Multi-agent collision risk prediction method fusing control barrier function and speed obstacle

Abstract

According to the multi-agent collision risk prediction scheme provided by the invention, based on the relative position and speed of any two agents, a control barrier function in a distance square difference form is firstly constructed, and a first-order derivative of the control barrier function is solved; generating a dimensionless risk gradient by using a control barrier function value and a derivative thereof, and obtaining a preliminary risk value through Sigmoid class continuous mapping; performing'bidirectional dynamic correction 'on the initial risk value in combination with speed obstacle analysis; a continuous and differentiable final risk value is output by weakening a false conflict with deceptive property and enhancing a hidden real collision threat; and finally, taking the maximum value of the risk values of the same subject and all other agents to form a subject overall risk, thereby realizing real-time risk quantification of the large-scale multi-agent system. Compared with a traditional method, the scheme has the advantages that the real collision risk can be described and quantified more accurately by fusing the instantaneous state and the dynamic evolution trend between the intelligent agents and the prospective prediction based on kinematics extrapolation, the problem of prediction one-sidedness caused by single information dimension of the traditional method is effectively solved, and the prediction accuracy is improved. And the prediction accuracy and rationality are effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent collision risk prediction, specifically involving a multi-agent collision risk prediction method that integrates control barrier function (CBF) and velocity barrier (VO). Background Technology

[0002] In the autonomous operation and collaborative work of multi-agent systems, effectively preventing and avoiding collisions between agents has always been a core issue and technical challenge in research and application. Currently, methods for predicting collision risks in multi-agent systems have made some progress, but many limitations still exist.

[0003] Traditional risk prediction methods often rely on Euclidean distance thresholds as the core criterion. These methods set a fixed minimum safe distance; if the actual distance between agents falls below this threshold, a collision risk is considered present, otherwise, the agent is deemed safe. While this static distance-based prediction method is simple, intuitive, and computationally inexpensive, it has significant inherent drawbacks:

[0004] First, the predictions are often overly conservative. Because the method doesn't fully consider the agents' motion states (such as speed, acceleration, and orientation) and future movement trends, it may misjudge many situations where there is actually no risk of collision as high-risk. For example, even if two agents are currently close, if their relative movement trend is towards moving away from each other, the actual probability of a collision is extremely low. However, distance-threshold-based methods will still trigger avoidance mechanisms, causing agents to perform unnecessary deceleration, steering, or stopping actions. This not only reduces the overall system efficiency and task completion speed, but also, in dense or confined environments, if each agent strictly adheres to a fixed minimum distance constraint, it can easily lead to "behavioral freeze" or "deadlock," causing the entire system to stagnate.

[0005] Secondly, the accuracy of risk characterization is insufficient. A simple distance threshold cannot reasonably reflect the true evolution of risk in a dynamic environment. On the one hand, for two intelligent agents traveling towards each other at high speeds, even with a large initial distance, there may be an extremely high risk of collision, while traditional methods may ignore this potential danger because the distance has not reached the threshold. On the other hand, for two intelligent agents that are close together but moving away from each other at a large relative speed, the actual risk is low, but it may be misjudged as high risk. This lack of understanding of dynamic interaction processes makes risk prediction lack foresight and detail.

[0006] Furthermore, existing technologies often struggle to achieve an ideal balance between computational real-time performance and predictive safety. Methods prioritizing high real-time performance typically rely on simplified models (such as the aforementioned distance threshold), which sacrifices prediction accuracy and adaptability to complex dynamics. To enhance safety margins, some methods introduce more complex collision prediction models, such as those based on multi-step trajectory simulation, probabilistic statistical risk calculations, or methods considering agent dynamics. While these methods provide more detailed risk profiles, their computational complexity increases significantly, potentially leading to decision delays and failing to meet the rapid response requirements of highly dynamic, large-scale agent systems.

[0007] Furthermore, many traditional risk measurement methods (such as hard threshold judgment) are inherently discontinuous or piecewise. When the agent's state undergoes a small change and crosses a preset threshold, the risk prediction value will experience a step-like jump. This discontinuity will pose challenges to the subsequent control system design, easily leading to jitter or instability in control commands, which is detrimental to the smooth transition of multi-agent system behavior and overall stability.

