A method and system for determining a safety separation between a manned aircraft turning leg and an unmanned aircraft straight leg

Abstract

The application discloses a kind of manned aircraft turning course and unmanned aircraft straight course safety interval determination method and system.The method comprises: obtaining manned aircraft turning course, unmanned aircraft straight course, aircraft performance, traffic flow and operation error data;The turning course of manned aircraft is segmented modeling for entry segment, platform turning segment and exit segment;The total error of manned aircraft and unmanned aircraft is respectively constructed;Collision risk chain is constructed based on airborne collision avoidance system;After decision consultation trigger, the horizontal, vertical and mixed collision avoidance maneuver of unmanned aircraft is simulated, and the closest point is determined;At the closest point, whether the aircraft collision box overlaps is judged based on position error sampling, the collision probability is obtained, and finally compared with target safety level, the safety interval meeting target safety level is output.

Description

Technical Field

[0001] This invention relates to the field of airspace operation safety risk assessment technology, and in particular to a method and system for determining the safe distance between manned aircraft turning routes and unmanned aerial vehicle straight routes. Background Technology

[0002] With the development of urban air traffic and the low-altitude economy, drones are being deployed in large numbers in scenarios such as airport shuttles, short-distance urban transportation, and emergency transport. Airport terminal areas typically have a high density of traditional manned aircraft. Manned aircraft often need to turn during approach, departure, waiting, or turning maneuvers. Therefore, when drones fly in a straight line in this area, they may encounter spatial proximity, conflict, or even collision risks with the turning routes of traditional manned aircraft.

[0003] Existing collision risk models typically abstract aircraft paths into straight segments and then assess safe separations using analytical or simulation models. However, in manned aircraft turning scenarios, the aircraft's track-keeping ability, heading changes, and relative motion relationships differ from those in straight-line level flight scenarios. Furthermore, collisions in actual operation are not directly caused by a single position error but usually involve multiple stages; a final collision determination only occurs if each stage fails sequentially. Existing methods do not adequately consider the coupling risk between the manned aircraft's turning process and the UAV's straight-line process, potentially leading to incorrect estimates of the true collision risk between the manned aircraft's turning path and the UAV's straight-line path, and making it difficult to quantify the collision probability at the closest point after collision avoidance maneuvers.

[0004] Therefore, it is necessary to propose a method for determining the safe distance between manned aircraft turning routes and unmanned aircraft straight routes. By assessing the operational risks of the aircraft, the minimum safe distance between the manned and unmanned aircraft routes can be calculated. Summary of the Invention

[0005] Purpose of the invention: To address the problems in existing technologies, such as the inability of the straight-line trajectory assumption to accurately characterize the risks of manned aircraft turning operations, insufficient modeling of the entire collision mitigation chain, and difficulty in quantifying the collision probability at the closest point after collision avoidance maneuvers, this invention proposes a method and system for determining the safe distance between manned aircraft turning routes and UAV straight-line routes based on operational risk assessment.

[0006] Technical solution:

[0007] This invention proposes a method for determining the safe interval between manned aircraft turning routes and unmanned aerial vehicle (UAV) straight-line routes, characterized by comprising:

[0008] S1: Collect the performance parameters of the aircraft, including manned and unmanned aircraft; establish discrete-time simulation models of the turning routes of manned aircraft and the straight routes of unmanned aircraft. The turning route of manned aircraft includes a straight segment, an entry segment, a turning segment, and an exit segment, while the straight route of unmanned aircraft includes a straight segment; set traffic flow conditions, design the total error of manned and unmanned aircraft, and simulate the turning routes of manned aircraft and the straight routes of unmanned aircraft in the simulation models respectively; set the safety interval for the turning routes of manned aircraft and the straight routes of unmanned aircraft, and generate the simulation scenario corresponding to the safety interval;

[0009] S2: In the current simulation scenario, enumerate the candidate maneuver strategies of the UAV and use the simulation model to generate the predicted trajectory, including the predicted trajectory of the manned aircraft turning route and the predicted trajectory of the UAV corresponding to the candidate maneuver strategies.

[0010] Calculate the squared slant distance function between the predicted trajectory of the UAV and the predicted trajectory of the manned aircraft turning route, record the discrete time interval in which the derivative of the squared slant distance function first changes from negative to non-negative, and search for the closest point between the manned and UAVs within this discrete time interval; if there are multiple candidate maneuver strategies, retain the predicted trajectory of the UAV with the largest slant distance function at the closest point.

[0011] S3: Based on the airborne collision avoidance system, calculate the collision risk value between the manned aircraft and the unmanned aircraft at the closest point and determine whether the current simulation scenario meets the target safety level;

[0012] S4: Change the safety interval in the simulation model, regenerate the simulation scene, and repeat steps S2 to S3 to obtain the minimum safety interval that meets the target safety level.

[0013] Furthermore, the collection of aircraft performance parameters and the establishment of discrete-time simulation models for manned aircraft turning routes and unmanned aircraft straight-line routes include:

[0014] The initial motion state of the aircraft in the simulation model is set according to the performance parameters, which include the aircraft's starting position, nominal flight altitude, nominal flight speed, flight acceleration, target turn rate, turn rate acceleration, and heading angle; the target turn rate and turn rate acceleration are zero on straight sections.

