Flexible intercept net space posture prediction and calculation method

Abstract

The present application relates to the field of flexible net dynamics prediction and launch control, in particular to a kind of flexible intercepting net space attitude prediction and calculation method, the nominal step is tried by fixing the force state of rope, the trajectory in step is reconstructed according to the elongation and its change rate of interval two ends, the relaxation-tightening event is positioned, and is recovered, segmented integration and repositioned according to the event in order;After energy closed check, the centroid of net body, main shaft and effective opening area are synthesized, the target state is synchronized, and the launch time or initial speed of traction not executed is adjusted.The present application positions the rope state event by the zero-crossing of trajectory in step, segmented integration according to causal order and energy check, combines attitude and target timing matching closed-loop correction launch parameters.

Description

Technical Field

[0001] This invention relates to the field of flexible net dynamics prediction and launch control technology, specifically to a method for predicting and calculating the spatial attitude of a flexible interceptor net. Background Technology

[0002] Flexible interception nets are a type of non-rigid capture device that relies on a traction mass to deploy flexible netting, thereby covering and constraining moving targets. The net typically consists of numerous nodes and rope units that only bear axial tension, characterized by its small storage volume, large deployment coverage, and good contact cushioning. Online attitude prediction and launch timing control of flexible interception nets are used to estimate the net's center of mass, net orientation, and effective opening area during launch, deployment, and approach to the target, providing a basis for setting the triggering time and initial velocity of the traction mass.

[0003] In missions where the target rapidly approaches the capture area, the time from the launch of the traction mass block to the formation of a usable capture area on the net is typically very short, and target tracking, execution feedback, and attitude calculation each have their own timestamps. The net is not constantly under tension during deployment; the same rope experiences slack and tautness as tension disturbances propagate, and the state transitions of adjacent areas have a clear sequential relationship. Therefore, the controller not only needs to determine whether the net can ultimately unfold, but also whether the net has formed a sufficient effective area and maintains an appropriate orientation when the target enters the capture envelope.

[0004] Current online calculations typically employ fixed step sizes, updating the force state only at the end of each step based on the rope length. To meet real-time control requirements, the calculation step size is generally set according to the control cycle, making it difficult to cover the minute timescales of rope state switching. When multiple switching occurs consecutively within a calculation step, or when the rope is first tightened and then relaxed, the length states at the beginning and end of the step may be the same, and related changes are easily missed; multiple switching events that should occur sequentially may also be concentrated at the end of the step. The resulting net deployment process will exhibit near-simultaneous force on adjacent areas and sudden increases in local tension, causing the predicted time when the effective opening area reaches the required value to deviate from the actual time. If the controller adjusts the launch based on this result, the net may not be fully deployed, the net may not be aligned, or the net may have already been prematurely retracted when the target arrives, making it easy for the target to pass through the net edge or uncovered areas. If a microsecond-level small step size is used uniformly throughout the deployment process to avoid the above phenomena, it will significantly increase the computational load of tens of thousands of nodes and rope elements, making it difficult to continuously output attitude within a millisecond-level control cycle. Therefore, the existing technology mainly suffers from the problem of distorted prediction of the effective deployment time of the net in high-speed deployment and capture scenarios, resulting in a mismatch between the launch timing and the target arrival time. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a method for spatial attitude prediction and calculation of a flexible interceptor net, comprising: S101, reading node states, rope topology, and material parameters, and correcting initial conditions according to measured traction speed and launch angle; calculating the current interval by fixing the tension or slack state of the rope unit that only transmits axial tension, and obtaining the event indication quantities and rates of change at both ends, wherein the event indication quantity is the ratio of axial elongation to natural length; S102, reconstructing the intra-step trajectory using the event indication quantities and rates of change, locating the effective zero crossing compatible with the current force state according to the trajectory monotonic interval, and writing the switching time into the candidate event queue; S103 1. Select the earliest switching time, restore the starting point of the interval and fix the state to re-integrate; after the zero crossing is verified, keep the node position and velocity continuous and update the force state, and relocate the remaining events based on the updated state until the nominal step ends; S104. Compare the change of mechanical energy of the nominal step with the work done by external forces to verify the energy closure, subdivide the non-closed sub-intervals and repeat the event processing, and if the verification fails, do not output the result of this step; S105. Synthesize the net body attitude based on the node states that have passed the verification, extrapolate the target state to the attitude time, and adjust the unexecuted launch time or traction initial velocity according to the order in which the predicted attitude meets the capture conditions and the target enters the capture envelope.

