Multi-variable-speed ship self-adaptive space-time step length coordination method based on collision risk potential field

Abstract

The invention discloses a multi-variable-speed ship adaptive space-time step length coordination method, a state updating method and a collision risk prediction method. The method comprises the following steps: acquiring real-time states of a ship and all target ships; calculating the recent meeting time among all ship pairs, finding out the minimum positive PAT value, and carrying out time interval calculation by adopting a time urgency constraint function; the minimum Euclidean distance between all ship pairs is calculated, and a spatial proximity constraint coordination function is adopted to carry out spatial proximity constraint step length calculation; the maximum absolute value of acceleration changes in all ships is calculated, and a self-adaptive step length is obtained through calculation based on a speed change feature constraint function; according to the method, the numerical integration of the ship motion state is updated, then the ship collision risk is predicted based on the collision risk potential field model, and the method aims at solving the limitation of a fixed step size algorithm and achieving the effects of high-risk speed change stage fine analysis and low-risk constant-speed stage efficient propulsion.

Description

Technical Field

[0001] This invention belongs to the field of intelligent navigation of ships and relates to an adaptive spatiotemporal step coordination method, state update and collision risk prediction method for multi-speed ships. Background Technology

[0002] With the widespread application of computer technology in complex systems such as ship navigation, intelligent transportation, and robot path planning, high-precision and high-efficiency numerical collision detection has become a key aspect of system design, verification, and evaluation. In these collision detection systems, the prediction of the trajectory of entities (such as ships) is usually achieved through numerical integration methods. The selection of its core parameter—the simulation time step (Δt)—directly determines the accuracy of the simulation results and the efficiency of computational resources.

[0003] Traditional collision detection models mostly employ a fixed time step strategy. While this method is simple to implement and computationally stable, it has inherent limitations when simulating dynamically changing scenarios. For example, in multi-ship collision detection, the motion states of ships vary significantly across different stages, such as long distance, safe distance, close approach, and emergency collision avoidance. To meet the accuracy and stability requirements of the most demanding stages (e.g., emergency collision avoidance), a fixed time step must be used throughout. This results in a large amount of unnecessary fine-grained calculations during most non-critical, low-dynamic-change detection periods, leading to a significant waste of computational resources and severely limiting the efficiency of collision detection. This is particularly detrimental to the real-time or ultra-real-time collision detection requirements in complex or busy navigation scenarios.

[0004] Conversely, if a large fixed step size is used simply to improve efficiency, significant truncation errors will be introduced at critical moments (such as near the closest meeting point between the two ships) due to the coarse granularity of the calculation. This will lead to problems such as distorted trajectory prediction and misjudgment of collision risk, making the collision detection results lose their reference value and unable to provide a reliable basis for the intelligent decision-making system.

[0005] In existing technologies, some improved methods attempt to adjust the step size simply based on a single condition (such as the distance between entities). However, the dynamic characteristics of complex systems are driven by multiple dimensions and multiple physical quantities. Relying solely on distance factors cannot effectively respond to the urgency of collisions represented by the most recent collision time step, nor can it handle sudden changes in motion state caused by ship acceleration, turning, or other maneuvers. This single-dimensional adaptive strategy is not refined or robust enough in dealing with complex scenarios involving multiple targets, high density, and strong interactions, making it difficult to achieve an optimal balance between computational efficiency and simulation accuracy globally. The instability risk of numerical integration still exists, and a systematic step size coordination mechanism capable of responding to multi-level spatiotemporal characteristics cannot be formed. Summary of the Invention

[0006] To address the core issue of the imbalance between accuracy and efficiency in existing ship collision risk detection methods when dealing with ships with multiple speeds and nonlinear motions due to the use of a fixed time step, the technical solution adopted in this invention is: an adaptive spatiotemporal step coordination method for ships with multiple speeds, comprising the following steps:

[0007] Obtain the real-time status of this ship and all target ships; Based on the real-time status of this ship and all target ships, calculate the nearest encounter time between all ship pairs, find the minimum positive PAT value, and use a time urgency constraint function to determine the time interval. calculate; Based on time interval Calculate the minimum Euclidean distance between all ship pairs, and use the spatial proximity constraint coordination function to determine the spatial proximity constraint step size. calculate; Step size based on spatial proximity constraint The maximum absolute value of acceleration change among all ships is calculated, and the adaptive step size is calculated based on the variable speed characteristic constraint function.

[0008] Furthermore, the expression for the time urgency constraint function is as follows:

[0009] in, As a safety factor, As an efficiency growth factor, As an emergency threshold, Small positive PAT values Time interval; Time urgency constrains step size.