[0008] To address the aforementioned issues, academia and industry have proposed several improvement schemes. For example, the "Velocity Obstacle" (VO) and its derivatives (such as RVO, HRVO, and ORCA) are widely used techniques. VO methods construct a "velocity obstacle region" in the agent's velocity space by assuming that other agents maintain a constant linear motion at their current velocity for a short period. The agent can avoid future collisions by choosing a velocity outside this region, based on the aforementioned assumptions. VO-type methods can effectively handle collision avoidance problems with multiple moving obstacles and exhibit good computational efficiency in large-scale dynamic scenarios. However, VO methods themselves are based on the constant velocity assumption and do not provide strict collision avoidance guarantees. When the agent's behavior is highly dynamic or there are significant acceleration changes, its prediction accuracy decreases, and collisions may still occur. Furthermore, directly and strictly applying VO constraints, especially in crowded environments, often leads to a sharp reduction in the agent's feasible velocity space, resulting in overly conservative behavior, or even "oscillations" or "no-solution" dilemmas, affecting system efficiency.

[0009] Another widely discussed technique is the "Control Barrier Function" (CBF). CBF constructs a scalar function (barrier function) that characterizes the safe state of a system and designs a controller to ensure that the function value and its derivative satisfy specific conditions (usually ensuring that its value is always non-negative or that its derivative points towards the safe region when approaching the safe boundary), thus providing a strict theoretical guarantee (forward invariance) for the system's safety (such as collision avoidance). However, control constraints generated solely by CBF can sometimes be too strict, unnecessarily restricting the agent's degrees of freedom and task execution efficiency, especially when facing complex constraints arising from the interaction of multiple agents. The feasible solution space may be excessively compressed, leading to a decline in system performance. Furthermore, CBF-based control strategies typically require online solving of one or more optimization problems (such as quadratic programming QP). In applications with limited computational resources or extremely high control frequency requirements, their real-time overhead remains a significant concern.

[0010] In summary, existing multi-agent collision risk prediction methods either suffer from inaccurate or overly conservative risk predictions due to model simplification, making them unsuitable for complex dynamic environments; or face real-time challenges due to high algorithm complexity; or lack continuity and differentiability in risk measurement, hindering the design of advanced control algorithms and system stability. Therefore, there is an urgent need to develop a novel risk prediction method that effectively integrates the advantages of existing technologies while overcoming their inherent shortcomings, to meet the comprehensive requirements of multi-agent systems in complex dynamic scenarios for accuracy, real-time performance, and stability in risk prediction. Summary of the Invention

[0011] The purpose of this invention is to address the problems of insufficient accuracy, excessive conservatism, lack of continuity, and difficulty in taking real-time into account in the existing technology for multi-agent collision risk prediction. It provides a multi-agent collision risk prediction method that integrates control barrier function and velocity barrier. By comprehensively considering the instantaneous safety margin between agents, the dynamic evolution trend of relative motion, and the probability of future trajectory conflict based on the constant velocity assumption, it achieves dynamic, continuous, and more accurate quantification of potential collision risks.

[0012] To achieve the above objectives, the present invention adopts the following technical solution:

[0013] A multi-agent collision risk prediction method that integrates control barrier functions and velocity barriers includes the following steps:

[0014] S1. For any pair of agents that may interact, obtain their positions. and speed According to the preset minimum safe distance Construct control barrier function And calculate its first derivative with respect to time. Specifically:

[0015] ;

[0016] ;

[0017] in, Represents intelligent agents and The Euclidean distance between them

[0018] S2. Based on the control barrier function Its first derivative The original risk characteristics are calculated, and then normalized and nonlinearly mapped to obtain preliminary continuous risk prediction values. ;

[0019] S3. Based on the speed barrier principle, calculate the predicted parameters assuming both parties maintain their current constant speeds. These predicted parameters include at least the predicted closest point time. and minimum prediction distance ;

[0020] S4. Predict the nearest point time based on the result obtained in step 3. sum and minimum prediction distance and safe distance The relationship between the initial continuous risk forecast value and the initial continuous risk forecast value. Make adjustments to obtain the revised risk value. ;

[0021] S5. For any intelligent agent Combine it with all other intelligent agents Between As the intelligent agent Final instantaneous collision risk value .

[0022] Furthermore, the implementation method of step S2 includes:

[0023] S21. Constructing basic risk trend indicators The formula for calculating the basic risk trend indicator is as follows:

[0024] ;

[0025] in, The constant coefficients are positive; take As a risk trend factor that quantifies the severity of risk evolution;

[0026] S22. Normalize the risk trend factors to obtain the normalized risk gradient. The formula for calculating the normalized risk gradient is:

[0027] ;

[0028] in, It is a very small positive number. Or according to The magnitude selection.

[0029] S23, Normalized Risk Gradient Perform truncation, so that This is to retain only trend values ​​indicating an increase in potential risk, excluding scenarios where risk decreases or there is no risk.