[0006] Compared to existing prediction methods that use fixed-step continuous integration and ignore the details of rope tension and slack switching, this invention can identify and accurately handle the switching of force states within a step during the deployment of a flexible interceptor net, reducing missed events, false switching, timing reversals, and the resulting attitude prediction deviations. By recovering and re-integrating at event boundaries and dynamically repositioning subsequent events, the node motion remains continuous before and after switching and conforms to the physical law that the rope only bears tension. Through energy closure verification and unqualified result blocking mechanisms, the invention avoids the accumulation of numerical errors that result in superficially reasonable but physically distorted attitude results. Furthermore, it matches the reliable net attitude with the target state at the same moment and adjusts the launch time or initial traction velocity that has not yet been executed, thereby forming a closed loop from dynamic prediction to launch control. This improves the time matching degree between the deployment attitude of the interceptor net and the target's arrival at the capture area, enhancing the accuracy, stability, and safety of online capture control in complex environments.

[0007] Furthermore, during initialization, the state is set to either tensioned or relaxed based on the sign of the event indicator; the trial calculation uses the velocity Werley integral, first updating the trial calculation endpoint position with the resultant force of the node at the starting point of the interval, then recalculating the node resultant force based on this position and the fixed stress state, and updating the trial calculation endpoint velocity with the acceleration at both ends of the interval; the tension of the relaxation unit is kept at zero, the tension unit calculates the tension according to the actual axial elongation, and the continuous environmental load is included in the node resultant force.

[0008] Compared to existing methods that uniformly apply elastic force to all rope elements or arbitrarily change the force state during integration, this invention avoids unrealistic compressive forces generated by slack ropes and coordinates the updating of node positions, resultant forces, and velocities under fixed force conditions, making the calculation results more accurately reflect the unilateral force characteristics of the flexible net. At the same time, incorporating continuous environmental loads into the resultant forces of nodes helps reduce trajectory deviations caused by neglecting external disturbances, balancing online calculation efficiency and node state prediction accuracy, and providing stable and reliable interval endpoint data for subsequent switching event positioning.

[0009] Furthermore, the intra-step trajectory is reconstructed using cubic Hermitian interpolation based on the event indicators and their rates of change at both ends of the interval; monotonic intervals are divided by the effective stationary points and interval endpoints of the intra-step trajectory, and the zero-crossing of each monotonic interval is checked; when the trajectory is tangent to the zero line but does not change its sign, it is not considered a switch, and the first switch with zero-crossing direction compatibility is retained according to the current force state.

[0010] Compared to existing methods that rely solely on the positive and negative changes of event indicators at both ends of the integration step to determine state switching, this invention can reconstruct the intra-step change trend using the values ​​and rates of change at both ends, and check for zero crossings within the monotonic interval, thereby discovering valid intra-step switching that may still exist even when the endpoints have the same sign. By excluding cases where the signal is only tangent to the zero line without a sign change, and retaining only the first zero crossing compatible with the current force state, false switching and repeated switching can be reduced, improving the completeness and directional accuracy of rope tension and slack event recognition.

[0011] Furthermore, for the monotonic intervals that cross zero, Newton's iterative method with interval constraints is first used to locate the root. When the iteration exceeds the monotonic interval or the derivative is too small, binary positioning is used instead. The numerical confirmation band is used to suppress repeated switching near the zero point, and a valid event is confirmed only after the trajectory leaves the numerical confirmation band along the switching direction. When the positioning does not converge, the zero-crossing interval is searched equally. If the time accuracy requirement is still not met, the starting point of the interval is restored and the interval is shortened.

[0012] Furthermore, after reaching the earliest switching time, the event indication quantity of the corresponding rope unit is recalculated, and the switching time is corrected by repeated integration in a fixed state and binary positioning when deviating from the zero point; the remaining candidate events are invalidated after the earlier event is updated; events with a time difference not exceeding the positioning error are sorted by time and unit number, and only events that simultaneously satisfy the zero point position and the correct zero crossing direction are updated in groups at the same event boundary.

[0013] Compared to existing methods that process events sequentially according to an initial candidate list without verifying their validity, this invention can reconfirm the zero-point position and zero-crossing direction when the earliest event arrives, and remove invalid candidate events from processing after state update, avoiding old candidate events from disrupting the true dynamic causal order. For multiple switches that occur approximately simultaneously in time, this invention adopts deterministic sorting and group update methods, which can reduce the differences in calculation results caused by different processing orders, more realistically reflect the working conditions of multiple ropes being simultaneously tensioned or relaxed, and improve the consistency and repeatability of simulation results.

[0014] Furthermore, after each event update, the node internal forces are recalculated and the remaining interval is trial-calculated; when the number of event boundaries exceeds the preset upper limit or when repeated checks without time advancement cause contradictory switching, the interval starting point is restored and the interval is shortened; when the calculation is not completed even after reaching the preset minimum interval length or the maximum number of consecutive backtracks, the nominal step is marked as invalid and its results are stopped from being output.

[0015] Compared to existing methods that continuously iterate and output abnormal results when dense events or contradictory transitions occur, this invention can recalculate the remaining interval based on the new node internal forces after each state update, and use interval backoff and shortening mechanisms to resolve event storms, time-limited transitions, and contradictory transitions. After reaching the computing capacity boundary, the nominal step is explicitly marked as invalid and output is stopped, which can prevent incomplete or unstable node states from continuing to propagate to the attitude prediction and control links, thereby improving the fault controllability and output reliability of online computing.