[0010] Furthermore, the expression for the spatial proximity constraint coordination function is as follows:

[0011]

[0012] in, The preset warning distance, when At that time, the step size will be reduced proportionally. Spatial proximity constraint step size; The minimum Euclidean distance between all ship pairs. , Coordinates of a certain ship.

[0013] Furthermore, the expression for the variable speed characteristic constraint function is as follows:

[0014]

[0015] in: : The maximum absolute value of acceleration change among all ships, β is the attenuation factor, and γ is the acceleration change threshold. Current acceleration, The acceleration at the next moment. : Acceleration change coordination step size.

[0016] The ship state update method according to any one of the described adaptive spatiotemporal step size coordination methods for multi-speed ships includes the following steps: Obtain the adaptive spatiotemporal coordination step size for multi-speed ships; Based on the adaptive spatiotemporal coordination step size of multi-speed ships, the ship's speed is updated; The ship's position is updated based on the updated ship speed, thus updating the ship's status.

[0017] A ship collision risk prediction method according to any one of the described states of a multi-speed ship includes the following steps: Get the current updated ship status; Based on the current updated ship status, the collision risk potential field function for the shortest collision avoidance distance and the shortest collision avoidance time between the two ships is constructed; Based on the shortest collision avoidance distance (PAS) and shortest collision avoidance time (PAT) of the two ships as core input variables and assigned different weight functions, the constructed collision risk potential field function is decomposed and simplified to obtain the simplified collision risk potential field function. Based on the ship's current state, and assuming the ship maintains its current state of motion, predict any future moment. The relative position and motion state of the objects will predict the shortest collision avoidance distance (PAS) at the next future moment. and shortest collision avoidance time PAT Substituting the above risk potential field function, we obtain the future risk potential field; Based on the overall risk potential field in which the ship is located, a comprehensive collision risk index is calculated. By analyzing the changing trend of the comprehensive collision risk index within a future time window, dynamic prediction of collision risk is achieved.

[0018] The simplified expression for the collision risk potential field function is as follows:

[0019] in, This is a normalized constant or a weighted coefficient related to ship size and type; distance risk factor. It is a monotonically decreasing function of the shortest collision avoidance distance (PAS) between the two ships, and its specific expression is as follows:

[0020] It is a distance scale parameter that controls the range of influence of the risk field. When PAS The risk is greatest at the highest PAS level; as PAS increases, the risk decreases exponentially. Time risk factor It is a monotonically decreasing function of the shortest collision avoidance time (PAT), used to characterize the urgency of the risk, for example:

[0021] in, It is a time constant. Control the decay rate; the smaller the PAT, the more imminent the collision, and the higher the risk factor. The closer it is to 1.

[0022] The comprehensive collision risk index is calculated by taking the ship's position p at this location. own The total risk field value is used to obtain the comprehensive collision risk index, which is expressed as follows:

[0023] Among them: CRI Indicates the trend of change within a future time window; The Collision Risk Index (CRI) for future moments is as follows: .

[0024] Furthermore: the ship's speed update, based on an adaptive time step Δt_final, assumes that the acceleration a(t) remains constant or changes linearly within this time interval. According to the basic formula for uniformly accelerated motion, the velocity v(t+Δt_final) at time t+Δt_final is calculated using the following formula:

[0025] Where v(t) is the velocity vector at the current moment, and a(t) is the acceleration of the ship at the current moment.

[0026] During the time interval Δt_final, assuming the ship's heading angle θ remains constant and the rate of change of velocity is steady, the expression for the ship's position update is as follows:

[0027]

[0028] in:[ , ] represents the current position coordinates of the ship in a two-dimensional plane, and θ is the ship's heading angle.

[0029] This invention provides an adaptive spatiotemporal step size coordination method, state update and collision risk prediction method for multi-speed ships. It constructs a dynamic adaptive spatiotemporal step size coordination mechanism that is coupled in real time with the characteristics of ship speed change, and drives the dynamic optimization of collision risk analysis accuracy by adjusting the simulation step size.

[0030] This method aims to overcome the limitations of fixed step size algorithms and achieve the effect of "detailed analysis in high-risk variable speed phases and efficient advancement in low-risk uniform speed phases", providing a new paradigm for simulation analysis of encounter safety for ships with multiple variable speeds.

