction results of the maneuvering target, a multi-stage interception planning model is constructed, which includes a passing-through interception segment planning model and a rolling optimization interception segment planning model.
[0046] The intercept trajectory generation unit generates an intercept trajectory based on a multi-stage intercept planning model, including: a transit point interception segment, which solves the transit point interception segment planning model to generate the transit point intercept trajectory; and a rolling optimization interception segment, in each cycle, the interceptor solves the rolling optimization interception segment planning model based on the current target state to generate the intercept trajectory for future time periods.
[0047] The interception judgment unit determines whether the interceptor has completed the interception based on the interception trajectory of the interception segment passing through the waypoints. If the interceptor has not completed the interception, it determines whether a new waypoint has been added. If a new waypoint appears, the target trajectory prediction unit, the multi-stage interception planning model construction unit, and the interception trajectory generation unit are re-executed to generate a new interception trajectory. If no new waypoint appears, and if the current waypoint is the last waypoint, the interceptor navigates according to the trajectory of the rolling optimized interception segment and dynamically intercepts the target in the last control cycle. If the current waypoint is not the last waypoint, the interception continues according to the interception trajectory generated by the interception segment passing through the waypoints.
[0048] Compared with existing technologies, this invention has the following significant advantages: 1) Dynamic adaptability: By using rolling time-domain control and online target prediction, the problem of intercept trajectory generation under target maneuvering is solved, realizing real-time intercept planning in dynamic environments. 2) Precise path tracking: Through multi-stage intercept planning modeling, waypoint constraints are incorporated into the terminal state constraints of each interception segment, supplemented by strict stage connection continuity constraints, ensuring that the interceptor can accurately and smoothly pass through all waypoints. 3) Balance between computational efficiency and accuracy: The hp-adaptive pseudospectral method is used for discretization, and the Warm-Start strategy is combined to initialize the nonlinear programming solution, effectively overcoming the disadvantage of high computational load in solving high-order nonlinear systems by the direct method, ensuring accurate target tracking while meeting real-time requirements. Attached Figure Description
[0049] Figure 1 This is a schematic diagram of the method flow of the present invention.
[0050] Figure 2 This is the interception trajectory diagram generated in the embodiments of the present invention.
[0051] Figure 3 This is a speed change diagram generated in each stage in an embodiment of the present invention.
[0052] Figure 4 This is a diagram showing the changes in state variables at each stage generated in an embodiment of the present invention.
[0053] Figure 5 This is a full-process energy change diagram generated in an embodiment of the present invention. Detailed Implementation
[0054] To address the problems of existing target interception planning methods in medium- and long-range interception applications, such as insufficient consideration of interception process security and decreased interception accuracy of maneuvering targets in the terminal phase, this invention discloses a method for generating maneuvering target interception trajectories that considers waypoint constraints. The principle is as follows: Figure 1 As shown. This method ensures smooth arrival and state transition of waypoints through multi-stage interception planning, and uses a rolling time-domain control approach to predict and intercept maneuvering targets simultaneously in the final stage of interception, guaranteeing the safety, accuracy, and dynamic responsiveness of the interception trajectory in medium- and long-range maneuvering target interception scenarios. The specific details are as follows:
[0055] 1. Establish a target prediction strategy for maneuvering targets.
[0056] A target motion model library is constructed, encompassing typical maneuvering modes such as uniform speed, uniform acceleration, and uniform speed turning. At the start of the interception, the interceptor uses a default target maneuvering mode for initial trajectory planning. During the interceptor's movement towards the first path point, online observation and model evaluation of the target's motion state are performed simultaneously. The rationality of the currently used target maneuvering model is evaluated by calculating and analyzing the distance prediction error between the interceptor and the target in real time. For the first Phase based on target maneuver model The distance prediction error satisfies:
[0057] ,
[0058] in, Based on the current model Predicted target location The actual observed target location, For the first The predicted duration of each stage. At each waypoint, based on the error trend throughout the stage, a decision is made regarding the rationality of the maneuver model; if the error... Always below the preset threshold If the error is within the expected range, the current model is considered accurate, and this model will continue to be used in subsequent stages. If the error increases significantly, the current model is considered inaccurate, and a model matching the observed data should be immediately selected from the model library. The most suitable model is selected, and the more accurate model is switched to in subsequent interception planning for target trajectory prediction.