[0016] Furthermore, the mechanical energy change includes the total kinetic energy change of all nodes and the elastic energy change of the rope unit in a taut and elongated state; the work done by the external force is determined based on the external force and node displacement of each sub-interval; when the difference between the mechanical energy change and the work done by the external force is not sufficient to meet the allowable condition of using the larger of the absolute values ​​of the starting mechanical energy and the work done by the external force as a reference, the sub-interval with the most obvious energy non-closure is located and subdivided, and then trial calculation, trajectory reconstruction, event location and segmented advancement are re-executed.

[0017] Furthermore, when the model includes damping, the damping dissipation energy is subtracted from the energy change; when the calculation range is extended to target contact, the energy change caused by the contact force or contact impulse is included; after each subdivision, the energy change of the entire nominal step is recalculated, and if the preset subdivision rounds are still not closed, the state is restored to the end state of the previous effective nominal step, and the unclosed state is prohibited from participating in attitude update and launch control.

[0018] Furthermore, the three-dimensional centroid of the mesh is calculated based on the node mass. An inertial tensor is constructed based on the position of the node relative to the centroid, and symmetric eigenvalue decomposition is performed to obtain the principal axis direction. Based on the continuity of the principal axis direction in the previous moment, the in-mesh direction is determined by combining the average extension direction of the principal axis and the boundary nodes in the previous moment when the difference between the two inertial eigenvalues ​​is less than a preset threshold. The effective opening area is obtained by the normal projection of the mesh surface. When the mesh surface is folded, the overlapping area of ​​the mesh projection polygon is only counted once and the hole area is deducted.

[0019] Furthermore, the timestamped target position and velocity are extrapolated to the attitude frame time, and the time interval for first meeting the capture conditions is determined by the minimum effective opening area, the allowable net surface normal deviation, and the allowable centroid deviation; the triggering is advanced or delayed, or the initial traction velocity is increased or decreased according to the time sequence; for independently triggered traction mass blocks, only those that have not yet been launched are adjusted; when the target data is invalid, the attitude is not updated, the execution feedback is saturated, or the energy verification fails, the most recent valid parameters are maintained, and the launch timing is re-aligned after the data is recovered.

[0020] The technical effects of this invention are as follows: The core innovation of this invention lies in constructing an event-driven prediction and launch closed-loop control mechanism for the unilateral force characteristics of flexible interception nets. Taking the axial elongation state of the rope as the event basis, it accurately locates and processes the tension and relaxation switching in sequence. Through state recovery, segmented re-integration, and energy closure verification, it ensures the physical credibility of the node motion results. On this basis, it stably extracts the net's centroid, principal axis, and true effective opening area, matches them with the target state after time synchronization, and dynamically adjusts the launch time or traction speed that has not been executed. This reduces the missed events, energy drift, and attitude misjudgment in traditional continuous integration, and improves the reliability of online prediction and the accuracy of interception control. Attached Figure Description

[0021] Figure 1 This is a flowchart of a method for spatial attitude prediction and calculation of a flexible interceptor network according to an embodiment of the present invention;

[0022] Figure 2 This is a schematic diagram of the location of the in-step trajectory reconstruction and force state switching time in an embodiment of the present invention. Detailed Implementation

[0023] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings. Figure 1 As shown, the method specifically includes the following steps: In this embodiment, the flexible interception net has an unfolded size of 20m × 20m, and is discretely arranged along the two net lines at natural intervals of 0.1m, forming 40,401 concentrated mass nodes and 80,400 rope units. Each rope unit transmits only axial tensile force, not axial compressive force, bending moment, or torque. The net line has an elastic modulus of 80 GPa, a material density of 970 kg / m³, a cross-sectional area of ​​1.5 mm², and a natural length of 0.1m per unit. The mass of each rope unit is determined according to its natural length, material density, and cross-sectional area, and is evenly distributed to the two end nodes; when multiple rope units are connected to the same node, the concentrated mass of the node is obtained by adding the masses distributed to the connected units. The mass of the traction mass block is separately included in the corresponding boundary node.

[0024] The initial velocity of the traction mass is set to 15 m / s, and the launch angle is set to 20°. In different capture missions, the initial traction velocity can be set within the range of 5 m / s to 30 m / s, and the launch angle can be set within the range of 5° to 45°. When the launch status detection data is valid, the actual traction velocity and actual launch angle are used to correct the initial conditions, instead of continuing to use the nominal parameters in the launch command.

[0025] Node status includes node position and node speed ,in Number the nodes. Rope element data includes two end node numbers and the natural length. Elastic modulus Cross-sectional area and force status labels ,in Number the rope unit. Status label. This indicates that the unit is in a taut state. This indicates that the unit is in a relaxed state.