[0031] The primary innovation of this method lies in the design of an adaptive spatiotemporal step size coordination method, state update method, and collision risk prediction method for multi-speed vessels. The adaptive spatiotemporal step size coordination method no longer treats the step size as a fixed parameter, but rather as a core variable that dynamically evolves with the vessel's motion state. It recursively optimizes candidate step sizes through three sequentially recursive constraint layers (PAT coordination layer, distance constraint layer, and acceleration change coordination layer). Each constraint function corresponds to different physical risk characteristics during vessel encounters: the PAT coordination layer reflects the urgency of collision time, the distance constraint layer controls spatial proximity, and the acceleration change coordination layer specifically addresses the core characteristic of multi-speed vessels—the abrupt change in motion state—by monitoring acceleration changes to suppress numerical integration errors and ensure the stability of the predicted variable-speed trajectory. This recursive hierarchical architecture ensures that the adaptive step size can accurately respond to the complex and nonlinear risk changes brought about by variable-speed vessels.

[0032] The core contribution of this invention lies in achieving deep coupling between adaptive step size and risk analysis of variable-speed ships. Specifically, this method utilizes the dynamic step size (Δt) output by the aforementioned coordination mechanism to directly control the update frequency and computational granularity of the collision risk potential field model. During the ship's acceleration and variable-speed maneuvering phase, the coordination mechanism automatically reduces the step size, allowing the risk potential field model to be calculated at a higher temporal resolution. This enables precise capture of the spatiotemporal evolution details of risks caused by variable-speed behavior, achieving refined analysis of instantaneous high-risk situations. Conversely, during the low-risk phase of the ship's uniform-speed navigation, the mechanism intelligently increases the step size, significantly improving analysis efficiency without significantly sacrificing accuracy. In summary, the risk analysis accuracy of this method is not statically fixed but dynamically assigned by the adaptive step size, thus solving the problem of optimizing the allocation of simulation computing resources in variable-speed scenarios.

[0033] This method overcomes the limitations of fixed-step-size and single-dimensional adaptive methods, intelligently sensing the dynamic changes in the collision risk potential field environment and accordingly adjusting the dynamic step size in a refined and multi-level coordinated manner. An ideal method should be able to balance multiple constraints such as time urgency, spatial proximity, and rate of change of motion state, achieving intelligent adjustment that is fast when necessary and slow when appropriate. This would significantly improve the computational efficiency of complex dynamic systems while ensuring numerical stability and collision accuracy. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is the overall architecture and flowchart of the dynamic adaptive spatiotemporal step size coordination method provided in this embodiment of the invention. Figure 2 These are schematic diagrams and graphs of the PAT constraint layer prediction scenario. (a) shows a schematic diagram of the time step prediction scenario under the PAT (Predicting Approach Time) constraint; (b) is a graph of the PAT value changing with the number of simulation steps. Figure 3 These are comparative diagrams and graphs, where (a) shows a comparative diagram of the decision-making between the distance constraint coordination layer and the PAT constraint layer (the next level), and (b) is a graph showing the change of the distance between ships with the number of simulation steps. Figure 4 Comparing the schematic diagram and the graph, (a) shows a schematic diagram comparing the decision-making of the acceleration change monitoring and coordination layer and the distance constraint layer (the next level), and (b) is a graph showing the change of ship acceleration with the number of simulation steps; Figure 5 It is a discrete grid 3D representation of the adaptive spatiotemporal step size coordination result. Detailed Implementation

[0036] It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0037] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] An adaptive spatiotemporal step coordination method for multi-speed ships includes the following steps: S11: At the start of each simulation step, acquire the real-time status of the current ship and all target ships; The state information includes velocity, acceleration, acceleration at the next moment, current coordinates (x, y), and ship size, i.e., ship collision radius; S12: Based on the real-time status of this ship and all target ships, calculate the nearest encounter time between all ship pairs, and find the minimum positive PAT value, based on the time urgency constraint function. calculate; S13: Based on time interval Calculate the minimum Euclidean distance between all ship pairs, and use the spatial proximity constraint coordination function to determine the spatial proximity constraint step size. calculate; S14: Step size based on spatial proximity constraints The maximum absolute value of acceleration change among all ships is calculated, and the adaptive step size is calculated based on the variable speed characteristic constraint function.

[0039] Steps S11 / S12 / S13 / S14 are executed sequentially; Furthermore, the expression for the time urgency constraint function is as follows:

[0040] in, As a safety factor, As an efficiency growth factor, As an emergency threshold, Small positive PAT values Time interval; Time urgency constrains step size.

[0041] Furthermore, the expression for the spatial proximity constraint coordination function is as follows:

[0042]

[0043] in, The preset warning distance, when At that time, the step size will be reduced proportionally. Spatial proximity constraint step size; The minimum Euclidean distance between all ship pairs. , Coordinates of a certain ship.

[0044] Furthermore, the expression for the variable speed characteristic constraint function is as follows:

[0045]

[0046] in: : The maximum absolute value of acceleration change among all ships, β is the attenuation factor, and γ is the acceleration change threshold.