[0059] 2. Construct a multi-stage interception planning model.
[0060] To achieve precise interception of maneuvering targets while meeting the mission requirements of passing through waypoints, the entire interception planning task is decomposed into two types of optimal control problems: one is the optimal control problem for the waypoint segment, focusing on precise path tracking; the other is the optimal control problem for the rolling optimization interception segment, focusing on dynamic target tracking. Each stage is smoothly connected through strict state transition constraints, forming a multi-stage interception planning problem.
[0061] For segments passing through points, consider including... The interception task at each path point is broken down into... Each stage must satisfy dynamic constraints. , Indicates the first Each stage, state variable constraints and control variable constraints To achieve precise arrival at each waypoint, terminal constraints are established at each waypoint. And set stage connection constraints between adjacent stages. This ensures that the initial state of the next stage is completely continuous with the terminal state of the previous stage in terms of position, velocity, and time. Performance metrics for the segments along the route are also constructed.
[0062]
[0063] The performance indicators comprehensively consider the trajectory tracking error throughout the entire process, the trajectory terminal error, and energy consumption. Among them, , These are adjustable weighting coefficients, corresponding to the weighting of the trajectory tracking error integral term, the terminal interception error term, and the control energy consumption term, respectively. The first term, the integral tracking error term, ensures close following of the target's predicted trajectory throughout the interception process. The second term, the terminal error term, forces the minimum position deviation to be achieved at the moment of interception. The third term, the energy consumption term, optimizes control efficiency and reduces energy consumption. By adjusting the weighting coefficients, a flexible trade-off can be made between interception accuracy, response speed, and energy consumption according to requirements.
[0064] For the rolling optimization intercept segment, each control cycle Within, the interceptor predicts the future of the target based on its current state. Trajectory within a time period generates the future. The target trajectory is predicted for a given time period. This process must satisfy the following constraints:
[0065] 1) Dynamic constraints ;
[0066] 2) State variable constraints ;
[0067] 3) Control variable constraints ;
[0068] 4) Prediction time domain constraints ;
[0069] 5) Target motion prediction constraints ;
[0070] 6) Intercepting terminal constraints .
[0071] The performance metrics for this stage are similar in form to those for the transit points, but optimization is only performed for the current prediction time domain. The performance metrics are as follows:
[0072]
[0073] in, It is a performance metric for the rolling optimization interception segment. This is the start time of the current control cycle. It predicts the length of the time domain. It predicts the terminal time in the time domain. Is the interceptor at any moment? The planar position vector, Is the interceptor at any moment? The planar position vector, The goal is at all times The predicted position vector, The goal is at all times The predicted position vector, For the energy consumption of the intercepting party, These are the weighting coefficients for trajectory tracking error, terminal error, and energy consumption, respectively.
[0074] This invention establishes a multi-stage interception planning model for intercepting medium- and long-range targets. This model simultaneously considers the waypoint constraints during the interception process and the target maneuvering patterns in the final stage of interception. It proposes an interception trajectory generation strategy for the waypoint segment, which takes into account the target maneuvering prediction results. This strategy reduces the accumulation of target trajectory prediction errors while ensuring accurate arrival at waypoints and smooth transitions between states before and after waypoints. Furthermore, it proposes a rolling optimization interception trajectory generation strategy, which uses the optimized solution of the previous prediction cycle as the initial guess for the next round of optimization, improving the accuracy of maneuvering target prediction and ensuring the dynamic response of the final interception trajectory.
[0075] 3. Generate interception trajectories for the passing points and segments.