[0026] Nominal step size The nominal step size is set to 0.5 ms and can be adjusted within the range of 0.1 ms to 1 ms depending on the control cycle and attitude output resolution. This nominal step size is used to control the overall advancement of the net's attitude timing and does not require scaling down to the time scale required for the tension wave to pass through a single rope unit. During the calculation, only the nominal step that actually involves force state switching is internally subdivided.

[0027] The computing platform employs an 8-core, 3.0GHz main processor and parallel computing units with over 4096 parallel processing cores and 16GB of video memory. The main processor is responsible for nominal step scheduling, event sorting, interval rollback, and control data output, while the parallel computing units are responsible for calculating the geometry, tension, and node internal forces of all rope elements. Node positions and velocities are stored as double-precision floating-point numbers. The data storage area includes at least a current state buffer, a trial state buffer, a rollback state buffer, and an event queue. The capacity of a single candidate record in the event queue is no less than the total number of rope elements to prevent record loss during near-simultaneous switching of a large number of net cables.

[0028] S101. Establish the state of the rope unit and complete the trial calculation of the current interval.

[0029] At the start of the calculation, all node positions, node velocities, node masses, rope element topology relationships, and material parameters are read, and the initial velocity direction of the boundary nodes is corrected based on the measured velocity of the traction mass block and the launch angle.

[0030] For connection nodes and nodes rope unit The normalized axial elongation is used as the event indicator for the change of force state: ; in, and These are the position vectors of the two end nodes, in meters; The natural length of the rope unit, in meters; It is a dimensionless quantity. This indicates that the element length is greater than the natural length, and that the geometric conditions for generating axial tension are met. This indicates that the unit length is less than the natural length and does not generate axial pressure.

[0031] The tension of the rope element is calculated based on a unidirectional force relationship: ; in, This refers to axial tension, expressed in N. This is the elastic modulus, expressed in Pa. The cross-sectional area is expressed in m². This relationship ensures that relaxed elements do not apply spurious compressive forces to the nodes.

[0032] At the initial moment, when When, set the unit state to the tense state; when When a cell is in a relaxed state, its state is set to relaxed. In subsequent calculations, the cell state is not repeatedly modified based on the result of a single floating-point calculation, but is updated only after a valid zero-crossing event is confirmed.

[0033] In the current calculation interval Within the trial calculation, the state labels of all elements are kept unchanged, and a trial calculation is completed. The trial calculation adopts the velocity Verlet integration method: first, the nodal acceleration is calculated based on the nodal resultant force at the starting point of the interval, and then the position of the trial calculation endpoint is updated; then, the nodal resultant force is recalculated based on the trial calculation endpoint position and the current unchanged element state; finally, the velocity of the trial calculation endpoint is updated using the accelerations at the starting point of the interval and the trial calculation endpoint.

[0034] During the trial calculation, the tension of the relaxation element is kept at zero, while the tension of the tensioning element is calculated based on the actual axial elongation. Gravity, traction force, and other continuous environmental loads are simultaneously included in the resultant force at the nodes. The target contact load is not directly applied across intervals in this step; when it is necessary to calculate the capture process after contact, the moment of contact start is treated as an independent event boundary.

[0035] Calculate at the start and end points of the interval respectively. and its rate of change over time The rate of change over time is obtained by dividing the projection of the relative velocity of the end nodes onto the current rope axis by the natural length. This calculation directly uses existing node positions and velocities without adding new nodal force assessments.

[0036] This step outputs the current starting point status of the interval, the trial ending point status, and all rope elements at both ends of the interval. and It is used for locating events within a step.

[0037] If the node position or velocity is not finite, the node velocity exceeds the preset physical upper limit of 100 m / s, or critical boundary conditions are missing, the current trial calculation result will not be processed further. The calculation program will revert to the most recent valid state and pause the output of new launch control parameters.

[0038] S102, Reconstruct the intra-step trajectory and locate the moment of force state switching.

[0039] Compare only the start and end points of the interval It can only reliably identify cases where the endpoints have opposite signs. When a cell first tightens and then relaxes within an interval, or first relaxes and then tightens and returns to its original state, the two ends of the interval may retain the same sign. To identify this type of intra-step switching, this step reconstructs the intra-step trajectory using the event indicators at both ends of the interval and their rates of change.

[0040] Let the length of the current calculation interval be... Normalized time is ,but The value ranges from 0 to 1. Rope unit The trajectory within this interval is represented in cubic Hermite form: ; in, and These are the event indicators for the start and end points of the interval, respectively; and These represent the rates of change at the corresponding time points; For the reconstructed trajectory within the interval.

[0041] right The derivative yields a quadratic function. Calculate the real roots of this quadratic function in the range of 0 to 1, and denote the effective stationary points and the endpoints of the intervals as several monotonic intervals. Then, check whether any intervals cross zero to identify the following cases: (1) The two ends of the interval have opposite signs, and there is at least one zero crossing within the interval; (2) The two ends of the interval have the same sign, but the internal extreme value crosses the zero line, and there are two zero crossings inside the interval; (3) If the trajectories are tangent at the zero line but the sign does not change, this is not considered a change in the force state; (4) The trajectory is at zero near the starting point of the interval, but the direction of change is inconsistent with the current force state. At this time, the starting point of the interval is taken as the moment of the event to be confirmed.