[0015] Let the motion state of aircraft i at the k-th discrete time be... ,in, and Indicates the aircraft's position coordinates. Indicates horizontal velocity. Indicates the heading angle. Indicates vertical velocity. Indicates the turning rate;

[0016] Let the step size of the discrete time be . The aircraft i updates its motion state from the k-th discrete time step to the k-th discrete time step according to the equation of motion. The motion states at discrete moments are simulated, and the equations of motion are expressed as follows:

[0017]

[0018] in, Indicates horizontal acceleration. Represents vertical acceleration. The turning rate acceleration is represented by the fourth-order Runge-Kutta integral method, and the motion state update is implemented using the turning rate acceleration method.

[0019] Furthermore, the total error between manned and unmanned aircraft includes navigation system error and flight technology error;

[0020] The navigation system error of manned aircraft is determined by the navigation and positioning system, and the same distribution model is used in the straight section, the entry section, the turning section, and the exit section. The flight technical error of manned aircraft is represented by a Gaussian distribution in the straight section and the turning section, and by a heavy-tailed distribution in the entry section and the exit section. The navigation system error and the flight technical error of unmanned aircraft are both represented by a Gaussian distribution.

[0021] Furthermore, the safety interval is either a lateral interval or a vertical interval, wherein the lateral interval refers to the distance in the horizontal plane between the centerline of the manned aircraft's straight-line segment and the centerline of the UAV's straight-line flight path, and the vertical interval refers to the absolute value of the difference between the nominal flight altitude of the manned aircraft and the nominal flight altitude of the UAV.

[0022] Furthermore, the candidate maneuvering strategy of the UAV is constructed based on the onboard collision avoidance system and includes at least one of horizontal turning, vertical maneuvering, and deceleration.

[0023] Furthermore, the discrete time interval in which the derivative of the recorded squared slope distance function first changes from negative to non-negative includes:

[0024] Manned aircraft turning trajectory prediction in time The predicted location is Prediction speed is The predicted trajectory of the drone's straight-line flight path in time The predicted location is Prediction speed is ;

[0025] The squared slope distance function Represented as:

[0026]

[0027] Set time window ,in This is the simulation start time. Given a preset window length, the squared slope distance function is calculated within the window at a fixed distance from the walking time. first derivative When it first appears At that time, the interval The discrete time interval is determined.

[0028] Furthermore, the search for the closest point of contact between the manned and unmanned aircraft includes:

[0029] Define the discrete time interval as the search interval. The binary search method is used for iterative calculation to approximate the closest point in time.

[0030] The iterative calculation includes: calculating the midpoint of the search interval. First derivative of the squared slope distance function at point subscript Indicates an iterative index; if Update the boundaries of the search range. ,make Proceed to the next iteration; if Update the boundaries of the search range. ,make Then proceed to the next iteration;

[0031] Repeat the iterative calculation until the length of the search interval is reached. , Given a preset time convergence threshold, output the moment when the midpoint of the search interval in the current iteration is the closest point. .

[0032] Furthermore, the calculation of the collision risk value between the manned aircraft and the unmanned aircraft at the closest point includes:

[0033] Calculate the probability of a collision between a manned aircraft and an unmanned aircraft. :

[0034]

[0035] in This indicates the probability that the airborne collision avoidance system will enter the tactical mitigation phase. This indicates the probability that the airborne collision avoidance system will enter the collision avoidance phase. This represents the probability that the manned aircraft and the drone will overlap in volume due to positional uncertainty at their closest point; the collision risk value is the probability that the manned aircraft and the drone will collide. .

[0036] Furthermore, determining whether the current simulation scenario meets the target safety level includes:

[0037] The collision risk value calculated in the current simulation scenario is compared with the preset collision risk assessment safety target. If the current simulation scenario risk value is greater than the preset collision risk assessment safety target, the corresponding lateral / vertical interval is considered not to meet the target safety level requirements.

[0038] On the other hand, this invention also proposes an operational risk assessment system for manned aircraft turning routes and unmanned aerial vehicle straight-line routes, including:

[0039] The simulation module is used to collect performance parameters of aircraft, including manned and unmanned aircraft; establish discrete-time simulation models of manned aircraft turning routes and unmanned aircraft straight routes, with the manned aircraft turning route including a straight segment, an entry segment, a turning segment, and an exit segment, and the unmanned aircraft straight route including a straight segment; set traffic flow conditions, design the total error of manned and unmanned aircraft, and simulate the manned aircraft turning route and the unmanned aircraft straight route in the simulation model respectively; set the safety interval for the manned aircraft turning route and the unmanned aircraft straight route, and generate the simulation scenario corresponding to the safety interval;

[0040] The closest point prediction module is used to enumerate candidate maneuver strategies for the UAV in the current simulation scenario, generate predicted trajectories using the simulation model, including predicted trajectories of manned aircraft turning routes and predicted UAV trajectories corresponding to candidate maneuver strategies; calculate the squared slant distance function between the predicted UAV trajectory and the predicted manned aircraft turning route trajectory, record the discrete time interval in which the derivative of the squared slant distance function first changes from negative to non-negative, and search for the closest point time between the manned aircraft and the UAV within this discrete time interval; if there are multiple candidate maneuver strategies, retain the UAV predicted trajectory with the largest slant distance function at the closest point time;

[0041] The risk assessment module is used to calculate the collision risk value between manned and unmanned aircraft at the closest point based on the airborne collision avoidance system, and to determine whether the current simulation scenario meets the target safety level.

[0042] The safety interval output module is used to change the safety interval in the simulation model, regenerate the simulation scene, and repeatedly call the trajectory generation module, the closest point prediction module, and the risk assessment module to obtain the minimum safety interval that meets the target safety level.