[0047] Furthermore, the formula for updating the numerical integral of the ship's motion state is as follows:

[0048] in: The ship's motion state at a given moment, including X and Y coordinates, ship speed, acceleration, turning, etc. : The calculated final spacetime step.

[0049] The ship state update method according to any one of the described adaptive spatiotemporal step size coordination methods for multi-speed ships includes the following steps: S21: Obtain the adaptive spatiotemporal coordination step size for multi-speed ships; S22: Based on the adaptive spatiotemporal coordination step size of multi-speed ships, the speed of the ship is updated; S23: Update the ship's position based on the updated ship speed to update the ship's status.

[0050] Steps S21 / S22 / S23 are executed sequentially; A ship collision risk prediction method according to any one of the described states of a multi-speed ship includes the following steps: S31: Get the current updated ship status; S32: Based on the current updated ship status, construct the collision risk potential field function for the shortest collision avoidance distance and the shortest collision avoidance time between the two ships; S33: Based on the shortest collision avoidance distance PAS and shortest collision avoidance time PAT of the two ships as core input variables and assigned different weight functions, the constructed collision risk potential field function is decomposed and simplified to obtain the simplified collision risk potential field function. S34: Based on the ship's current state, predict any future moment assuming the ship maintains its current motion. The relative position and motion geometry will predict the shortest collision avoidance distance (PAS) at the next future moment. and shortest collision avoidance time PAT Substituting the above risk potential field function, we obtain the future risk potential field; Based on the overall risk potential field in which the ship is located, S35 calculates a comprehensive collision risk index and analyzes the changing trend of the comprehensive collision risk index within a future time window to achieve dynamic prediction of collision risk.

[0051] Steps S31 / S32 / S33 / S34 / S35 are executed sequentially; Furthermore, the simplified expression for the collision risk potential field function is as follows:

[0052] in, This is a normalized constant or a weighted coefficient related to ship size and type; distance risk factor. It is a monotonically decreasing function of the shortest collision avoidance distance (PAS) between the two ships, and its specific expression is as follows:

[0053] It is a distance scale parameter that controls the range of influence of the risk field. When PAS The risk is greatest at the highest PAS level; as PAS increases, the risk decreases exponentially. Time risk factor It is a monotonically decreasing function of the shortest collision avoidance time (PAT), used to characterize the urgency of the risk, for example:

[0054] in, It is a time constant. Control the decay rate; the smaller the PAT, the more imminent the collision, and the higher the risk factor. The closer it is to 1.

[0055] Furthermore: the comprehensive collision risk index is obtained by calculating the total risk field value of p_own at the ship's current position, and the expression for the comprehensive collision risk index is as follows:

[0056] Among them: CRI Indicates the trend of change within a future time window; The Collision Risk Index (CRI) for future moments is as follows: .

[0057] Furthermore: the ship's speed update, based on an adaptive time step Δt_final, assumes that the acceleration a(t) remains constant or changes linearly within this time interval. According to the basic formula for uniformly accelerated motion, the velocity v(t+Δt_final) at time t+Δt_final is calculated using the following formula:

[0058] Where v(t) is the velocity vector at the current moment, and a(t) is the acceleration of the ship at the current moment.

[0059] During the time interval Δt_final, assuming the ship's heading angle θ remains constant and the rate of change of velocity is steady, the expression for the ship's position update is as follows:

[0060]

[0061] in:[ , ] represents the current position coordinates of the ship in a two-dimensional plane, and θ is the ship's heading angle.

[0062] Figure 1 This is the overall architecture and flowchart of the dynamic adaptive spatiotemporal step size coordination method provided in the embodiments of the present invention; This flowchart illustrates the closed-loop workflow of the dynamic adaptive spatiotemporal step-size coordination algorithm. At its core is a decision system comprising four layers of sequential coordination and one layer of feedback verification. The entire process begins with the input of the system's initial state and forms a continuous optimization loop.

[0063] First: The core computational aspect of the method—dynamically calculating the time step. (Green module in the diagram) – encapsulates a three-layer recursive coordination mechanism. Data undergoes the following processing sequentially: Time urgency constraint layer (collision urgency assessment): such as Figure 1 The first step within the green module is to activate this layer.

[0064] Based on the motion states of all ships, the minimum nearest encounter time is calculated using formulas (9), (10), (11), and (12). ).

[0065] (9) (10) (11) (12) according to Is it less than the threshold? ) Make a decision branch: if If the value is less than the threshold, a conservative approach is adopted. Directly related step size ( This ensures high-precision prediction capabilities under collision risk; otherwise, an increasing step size is used ( (to improve efficiency during free navigation).