[0042] For confirmed monotonic intervals crossing zero, Newton's iteration with interval constraints is first used to locate the root. When the Newton iteration exceeds the current monotonic interval or the derivative becomes too small, the bisection method is used to continue locating the root. The time error for root location is no more than 1 μs, and the maximum number of iterations is set to 12.

[0043] Let the normalized root be... The corresponding event time is The event log includes the event time. Rope unit number, current status, expected switching status, and zero-crossing direction.

[0044] For the same rope element, even if the reconstructed trajectory contains multiple roots, only the first zero-crossing compatible with the current state is added to the candidate event queue in this round. For example, when the current element is in a relaxed state, the first zero-crossing from a negative value to a positive value is prioritized; when the current element is in a taut state, the first zero-crossing from a positive value to a negative value is prioritized. After the event is processed, subsequent events are repositioned based on the updated node state to avoid directly using invalid subsequent roots.

[0045] To suppress repeated switching near zero caused by floating-point errors, the numerical confirmation bandwidth is set to [value]. After the trajectory crosses zero, it should leave the confirmation zone in the corresponding direction for the zero-crossing to be considered a valid switch. A unit that has completed one switch will not accept a repeating event in the opposite direction until it leaves the confirmation zone again. This setting is only used to suppress numerical jitter and does not change the principle that the event timing is still based on the zero point as the boundary.

[0046] If the root localization of the Hermite trajectory fails to converge within 12 iterations, the corresponding monotonic interval is divided into 16 smaller intervals. The sign changes are checked segment by segment, and binary localization is performed on the smaller intervals where zero crossings are found. If a time accuracy of 1 μs is still not achieved, the current interval is rejected, the interval starting state is returned, the interval length is halved, and the calculation is retried.

[0047] If no valid candidate events exist in any of the rope units, the trial endpoint state of the current interval can be directly accepted without further subdivision.

[0048] like Figure 2 As shown in the figure, the three sets of trajectories sharing the current calculation interval illustrate three cases: endpoints with different signs, endpoints with the same sign but internal extreme values ​​crossing the zero line, and trajectories tangent to the zero line.

[0049] S103. Proceed in stages according to the causal sequence of events.

[0050] When the candidate event queue is not empty, select the earliest event time from the queue. The original trial endpoint is only used for event detection and is not directly used as the final calculation result. The calculation program restores the current interval's starting state and, under the condition that all cell states are fixed, starts from... Reintegration .

[0051] arrive Then, the actual value of the corresponding rope unit is recalculated. When the deviation of the actual value from zero does not exceed When the deviation exceeds this range, the event time is accepted; when the deviation exceeds this range, the starting point of the current interval is compared with... The time interval is re-established, and the event timing is corrected through repeated integration in a fixed state and binary positioning. This process is used to avoid Hermite trajectory errors causing state transitions to occur at positions significantly deviating from the natural length.

[0052] When the event occurs, the node position and velocity remain continuous; no artificial velocity jumps are applied to the nodes. The calculation program only modifies the force state label of the corresponding rope element and reassembles the node internal forces according to the new state. Because the switching occurs... Nearby, the rope tension either builds up from zero or decays to zero at the event boundary, without the need to set additional impulse.

[0053] For multiple candidate events with a time difference greater than the root positioning error, they are processed strictly according to their event time order. After earlier events are processed, all events in the original candidate queue that have not yet occurred become invalid. Their original predicted times are not directly used; instead, they are considered in the remaining interval. The trial calculation and trajectory reconstruction are then re-executed. Therefore, subsequent event times are obtained again under the condition that the upstream rope state has changed.

[0054] For candidate events whose time difference does not exceed the root positioning error, they are first sorted by event time and element number, and then each candidate element is checked to see if it simultaneously satisfies the zero-point position and the correct zero-crossing direction in the current node state. Events that pass the check can be updated in groups at the same time boundary; events that fail the check are not updated and are repositioned in the remaining interval. This process avoids unconditionally synchronizing events that are only close to each other, while allowing switching that actually occurs simultaneously at geometrically symmetrical positions to be processed at the same boundary.

[0055] Each time an event update is completed, the internal forces of the nodes are recalculated, and a new trial calculation is performed for the remaining time interval. This process continues until no valid switching events exist at the end of the current nominal step. Ultimately, a nominal step is divided into several sub-intervals consisting of the nominal step start point, each event time, and the nominal step end point. The rope force state within each accepted sub-interval remains unchanged.