[0043] Beneficial effects:

[0044] This invention incorporates manned aircraft turning tracks into route operation risk assessment, reflecting the differences in track maintenance capabilities during the entry, platform turn, and exit phases. Combined with the collision avoidance failure of the Airborne Collision Avoidance System Xu (ACAS Xu), a conditional probability chain is formed, characterizing the entire process of a collision event and effectively improving the accuracy of route operation risk assessment.

[0045] This invention quantifies the collision probability by sampling the position error at the closest point and determining the overlap of collision boxes, thereby obtaining the route risk value. It then iteratively calculates and outputs the minimum safety interval (including lateral and vertical intervals) that meets the Target Level of Safety (TLS) requirements, providing a basis for UAV route planning and integrated operation safety assessment in airport terminal areas. Attached Figure Description

[0046] Figure 1 This is a flowchart of the method of the present invention;

[0047] Figure 2 This is a segmented diagram of a manned aircraft turning route;

[0048] Figure 3 A schematic diagram illustrating the geometric relationship between the turning path of a manned aircraft and the straight-line path of an unmanned aircraft.

[0049] Figure 4 Timeline of the ACAS (Airborne Collision Avoidance System) Xu;

[0050] Figure 5 A flowchart for selecting collision avoidance strategies between manned aircraft turning routes and unmanned aircraft straight-line routes;

[0051] Figure 6 This is a schematic diagram of the conflict and collision mitigation phase.

[0052] Figure 7 A diagram illustrating the collision avoidance process for ACAS Xu;

[0053] Figure 8 The Monte Carlo simulation shows the positional relationship between manned and unmanned aircraft;

[0054] Figure 9 This is a schematic diagram of the minimum horizontal / vertical interval output in this embodiment. Detailed Implementation

[0055] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments. Figure 1 The flowchart shown is a process for the method of the present invention, which specifically includes the following steps:

[0056] S1: Establish a simulation model that includes manned aircraft turning routes and unmanned aerial vehicle straight-line routes.

[0057] In this embodiment, the UAV is specifically an electric vertical take-off and landing aircraft (eVTOL). In the scenario designed in this invention, a manned aircraft enters a turning segment from a straight segment, completes the turn, and then enters a subsequent straight segment, while the eVTOL flies along a predetermined straight flight path. Therefore, the simulation model of the eVTOL's straight flight path is a straight trajectory model; the simulation model of the manned aircraft's turning flight path includes a pre-turn straight segment, an entry segment, a platform turning segment, and an exit segment. The turning rate of the pre-turn straight segment is 0, and the turning rates of the entry segment, platform turning segment, and exit segment are determined according to a preset target turning rate and turning rate acceleration. Specifically, the construction of the simulation model includes the following sub-steps:

[0058] (1.1) Collect data on manned aircraft turning routes, eVTOL straight routes, aircraft performance, traffic flow and operational errors.

[0059] The eVTOL uses the size, speed, acceleration, climb rate, descent rate, and maximum turning rate of the known or to be evaluated models, and is determined in conjunction with materials such as the ACAS Guide Airborne Collision Avoidance Systems. The eVTOL performance parameters in this embodiment are shown in Table 1.

[0060] Table 1 eVTOL performance parameters in this embodiment

[0061] parameter Value parameter Value long 6.05 m Width 5.73 m high 1.933 m Vertical acceleration 0.25 g Maximum rate of climb 6 m / s Maximum rate of decline 5 m / s Maximum acceleration 5 m / s² Maximum deceleration -5 m / s² Maximum level flight speed 90 km / h Speed ​​that cannot be exceeded 105 km / h Target turning rate 3° / s Turning rate acceleration 1° / s²

[0062] Obtain the target turning rate of the manned aircraft turning route Turning rate acceleration Total Angle The specific settings for the turning parameters of the manned aircraft in this embodiment are shown in Table 2.

[0063] Table 2. Human-machine turning parameters in this embodiment

[0064] parameter Value Target turning rate 3° / s Turning rate acceleration 1° / s² Total angle 90°

[0065] The turning process is divided into the entry section, the plateau turning section, and the exit section: the turning rate gradually increases from 0 to [missing information] in the entry section. The turning rate remains constant during platform turning sections. The turning rate in the exit section is changed from... Gradually decreasing to 0. This segmentation method can reflect the difference in track maintenance between the manned aircraft's turn transition phase and the stable turn phase.

[0066] (1.2) Based on the data obtained in the previous step, establish simulation models of manned aircraft turning routes and eVTOL straight routes.

[0067] For ease of standardized description, a three-dimensional Cartesian coordinate system O-XYZ is established, where the X and Y axes are perpendicular to each other and lie in the horizontal plane, and the Z axis represents the altitude direction. The position of the aircraft when entering the segment to be evaluated is used as the coordinate reference point O.

[0068] Let the motion state of aircraft i at the k-th discrete time be represented as: :

[0069]

[0070] in, and These represent the aircraft's position coordinates. Indicates horizontal velocity. Indicates the heading angle. Indicates vertical velocity. Indicates the turning rate. At a time step of... Under these conditions, the aircraft's motion state is updated according to the following formula:

[0071]

[0072] in, Indicates horizontal acceleration. Represents vertical acceleration. This represents the turning rate acceleration. The above state update is implemented using the fourth-order Runge-Kutta integral method or other equivalent numerical integration methods. In this embodiment, a discrete time step of 1 second is used when generating the nominal trajectory. In subsequent detailed simulations of candidate collision avoidance maneuvers, a time step of 0.5 seconds or less is used.

