Unmanned aerial vehicle normalization security model calibration method based on risk driving
By constructing a risk-driven normalized safety model for UAVs, the problem of poor generalization ability of existing UAV safety interval models is solved. It achieves adaptive dynamic calibration and efficient safety interval calculation, which is applicable to various UAV models and improves the operating efficiency and safety of UAVs in complex environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-03
- Publication Date
- 2026-03-10
AI Technical Summary
Existing UAV safety interval models have poor generalization capabilities and cannot dynamically adapt to real-time changes in positioning accuracy or perception conditions during flight. This means that a complex simulation calibration process must be re-executed every time the UAV model or operating conditions change, hindering the large-scale standardized application of heterogeneous UAV fleets.
A risk-driven normalized safety model calibration method for unmanned aerial vehicles (UAVs) is adopted. This method constructs a safety interval model based on the optimal control physics principle and uses risk-driven simulation to calibrate the basic physical parameter set, including initializing a gradient-free optimizer, Monte Carlo simulation, and high-fidelity risk injection, to optimize and generate the optimal basic physical parameter set.
It achieves adaptive dynamic calibration under different aircraft models, speeds, weather and environmental constraints, reduces calibration costs, and improves the operational efficiency and safety of UAVs in complex urban environments. The model only needs to be calibrated once to generalize to multiple UAVs.
Smart Images
Figure CN121635002A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of unmanned aerial vehicle flight control systems, and particularly relates to a risk-driven unmanned aerial vehicle normalization safety model calibration method. BACKGROUND
[0002] When an unmanned aerial vehicle (UAV) operates in a city low-altitude environment, it needs to determine its safety interval. To ensure city low-altitude safety, existing technologies mostly use a collision probability model to calibrate the safety interval of the UAV and static obstacles. However, the safety interval value calibrated by this kind of method is a specific value coupled with the specific model of the UAV, flight speed, and environmental assumption depth. This leads to poor generalization ability and the inability to dynamically adapt to real-time changes in positioning accuracy or sensing conditions (such as rain, fog, and weak light) during flight. Therefore, whenever the UAV model or operating conditions change, a complex simulation calibration process must be re-executed, which seriously hinders the large-scale standardized application of heterogeneous UAV teams. SUMMARY
[0003] The purpose of the present application is to provide a risk-driven UAV normalization safety model calibration method to solve the problems of poor generalization ability, high calibration cost, and inability to dynamically adapt to real-time operating conditions of existing safety interval models.
[0004] To achieve the above purpose, the technical solution adopted by the present application is as follows: A risk-driven UAV normalization safety model calibration method, comprising the following steps: S1, constructing a UAV normalization safety interval model based on optimal control physical principles; S2, using risk-driven simulation to calibrate the basic physical parameter set of the UAV normalization safety interval model.
[0005] Further, in S1, the UAV normalization safety interval model is represented as: In the formula, is the total forward distance accumulated in time sequence for a series of physical events; is the dynamic reaction buffer during which the UAV continues to fly from sensing to executing maneuvers; is the shortest forward distance required for the UAV to execute an optimal hybrid evasion strategy; is the static uncertainty buffer covering all non-dynamic sensing and positioning errors; is the geometric radius of the UAV.
[0006] Further, the static uncertainty buffer covering all non-dynamic sensing and positioning errors is The system is decoupled into two categories: localization and perception. Environmental condition factors based on real-time contextual variables are used for adjustment, thereby obtaining... The derivation expression: In the formula, This is the positioning error; For perceived error; , Environmental condition factors for real-time scenario variables; This refers to the baseline positioning error; The baseline perceived error.
[0007] Furthermore, by using the flight distance within the total reaction delay at the net forward velocity, the dynamic reaction buffer for the UAV to continue flying during the period from perception to execution of the maneuver is calculated. It is represented as: In the formula, The real-time horizontal cruising speed of the drone; This is the projection of the wind speed vector onto the flight direction; Total reaction delay; Baseline perception-execution latency.