[0030] S24, Based on nonnegative normalized risk gradient Using a generalized Sigmoid class function to Mapped to continuous risk prediction values ​​between 0 and 1 This enables tiered decision-making and early warning operations; its function expression is:

[0031] ;

[0032] Where k is a real number controlling the steepness of the mapping curve, i.e., the risk value pair. Sensitivity to change.

[0033] Furthermore, step S23, the truncation process, is used to reduce negative or risk-reducing trends. Setting the value to zero focuses only on and quantifies scenarios where potential risks increase.

[0034] Furthermore, the implementation method of step S3 includes:

[0035] S31. Calculate the predicted closest point time assuming both parties maintain their current constant speeds. Specifically:

[0036] Make intelligent agents and The current relative position is The relative speed is ; Calculate the most recent time point for prediction ;in, Represents the vector dot product. Denotes the Euclidean norm of a vector; only if At that time, it was determined that the two would be closer in the future;

[0037] S32, Based on the nearest point time predicted in step S31 Computational intelligent agents and Minimum predicted distance between The minimum prediction distance Calculate using any of the following methods:

[0038] Method 1: The direct formula is: ;

[0039] Method 2: The square form is: ;

[0040] In the three-dimensional case, The cross product; in the two-dimensional case, the squared modulus of the cross product is defined as: );

[0041] Where a and b are two-dimensional vectors; , Let x and y represent the components of vector a, respectively. , Let the x-component and y-component of vector b be represented respectively; () represents the scalar result of the cross product of two-dimensional vectors;

[0042] S33, Based on the predicted nearest point time and minimum prediction distance Assess collision risk: If all conditions are met and or Then determine the intelligent agent. speed Located in the intelligent agent The collision speed obstacle zone, in which A positive time threshold. This is the preset safe distance threshold.

[0043] Furthermore, the correction in step S4 falls into two categories:

[0044] First, eliminate spurious conflicts: when the risk value obtained in step S2... Higher than the preset threshold However, the assessment of collision risks indicates future actual safety. or At that time, through the attenuation coefficient reduce ;

[0045] Second, strengthen the real collision warning: when the risk value obtained in step S2 Below the preset threshold However, assessing collision risk clearly predicts collisions. and At that time, through the enhancement coefficient promote .

[0046] This method provides a multi-agent collision risk prediction scheme. Based on the relative position and velocity of any two agents, it first constructs a control barrier function in the form of the squared difference of distance and solves its first derivative. A dimensionless risk gradient is generated using the control barrier function value and its derivative, and a preliminary risk value is obtained through a Sigmoid-type continuous mapping. A "bidirectional dynamic correction" is implemented on the preliminary risk value using velocity barrier analysis. By weakening deceptive "pseudo-collisions" and enhancing concealed "real collision threats," a continuously differentiable final risk value is output. Finally, the maximum risk value of the same agent with all other agents is taken to form the overall risk of the agent, thereby achieving real-time risk quantification for large-scale multi-agent systems. Compared with traditional methods, this scheme, by integrating the instantaneous states and dynamic evolution trends between agents and forward-looking predictions based on kinematic extrapolation, can more accurately characterize and quantify real collision risks, effectively solving the problem of predictive bias caused by the single information dimension in traditional methods, and effectively improving the accuracy and rationality of predictions. Compared with existing technologies, this invention has the following beneficial effects:

[0047] 1. This invention employs the Sigmoid function with adjustable kurtosis, a nonlinear continuous mapping function, to smoothly map the normalized risk gradient to the [0,1) interval, ensuring that the risk value is continuous and differentiable everywhere. This processing method guarantees that the final output risk prediction value transitions smoothly and continuously within the interval, which is not only convenient for subsequent optimization control algorithms to use directly, but also crucial for achieving more stable and less jittery behavior control and path planning in multi-agent systems.

[0048] 2. This invention introduces a forward-looking two-way risk correction mechanism based on VO to intelligently correct the risk prediction results based on CBF: by calculating the shortest predicted convergence time. and minimum prediction distance If the VO criterion indicates safety but the initial risk is high, the risk value is reduced by a set attenuation coefficient; if the VO criterion indicates an impending collision and the initial risk is low, the risk value is amplified by an enhancement coefficient. This mechanism balances immediate safety margins with future trajectory conflicts, effectively reducing unnecessary avoidance actions caused by overly conservative predictions while ensuring that the safety baseline is not breached. It avoids both underreporting of risks and overprotection, ultimately improving the overall operational efficiency and ability to navigate complex environments of the multi-agent system.