[0056] In this embodiment, the maximum number of event boundaries allowed in a single nominal step is set to 256, and each event boundary can contain multiple confirmed simultaneous events. The capacity of the event record buffer is set to 80,400 records to store candidate records for all rope units within a trial interval. If the number of event boundaries exceeds 256, it indicates that the current nominal step size is insufficient to stably distinguish the event propagation process, and the calculation program returns to the nominal step starting point and halves the nominal step size.

[0057] No more than 6 rounds of time-independent repeated checks are allowed at the same event moment. If 6 consecutive rounds generate contradictory switching results near the same time, the current interval is considered to have numerical jitter, and the interval is returned to its starting point and shortened. The minimum interval length is set to 1 μs, and a maximum of 8 consecutive backtrackings are allowed. If the calculation cannot be completed after reaching the above limits, the current nominal step is marked as invalid, and the result of this step is not output to subsequent control processes.

[0058] After the above processing, the earlier rope switching can change the force and motion trajectory of subsequent nodes. Subsequent events are no longer directly executed based on the one-time prediction of the nominal step starting point, thus preserving the order of propagation of tension disturbances along the network line.

[0059] S104. Perform energy closure check and handle hidden events.

[0060] After all subintervals of the current nominal step have been integrated, an energy closure check is performed on the starting and ending points of the nominal step.

[0061] First, calculate the total kinetic energy of all nodes at the nominal step start and end points. Then, calculate the elastic energy stored in the taut rope element with positive axial elongation. Elastic energy of relaxed elements is not included. Next, calculate the work done by gravity, traction, and other continuous loads based on the external forces and node displacements in each sub-interval. When external forces change over time, the average value of the external forces at both ends of the sub-interval is used to calculate the corresponding work.

[0062] When the model includes damping, damping dissipation energy should be deducted separately; when the calculation range is extended to after target contact, the work done by contact force or the energy change caused by contact impulse should be included. Unaccounted damping or contact dissipation must not be incorrectly judged as missed rope switching detection.

[0063] The total change in kinetic and elastic energy within the nominal step is compared with the work done by the external force. The current nominal step passes the verification when the absolute value of the difference between the two does not exceed 0.5% of the reference energy. The reference energy is the larger of the mechanical energy at the starting point of the nominal step and the absolute value of the work done by the external force in this step; when both are less than 1J, 0.005J is used as the minimum allowable difference.

[0064] If the energy difference exceeds the allowable range, check the kinetic energy change, elastic energy change, and external work done in each sub-interval to determine the sub-interval with the most obvious energy non-closure. Divide this sub-interval in half and re-execute state trial calculation, trajectory reconstruction, event localization, and segmented advancement in the two new sub-intervals.

[0065] After each binary search, the energy change of the entire nominal step is recalculated. If the recalculation meets the allowable range, the corrected nominal step result is accepted; otherwise, the sub-interval with the most obvious energy non-closure is further subdivided. A single nominal step can perform a maximum of 8 rounds of energy verification subdivision.

[0066] If the verification fails after 8 rounds of subdivision, the system reverts to the endpoint state of the previous valid nominal step and marks the current nominal step as unclosed. The unclosed state does not participate in attitude timing updates, nor is it used to generate new launch velocities or launch timing commands.

[0067] Energy verification does not replace geometric zero-crossing judgment, but is used to check complex intra-step motions that were not identified by the three-dimensional trajectory reconstruction. In particular, when the actual trajectory crosses zero more than three times in a certain interval, or when the local motion cannot be fully described by the three-dimensional trajectory, the incorrect force state usually manifests as an inconsistency between the change in mechanical energy and the work done by the external force, thus triggering interval refinement.

[0068] S105, Synthetic net body attitude and feedback launch timing control.

[0069] After energy verification, the node position and velocity of the nominal step endpoint are written into the current state buffer, and the net body attitude is synthesized based on the node configuration.

[0070] First, the 3D centroid of the network is calculated based on the node mass. Then, a 3D inertial tensor is constructed using the positions of all nodes relative to the centroid, and symmetric eigenvalue decomposition is performed to obtain the three principal axis directions of the network. Continuity checks are performed on the principal axis directions between adjacent nominal steps. If the principal axis obtained from the eigenvalue decomposition is opposite to the principal axis direction of the previous time step, the current principal axis is inverted to avoid instantaneous attitude reversal due to uncertain eigenvector signs.

[0071] When two inertial eigenvalues ​​are too close, causing instability in the corresponding principal axis direction, the eigenvector of the current frame is not used directly. Instead, the direction within the current mesh surface is determined by the principal axis direction of the previous frame and the average extension direction of the mesh boundary nodes. The mesh surface normal is determined by the cross product direction of the two principal axes within the mesh surface, and its positive and negative directions are also continuous with the normal of the previous frame.

[0072] Project all nodes along the normal to the mesh surface onto the current mesh coordinate system. When the mesh body is approximately planar unfolded, the area of ​​the outer contour formed by the projection of the boundary nodes is used as the effective open area. When the mesh surface has obvious folds, each mesh cell is projected as a two-dimensional polygon, and the overlapping part is counted only once. The hole area not covered by the mesh is deducted to obtain the actual effective open area, avoiding the overestimation of the area caused by directly using the convex hull.