[0073] The simulation model takes manned aircraft turning path data, eVTOL straight-line path data, aircraft performance parameters, traffic flow parameters, and simulation duration as input. It calculates the position, velocity, heading, turn rate, and vertical velocity of both the manned aircraft and eVTOL at each time step, outputting the time-series trajectories of the aircraft (manned aircraft and eVTOL). Subsequent steps will superimpose the total system error onto the nominal time-series trajectories and calculate the relative motion relationships of the aircraft under different candidate maneuvering strategies.

[0074] Figure 2This is a segmented schematic diagram of the manned aircraft turning trajectory in the simulation model, including the pre-turn straight section, the entry section, the platform turning section, and the exit section. The entry section begins when the turning rate becomes greater than 0 and ends when the turning rate reaches the target turning rate; the platform turning section maintains the target turning rate; the exit section begins when the turning rate begins to decrease and ends when the turning rate decreases to 0. The section preceding the entry section is the pre-turn straight section. The manned aircraft's heading angle and position are updated hourly according to the motion state equations to obtain the complete nominal trajectory of the manned aircraft turning path.

[0075] In this embodiment, the manned aircraft maintains a given horizontal speed within each of the above flight segments, while maintaining a constant nominal altitude; that is, the horizontal acceleration of the manned aircraft satisfies... The vertical velocity satisfies The target turning rate of the human-machine interface is set. The turning rate acceleration is The total turning angle is The turning rate on the straight section before the turn is 0; during the turn entry phase, the turning rate changes from 0 according to the turning rate acceleration. Gradually increase to the target turning rate The duration of the turn is The angle generated during the entry phase of the curve is During the platform's turning phase, the turning rate remains at the target turning rate. When the entry and exit sections are symmetrical, the duration of the platform turning phase is: During the exit phase of a turn, the turning rate changes from the target turning rate. According to the turning rate acceleration Gradually decrease to 0, the exit time is the same as the entry time.

[0076] Figure 3 This diagram illustrates the geometric relationship between the manned aircraft's turning path and the eVTOL's straight-line path in the simulation model. The eVTOL's straight-line path is determined by its starting position, nominal altitude, heading angle, and nominal flight speed. The manned aircraft enters the turning segment from the straight section before the turn and ends the turn after completing the predetermined total turn angle; the eVTOL operates along the predetermined straight-line path. During operation, the eVTOL may deviate from the nominal path (e.g., ...). Figure 3 (As shown by the dashed line corresponding to eVTOL), which in turn triggers conflict or decision-making consultation.

[0077] When no conflict is triggered, the eVTOL flies along a given straight path with a turn rate, horizontal acceleration, and vertical speed all of 0. Based on the eVTOL's initial position, nominal speed, and heading angle, the nominal trajectory of the eVTOL traveling along the straight path can be obtained using the motion state update equation.

[0078] Define horizontal spacing The distance in the horizontal plane between the nominal track centerline of the manned aircraft's straight section before turning and the nominal track centerline of the eVTOL straight route, and the vertical separation. This refers to the absolute value of the difference between the nominal flight altitude of the manned aircraft and the nominal flight altitude of the eVTOL, and the safety interval (lateral / vertical interval) is changed to construct different simulation scenarios.

[0079] (1.3) Further construct the total system error model of manned machine and eVTOL in the simulation model.

[0080] The total system error (TSE) for manned aircraft and eVTOL includes navigation system error (NSE), flight technique error (FTE), and path definition error (PDE). Since the present invention has established an accurate flight path simulation model in the aforementioned steps, the path definition error PDE is negligible relative to the navigation system error NSE and the flight technique error FTE. Therefore, the TSE is mainly determined by NSE and FTE.

[0081] For manned aircraft, the NSE (Network Sequence) is primarily determined by the navigation and positioning system, employing the same distribution model for the pre-turn straight segment, the entry segment, the platform turn segment, the exit segment, and the mid-turn segment. FTE (Field-Track Equivalent) is modeled separately for each segment: straight segment, entry segment, platform turn segment, and exit segment. For the pre-turn straight segment, the aircraft is in a relatively stable track-tracking state, and the horizontal FTE is represented by a Gaussian distribution. For the entry and exit segments, due to roll transition, heading acquisition, and short-term overshoot, outlier deviations are more likely to occur; therefore, the horizontal FTE is represented by a Student-t distribution or a heavy-tailed distribution. For the platform turn segment, the aircraft is in a relatively stable turning state, and the horizontal FTE is represented by a Gaussian distribution. The vertical FTE for each segment of a manned aircraft can be represented by a Gaussian distribution based on the vertical track-keeping characteristics. For eVTOL (Extreme Vertical Tunneling) straight segments, both the NSE and FTE are represented by Gaussian distributions.

[0082] The relationship between TSE, NSE, and FTE is as follows: When simulating the flight paths of manned aircraft and eVTOLs, the TSE obtained at each moment is added to their respective nominal positions to obtain the actual positions of manned aircraft and eVTOLs during the simulation.

[0083] (1.4) Set the route to be evaluated.

[0084] The flight segment to be evaluated includes at least a straight section and a complete curve with conflict. For example... Figure 4The diagram shows a timeline of the Airborne Collision Avoidance System Xu (ACAS Xu). If a manned aircraft and an eVTOL reach their Closest Point of Approach (CPA) within 55 seconds, and the collision boxes of the two aircraft intersect at the CPA, then a collision is considered to have occurred between the manned aircraft and the eVTOL. The collision box represents the three-dimensional shape of the aircraft in the simulation model.