[0076] From the starting point to the... For each path segment, a solution framework based on the hp-adaptive Radau pseudospectral method is used, which divides each stage... time interval pass The transformation is mapped to the standard interval [-1, 1]. At each stage, N+1 discrete points are selected to approximate the state and control variables using a global interpolation polynomial. The constraints of the dynamic differential equation are transformed into algebraic constraints using a differential matrix. The integral term in the objective function is discretized into a weighted summation form using numerical integration, which, together with path constraints and boundary constraints, constitutes a nonlinear programming problem. An adaptive grid optimization strategy is employed during the solution process. The grid density is dynamically adjusted based on the approximation error. The grid is subdivided in regions of drastic state changes, while a higher-order approximation is used in smooth regions. Iterative optimization is performed using the current solution as the initial value until the error requirement is met. Finally, continuous optimal trajectories are obtained through interpolation reconstruction, ensuring the generation of smooth and feasible path points.
[0077] 4. Generate the interception trajectory for the rolling optimized interception segment. This is also based on the numerical solution framework of the hp-adaptive Radau pseudospectral method, and employs a local programming strategy to handle target maneuvering. In each prediction time domain... Inside, the interceptor predicts the future of the target based on its current state. For the trajectory within a time period, construct a locally finite time-domain optimization model. This generates the future trajectory. Predict the target trajectory over a time period but only execute ( The interception planning results, among which It is a prediction of time. This involves controlling the time frame. Through this periodic iteration, dynamic interception of the target is achieved within the final control cycle. A Warm-Start strategy is employed within each control cycle, using the optimized solution from the previous cycle as the initial guess for the current optimization, improving the accuracy of the search direction for each iteration. Simultaneously, by setting upper limits on the number of grid points, control parameter ranges, and the maximum number of iterations, the scale of a single optimization problem is limited, ensuring the real-time requirements of rolling optimization while maintaining computational accuracy.
[0078] The above target interception trajectory generation process can adapt to the dynamic updates of the path points.
[0079] 5. Perform waypoint update judgment. First, determine if the interception is complete. If not, check if any new waypoints have been added. If a new waypoint appears, update the interception phase, replan based on the latest waypoint sequence, and immediately update the interception planning model for the next phase. If no waypoint update is determined, continue using the original waypoint sequence for either over-the-waypoint interception or rolling optimization interception. This mechanism ensures the flexibility and adaptability of the interception strategy in dynamic environments, enabling the interceptor to autonomously adjust the route when mission conditions change, maintaining effective interception capability against maneuvering targets at all times.
[0080] This invention also provides a maneuvering target interception trajectory generation system considering waypoint constraints, employing the aforementioned maneuvering target interception trajectory generation method, comprising:
[0081] The parameter setting unit sets the initial parameters for the interceptor's status, target motion model library, and waypoint location;
[0082] The target trajectory prediction unit predicts the trajectory of the maneuvering target based on the interceptor's status, the target's motion model, and the location of the waypoints.
[0083] The multi-stage interception planning model construction unit divides the interception path into a passing-through interception segment and a rolling optimization interception segment, with the last waypoint as the dividing point. Based on the trajectory prediction results of the maneuvering target, a multi-stage interception planning model is constructed, which includes a passing-through interception segment planning model and a rolling optimization interception segment planning model.
[0084] The intercept trajectory generation unit generates intercept trajectories based on a multi-stage intercept planning model, including: for interception segments that pass through points, solving the planning model of the interception segment that passes through points to generate the intercept trajectory of the interception segment that passes through points; for rolling optimization interception segments, within each cycle, the interceptor solves the planning model of the rolling optimization interception segment based on the current target state to generate the intercept trajectory for future time periods.
[0085] The interception judgment unit determines whether the interceptor has completed the interception based on the interception trajectory of the interception segment passing through the waypoints. If the interceptor has not completed the interception, it determines whether a new waypoint has been added. If a new waypoint appears, the target trajectory prediction unit, the multi-stage interception planning model construction unit, and the interception trajectory generation unit are re-executed to generate a new interception trajectory. If no new waypoint appears, and if the current waypoint is the last waypoint, the interceptor navigates according to the trajectory of the rolling optimized interception segment and dynamically intercepts the target in the last control cycle. If the current waypoint is not the last waypoint, the interception continues according to the interception trajectory generated by the interception segment passing through the waypoints.