[0008] Furthermore, the shortest forward distance required for the UAV to execute the optimal hybrid avoidance strategy is derived. It includes: Based on the drone's current speed Decelerate to target turning speed Then, turn the speed at the target. lateral evasion The required total forward distance constructs the hybrid maneuver function, which is expressed as: In the formula, For hybrid maneuver functions; This is the deceleration distance; This refers to the turning distance; Based on aerodynamics and Newton's second law, the deceleration distance and turning distance are corrected, thus yielding the corrected hybrid maneuver function. The corrected hybrid maneuver function is then applied within physical constraints. All feasible target turning speeds The minimum value in the interval is the shortest forward distance required for the drone to execute the optimal hybrid avoidance strategy. It is represented as: In the formula, Forward braking acceleration calibrated for the drone; for the aerodynamic correction term, representing the beneficial braking acceleration due to air resistance; for the calibrated lateral acceleration; for the aerodynamic correction term, representing the resistance acceleration due to the forward airflow impacting the sides of the body, which hinders lateral maneuvering.
[0009] Further, in S2, a risk-driven simulation is used to calibrate the basic physical parameter set of the normalized safety margin model of the UAV, aiming to minimize the simulation accident rate, which specifically includes the following sub-steps: S21, initialize the gradient-free optimizer; S22, the gradient-free optimizer generates the basic physical parameter set to be tested , wherein, is the reference positioning error attempted in the i-th iteration process, is the reference perception error attempted in the i-th iteration process, is the reference perception-execution delay attempted in the i-th iteration process; S23, the basic physical parameter set to be tested is input into the Monte Carlo simulation evaluation system; S24, construct a heterogeneous simulation instance, including randomized performance parameters and randomized scenario variables ; S25, based on the constructed heterogeneous simulation instance and the input basic physical parameter set to be tested , calculate the dynamic safety margin using the normalized safety margin model of the UAV; S26, inject high-fidelity risks of positioning noise, perception noise and reaction delay in the Monte Carlo simulation evaluation system; S27, based on the injected high-fidelity risks, the Monte Carlo simulation evaluation system runs all flight plans of the UAV, and records all collision events that occur; S28, calculate the simulation accident rate ; S29, deliver the accident rate to the gradient-free optimizer, which generates the next basic physical parameter set to be tested , and executes S21-S29 in a loop until the accident rate converges, and the gradient-free optimizer outputs the optimal basic physical parameter set .
[0010] Further, in S26, a first-order Gaussian-Markov process modeling is used for positioning noise injection, specifically: superimpose a time-correlated noise on the real position of the UAV Self-position perception of UAV ; The time-dependent noise is discretized to obtain a discrete-time representation of the noise: where, is the positioning error vector at discrete time k+1; is the inverse coefficient related to the drift-dependent time ; is the positioning error vector at discrete time k; is a discrete white noise with covariance satisfying: where, is the steady-state standard deviation of the Gaussian-Markov process; is the inverse of the drift-dependent time; is the steady-state standard deviation of the Gaussian-Markov process is associated with the static uncertainty buffer and is expressed as: where, is the positioning condition factor of the UAV j at present, is the reference positioning error to be tested in the i-th iteration; Then, based on the set of basic physical parameters in S23 and the randomized scenario variables in S24 , the and are calculated and iteratively generated in the time domain to be superimposed on the real position of the UAV .
[0011] Further, in S26, a zero-mean Gaussian white noise is used to inject the perception noise, which is expressed as: where: where, is the perception distance of the UAV j to the obstacle at t; is the real distance of the UAV to the obstacle at t; is the standard deviation of the zero-mean Gaussian white noise; is the perception condition factor of the UAV j at present; The reference perception error to be tested in the ith iteration.
[0012] Further, in the S26, the injection reaction delay comprises: In the Monte Carlo simulation evaluation system, when The first time is less than the dynamic safety interval At this moment, it is recorded as The actual execution time of the evasion maneuver Is delayed, which is expressed as: In the formula, The simulation time at which the UAV j actually starts to execute the evasion maneuver; The simulation time at which the UAV j first detects that the safety interval is broken; The delay mean; The Gaussian distribution standard deviation of the reaction delay, used to quantify the instability of the processing time; Wherein, the delay mean is: In the formula, The reference perception-execution delay to be tested in the ith iteration.
[0013] The risk-driven UAV normalized safety model calibration method provided by the application has the following beneficial effects: 1、The application combines the perception delay, maneuver execution and static buffer three event chains in the UAV operation process, can realize the self-adaptation of different models, speeds, weather, positioning and environmental constraints, and dynamically calibrate the reasonable safety interval of the UAV relative to the urban low-altitude static obstacles.