[0066] Distance constraint layer (spatial approximation verification): as per the process Figure 1 As shown, after the time urgency constraint layer makes a decision, the step size is immediately adjusted in this layer. This layer calculates the minimum real-time distance between ships ( ), and based on its distance from the warning ( The ratio of the two factors is used to calculate a continuous attenuation coefficient. This step ensures that even in scenarios where there is no imminent collision time risk but the space is very close, the step size can be adaptively reduced to guarantee the accuracy of the close proximity urgency calculation.

[0067] Acceleration Variation Layer (Motion State Stability Monitoring): Subsequently, the step size is passed to this layer. This layer monitors abrupt changes in the ship's acceleration. ).

[0068] The process path indicates that when the acceleration change exceeds the stability threshold ( When ), the step size will be reduced by a decay factor ( The step size should be reduced to address numerical instability caused by drastic changes in acceleration; otherwise, the step size will be... The growth factor (≥1) is adjusted appropriately and flows directly to the next layer.

[0069] The new step size is calculated in the green module. The process doesn't end there; instead, it enters a collision accuracy verification phase. This phase forms a feedback loop, verifying the accuracy of numerical integration at this step size. If the verification fails, the algorithm backtracks along the feedback path, triggering step size reduction and recalculation until a more accurate step size is found. If the verification passes, this step size is used to advance the simulation, outputting the result of this step and completing one collision detection cycle. Subsequently, the process loops to the beginning of the next spatiotemporal step, and then sequentially detects collisions.

[0070] Example 1: An adaptive spatiotemporal step coordination method for multi-speed ships, comprising the following steps: S1: Real-time system status acquisition and four-layer decision-making process initiation; At the start of each simulation step, the system collects the real-time states of its own vessel and all target vessels, forming a set of state vectors. ,in Subsequently, the decision-making process was based on... Figure 1 The logic is as shown. A candidate step size (initially the step size of the previous frame or the baseline step size) is input from the process entry point and begins to be evaluated and filtered by four layers of constraints in sequence.

[0071] S2: Step size prediction dominated by time urgency constraints; This is the first layer of constraints, designed to adjust the step size based on the urgency of the collision. The core of this layer is calculating the nearest encounter time (PAT) between all ship pairs and finding the smallest positive PAT value. .

[0072] like Figure 2 As shown in (a), in an example scenario, the system contains three ships, ship 2 and ship 3. The time is 6.3 seconds. At this point, the decision logic of this layer is activated, and its constraint function is:

[0073] in, The safety factor is <1. The efficiency growth factor is greater than 1. This is the emergency threshold. Figure 2 (a) In the scenario, due to the detection of small This layer is identified as being in a critical state and a short step size (0.939 seconds) dominated by the PAT value is calculated. This step size will be passed to the next layer as a new candidate value. Figure 2 (b) By showing the dynamic changes of three PAT values ​​over 100 simulation steps, it is further explained why the step size must be adjusted in real time according to PAT: the PAT value fluctuates dramatically over time, and the step size must also be adapted accordingly. Time interval; S3: Step size prediction dominated by spatial proximity constraints; The candidate step sizes, processed by the time urgency constraint layer, proceed to the second layer—the distance constraint layer. This layer focuses on the actual spatial distances between ships, aiming to ensure spatial resolution accuracy during ship approach. This layer calculates the minimum Euclidean distance between all ship pairs. .

[0074] like Figure 3As shown in (a), in a comparative analysis scenario, the current distance between ship 1 and ship 3 is... The distance is 141.4 meters. The distance constraint layer is triggered, and compared with the PAT constraint decision from the previous time step, the constraint function of this layer is:

[0075]

[0076] in, This is the preset warning distance. When At that time, the step size will be reduced proportionally. Figure 3 (a) Displayed in the upper left corner, at this time , (0.939 seconds) multiplied by ,thereby Further expand and replace the PAT constraint as the dominant decision in the current step, finally It was calculated as 2.0 seconds. Figure 3 (b) The distance between the three ships is confirmed to be dynamic. The constraints at this level ensure that the simulation step size is automatically reduced when the ships approach each other to match the higher spatial resolution requirements.

[0077] S4: Step size prediction dominated by variable speed characteristic constraints; This is the core constraint layer specifically designed for the motion characteristics of ships with multiple speeds. This layer monitors changes in ship acceleration to prevent severe truncation errors caused by excessively large step sizes during drastic speed changes such as rapid acceleration, deceleration, or turning. This layer calculates the maximum absolute value of acceleration change Δa_max for all ships.