[0086] This invention takes into account both the constraints of waypoints during the interception process and the target maneuvering mode at the end of the interception, ensuring the accurate arrival of waypoints, the smooth transition of states before and after waypoints, and the dynamic response of the interception trajectory at the end. It can be applied to medium- and long-range target interception missions in the air or at sea.
[0087] Example
[0088] To better illustrate the purpose and function of the present invention, the present invention will be described in further detail below with reference to specific examples.
[0089] Consider a scenario where an unmanned aerial vehicle (UAV) intercepts a mid-range maneuvering target. The UAV needs to pass through two waypoints before intercepting the target, and the target performs a Singer maneuver. The target's initial state is... ,in m, m, m / s, m / s, m / s², target attenuation coefficient Acceleration standard deviation m / s².
[0090] S1. Initial system parameter settings.
[0091] S11. Set the initial state of the unmanned aerial vehicle (UAV). The initial state vector of the UAV is defined as follows: .in The initial position in the coordinate system. The initial heading angle, These represent the forward speed, drift speed, and bow roll rate in the ship's coordinate system, respectively. This represents the initial accumulated energy consumption. Let the initial state be... m, m, rad, m / s, rad / s, J.
[0092] S12. Set waypoints. The two waypoints are as follows: ,in m, m, m, m.
[0093] S13. Target Motion Model Library Settings. The model library includes uniform linear motion models (CV model), uniformly accelerated linear motion models (CA model), uniform circular motion models (CT model), and Singer maneuvering models (Singer model). Key parameters for each motion model are shown in Table 1. At the start of the interception planning, according to the maneuvering target prediction strategy of this invention, the unmanned aerial vehicle defaults to using the uniform linear motion model for the target.
[0094] Table 1 Key parameters of each model in the target motion model library of the present invention.
[0095]
[0096] S2, Predicting Maneuvering Targets.
[0097] As the UAV passes each waypoint, online observation of the target's motion state is initiated simultaneously. The system calculates the distance prediction error between the interceptor and the target in real time based on the current maneuvering model and records the cumulative error throughout the entire phase. The initial target maneuvering model is the CV model. When the UAV passes the first waypoint and moves towards the second waypoint, it predicts the target's maneuvering type and makes a decision. The target actually performs a movement closer to the Singer maneuver, and the prediction error using the CV model significantly exceeds a preset threshold. Therefore, the current CV model is determined to be inaccurate, and the system immediately switches from the model library to the Singer model, which best matches the observed data, for subsequent target trajectory prediction.
[0098] S3, Multi-stage interception planning modeling.
[0099] S31. Unmanned Aerial Vehicle (UAV) Modeling. The dynamic model of the UAV is defined as follows:
[0100] ,
[0101] in, For velocity vectors, This is the vector of control force and torque.
[0102] S32. Interception planning and modeling for transit points. For this task containing two preset transit points, the task is divided into three phases: Phase 1: From the initial time... At the terminal time ,from Exercise to Phase 2: From the initial moment At the terminal time ,from Exercise to Phase 3: From the initial moment At the terminal time ,from Exercise to ( For the first two stages, the interception planning modeling for transit points must satisfy dynamic constraints. State variable constraints and control variable constraints Terminal constraints are set up at the route points. Set stage connection constraints between two adjacent stages. And construct performance metrics for the route segments:
[0103]
[0104] Among them, tracking error weights Terminal error weights Energy consumption weight .
[0105] S33. Rolling optimization interception segment planning and modeling. Rolling optimization interception segment planning and modeling are performed for stage 3. This stage should satisfy dynamic constraints. State variable constraints Control variable constraints Prediction time domain constraints Target motion prediction constraints Intercepting terminal constraints And construct performance metrics for the interception phase:
[0106]
[0107] Among them, tracking error weight Terminal error weights Energy consumption weight .
[0108] S4. Interception trajectory generation.