[0014] 2、The application constructs a normalized safety interval model structure with clear physical meaning, and adopts a closed-loop optimization calibration method, so that the model only needs to be calibrated once and can be generalized to different types of UAVs. At the same time, the model can also enable the UAV flight control system to dynamically calculate an optimal safety interval according to the real-time speed, positioning signal quality and weather perception conditions in flight, so as to greatly improve the operation efficiency under the premise of ensuring safety.
[0015] 3、The application generates a normalized optimal physical model through a risk-driven closed-loop calibration method with objective accident rate as the target; compared with the traditional calibration method deeply coupled with the model, running speed and running condition, the model can be calibrated once and applied to various unmanned aerial vehicles, greatly reducing the application cost; and the unmanned aerial vehicle can dynamically calculate the physically optimal safety interval according to the real-time flight speed, positioning signal quality and weather sensing condition, thereby significantly improving the running efficiency in the complex urban environment on the premise of ensuring absolute safety. BRIEF DESCRIPTION OF DRAWINGS
[0016] Figure 1 The flowchart of the risk-driven unmanned aerial vehicle normalization safety model calibration method of the embodiment of the application is shown.
[0017] Figure 2 The closed-loop process block diagram of the simulation simulation calibration unmanned aerial vehicle normalization safety interval model basic physical parameter set of the embodiment of the application is shown. DETAILED DESCRIPTION
[0018] The specific embodiments of the application are described below to facilitate the understanding of the application by those skilled in the art, but it should be clear that the application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the application defined and determined by the appended claims, and all applications utilizing the concept of the application are within the scope of protection.
[0019] The risk-driven unmanned aerial vehicle normalization safety model calibration method of the embodiment mainly includes two core components in structure: a normalized safety interval model based on optimal control physical principle is proposed, which is used for real-time calculation of safety interval on the unmanned aerial vehicle device; a closed-loop optimization method for calibrating key basic physical parameters in the model is proposed, which reversely solves the model parameters through risk-driven simulation, and references Figure 1 , which specifically includes the following contents: S1, constructing an unmanned aerial vehicle normalization safety interval model based on optimal control physical principle; In some embodiments, the safety interval of the unmanned aerial vehicle and the static obstacle (such as a building) is constructed as an accumulation model based on a physical event chain, which discards the suboptimal method of simply selecting between multiple discrete strategies, and instead finds the physically optimal solution in a continuous system of all possible mixed avoidance strategies.
[0020] In a specific embodiment, the total forward distance accumulated in time sequence for a series of physical events is defined , and based on this, the unmanned aerial vehicle normalization safety interval model of the embodiment is represented as: where, is the dynamic reaction buffer for UAV to continue flying during the period from perception to execution maneuver; is the minimum forward distance required for UAV to execute the optimal hybrid evasion strategy; is the static uncertainty buffer covering all non-dynamic perception and localization errors; is the geometric radius of UAV.
[0021] In a specific embodiment, the uncertainty is further decoupled into two categories of localization and perception, and adjusted by environmental condition factors of corresponding real-time situational variables and ; Specifically, the static uncertainty buffer covering all non-dynamic perception and localization errors is decoupled into two categories of localization and perception, and adjusted by environmental condition factors of corresponding real-time situational variables, and then the derivation expression of is obtained: where, is the localization error; is the perception error; , is the environmental condition factor of real-time situational variables; is the reference localization error, is the reference perception error, and are the underlying physical parameters to be calibrated.
[0022] In a specific embodiment, is the net forward velocity is the flight distance within the total reaction delay ; the total reaction delay is affected by the perception condition , and the dynamic reaction buffer for UAV to continue flying during the period from perception to execution maneuver is derived as follows: where, is the real-time cruising speed of UAV in horizontal direction; is the projection of wind speed vector in the flight direction; is the total reaction delay; is the minimum physical time required for the onboard computing platform of UAV to process a series of perception algorithms from receiving sensor raw data to outputting motor instructions at the bottom level, which is specified as the reference perception-execution delay, and is the underlying physical parameter to be calibrated.