[0078] like Figure 4 As shown in (a), at a certain simulation moment, the system detects a significant change in acceleration. The constraint function for this layer is:

[0079]

[0080] Where β is the decay factor (<1). γ is the growth factor (≥1), and γ is the acceleration change threshold.

[0081] exist Figure 4 In example (a), the acceleration constraint layer is activated, which is when it belongs to In this case, the original constraint layer calculation (1 second) step length is multiplied by The growth factor is used to calculate the final step size. (2 seconds), and replaced the distance constraint of the previous time step, becoming the dominant decision; Figure 4 (b) The acceleration variation curves of the three ships clearly show that there are significant acceleration abrupt changes near simulation steps 20 and 80. This is precisely when the constraints of this layer play a crucial role, forcibly reducing the step size to maintain numerical stability and motion prediction accuracy. After processing by this layer, the adaptive step size Δt_final of this simulation step is finally output.

[0082] Example 2 A ship state update method based on an adaptive spatiotemporal step size coordination method for multi-speed ships, the specific steps of which are as follows: S21: Obtain the adaptive spatiotemporal coordination step size for multi-speed ships; S22: Integral update of velocity state The ship's speed is updated based on the integral of acceleration over time. Within the adaptive time step Δt_final, assuming the acceleration a(t) remains constant or changes linearly during this time interval, the velocity v(t+Δt_final) at time t+Δt_final can be calculated using the following formula, according to the basic formula for uniformly accelerated motion:

[0083] Where v(t) is the velocity vector at the current moment (or its scalar magnitude, depending on the model dimension), and a(t) is the ship's acceleration at the current moment. This formula is essentially an application of Euler's forward integral method to velocity updates, and its accuracy depends on the selection of the step size Δt_final. To ensure physical realism, the updated velocity must be constrained within the limits allowed by the ship's maneuverability, i.e., v_min ≤ v(t + Δt_final) ≤ v_max.

[0084] S23: Integral update of position status Ship position update is the core of kinematic integration, achieved by integrating velocity. During the time interval Δt_final, assuming the ship's heading angle θ remains constant and the rate of change of velocity is stationary, the position update can be expressed as:

[0085]

[0086] Here, [x(t), y(t)] represent the ship's current position coordinates in a two-dimensional plane, and θ is the ship's heading angle (usually 0 degrees for due east and increasing counterclockwise). This model simplifies the ship as a point mass, whose direction of motion is uniquely determined by the heading angle. The accuracy of the position update is directly affected by the accuracy of the velocity v(t) and the size of the step size Δt_final.

[0087] Furthermore: Considerations and handling of heading status In the basic kinematic model of a point mass, the heading angle θ can be considered a variable independently controlled by the ship maneuvering model, rather than directly derived from the linear motion formulas described above. Therefore, the heading angle update logic within the time interval Δt_final depends on the specific maneuvering model. If a constant heading model is used, the heading angle remains unchanged: θ(t+Δt_final) = θ(t). If a more complex motion model is used, such as considering the turning angular velocity r, the heading update formula becomes: θ(t+Δt_final) = θ(t) + r Δt_final. In actual simulations, a suitable heading change model needs to be selected based on the ship's maneuvering characteristics.

[0088] Furthermore, the relationship between adaptive step size and integration accuracy is discussed. The introduction of the adaptive step size Δt_final aims to balance computational efficiency with the accuracy of numerical integration. When the ship's motion changes drastically (e.g., high relative speed, close encounters leading to a decrease in DCPA / TCPA), the algorithm automatically reduces Δt_final to meet the requirements of local truncation error. The local truncation error of the Euler integral method described above is proportional to (Δt_final)^2, while the global error is proportional to Δt_final. Therefore, by dynamically adjusting the step size, the cumulative error of the numerical solution can be effectively controlled, ensuring the reliability of key calculation results such as collision detection.

[0089] The final Δt_final is applied to the numerical integral update of the ship's motion state, for example:

[0090] The key point is that this This directly determines the accuracy of subsequent risk analysis. When A smaller value indicates that the system employs a refined calculation mode during "high-risk acceleration moments" characterized by "high time urgency" (small PAT), "high spatial risk" (close distance), or "high dynamic change" (large acceleration), thus enabling it to accurately capture the transient evolution of collision risk. Conversely, in low-risk phases, a larger value indicates a more complex system. This ensures the overall simulation efficiency.