[0109] S41. Trajectory Generation for Passing Through Waypoints. Based on the optimal control model for passing through waypoints constructed in S32, a global optimization approach is adopted to solve the multi-stage optimal control problem in one go. Considering the task time of the entire passing through-waypoint stage, a complete optimal trajectory from the starting point to all waypoints is generated, ensuring accurate arrival at waypoints and smooth transitions between stages. The hp-adaptive Radau pseudospectral method is used for numerical solution to generate a globally optimal trajectory that accurately satisfies the waypoint constraints. The time interval of each stage is defined. pass The transformation map is mapped to the standard interval [-1, 1]. Selection is made at each stage. Discrete points, including Radau point and a left endpoint . State variables and control variables Approximate these expressions using global Lagrange interpolation polynomials:
[0110]
[0111] in and These are the Lagrange interpolation basis functions for state and control, respectively. ,in and These are the Lagrange interpolation basis functions for state and control, respectively. (At the collocation point) The differential matrix is used to pass through the point. Discrete with algebraic constraints: Continue to apply Radau integral weights to performance metrics. Perform discrete approximation: .
[0112] By combining all discretized algebraic constraints, path constraints, boundary constraints, and discrete performance indices, a large-scale sparse nonlinear programming problem is constructed. The Snopt solver is then used to perform a global, one-time solution to this NLP problem, yielding the discrete optimal solution. and Then, the optimal state trajectory in continuous time is reconstructed using the Lagrange interpolation basis function. and optimal control trajectory To further improve accuracy, an hp-adaptive mesh optimization strategy is adopted. This strategy analyzes the approximation error of the current solution in each time period, and subdivides the mesh or increases the polynomial order for sections with large errors until the predetermined error tolerance is met across the entire time domain.
[0113] S42. Rolling Optimization Segment Interception Trajectory Generation. Based on the rolling optimization interception segment planning model constructed in S33, local optimization is employed, and an online adaptive interception of maneuvering targets is achieved through a rolling time-domain control strategy. In this optimization stage, the time-domain prediction... Control time domain Interception radius In each prediction time domain Internally, predict the future based on the current target state. The trajectory within time is similarly discretized into an NLP problem using the hp-adaptive Radau pseudospectral method, as in S41. However, only the optimization solution for the first control step is executed, and then a new round of optimization is immediately restarted based on the updated system state and target state, forming a closed-loop rolling mechanism of "prediction-optimization-execution," thereby achieving dynamic prediction and adaptive interception of the target motion. To improve real-time performance, a Warm-Start strategy is adopted: using the optimal solution of the previous cycle as the initial guess for the current cycle optimization, significantly accelerating the solution convergence.
[0114] S5, Interception End Judgment.
[0115] Calculate the real-time distance between the interceptor and the target. If the interception is successful, the optimization continues; otherwise, it checks whether further waypoints are needed before optimization. In this simulation, when the unmanned aerial vehicle reaches the first waypoint... At that time, calculate the relative distance between path point 1 and the target. and Comparison Then, it is determined whether there is a new waypoint, and the result is that there is a new waypoint. Returning to step S2, multi-stage global trajectory planning is performed again based on the updated waypoint sequence. If there are no new waypoints and the current waypoint is not the last waypoint, interception is carried out according to the trajectory generated in step S41. Similarly, when the unmanned vehicle reaches the second waypoint... If it is determined that there are no new waypoints and the last waypoint has been reached, then interception is initiated according to the trajectory generated in step S42, and rolling optimization interception begins. At the end of the final interception, the real-time distance between the interceptor and the target is calculated. The interception was deemed successful. Thus, the complete trajectory generation from the starting point through the preset waypoints to the final interception of the mobile target was completed. The simulated interception trajectory is as follows: Figure 2 As shown in the figure, the velocity-time curves at each stage during the simulation are as follows: Figure 3 As shown in the figure, the curves of the control quantity changing with time at each stage are as follows: Figure 4 As shown, the energy change curve over time throughout the entire process is as follows: Figure 5 As shown.