[0023] In one specific embodiment, the shortest forward distance required for the UAV to execute the optimal hybrid avoidance strategy is... The derivation is obtained by solving an optimal control problem. First, a parameter related to the target turning speed is defined. Continuous functions It represents the drone starting from its current speed. Decelerate to target turning speed Then, turn the speed at the target. lateral evasion Total forward distance required; the hybrid maneuver function It consists of the sum of the distances during the deceleration phase and the steering phase, and is expressed as: In the formula, For hybrid maneuver functions; This is the deceleration distance; This refers to the turning distance; By introducing aerodynamic correction terms, the deceleration distance is reduced. Represented as: This revision Based on standard fluid dynamics And from the derivation of Newton's second law: In the formula, air density, The total weight of the drone and These are the forward drag coefficient and the frontal area, respectively.
[0024] Similarly, in the turning distance It is represented as: Ultimately, the modified hybrid maneuver function is subject to physical constraints. All feasible target turning speeds The minimum value in the interval is the shortest forward distance required for the drone to execute the optimal hybrid avoidance strategy. It is represented as: In the formula, Forward braking acceleration calibrated for the drone; This is an aerodynamic correction term, representing the beneficial braking acceleration caused by air resistance; The calibrated lateral acceleration; for aerodynamic correction term, representing the resistance acceleration generated by the forward airflow impacting the body side, which hinders the lateral maneuvering.
[0025] S2, calibrating the normalized safety margin model of the UAV based on risk-driven simulation; In some embodiments, this step requires calibrating the normalized safety margin model of the UAV based on risk-driven simulation , specifically aiming at the minimum simulation accident rate, and the reference Figure 2 , which specifically includes the following sub-steps: S21, initializing the gradient-free optimizer; On one or more processors, initialize a gradient-free optimization algorithm, using the Nelder-Mead downhill simplex method, which generates an initial simplex in the N-dimensional space of the parameters to be calibrated .
[0026] S22, the gradient-free optimizer generates the set of basic physical parameters to be tested , wherein, is the reference positioning error in the i-th iteration process, is the reference perception error in the i-th iteration process, is the reference perception-execution delay in the i-th iteration process.
[0027] S23, input the set of basic physical parameters to be tested into the Monte Carlo simulation evaluation system, and start a high-fidelity Monte Carlo simulation evaluation.
[0028] S24, construct a heterogeneous simulation instance, including randomized performance parameters and randomized scenario variables . Specifically, the Monte Carlo simulation evaluation system instantiates a UAV entity in a simulation space with a real urban scene topology, which has randomized performance parameters and randomized scenario variables , such as different .
[0029] S25, based on the constructed heterogeneous simulation instance and the input set of basic physical parameters to be tested , calculate the dynamic safety margin using the normalized safety margin model of the UAV; Specifically, at the beginning of the simulation, each UAV entity , according to its unique randomized performance parameters and randomized situational variables and the set of basic physical parameters received from S23 Using the UAV normalized safety interval model in S1 It calculates its own unique, dynamic safety interval in real time. .
[0030] S26. Inject high-fidelity risks of localization noise, perception noise, and reaction delay into the Monte Carlo simulation evaluation system to physically reproduce these risks in the simulation. The real risks represented specifically include the following: (1) Regarding positioning noise; To more realistically simulate the low-frequency drift characteristics of GNSS multipath and IMU integral drift, a first-order Gaussian-Markov process is used for localization noise injection. Specifically, the actual position of the UAV is... Add a time-dependent noise As a means for drones to perceive their own position : In the formula, It is a zero-mean Gaussian white noise process. It is the time related to drift. The relevant inverse coefficient; Time-related noise Discretization yields the simulation results in discrete time (step size). The iterative expression of the noise in ) is: In the formula, Let be the positioning error vector at discrete time k+1; For drift-related time The relevant inverse coefficient; Let be the positioning error vector at discrete time k; For a discrete white noise, its covariance satisfy: In the formula, The steady-state standard deviation of this Gaussian-Markov process represents the statistical characteristic of the noise model after long-term operation, indicating the magnitude of the positioning drift. In the simulation, it is necessary to ensure that the generated noise standard deviation is consistent. This is exactly equal to the total positioning error predicted by the model in this invention; It is the reciprocal of the drift-related time; Its steady-state standard deviation The association with the static uncertainty buffer is represented as follows: In the formula, Let be the current positioning condition factor for UAV j. Let be the baseline positioning error to be tested in the i-th iteration; Then, based on the fundamental physical parameter set in S23 and the randomized scenario variables in S24 ,calculate and Iteratively generate in the time domain Overlay on drones In its true location.