[0085] If the system predicts that the two aircraft will reach the Collision Point (CPA) within 35 seconds, and the two aircraft's collision boxes intersect at the CPA, then a Resolution Advisory (RA) is triggered, and the eVTOL begins to perform collision avoidance. In this embodiment's simulation model, when the eVTOL performs candidate collision avoidance maneuvers, all motion state parameters must not exceed the boundaries defined in Table 1. If an RA is triggered in a simulation scenario, the manned aircraft continues to fly along the given turning route and does not participate in collision avoidance strategy enumeration; the collision avoidance action is performed by the eVTOL. Therefore, the manned aircraft uses a fixed route, while the eVTOL, in addition to using a straight route, also has candidate maneuver strategies.

[0086] Within the simulation duration T, the entry times of manned and eVTOL aircraft into the segment to be evaluated are generated based on the traffic flow of manned and eVTOL routes. The manned aircraft traffic flow is determined based on historical airport operational data, and manned aircraft samples are generated using the larger flow value within the historical observation period or a preset flow value. The eVTOL traffic flow is generated based on wake separation or the minimum longitudinal separation requirement of the route. The minimum longitudinal separation requirement refers to the minimum separation between two aircraft on a route, which is manually specified.

[0087] S2: For those... , In a given simulation scenario, after decision consultation is triggered, the slant distance function between the eVTOL trajectory and the manned aircraft trajectory under different maneuvering strategies is calculated. The CPA time is approximated using the bisection method, and the maneuvering strategy with the largest slant distance function at the closest point is selected as the collision avoidance strategy.

[0088] The process for this step is as follows: Figure 5 As shown, the specific steps include the following:

[0089] (2.1) In the current simulation scenario, generate the predicted aircraft trajectories corresponding to different candidate maneuver strategies.

[0090] Let the moment when RA is triggered be . Simulations were performed on the candidate maneuver strategies for eVTOL. Based on ACAS Xu, a set of candidate maneuver strategies was constructed: [horizontal turning only, horizontal turning + maximum deceleration, vertical maneuver only, horizontal turning + vertical maneuver, horizontal turning + maximum deceleration + vertical maneuver].

[0091] The number and parameters of the aforementioned candidate maneuver strategies can be increased, decreased, or adjusted according to the eVTOL model, operating rules, and the type of executable decision advice output by ACAS Xu. For example, multiple intensity levels can be set within the range of maximum permissible turning rate, maximum permissible climb rate, and maximum permissible descent rate, thereby forming a set of candidate strategies that include different maneuver directions and different maneuver intensities.

[0092] For any candidate maneuver strategy, based on the simulation model established in step S1, the manned aircraft and eVTOL are calculated respectively within the preset simulation time window. Predicted location and prediction speed within, The typical time is 35 seconds.

[0093] In this embodiment, the predicted location of the manned aircraft is represented as follows: The predicted speed is expressed as The predicted position of eVTOL under the candidate maneuver strategy is represented as follows: The predicted speed is expressed as .

[0094] (2.2) Calculate the slant range function and its rate of change under different candidate maneuver strategies.

[0095] Calculate the slant range function between the eVTOL trajectory and the manned aircraft trajectory, and find the earliest time interval where the derivative of the slant range function changes from negative to non-negative. For candidate maneuver strategies, define the relative position vector of the eVTOL relative to the manned aircraft as... The three-dimensional slant range function between the manned machine and the eVTOL is:

[0096]

[0097] To avoid directly processing the square root and simplify the calculation of the nearest point, we further define the squared slope distance function:

[0098]

[0099] The first derivative of the squared slope distance function is:

[0100]

[0101]

[0102]

[0103] when When, it indicates that the slant distance between the two aircraft is decreasing; when When this occurs, it indicates that the slant distance between the two aircraft is increasing. Therefore, when When the value changes from negative to non-negative, the corresponding time is the local minimum of the squared slope distance function, i.e., the candidate CPA time.

[0104] Using a preset discrete time step Perform a coarse search on the simulation time window: In the formula This indicates the start time of the current search time window. The values ​​for each discrete time point are calculated sequentially. When it first appears At that time, the interval The timeframe for the CPA exam was determined. This indicates the start time of the next search time window. In this embodiment, the discrete time step... Take 1 second.

[0105] (2.3) Use the bisection method to approximate the closest point (CPA) time.

[0106] The interval containing the CPA time obtained in step (2.2) is defined as the initial search interval. Read the predicted trajectory corresponding to the candidate maneuver strategy generated in step (2.1), and iteratively calculate the aircraft position, velocity, and first derivative of the square slant range function at the midpoint of the interval.

[0107] For the m-th iteration, the midpoint of the interval is represented as The first derivative of the squared slope distance function is expressed as: .like This indicates that the CPA is within the range. Therefore, Update the boundaries of the search interval, and let Proceed to the next iteration; if This indicates that CPA is within the range Therefore, Update the boundaries of the search interval, and let Proceed to the next iteration.

[0108] Repeat the binary search process described above until the length of the search interval is satisfied: ,in This is a preset time convergence threshold. In this embodiment, Set the time interval to 0.01s. Use the midpoint of the final search interval as the closest point for the candidate maneuver strategy. The slant distance of the closest point corresponding to the candidate maneuver strategy is denoted as . .

[0109] When multiple candidate maneuver strategies exist, the strategy with the largest slant range is selected as the target collision avoidance strategy based on the CPA results obtained from the multiple strategies.