[0116] This invention constructs a multi-stage interception planning model based on target maneuver prediction results, designs interception trajectory generation strategies for both the waypoint segment and the rolling optimization interception segment, and provides interception trajectory generation rules under dynamic waypoint updates. Compared with existing technologies, this invention simultaneously considers waypoint constraints during the interception process and the target maneuvering mode in the final interception stage, ensuring accurate arrival at waypoints, smooth transitions between states before and after waypoints, and dynamic response of the final interception trajectory. It can be applied to medium- and long-range target interception missions in the air or at sea.
[0117] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A method for generating interception trajectories for maneuvering targets considering waypoint constraints, characterized in that, include: Step 1: Set the initial parameters for the interceptor's status, target motion model library, and waypoint locations; Step 2: Predict the trajectory of the maneuvering target based on the interceptor's status, target motion model, and waypoint location; Step 3: Using the last waypoint as the dividing point, the interception path is divided into a waypoint interception segment and a rolling optimization interception segment. A multi-stage interception planning model is constructed based on the maneuver target trajectory prediction results. The multi-stage interception planning model includes a waypoint interception segment planning model and a rolling optimization interception segment planning model. Step 4: Generate the interception trajectory based on the multi-stage interception planning model, including: for the interception segment that passes through the waypoint, solve the planning model of the interception segment that passes through the waypoint to generate the interception trajectory of the segment that passes through the waypoint; for the rolling optimization interception segment, within each cycle, the interceptor solves the planning model of the rolling optimization interception segment based on the current target state to generate the interception trajectory for future time periods. Step 5: The interceptor navigates and intercepts based on the interception trajectory of the interception segment passing through the waypoints. When the interceptor passes through each waypoint, it determines whether the interception is complete. If the interception is not complete, it determines whether a new waypoint has been added. If a new waypoint appears, steps 2-4 are re-executed to generate a new interception trajectory. If no new waypoint appears, and if the current waypoint is the last waypoint, the interceptor navigates according to the trajectory of the rolling optimized interception segment and dynamically intercepts the target in the last control cycle. If the current waypoint is not the last waypoint, the interception continues according to the interception trajectory generated by the interception segment passing through the waypoints. The planning model for the interception segment via the transit point is as follows: ； in, For the performance indicators of the route segments, These are adjustable weighting coefficients. For the first The start time of the phase, For the first The end time of the phase, For the intercepting party The position vector at time , For the goal The position vector at time , For the first The position vectors of the points along the way For the first Energy consumed by the interceptor in each phase; The performance indicators The constraints include: Dynamic constraints ; State variable constraints ; Control variable constraints ; Terminal constraints ; Phase transition constraints ; in, For the first stage The derivative of the state vector at time t, For the first stage The state vector at time t, For the first stage The control input vector at time t, This is the state transition function. This refers to the upper and lower bounds of the state variables throughout the entire interception process. This refers to the upper and lower bounds of the control variables throughout the entire interception process. For the first The position vector of the interceptor at the end of the phase. For the first At the initial moment of the phase, For the first The position vectors of the points along the way For the first The state of the interceptor at the initial moment of the phase. For the first The state of the interceptor at each stage terminal.
2. The method for generating interception trajectories for maneuvering targets considering waypoint constraints according to claim 1, characterized in that, The interceptor's state includes the interceptor's position and the interceptor's motion state. The target motion model library includes uniform linear motion model, uniformly accelerated linear motion model, uniform circular motion model, and Singer maneuver model.
3. The method for generating interception trajectories for maneuvering targets considering waypoint constraints according to claim 2, characterized in that, The interceptor is an unmanned aerial vehicle, and the initial value of the interceptor's state is... ,in The initial position in the coordinate system. The initial heading angle, These represent the forward speed, drift speed, and bow roll rate in the ship's coordinate system, respectively. This represents the initial accumulated energy consumption.
4. The method for generating interception trajectories for maneuvering targets considering waypoint constraints according to claim 1, characterized in that, Step 2 specifically includes: At the start of the interception, the initial target motion model is used to predict the trajectory of the initial maneuvering target. As the interceptor passes each waypoint, the distance prediction error between the interceptor and the target is calculated and analyzed in real time. If the error is always lower than the preset threshold, the current target motion model is used to predict the trajectory of the maneuvering target. Otherwise, the target motion model that best matches the actual observation data of the target is selected from the target motion model library to predict the trajectory of the maneuvering target.