[0091] Example 3: A ship collision risk prediction method based on a state update method for multi-speed ships, comprising the following steps: S31 retrieves the current updated ship status; S32: Basic Definition and Construction of Collision Risk Potential Field. The core idea of ​​the collision risk potential field model is to establish a scalar field function. This function defines the time at a specific moment. any point on a two-dimensional plane This represents the collision risk value relative to the vessel. This potential field is typically the superposition of independent risk potential fields generated by the vessel and multiple other vessels. For a single other vessel... The risk field it generates It is a function of the relative motion geometry between the other vessel and the ship, primarily depending on two key parameters: the predicted avoidance distance (PAS) and the predicted avoidance time (PAT). Its general form can be expressed as:

[0092] in, and These are the velocity vectors of the other vessels and the vessel itself, respectively. The total risk field is then the linear or nonlinear superposition of the risk fields generated by all other vessels: The essence of prediction lies in calculating and visualizing this time-varying scalar risk field based on the motion parameters measured at the current moment.

[0093] S33: Modeling the Risk Potential Function Based on PAS and PAT The specific construction typically uses PAS and PAT as core input variables, assigning them different weighting functions. A typical risk potential field function can be decomposed into distance risk factors. and time risk factors The product or summation form:

[0094] in, This is a normalized constant or a weighted coefficient related to ship size and type. Distance risk factor. It is a monotonically decreasing function of PAS, commonly in exponential or Gaussian form, for example:

[0095] here, It is a distance scale parameter that controls the range of influence of the risk field. When PAS The risk is greatest at the highest point; as PAS increases, the risk decreases exponentially. Time risk factor. It is a monotonically decreasing function of PAT, used to characterize the urgency of the risk, for example:

[0096] in, It is a time constant. Control the decay rate. A smaller PAT indicates a more imminent collision and a higher risk factor. The closer it is to 1.

[0097] S34: Risk Prediction and Dynamic Evolution. Risk prediction is achieved by calculating the evolution of the risk potential field over a future period. Given the current moment... Given the ship's state (position, speed, heading), and assuming the ship maintains its current motion (uniform linear motion), it is possible to predict any future moment. The relative position and motion geometry.

[0098] By predicting the future PAS and PAT Substituting the above risk potential function, we can obtain the future risk field. By traversing a time window (e.g., 0 to 30 minutes into the future), a profile of risk evolution over time can be generated, identifying when the risk peaks and the spatial distribution of high-risk areas. This prediction allows ship operators or autopilot systems to proactively assess the situation, rather than relying solely on the current instantaneous state.

[0099] Section S35: Potential Field Superposition and Comprehensive Risk Quantification. In multi-ship encounter scenarios, the total risk potential field of the vessel is the vector sum of the risk potential fields generated by all surrounding vessels. The Comprehensive Collision Risk Index (CRI) is typically calculated by measuring the risk potential fields generated by all surrounding vessels at the vessel's position. The total risk field value is used to obtain:

[0100] This CRI value provides an intuitive, quantitative measure of overall risk. For prediction, also based on motion extrapolation, the CRI for future times is calculated:

[0101] By analyzing CRI The changing trends within a future time window, such as its maximum value, the time to reach the maximum value, and the time to exceed a certain safety threshold, can enable dynamic prediction of collision risk, providing a quantitative basis for the timing and magnitude of risk avoidance decisions (such as steering and speed change).

[0102] like Figure 5As shown, the final effect of this method can be comprehensively displayed through a three-dimensional decision space grid. The graph uses "PAT constraint value" and "distance constraint value" as the base plane coordinate axes, "final adaptive time step" as the height, and color mapping to "acceleration constraint strength." This three-dimensional surface vividly illustrates that the final step size decision is the result of the comprehensive competition and coordination of three dimensions of constraints: time urgency, spatial proximity, and acceleration change. Its value is dynamic, discrete, and intelligently optimized, effectively balancing the simulation accuracy and computational efficiency requirements of variable-speed ships under different situations. The upper left shows an adaptive adjustment diagram of the ship's spatiotemporal step size under two different scenarios: the left side shows a scenario where the spatiotemporal step size gradually decreases under an emergency collision risk situation, and the right side shows a scenario where the step size gradually increases under a low collision risk situation.

[0103] In summary, this invention achieves dynamic adaptive coordination of the spatiotemporal step size for collision detection through a three-layer step size coordination mechanism deeply coupled with the multi-speed ship motion characteristics (PAT, distance, acceleration). This method drives the collision detection system to adaptively decrease the step size in high-risk areas for refined risk analysis, while adaptively increasing the step size in low-risk areas, providing an efficient and reliable computational foundation for safety assessment and decision-making under complex encounter situations.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for adaptive spatiotemporal step size coordination of multi-speed ships, characterized in that: Includes the following steps: Obtain the real-time status of this ship and all target ships; Based on the real-time status of this ship and all target ships, calculate the nearest encounter time between all ship pairs, find the minimum positive nearest encounter time (PAT) value, and use a time urgency constraint function to determine the time interval. calculate; Based on time interval Calculate the minimum Euclidean distance between all ship pairs, and use the spatial proximity constraint coordination function to determine the spatial proximity constraint step size. calculate; Step size based on spatial proximity constraint The maximum absolute value of acceleration change among all ships is calculated, and the adaptive step size is calculated based on the variable speed characteristic constraint function.