[0031] (2) For perceived noise; Since the single-point ranging noise of the sensor is mainly high-frequency thermal noise and does not have time-series correlation, this embodiment uses zero-mean white Gaussian noise. Injecting perceived noise is represented as follows: Among them, the standard deviation of zero-mean Gaussian white noise Determined by the parameter to be calibrated and the scenario factor: In the formula, Let be the distance (observed value) that UAV j perceives as an obstacle at time t. Let t be the true distance (true value) between the drone and the obstacle at time t. The standard deviation of zero-mean Gaussian white noise; The current perception condition factor (real-time scenario variable) of UAV j. Let be the baseline sensing error to be tested in the i-th iteration.
[0032] (3) Regarding reaction delay; In the simulator First less than the dynamic safety interval Time, this moment is recorded as Avoiding the actual execution time of maneuvering It must be delayed. This delay is necessary to simulate jitter calculations. It can be modeled as a random variable.
[0033] Among them, the actual execution time of evasion maneuvers Delay is represented as: In the formula, The simulation time at which the UAV actually begins to perform evasive maneuvers is time j; is the simulation time when the safety margin is first detected to be breached by drone j; is the delay mean; is the standard deviation of the Gaussian distribution of reaction delays, quantifying the instability of the processing time; wherein the delay mean is: wherein, is the benchmark perception-execution delay to be tested in the i-th iteration.
[0034] S27, based on the injected high-fidelity risk, the Monte Carlo simulation evaluates the system running the flight plan of all drones and records all the collision events that occur; S28, calculate the accident rate ; S29, deliver the accident rate to the gradient-free optimizer, whose goal is to minimize the accident rate, update its internal state, and propose (generate) the next set of basic physical parameters to be tested , and execute S21~S29 in a closed loop automatically iterated until the accident rate converges, while the gradient-free optimizer outputs the optimal set of basic physical parameters .
[0035] Although the specific embodiments of the invention are described in detail with reference to the accompanying drawings, it should not be understood as limiting the scope of protection of the patent. Various modifications and variations made by those skilled in the art within the scope described in the claims are still within the scope of protection of the patent.
Claims
1. A risk-driven based UAV normalized security model calibration method, characterized in that, The method comprises the following steps: S1, constructing a UAV normalized safety margin model based on optimal control physical principles; S2, calibrating the basic physical parameter set of the UAV normalized safety margin model by using risk-driven simulation.
2. The risk-driven based UAV normalized security model calibration method of claim 1, wherein, In the S1, the UAV normalized safety margin model is expressed as: wherein, is the total forward distance accumulated in time series for a series of physical events; is the dynamic reaction buffer for the UAV to continue flying during the time from sensing to executing the maneuver; is the shortest forward distance required for the UAV to execute the optimal hybrid evasion strategy; is the static uncertainty buffer to cover all non-dynamic sensing and localization errors; is the geometric radius of the UAV.
3. The risk-driven based UAV normalized security model calibration method of claim 2, wherein, Static uncertainty buffer covering all non-dynamic perception and localization errors Decoupling into localization and perception categories, and adjusting with real-time situational variable environmental condition factors, yields derived expression: wherein is the positioning error; is the perception error; , is an environmental condition factor of the real-time situational variable; is the reference positioning error; is the reference perception error.
4. The risk-driven based UAV normalized security model calibration method of claim 3, wherein, A dynamic reaction buffer is calculated for the UAV to continue flying during the time from perception to execution of the maneuver using the net forward velocity flown distance within the total reaction delay which is expressed as: In the formula, is the real-time cruising speed of the UAV in the horizontal direction; is the projection of the wind speed vector in the flight direction; is the total reaction delay; is the reference perception-execution delay.