5. The method for generating interception trajectories for maneuvering targets considering waypoint constraints according to claim 1, characterized in that, The rolling optimization interception segment planning model is as follows: ； in, It is a performance metric for the rolling optimization interception segment. This is the start time of the current control cycle. It predicts the length of the time domain. It predicts the terminal time in the time domain. Is the interceptor at any moment? The planar position vector, Is the interceptor at any moment? The planar position vector, The goal is at all times The predicted position vector, The goal is at all times The predicted position vector, For the energy consumption of the intercepting party, These are adjustable weighting coefficients; The performance indicators The constraints include: Dynamic constraints ; State variable constraints ; Control variable constraints ; Prediction Time Domain Constraints ; Target motion prediction constraints ; Intercepting terminal constraints ; in, For the first stage The derivative of the state vector at time t, For the first stage The state vector at time t, For the first stage The control input vector at time t, This is the state transition function. This refers to the upper and lower bounds of the state variables throughout the entire interception process. This refers to the upper and lower bounds of the control variables throughout the entire interception process. To predict the minimum length in the time domain, To predict the maximum length in the time domain, Let be the target motion prediction function. The current observed target state, The attenuation coefficient of the target model. The radius of successful interception. This is the terminal moment of the rolling interception process. Is the interceptor at any moment? The planar position vector, The goal is at all times The predicted position vector.
6. The method for generating interception trajectories for maneuvering targets considering waypoint constraints according to claim 1, characterized in that, Step 4 uses the hp-adaptive Radau pseudospectral method to solve the planning model for the interception segment via the waypoint and the rolling optimization interception segment planning model.
7. The method for generating interception trajectories for maneuvering targets considering waypoint constraints according to claim 6, characterized in that, For the rolling optimization interception segment, a Warm-Start strategy is adopted in each control cycle, using the optimization solution of the previous cycle as the initial guess for this optimization, and achieving dynamic interception of the target in the last control cycle.
8. The method for generating interception trajectories for maneuvering targets considering waypoint constraints according to claim 1, characterized in that, If the real-time distance between the interceptor and the target is less than a set value, the interception is considered successful.
9. A trajectory generation system for intercepting maneuvering targets considering waypoint constraints, characterized in that, The method for generating interception trajectories for maneuvering targets according to any one of claims 1-8 includes: The parameter setting unit sets the initial parameters for the interceptor's status, target motion model library, and waypoint location; The target trajectory prediction unit predicts the trajectory of the maneuvering target based on the interceptor's status, the target's motion model, and the location of the waypoints. The multi-stage interception planning model construction unit divides the interception path into a passing-through interception segment and a rolling optimization interception segment, with the last waypoint as the dividing point. Based on the trajectory prediction results of the maneuvering target, a multi-stage interception planning model is constructed, which includes a passing-through interception segment planning model and a rolling optimization interception segment planning model. The intercept trajectory generation unit generates intercept trajectories based on a multi-stage intercept planning model, including: for interception segments that pass through points, solving the planning model of the interception segment that passes through points to generate the intercept trajectory of the interception segment that passes through points; for rolling optimization interception segments, within each cycle, the interceptor solves the planning model of the rolling optimization interception segment based on the current target state to generate the intercept trajectory for future time periods. The interception judgment unit determines whether the interceptor has completed the interception based on the interception trajectory of the interception segment passing through the waypoints. If the interceptor has not completed the interception, it determines whether a new waypoint has been added. If a new waypoint appears, the target trajectory prediction unit, the multi-stage interception planning model construction unit, and the interception trajectory generation unit are re-executed to generate a new interception trajectory. If no new waypoint appears, and if the current waypoint is the last waypoint, the interceptor navigates according to the trajectory of the rolling optimized interception segment and dynamically intercepts the target in the last control cycle. If the current waypoint is not the last waypoint, the interception continues according to the interception trajectory generated by the interception segment passing through the waypoints.