[0049] 3. The method of this invention combines computational efficiency with good real-time performance. Its core lies in employing a CBF (Cross-Cumulative Distance) safety margin and risk trend quantification method based on the squared difference of distance: the difference between the squares of the actual distance and the square of the safe distance threshold is defined as CBF, thus avoiding square root calculations and ensuring function smoothness; simultaneously, a risk trend index is obtained by combining CBF with its derivative. This index is highly sensitive to situations approaching the safety boundary and moving in a dangerous direction, and can expose potential collision risks in advance. Furthermore, the core computational steps involved in this method, such as vector operations of distance and velocity, dot products, nonlinear function evaluation, and simple logical judgments, are all analytical operations, resulting in controllable overall computational complexity, which can meet the needs of most multi-agent systems for online real-time risk prediction. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the multi-agent collision risk prediction method of the present invention;

[0051] Figure 2 The flowchart of the multi-agent collision risk prediction method is shown in the embodiment.

[0052] Figure 3 For safe distance Risk prediction comparison chart under pseudo-conflict scenario at a distance of 2.5 meters; where a is the traditional assessment based on fixed distance threshold method; b is the assessment by the method of this invention;

[0053] Figure 4 For safe distance Risk prediction comparison chart in pseudo-conflict scenario when the distance is 2.5 meters; where a is the traditional assessment based on fixed distance threshold method; b is the assessment by the method of this invention;

[0054] Figure 5 This is a comparison of the risk prediction curves of the present invention with those of traditional distance-based methods as a function of the relative distance between agents. Detailed Implementation

[0055] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0056] like Figure 1 , Figure 2 As shown, the present invention provides a multi-agent collision risk prediction method that integrates control barrier functions and velocity barriers, comprising the following steps:

[0057] S1. For any pair of agents that may interact, obtain their positions. and speed According to the preset minimum safe distance Construct control barrier function And calculate its first derivative with respect to time. .

[0058] S2. Based on the control barrier function Its first derivative The original risk characteristics are calculated, and then normalized and nonlinearly mapped to obtain preliminary continuous risk prediction values. .

[0059] S3. Based on the speed barrier principle, calculate the predicted parameters assuming both parties maintain their current constant speeds. These predicted parameters include at least the predicted closest point time. and minimum prediction distance .

[0060] S4. Predict the nearest point time based on the result obtained in step 3. sum and minimum prediction distance and safe distance The relationship between the initial continuous risk forecast value and the initial continuous risk forecast value. Make adjustments to obtain the revised risk value. .

[0061] S5. For any intelligent agent Combine it with all other intelligent agents Between As the intelligent agent Final instantaneous collision risk value .

[0062] In some embodiments, step S1 draws on the theory of control barrier functions to construct a scalar function that characterizes the current safety state of each pair of agents that may interact. In practice, the squared difference of distance form is chosen as the preferred option after comprehensively balancing computational efficiency and the convenience of derivative derivation. In a general sense, any function that satisfies the conditions of being non-negative in a safe state, negative in a dangerous state, and possessing appropriate regularity can be used as a candidate control barrier function. This function not only directly reflects the current safety distance margin between agents or its equivalent measure, i.e., the difference between the squared distance and the squared safety threshold; more importantly, by analyzing the rate of change of this scalar function over time, i.e., its first derivative, it can capture the immediate dynamic trend of whether the safety margin is decreasing (indicating increased risk) or increasing (indicating decreased risk). This embodiment further combines the current safety margin information with this dynamic trend information to form a comprehensive original risk indication feature. The implementation process of step S1 includes:

[0063] S11. Defining Variables and the Foundations of Collision Risk Quantification:

[0064] Assuming the environment has An intelligent agent. To quantize any two intelligent agents... and The risk of collisions between them is mitigated by introducing a Control Barrier Function (CBF). To describe intelligent agents and The safety state relationship between them. Wherein, the system state vector... Defined as , For intelligent agents Location, For intelligent agents speed, For intelligent agents Location, For intelligent agents The speed.

[0065] S12. Redefine the control barrier function (CBF):

[0066] Based on the requirements of system security and computational convenience, a distance squared difference method is adopted to construct... Specifically defined as:

[0067] ;

[0068] in, Represents intelligent agents and The Euclidean distance between them; The minimum safe distance threshold is a pre-set value, determined based on the agent's physical size, motion characteristics, or specific safety regulations. This is the square of the preset minimum safe distance threshold.