[0110] S3: Calculate the probability of a collision between the manned aircraft turning route and the eVTOL straight route under the collision avoidance strategy, compare the probability with the target level of safety (TLS), and output the minimum lateral clearance / minimum vertical clearance that meets the target level of safety.

[0111] The collision process between a manned aircraft and an eVTOL aircraft can be divided into three sequentially acting mitigation phases: failure of strategic mitigation measures, failure of tactical mitigation measures, and failure of the airborne collision avoidance system (ACAS Xu). The relationship between these phases is as follows: Figure 6 As shown. Based on the above three mitigation stages, the collision risk chain of this invention is constructed as follows: strategic mitigation measures failure, tactical mitigation measures failure, ACAS, and collision avoidance failure.

[0112] The probability of a collision between a manned aircraft and an eVTOL. Represented as the product of conditional probabilities at each stage:

[0113]

[0114] in Indicates the probability of collision; This indicates the probability of entering the tactical mitigation phase after strategic mitigation measures have failed; This indicates the probability of entering the ACAS Xu RA collision avoidance phase after tactical mitigation measures fail; The probability of volume overlap between the manned aircraft and the eVTOL at the CPA point due to positional uncertainty after collision avoidance measures (hereinafter referred to as the CPA collision probability).

[0115] The probability values ​​for each mitigation stage will be explained below:

[0116] (3.1) The probability of entering the tactical mitigation phase after the failure of strategic mitigation measures :

[0117]

[0118] (3.2) Probability of entering the ACAS Xu RA collision avoidance phase after tactical mitigation measures fail :

[0119] ACAS collision avoidance logic diagram is shown below. Figure 7As shown, tactical mitigation measures and collision avoidance maneuvers are divided into six phases: surveillance, spacing service, communication, pilot response, control link, and maneuver. The surveillance phase is used to obtain the aircraft's status and complete track processing; the spacing service phase is used for conflict detection and conflict solution generation; the communication phase is used to transmit instructions to the pilot or remote operator; the pilot response phase is used for the pilot to understand the instructions and take action; the control link phase is used for transmitting control instructions to the aircraft and preparing for execution; and the maneuver phase is used for the aircraft to perform collision avoidance maneuvers.

[0120] Surveillance delay, interval service delay, communication delay, pilot response delay, and control link delay are all represented by Gaussian distributions, with the total delay time being... This is the sum of the individual delay components. Exemplary parameters are shown in Table 3.

[0121] Table 3. Time parameters of tactical mitigation process

[0122] step Mean μ / s Standard deviation σ / s Surveillance 2 0 Interval service 6.9 4.9 communication 1 2 Pilot response 4.77 3.11 Control Link 6.13 0 The above total 20.8 6.14

[0123] Total delay time The probability distribution function is: In the formula This represents the sum of the average times taken for each stage of the tactical mitigation process. This represents the sum of the time variances for each stage of the tactical mitigation process. By incorporating communication delay, interval service delay, pilot response delay, control link delay, and eVTOL maneuverability into decision-making consultation and conducting collision avoidance simulations, the closest approach point can be obtained more accurately.

[0124] The length of the straight segment before the start of the turn is determined by a conflict time threshold. In this embodiment, the straight segment corresponding to 55 seconds before the manned aircraft begins to turn is taken as the straight segment before entering the turn. For straight segment conflicts at earlier times, existing straight-line collision risk assessment methods can be used.

[0125] The estimated collision time, calculated based on the current relative positions and relative velocities of the two aircraft, is: The triggering time threshold for ACAS Xu decision-making consultation is The available time for tactical mitigation measures is .

[0126] The total time required for the tactical mitigation process is ,use This represents the remaining time from the current moment until ACAS Xu triggers RA, which is the time available for surveillance, interval services, communications, pilot response, and control link execution. It is equivalent to the available time for tactical mitigation measures mentioned earlier. .when At that time, it is assumed that the tactical mitigation measures failed to resolve the conflict before the RA was triggered. Therefore, the probability of the tactical mitigation measures failing is:

[0127]

[0128] in, This is the cumulative distribution function of the standard normal distribution. In this embodiment, , , ,but:

[0129]

[0130] when At that time, it was considered that they had directly entered the RA stage, and took .

[0131] (3.3) Collision probability of CPA after collision avoidance measures :

[0132] Figure 8 This diagram illustrates the positional relationship between the manned aircraft and the eVTOL in a Monte Carlo simulation, used to determine whether the aircraft's collision boxes overlap at the CPA (Collision Point of Approach). Both the manned aircraft and eVTOL collision boxes are represented as cylinders. The radius of the manned aircraft cylinder is determined by its maximum horizontal projection dimension, and its half-height is determined by its vertical dimension. The radius of the eVTOL cylinder is determined by its maximum length and width, and its half-height is determined by its height.

[0133] In this invention, it is assumed that the nominal location of the human-machine interface is reached when the CPA is reached. The nominal location of eVTOL is Manned aircraft position error is The eVTOL position error is The actual relative positions of the two machines can be determined by ( ). + )−( + Determine if the horizontal relative distance is not greater than the sum of the radii of the two cylinders. And the vertical relative distance is no greater than the sum of the half heights of the two cylinders. If so, it is determined that the two machines are spatially overlapping.