2. The adaptive spatiotemporal step size coordination method for multi-speed ships according to claim 1, characterized in that: The expression for the time urgency constraint function is as follows: in, As a safety factor, As an efficiency growth factor, As an emergency threshold, Small positive PAT values Time interval; Time urgency constrains step size.

3. The adaptive spatiotemporal step size coordination method for multi-speed ships according to claim 1, characterized in that: The expression for the spatial proximity constraint coordination function is as follows: in, The preset warning distance, when At that time, the step size will be reduced proportionally. Spatial proximity constraint step size; The minimum Euclidean distance between all ship pairs. , Coordinates of a certain ship.

4. The adaptive spatiotemporal step size coordination method for multi-speed ships according to claim 1, characterized in that: The expression for the variable speed characteristic constraint function is as follows: in: : The maximum absolute value of acceleration change among all ships, β is the attenuation factor, and γ is the acceleration change threshold. Current acceleration, The acceleration at the next moment. : Acceleration change coordination step size.

5. The ship state update method according to any one of claims 1-4, characterized in that: Includes the following steps: Obtain the adaptive spatiotemporal coordination step size for multi-speed ships; Based on the adaptive spatiotemporal coordination step size of multi-speed ships, the ship's speed is updated; The ship's position is updated based on the updated ship speed, thus updating the ship's status.

6. The ship collision risk prediction method according to any one of claims 1-4 of the state update method for multi-speed ships, characterized in that: Includes the following steps: Get the current updated ship status; Based on the current updated ship status, the collision risk potential field function for the shortest collision avoidance distance and the shortest collision avoidance time between the two ships is constructed; Based on the shortest collision avoidance distance (PAS) and shortest collision avoidance time (PAT) of the two ships as core input variables, and assigned different weight functions, the constructed collision risk potential field function is decomposed and simplified to obtain the simplified collision risk potential field function. Based on the ship's current state, and assuming the ship maintains its current motion, predict any future moment. The relative position and motion state of the objects will predict the shortest collision avoidance distance (PAS) at the next future moment. and shortest collision avoidance time PAT Substituting the collision risk potential field function, we obtain the future risk potential field; Based on the overall risk potential field in which the ship is located, a comprehensive collision risk index is calculated. By analyzing the changing trend of the comprehensive collision risk index within a future time window, dynamic prediction of collision risk is achieved.

7. The method for predicting collision risk of multi-speed ships according to claim 6, characterized in that: The simplified expression for the collision risk potential field function is as follows: in, This is a normalized constant or a weighted coefficient related to ship size and type; distance risk factor. It is a monotonically decreasing function of the shortest collision avoidance distance (PAS) between the two ships, and its specific expression is as follows: It is a distance scale parameter that controls the range of influence of the risk field. When PAS The risk is greatest at the highest PAS level; as PAS increases, the risk decreases exponentially. Time risk factor It is a monotonically decreasing function of the shortest collision avoidance time (PAT), used to characterize the urgency of the risk. in, It is a time constant. Control the decay rate; the smaller the PAT, the more imminent the collision, and the higher the risk factor. The closer it is to 1.

8. The method for predicting collision risk of multi-speed ships according to claim 6, characterized in that: The comprehensive collision risk index is obtained by calculating the total risk field value of p_own at the ship's current position. The expression for the comprehensive collision risk index is as follows: Among them: CRI Indicates the trend of change within a future time window; The Collision Risk Index (CRI) for future moments is as follows: 。 9. The method for updating the state of a multi-speed ship according to claim 5, characterized in that: The ship's speed update is based on an adaptive time step Δt_final, assuming that the acceleration a(t) remains constant or changes linearly within this time interval. According to the basic formula of uniformly accelerated motion, the velocity v(t+Δt_final) at time t+Δt_final is calculated by the following formula: Where v(t) is the velocity vector at the current moment, and a(t) is the acceleration of the ship at the current moment. During the time interval Δt_final, assuming the ship's heading angle θ remains constant and the rate of change of velocity is steady, the expression for the ship's position update is as follows: in:[ , ] represents the current position coordinates of the ship in a two-dimensional plane, and θ is the ship's heading angle.

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