[0069] The value of directly corresponds to the system security status: when At that time, the distance between the two agents is not less than the minimum safety threshold. That is, the square of the distance is not less than The system is in a safe state; when At that time, the distance between the two had exceeded the safe distance threshold, posing a risk of collision or indicating a highly unsafe situation.

[0070] The core advantages of defining CBF using the squared difference of distance form include the following:

[0071] a. Advantage of smoothness: It's about location. The continuous differentiable function avoids the singularity problem that may occur when calculating the derivative of the absolute value function in the traditional distance difference form, such as the discontinuity of the derivative when the distance between two agents is zero.

[0072] b. Computational simplicity: Its derivative expression does not contain square root operations, making it more concise and effectively reducing the complexity of subsequent control law solutions and real-time calculations.

[0073] c. Security equivalence: and They are equivalent in terms of safety determination and can accurately characterize safety constraints.

[0074] S13. Calculation of the first derivative of the control barrier function:

[0075] The first derivative of the control barrier function with respect to time This reflects the dynamic trend of safety margin changes. (Regarding...) The time derivative is derived as follows:

[0076] ;

[0077] in,( For intelligent agents point to The relative position vector, ( ) for intelligent agents Compared to intelligent agents The relative velocity vector. The sign of the dot product is determined by the dot product of the two vectors: when the dot product is negative, This indicates that the two agents are approaching each other and the distance decreases; when the dot product is positive, This indicates that the two agents are moving further apart, and the distance between them is increasing.

[0078] Control barrier function It represents the square of the safety margin between two agents in the current state, and its core safety criterion and safety margin are related. Equivalently, the first derivative of this function with respect to time, ḣij (x), reflects the dynamic trend of this safety margin, which can be used to determine whether the system is approaching a safe or dangerous state.

[0079] In traditional CBF safety control, constraints are typically used. ,in Adjustable parameters are used to ensure that the system not only does not tend towards danger, but also "bounces" back to its original state when approaching the danger boundary.

[0080] Based on this idea, in some embodiments, step S2 is designed with the following multi-level calculation process to generate continuous and interpretable risk prediction values, so as to achieve hierarchical decision-making and early warning; the specific steps include:

[0081] S21. Constructing basic risk trend indicators The risk depends not only on... Speed ​​also depends on the current Therefore, the formula for calculating the basic risk trend indicator is:

[0082] ;

[0083] in, The constant coefficient is positive. This indicates that the system state tends to evolve towards an unsafe region, and when When the value approaches zero (i.e., close to the safety boundary) or is negative (i.e., has entered the unsafe zone), even if Even for small negative values ​​(such as -0.1), due to the amplification effect of γ, It may still show a large negative value, thus indicating risk earlier. Therefore, we take... As a risk trend factor that quantifies the severity of risk evolution.

[0084] S22. To obtain a dimensionless and easily comparable risk indicator, the risk trend factor is normalized to obtain the normalized risk gradient. The formula for calculating the normalized risk gradient is:

[0085] ;

[0086] in, It is a very small positive number. Or according to The magnitude selection; the The physical meaning can be understood as:

[0087] when That is, in a safe state, The magnitude of the value reflects the "rush" toward the zero level set, that is... The relative velocity at which the corresponding critical state "rushes". If If gij > 1, it means that the rate of safety margin consumption exceeds the unit threshold, indicating that the safety margin is being consumed rapidly.

[0088] when Approaching zero, even the smallest negative value representing a dangerous trend... Its value will also be significantly amplified, thus clearly indicating that the system has a high sensitivity near the critical state;

[0089] when That is, when the system has entered an unsafe region, the denominator is negative. or values ​​close to At this point, if the molecule is still positive, that is... The system continues to trend towards a more dangerous state. When the absolute value is greater than 1, the specific result is determined by... The sign and size are both determined.

[0090] S23, Normalized Risk Gradient Perform truncation, so that This process retains only trend values ​​indicating an increase in potential risk, excluding cases of decreased or no risk; the truncation process is used to exclude negative or decreasing trends. Setting the value to zero focuses only on and quantifies scenarios where potential risks increase.

[0091] S24, Based on nonnegative normalized risk gradient By employing a nonlinear continuous mapping function with saturation characteristics, Mapped to continuous risk prediction values ​​between 0 and 1 This enables hierarchical decision-making and early warning operations. The mapping function is a generalized Sigmoid class function, and its function expression is:

[0092] ;

[0093] Where k is a real number controlling the steepness of the mapping curve, i.e., the risk value pair. Sensitivity to change.