[0134] CPA collision probability The samples were obtained through Monte Carlo sampling, referencing the research of Yang Jin et al. (Yang Jin, Hang Xu, Wang Yanjun. Safety risk assessment of UAV operation in airport controlled airspace [J]. Acta Aeronautica Sinica, 2025, 46(11): 418-431). A maximum number of Monte Carlo samplings and a probability convergence threshold were set. When the collision probability fluctuation of multiple consecutive sampling batches was less than the set threshold, sampling was considered converged and sampling was terminated.

[0135] Specifically, at the CPA, multiple sets of samples are generated according to the position error distributions of manned aircraft and eVTOL, and spatial overlap determination is performed on each set. The proportion of samples with spatial overlap to the total number of samples is used as the criterion. Finally, a convergent value is found as the CPA collision probability.

[0136]

[0137] in It is the total number of samples. It represents the number of samples that have spatial overlap.

[0138] For a flight path operation scenario consisting of multiple manned aircraft and multiple eVTOL aircraft, the flight path operation risk value is obtained by summing the simulation duration T and the collision probabilities of all paired aircraft:

[0139]

[0140] in, This represents the number of manned and machine-generated objects generated within the simulation duration T. This indicates the number of eVTOLs, where i represents the number of human-machine indexes and j represents the number of eVTOL indexes.

[0141] The International Civil Aviation Organization (ICAO) defines TLS as "a level of risk considered acceptable under specific circumstances," typically expressed as fatal accidents per aircraft flying hour (fapfh), and stipulates that the safety objective for manned aircraft mid-air collision risk assessment is... fapfh. When the risk value of the current simulation scenario is calculated by the method of this invention... When the security level is greater than the target TLS level, the corresponding lateral movement is considered to be... / Vertical spacing It does not meet the operational safety requirements.

[0142] S4: Change the horizontal / vertical spacing, redefine the simulation scenario, and search for the minimum horizontal and minimum vertical spacing that meet the target safety level.

[0143] Specifically, the minimum lateral spacing is determined within parallel, same-height, and same-direction simulation scenarios, and the minimum vertical spacing is determined within simulation scenarios where horizontal projections of straight line segments overlap, are of different heights, and are in the same direction. The spacing to be evaluated is then set. According to the preset step size Gradually increase the interval ,in For the initial interval, For the current candidate interval, In this embodiment For each candidate interval Reconstruct the corresponding route geometry scenario and calculate the route operation risk value according to step S3. Risk value Compare with the target security level TLS. When the first satisfaction... And the previous candidate interval satisfies At that time, The minimum horizontal / vertical interval that satisfies the target safety level under the current search accuracy is determined.

[0144] Alternatively, a dichotomy can be used to refine the intervals between those that do not satisfy TLS and those that do satisfy TLS, to obtain the minimum horizontal / vertical interval that satisfies the target security level.

[0145] This embodiment uses actual manned aircraft turning data and a predetermined UAV eVTOL straight-line flight path to perform the Monte Carlo simulation designed in this invention, setting the TLS to 5×10. -9 times / hour, output results are as follows Figure 9 As shown, the minimum lateral spacing that satisfies the safety constraints is 4651.36m, and the minimum vertical spacing is 140.00m.

Claims

1. A method for determining the safe interval between a manned aircraft turning route and an unmanned aerial vehicle (UAV) straight-line route, characterized in that, include: S1: Collect the performance parameters of the aircraft, including manned and unmanned aircraft; establish discrete-time simulation models of the turning routes of manned aircraft and the straight routes of unmanned aircraft. The turning route of manned aircraft includes a straight segment, an entry segment, a turning segment, and an exit segment, while the straight route of unmanned aircraft includes a straight segment; set traffic flow conditions, design the total error of manned and unmanned aircraft, and simulate the turning routes of manned aircraft and the straight routes of unmanned aircraft in the simulation models respectively; set the safety interval for the turning routes of manned aircraft and the straight routes of unmanned aircraft, and generate the simulation scenario corresponding to the safety interval; S2: In the current simulation scenario, enumerate the candidate maneuver strategies of the UAV and use the simulation model to generate the predicted trajectory, including the predicted trajectory of the manned aircraft turning route and the predicted trajectory of the UAV corresponding to the candidate maneuver strategies. Calculate the squared slant distance function between the predicted trajectory of the UAV and the predicted turning route of the manned aircraft, record the discrete time interval in which the derivative of the squared slant distance function first changes from negative to non-negative, and search for the closest point between the manned aircraft and the UAV within this discrete time interval. If there are multiple candidate maneuver strategies, retain the UAV predicted trajectory with the largest slant range function at the closest point; S3: Based on the airborne collision avoidance system, calculate the collision risk value between the manned aircraft and the unmanned aircraft at the closest point and determine whether the current simulation scenario meets the target safety level; S4: Change the safety interval in the simulation model, regenerate the simulation scene, and repeat steps S2 to S3 to obtain the minimum safety interval that meets the target safety level.

2. The operational risk assessment method according to claim 1, characterized in that, The collection of aircraft performance parameters and the establishment of discrete-time simulation models for manned aircraft turning routes and unmanned aerial vehicle straight-line routes include: The initial motion state of the aircraft in the simulation model is set according to the performance parameters, which include the aircraft's starting position, nominal flight altitude, nominal flight speed, flight acceleration, target turn rate, turn rate acceleration, and heading angle; the target turn rate and turn rate acceleration are zero on straight sections. Let the motion state of aircraft i at the k-th discrete time be... ,in, and Indicates the aircraft's position coordinates. Indicates horizontal velocity. Indicates the heading angle. Indicates vertical velocity. Indicates the turning rate; Let the step size of the discrete time be . The aircraft i updates its motion state from the k-th discrete time step to the k-th discrete time step according to the equation of motion. The motion states at discrete moments are simulated, and the equations of motion are expressed as follows: in, Indicates horizontal acceleration. Represents vertical acceleration. The turning rate acceleration is represented by the fourth-order Runge-Kutta integral method, and the motion state update is implemented using the turning rate acceleration method.