[0073] Each nominal step outputs one frame of attitude data, including at least: timestamp, three-dimensional centroid position and centroid velocity, three principal axis directions, mesh normal, effective opening area, number of events in the current nominal step, whether the energy check passed, maximum rope tension and corresponding cell number.

[0074] Attitude data is written to a circular buffer with a capacity of 10 seconds. Target tracking data is input at a frequency of 100Hz and carries a sampling timestamp. The controller extrapolates the target state to the current attitude frame based on the target position and velocity, avoiding direct comparison of data with different timestamps.

[0075] Based on the target size, relative velocity, and allowable capture attitude, the minimum effective opening area, allowable net surface normal deviation, and allowable centroid deviation are preset. The controller determines the time interval from the predicted attitude sequence in which the net first meets the above conditions and compares it with the time when the target is expected to enter the capture envelope.

[0076] When the predicted time for the net to reach its effective deployment state is later than the time when the target enters the capture envelope, the controller will advance the trigger time or increase the initial velocity of the traction mass block before launch is executed. When the predicted time for the net to reach its effective deployment state is too early, the trigger time will be delayed or the initial traction velocity will be reduced. Within a single control cycle, the adjustment amount for the launch time shall not exceed 2ms, the adjustment amount for the initial traction velocity shall not exceed 0.5m / s, and the adjustment amount for the launch angle shall not exceed 0.5°.

[0077] For multiple independently triggerable traction mass blocks, the initial parameters of mass blocks that have already been launched are no longer modified; only the mass blocks that have not yet been launched are adjusted. After all mass blocks have been launched, the attitude calculation results are only used for acquisition state prediction and subsequent processing, and no unexecutable initial parameter correction instructions are generated.

[0078] The launch control cycle is set to 1ms, and control commands are sent via the CANFD interface. The traction speed sensor sampling frequency is 2000Hz, and the launch angle sensor sampling frequency is 1000Hz. When the actual initial traction velocity deviates from the command value by more than 0.2m / s for three consecutive control cycles, or the actual launch angle deviates from the command value by more than 0.5° for three consecutive control cycles, the boundary conditions are reinitialized using the measured values, and subsequent attitude predictions are updated.

[0079] If target tracking data is invalid for three consecutive sampling cycles, attitude results are not updated for more than one control cycle, launch actuator feedback is saturated, or the current nominal step fails energy verification, the controller retains the most recently valid parameters and does not continue to increase the initial traction velocity. Launch commands that have not yet been executed are canceled if target tracking data remains invalid. After target data, attitude data, and execution feedback are restored to validity for five consecutive control cycles, launch timing alignment is re-performed.

[0080] Fixed-step-size calculations tend to concentrate multiple switches within the same nominal step at the end of the step, resulting in near-simultaneous tensioning in adjacent areas and sudden increases in local tension. This embodiment divides the space into sub-intervals based on event time and relocates the remaining events after each state update, resulting in a tension propagation sequence and mesh attitude change process that more closely approximates the global small-step-size reference result. No-event nominal steps still only perform one trial calculation and one acceptance operation, thus eliminating the need to uniformly adopt microsecond-level step sizes throughout the entire unfolding process.

Claims

1. A method for spatial attitude prediction and calculation of a flexible interceptor network, characterized in that, The method includes: S101, reading node status, rope topology and material parameters, correcting initial conditions according to measured traction speed and launch angle; calculating the current interval by fixing the tension or slack state of the rope unit that only transmits axial tension, and obtaining the event indication quantity and rate of change at both ends, wherein the event indication quantity is the ratio of axial elongation to natural length; S102. Reconstruct the intra-step trajectory using the event indication and rate of change, locate the effective zero crossing compatible with the current force state according to the monotonic interval of the trajectory, and write the switching time into the candidate event queue. S103. Select the earliest switching time, restore the starting point of the interval and fix the state to re-integrate; after the zero crossing is verified, keep the node position and velocity continuous and update the force state, and relocate the remaining events based on the updated state until the nominal step ends. S104. Compare the change in nominal mechanical energy with the work done by external forces to verify energy closure. Subdivide non-closed sub-intervals and repeat event processing. If the verification fails, do not output the result of this step. S105. Based on the verified node states, synthesize the network attitude, extrapolate the target state to the attitude time, and adjust the unexecuted launch time or traction initial velocity according to the order in which the predicted attitude meets the capture conditions and the target enters the capture envelope.

2. The method for spatial attitude prediction and calculation of a flexible interceptor network according to claim 1, characterized in that, During initialization, the state is set to either tensioned or relaxed based on the sign of the event indicator. The trial calculation uses the velocity Werley integral. First, the position of the trial endpoint is updated with the resultant force of the nodes at the starting point of the interval. Then, the resultant force of the nodes is recalculated based on the position and the fixed force state. Finally, the velocity of the trial endpoint is updated with the acceleration at both ends of the interval. The tension of the relaxation unit is kept at zero, the tension of the tensioning unit is calculated according to the actual axial elongation, and the continuous environmental load is included in the resultant force of the nodes.