[0094] This embodiment uses a Sigmoid mapping function to ensure... It possesses continuity, smoothness, and differentiability, while also being clearly defined. Follow A monotonically increasing mathematical mapping relationship; based on this, a specific method for calibrating the risk prediction sensitive interval by adjusting the parameter k is described, with the specific technical effects and value rules as follows:

[0095] Depending on the system state and Continuous and smooth changes avoid the risk value jump problem that may be caused by hard threshold judgment, which helps to improve the stability of subsequent control decisions; The value of is normalized within the interval [0,1), and its value can theoretically approach 1, where 0 intuitively corresponds to a low-risk state, and a value close to 1 corresponds to a high-risk state. This provides convenience for setting risk alarm levels and integrating multiple risk sources; the mapping function has differentiable properties. The gradient relative to the system state can be calculated, providing feasibility for implementing gradient-based risk optimization control algorithms. Meanwhile, It exhibits a clear monotonically increasing pattern, and its value corresponds precisely to the system's risk state:

[0096] when At times, such as when the system is far from an insecure area or The value is greater than the safety boundary, such as Greater than the safety boundary threshold and , ,but This indicates that there is no immediate risk of collision; when For example, Approaching zero and For significantly negative values, ,but This indicates an extremely high risk of collision; therefore, it is evident that with... The increase, It can smoothly transition from 0 to 1, enabling accurate and continuous quantitative assessment of system collision risks.

[0097] By adjusting the parameters This allows for the calibration of the sensitive range for risk prediction; for example, it allows setting a range such that when... When it reaches a certain level that represents "significant urgency", The risk level can be adjusted to 0.5 or another preset intermediate risk level. This adjustable feature further enhances the adaptability of the solution in this embodiment to different application scenarios and meets diverse risk assessment needs.

[0098] The above process ensures that the obtained preliminary risk prediction value is continuous and differentiable everywhere, effectively overcoming the problem of sudden changes in risk prediction value caused by traditional hard threshold methods, and laying a solid foundation for subsequent stable control or decision-making algorithms based on this risk value.

[0099] The above calculations are based on CBF and its derivative. It can effectively reflect the current system safety margin and its changing trends. However, it is essentially still a prediction based on the current instantaneous state and may not fully capture the long-term collision probability implied by the future trajectories of the agents, especially in certain geometric interaction scenarios. For example, if the current distance between two agents is still manageable... The collision is not high, but its velocity vector foreshadows an inevitable collision in the near future. Conversely, the two agents might approach each other at high speed, leading to an instantaneous... Very high, The speed also increases accordingly, but they will actually pass each other safely. To compensate for this deficiency, a velocity obstacle (VO) is introduced in some embodiments. Make forward-looking revisions. Specifically:

[0100] S3. Speed ​​Obstacle Criterion: Based on the speed obstacle principle, predictive parameters are calculated under the assumption that both parties maintain their current constant speed. Specifically:

[0101] S31, Command the intelligent agent and The current relative position is The relative speed is Computational intelligent agents and The moment when they approach each other and reach the closest distance ;in, Represents the vector dot product. Denotes the Euclidean norm of a vector; only if At that time, it was determined that the two would be closer in the future;

[0102] S32, for calculating energy bodies and The risk of collision at some future time is defined by the following criteria:

[0103] At any moment Computational intelligent agents and Minimum predicted distance between If both conditions are met or (or equivalent land, or) Then determine the intelligent agent; speed Compared to intelligent agents Located within the collision speed barrier zone, this indicates that if both parties maintain their current speeds, a future collision or a distance less than the safe distance is possible; among which... A positive time threshold is used to ensure that the timeframe is in the future. This is the preset safe distance threshold.

[0104] This embodiment calculates the intelligent agent. and Minimum predicted distance between The method is as follows:

[0105] The direct formula is: ;

[0106] The square form is: ;

[0107] Choose one of the two; among which:

[0108] For the three-dimensional case, It is a cross product;

[0109] In the two-dimensional case, the squared modulus of the cross product is defined as: The formula in square form is... Valid for a period of time, among which It is a positive number close to zero. In this embodiment, the value is taken as 0.001~0.01 to avoid division by zero error.

[0110] S4. Risk Cost Correction: Based on the predicted nearest point time obtained in step 3. sum and minimum prediction distance and safe distance The relationship between the initial continuous risk forecast value and the initial continuous risk forecast value. Perform a cost adjustment to obtain the adjusted risk value. Specifically, there are two situations:

[0111] First, eliminate false collisions to reduce the risk of false alarms: if the risk value obtained in step S2... Higher than the preset threshold The analysis results based on the VO criterion satisfy... or This means that no actual collision will occur in the future; in other words, the current situation... This falls under the category of "pseudo-conflict" or "high-risk in the short term but safe in the long term." In this case, the current situation is adjusted according to the following formula. Attenuation is performed to obtain the corrected risk value. :

[0112] ;

[0113] in, It is an attenuation coefficient, and in this embodiment, it is selected as 0.3 or 0.5.