5. The risk-driven based UAV normalized security model calibration method of claim 4, wherein, Deriving the shortest forward distance required for a drone to execute an optimal mixed evasion strategy comprising: Based on the current speed of the UAV decelerate to a target turn speed and execute a lateral evasion at the target turn speed The total forward distance required builds a hybrid maneuver function, which is represented as: wherein is a mixing machine function; is a deceleration distance; is a turning distance; Based on aerodynamics and Newton's second law, the deceleration distance and turning distance are corrected, thus yielding the corrected hybrid maneuver function. The corrected hybrid maneuver function is then applied within physical constraints. All feasible target turning speeds The minimum value in the interval is the shortest forward distance required for the drone to execute the optimal hybrid avoidance strategy. It is represented as: wherein is the forward braking acceleration for the drone calibration; is the aerodynamics correction term, representing the beneficial braking acceleration due to air resistance; is the lateral acceleration for the drone calibration; is the aerodynamics correction term, representing the resistance acceleration due to the forward airflow impacting the sides of the body, which hinders lateral maneuvering.
6. The risk-driven based UAV normalized security model calibration method of claim 4, wherein, In the S2, the basic physical parameter set of the UAV normalized safety margin model is calibrated by using risk-driven simulation with the minimum simulation accident rate as the target, and the specific steps include the following sub-steps: S21, initializing a gradient-free optimizer; S22, the gradient-free optimizer generates a set of base physical parameters to be tested wherein, is the reference positioning error for the attempt in the i-th iteration process, is the reference perception error for the attempt in the i-th iteration process, is the reference perception-execution delay for the attempt in the i-th iteration process; S23, a set of base physical parameters to be tested input into the Monte Carlo simulation evaluation system; S24, constructing a heterogeneous simulation instance, including randomized performance parameters and randomized scenario variables ; S25, based on the constructed heterogeneous simulation instance and the input set of basic physical parameters to be tested a dynamic safety margin is calculated using a drone normalization safety margin model; S26, injecting high-fidelity risks of positioning noise, perception noise and reaction delay into a Monte Carlo simulation evaluation system; S27, based on the injected high-fidelity risks, the Monte Carlo simulation evaluation system runs all flight plans of the UAVs and records all collision events occurring; S28, calculate simulated accident occurrence rate ; S29, the accident rate to the gradient-free optimizer, the gradient-free optimizer generates the next set of basic physical parameters to be tested , and the S21-S29 are executed in a loop until the accident rate converges, while the gradient-free optimizer outputs the optimal set of basic physical parameters .
7. The risk-driven based UAV normalized security model calibration method of claim 6, wherein, In the S26, a first-order Gauss-Markov process modeling is adopted for positioning noise injection, specifically: the real position of the unmanned aerial vehicle is superimposed with a time-dependent noise as the unmanned aerial vehicle's perception of its own position ; correlated noise discretization, resulting in a discrete-time representation of the noise: wherein is the positioning error vector at discrete time k + 1 ; is the time related to the drift the inverse coefficient related to the drift; is the positioning error vector at discrete time k; is a discrete white noise with covariance satisfies: wherein is the steady state standard deviation of the Gaussian-Markov process; is the inverse of the drift correlation time; its steady state standard deviation Associated with the static uncertainty buffer, denoted as: In the formula, is a positioning condition factor of the current position of the UAV j, is the reference positioning error to be tested in the i th iteration; Then, based on the set of base physical parameters in S23 and the randomized scenario variables in S24 , the calculations and are made and iteratively generated in the time domain to be superimposed on the real position of the drone .
8. The risk-driven based UAV normalized security model calibration method of claim 6, wherein, In the S26, the zero-mean Gaussian white noise is adopted The injection of the perceived noise is represented as: In the S26, the reaction delay is injected, which includes: wherein, is the sensing distance of the UAV j to the obstacle at time t; is the real distance of the UAV to the obstacle at time t; is the standard deviation of the zero-mean Gaussian white noise; is the sensing condition factor of the UAV j at the current time; is the benchmark sensing error to be tested in the i-th iteration.
9. The risk-driven based UAV normalized security model calibration method of claim 6, wherein, Wherein, the delay mean is: In the Monte Carlo simulation evaluation system, when the first time is less than the dynamic safety interval , the moment is recorded as , and the actual execution time of the evasion maneuver is delayed, which is expressed as: In the formula, is the simulation time at which the UAV j actually starts to perform the evasion maneuver; is the simulation time at which the UAV j first detects that the safety margin is breached; is the delay mean value; is the standard deviation of the Gaussian distribution of the reaction delay, which quantifies the instability of the processing time; In the formulae, is the reference perception-execution delay to be tested in the i-th iteration.