3. The operational risk assessment method according to claim 2, characterized in that, The total error between manned and unmanned aircraft includes navigation system error and flight technology error; The navigation system error of manned aircraft is determined by the navigation and positioning system, and the same distribution model is used in the straight section, the entry section, the turning section, and the exit section. The flight technical error of manned aircraft is represented by a Gaussian distribution in the straight section and the turning section, and by a heavy-tailed distribution in the entry section and the exit section. The navigation system error and the flight technical error of unmanned aircraft are both represented by a Gaussian distribution.

4. The operational risk assessment method according to claim 3, characterized in that, The safety interval is either a lateral interval or a vertical interval. The lateral interval refers to the distance in the horizontal plane between the centerline of the manned aircraft's straight-line segment and the centerline of the UAV's straight-line flight path. The vertical interval refers to the absolute value of the difference between the nominal flight altitude of the manned aircraft and the nominal flight altitude of the UAV.

5. The operational risk assessment method according to claim 4, characterized in that, The candidate maneuvering strategies of the UAV are constructed based on the onboard collision avoidance system and include at least one of horizontal turning, vertical maneuvering, and deceleration.

6. The operational risk assessment method according to claim 5, characterized in that, The discrete time interval in which the derivative of the squared slope distance function first changes from negative to non-negative includes: Manned aircraft turning trajectory prediction in time The predicted location is Prediction speed is The predicted trajectory of the drone's straight-line flight path in time The predicted location is Prediction speed is ; The squared slope distance function Represented as: Set time window ,in This is the simulation start time. Given a preset window length, the squared slope distance function is calculated within the window at a fixed distance from the walking time. first derivative When it first appears At that time, the interval The discrete time interval is determined.

7. The operational risk assessment method according to claim 6, characterized in that, The search for the closest point between manned and unmanned aircraft includes: Define the discrete time interval as the search interval. The binary search method is used for iterative calculation to approximate the closest point in time. The iterative calculation includes: calculating the midpoint of the search interval. First derivative of the squared slope distance function at point subscript Indicates an iterative index; if Update the boundaries of the search range. ,make Proceed to the next iteration; if Update the boundaries of the search range. ,make Then proceed to the next iteration; Repeat the iterative calculation until the length of the search interval is reached. , Given a preset time convergence threshold, output the moment when the midpoint of the search interval in the current iteration is the closest point. .

8. The operational risk assessment method according to claim 7, characterized in that, The calculation of the collision risk value between the manned aircraft and the unmanned aircraft at the closest point includes: Calculate the probability of a collision between a manned aircraft and an unmanned aircraft. : in This indicates the probability that the airborne collision avoidance system will enter the tactical mitigation phase. This indicates the probability that the airborne collision avoidance system will enter the collision avoidance phase. This represents the probability that the manned and unmanned aircraft will overlap in volume due to positional uncertainty at their closest point; the collision risk value is the probability that the manned and unmanned aircraft will collide. .

9. The operational risk assessment method according to claim 8, characterized in that, The determination of whether the current simulation scenario meets the target safety level includes: The collision risk value calculated in the current simulation scenario is compared with the preset collision risk assessment safety target. If the current simulation scenario risk value is greater than the preset collision risk assessment safety target, the corresponding lateral / vertical interval is considered not to meet the target safety level requirements.

10. A system for assessing operational risks of manned aircraft turning routes and unmanned aerial vehicle (UAV) straight-line routes, characterized in that, include: The simulation module is used to collect performance parameters of aircraft, including manned and unmanned aircraft; establish discrete-time simulation models of manned aircraft turning routes and unmanned aircraft straight routes, with the manned aircraft turning route including a straight segment, an entry segment, a turning segment, and an exit segment, and the unmanned aircraft straight route including a straight segment; set traffic flow conditions, design the total error of manned and unmanned aircraft, and simulate the manned aircraft turning route and the unmanned aircraft straight route in the simulation model respectively; set the safety interval for the manned aircraft turning route and the unmanned aircraft straight route, and generate the simulation scenario corresponding to the safety interval; The closest point prediction module is used to enumerate candidate maneuver strategies for the UAV in the current simulation scenario, generate predicted trajectories using the simulation model, including predicted trajectories of manned aircraft turning routes and predicted UAV trajectories corresponding to candidate maneuver strategies; calculate the squared slant distance function between the predicted UAV trajectory and the predicted manned aircraft turning route trajectory, record the discrete time interval in which the derivative of the squared slant distance function first changes from negative to non-negative, and search for the closest point time between the manned aircraft and the UAV within this discrete time interval; if there are multiple candidate maneuver strategies, retain the UAV predicted trajectory with the largest slant distance function at the closest point time; The risk assessment module is used to calculate the collision risk value between manned and unmanned aircraft at the closest point based on the airborne collision avoidance system, and to determine whether the current simulation scenario meets the target safety level. The safety interval output module is used to change the safety interval in the simulation model, regenerate the simulation scene, and repeatedly call the trajectory generation module, the closest point prediction module, and the risk assessment module to obtain the minimum safety interval that meets the target safety level.

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