[0114] Will Designed for and A function of the difference, which satisfies the following relationship: The larger and The larger the difference, that is Far exceeding the safe distance threshold ; The smaller the value of , the more significant the decrease in risk value.

[0115] Second, strengthen real collision warnings to improve the risk of missed reports: If the risk value obtained in step S2 Below the preset threshold The analysis results based on the VO criterion meet the conditions. and That is, in the future Collisions or entry into unsafe zones may occur at any time; that is to say, the current... This constitutes a serious threat situation. In this case, the current situation should be assessed using the following formula. Make corrections to improve risk predictions and ensure the system can respond promptly:

[0116] ;

[0117] in, This is an enhancement coefficient, which is selected as 0.3 or 0.5 in this embodiment; the effect of this formula is that when the value obtained in step S2 is... At very low levels, 1- Close to 1, after correction It will significantly improve (for example, if) ,but If the result obtained in step S2 There is already a medium risk value, such as This will further push it towards 1. This measure aims to provide early warning of potential collision risks that are not fully reflected in the instantaneous CBF index.

[0118] Through the above two-way correction, the risk prediction method of the present invention can incorporate consideration of future trends while maintaining sensitivity to immediate dangers, thereby achieving a better balance between avoiding over-conservatism and preventing the underreporting of key risks.

[0119] S5: Aggregate computation for final risk prediction: For a system with multiple agents, the above risk prediction method can be applied to each pair of agents. For a specific intelligent agent It faces challenges from all other intelligent agents in the environment. ( The collision risk can be assessed by summarizing all relevant information. (or revised) This is obtained by using the maximum risk criterion. A direct and commonly used strategy is to adopt the maximum risk criterion, that is, the agent... Overall instantaneous risk Defined as its relationship with any other intelligent agent Maximum pairwise risk value:

[0120] ;

[0121] in This represents the final risk value calculated through steps 1-4 and possibly adjusted by VO.

[0122] The pseudocode structure for the multi-agent collision risk prediction method that integrates the control barrier function and velocity barrier is as follows:

[0123]

[0124] To verify the effectiveness and superiority of the multi-agent collision risk prediction method integrating CBF and VO proposed in this invention, such as... Figure 3As shown in a and b in the diagram, in a typical "pseudo-collision" scenario, although the three agents are relatively close at the current moment and have a certain approaching speed, their future trajectories will not actually intersect, and there is no risk of collision. Traditional methods based on fixed distance thresholds, which only focus on instantaneous distance, may overestimate the risk in such situations, leading to unnecessary avoidance behaviors. However, the method of this invention, through the forward-looking judgment of VO in step S4, identifies this as a pseudo-collision, thereby attenuating the initial risk value obtained in step S3 based on CBF and Sigmoid mapping, and outputting a lower risk value that is more in line with the actual situation, avoiding over-conservatism.

[0125] In contrast, such as Figure 4 As shown in a and b in the diagram, in a "potential real collision" scenario, the initial distance between two agents is acceptable, but if they maintain their current speed and orientation and take no action, a collision will occur in the future. Traditional distance-based methods underestimate or even ignore this risk because the current distance has not reached a threshold. The method of this invention, however, by leveraging the sensitive capture of dangerous trends by CBF and its derivative in step S2 and the accurate prediction of future trajectory conflicts by VO in step S4, can significantly enhance the warning of such real collision threats, output high risk values ​​in a timely manner, and provide sufficient early warning for agents to take avoidance measures.

[0126] like Figure 5 As shown, the overall curves of risk prediction values ​​as a function of relative distance between agents are compared between the method of this invention and the traditional distance-based method. It can be seen that the risk value of the traditional method exhibits a step-like abrupt change near the safe distance threshold, lacking smoothness. In contrast, the method of this invention, benefiting from the continuous mapping characteristics of the Sigmoid function in step S3 and the comprehensive consideration of dynamic trends (CBF derivative) and future predictions (VO correction), produces risk prediction values ​​that change more smoothly and continuously with distance. Furthermore, it reflects the risk growth trend earlier, starting to increase gradually when far from the collision boundary and rapidly reaching high values ​​when truly dangerous, making the risk prediction more forward-looking and scientific.