3. The method for spatial attitude prediction and calculation of a flexible interception network according to claim 2, characterized in that, The intra-step trajectory is reconstructed using cubic Hermitian interpolation based on the event indicators at both ends of the interval and their rates of change. Divide the monotonic intervals by the effective stationary points and interval endpoints of the in-step trajectory, and check the zero crossings of each monotonic interval respectively; If the trajectory is tangent to the zero line but the sign does not change, it is not considered a switch, and the first switch with zero-crossing direction compatibility is retained according to the current force state.

4. The method for spatial attitude prediction and calculation of a flexible interceptor network according to claim 3, characterized in that, For the monotonic intervals that cross zero, Newton's iteration with interval constraints is first used to locate the root. If the iteration exceeds the monotonic interval or the derivative is too small, binary search is used to locate the root. The numerical confirmation band is used to suppress repeated switching near the zero point, and a valid event is only confirmed after the trajectory leaves the numerical confirmation band along the switching direction. If the localization fails to converge, the search interval is divided into equal parts. If the time accuracy requirement is still not met, the starting point of the interval is restored and the interval is shortened.

5. The method for spatial attitude prediction and calculation of a flexible interceptor network according to claim 1, characterized in that, After reaching the earliest switching time, the event indication quantity of the corresponding rope unit is recalculated, and the switching time is corrected by repeated integration in a fixed state and binary positioning when it deviates from the zero point; The earlier event update invalidates the remaining candidate events; Events with time differences not exceeding the positioning error are sorted by time and unit number, and only events that simultaneously satisfy the zero position and correct zero crossing direction are updated in groups at the same event boundary.

6. The method for spatial attitude prediction and calculation of a flexible interception network according to claim 5, characterized in that, After each event update, recalculate the nodal internal forces and test the remaining interval; When the number of event boundaries exceeds the preset limit or when conflicting switching occurs due to repeated checks without time progress, restore the starting point of the interval and shorten the interval. If the calculation is not completed even after reaching the preset minimum interval length or the maximum number of consecutive backtracks, the nominal step is marked as invalid and the output of its result is stopped.

7. The method for spatial attitude prediction and calculation of a flexible interceptor network according to claim 1, characterized in that, The mechanical energy change includes the total kinetic energy change of all nodes and the elastic energy change of the rope unit in a taut and elongated state; The work done by the external force is determined based on the external force and nodal displacement in each sub-interval. When the difference between the change in mechanical energy and the work done by external forces is not sufficient to meet the allowable condition of using the larger of the absolute values ​​of the starting mechanical energy and the work done by external forces as a reference, the sub-interval with the most obvious energy non-closure is located, subdivided, and then trial calculation, trajectory reconstruction, event location, and segmented advancement are re-executed.

8. The method for spatial attitude prediction and calculation of a flexible interceptor network according to claim 7, characterized in that, When the model includes damping, the damping dissipation energy is subtracted from the energy change. When the calculation scope is extended to target contact, the energy change caused by the work done by the contact force or the contact impulse is taken into account. After each subdivision, the energy change of the entire nominal step is recalculated. If the state is still not closed after the preset subdivision rounds, it is restored to the end state of the previous valid nominal step, and the unclosed state is prohibited from participating in attitude update and launch control.

9. The method for spatial attitude prediction and calculation of a flexible interceptor network according to claim 1, characterized in that, The three-dimensional centroid of the network is calculated based on the node mass. An inertial tensor is constructed based on the position of the node relative to the centroid, and symmetric eigenvalue decomposition is performed to obtain the principal axis direction. Based on the fact that the main axis maintains a continuous direction in the previous moment, the direction within the mesh is determined by combining the average extension direction of the main axis and the boundary node in the previous moment when the difference between the two inertial characteristic values ​​is less than a preset threshold. The effective opening area is obtained by projecting the mesh surface normally. When the mesh surface is folded, the overlapping area of ​​the mesh projection polygon is counted only once and the hole area is deducted.

10. The method for spatial attitude prediction and calculation of a flexible interceptor network according to claim 9, characterized in that, The timestamped target position and velocity are extrapolated to the attitude frame time, and the time interval for the first time to meet the capture conditions is determined by the minimum effective opening area, the allowable net surface normal deviation and the allowable centroid deviation. The triggering time may be advanced or delayed, or the initial traction velocity may be increased or decreased, depending on the timing of the event. For independently triggered traction mass blocks, only those that have not yet been launched are adjusted; When the target data is invalid, the attitude is not updated, the execution feedback is saturated, or the energy verification fails, the most recent valid parameters are retained, and the launch timing is re-aligned after the data is recovered.

Images