[0127] This invention's method is not only applicable to risk prediction among autonomous vehicles, but can also be widely applied to various multi-agent systems such as drone swarms, multi-robot collaboration, and human-machine integration, providing crucial risk measurement data for their autonomous decision-making and safe behavior planning. By adjusting parameters at each stage (e.g., (Including the time / distance threshold in the VO criterion), the method of this invention can flexibly adapt to the security requirements and dynamic characteristics of different application scenarios. This invention provides a risk prediction framework that takes into account real-time performance, accuracy, and foresight, and can perform timely and accurate risk prediction for interactions between multiple agents to support autonomous navigation, trajectory planning, and collaborative control decisions of multi-agent systems, thereby improving the overall system's safety margin, operational efficiency, and intelligence level.

[0128] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A multi-agent collision risk prediction method that integrates control barrier functions and velocity barriers, characterized in that, Includes the following steps: S1. For any pair of agents that may interact, obtain their positions. and speed According to the preset minimum safe distance Construct control barrier function And calculate its first derivative with respect to time. Specifically: ； ； in, Represents intelligent agents and The Euclidean distance between them S2. Based on the control barrier function Its first derivative The original risk characteristics are calculated, and then normalized and nonlinearly mapped to obtain preliminary continuous risk prediction values. ; S3. Based on the speed barrier principle, calculate the predicted parameters assuming both parties maintain their current constant speeds. These predicted parameters include at least the predicted closest point time. and minimum prediction distance ; S4. Predict the nearest point time based on the result obtained in step 3. sum and minimum prediction distance and safe distance The relationship between the initial continuous risk forecast value and the initial continuous risk forecast value. Make adjustments to obtain the revised risk value. ; S5. For any intelligent agent Combine it with all other intelligent agents Between As the intelligent agent Final instantaneous collision risk value .

2. The method as described in claim 1, characterized in that, The implementation method of step S2 includes: S21. Constructing basic risk trend indicators The formula for calculating the basic risk trend indicator is as follows: ； in, The constant coefficients are positive; take As a risk trend factor that quantifies the severity of risk evolution; S22. Normalize the risk trend factors to obtain the normalized risk gradient. The formula for calculating the normalized risk gradient is: ； in, It is a positive number. Or according to The magnitude selection. 3.S23, Normalized Risk Gradient Perform truncation, so that This is to retain only trend values ​​indicating an increase in potential risk, excluding scenarios where risk decreases or there is no risk. S24, Based on non-negative normalized risk gradient Using a generalized Sigmoid class function to Mapped to continuous risk prediction values ​​between 0 and 1 This enables tiered decision-making and early warning operations; its function expression is: ； Where k is a real number controlling the steepness of the mapping curve, i.e., the risk value pair. Sensitivity to change.

4. The method as described in claim 2, characterized in that, The truncation process in step S23 is used to truncate negative or risk-reducing trends. Setting the value to zero focuses only on and quantifies scenarios where potential risks increase.

5. The method as described in claim 1, characterized in that, The implementation method of step S3 includes: S31. Calculate the predicted closest point time assuming both parties maintain their current constant speeds. Specifically: Make intelligent agents and The current relative position is The relative speed is ; Calculate the most recent time point for prediction ;in, Represents the vector dot product. Denotes the Euclidean norm of a vector; only if At that time, it was determined that the two would be closer in the future; S32, Based on the nearest point time predicted in step S31 Computational intelligent agents and Minimum predicted distance between The minimum prediction distance Calculate using any of the following methods: Method 1: The direct formula is: ; Method 2: The square form is: ; In the three-dimensional case, The cross product; in the two-dimensional case, the squared modulus of the cross product is defined as: ; Where a and b are two-dimensional vectors; , Let x and y represent the components of vector a, respectively. , Let the x-component and y-component of vector b be represented respectively; () represents the scalar result of the cross product of two-dimensional vectors; S33, Based on the predicted nearest point time and minimum prediction distance Assess collision risk: If all conditions are met and or Then determine the intelligent agent. speed Located in the intelligent agent The collision speed obstacle zone, in which A positive time threshold. This is the preset safe distance threshold.

6. The method as described in claim 1, characterized in that, The correction in step S4 has two cases: First, eliminate spurious conflicts: when the risk value obtained in step S2... Higher than the preset threshold However, the assessment of collision risks indicates future actual safety. or At that time, through the attenuation coefficient reduce ; Second, strengthen the real collision warning: when the risk value obtained in step S2 Below the preset threshold However, assessing collision risk clearly predicts collisions. and At that time, through the enhancement coefficient promote .

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