A time elastic band trajectory planning method based on dynamic parabolic control barrier function and game enhancement

Abstract

The application relates to the technical field of automatic control, in particular to a time-elastic track planning method based on a dynamic parabolic control barrier function and game enhancement, which jointly optimizes track nodes and time intervals to obtain a track node sequence with time stamps, inputs a dynamic parabolic control barrier function module to calculate a dynamic safety cost based on relative motion states, simultaneously inputs a game enhancement module to calculate a game guide cost based on a non-cooperative dynamic game Nash equilibrium, calculates weight coefficients of each cost according to an environment complexity index, and weights and sums a static basic item and the above-mentioned costs to form a target function to solve an optimal track. The application can consider the relative speed and acceleration of obstacles to enhance time foresight, generate a collision-free track in a time-space joint domain to improve time-space consistency, generate a consistent interaction reference through Nash equilibrium to improve multi-agent interaction coordination, and reduce calculation complexity based on a dynamic clipping mechanism.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, specifically to trajectory planning, obstacle avoidance control, control barrier function (CBF) application, and multi-agent game decision-making techniques and methods for unmanned aerial vehicles or aircraft in complex dynamic environments. Background Technology

[0002] With the widespread application of unmanned systems in complex environments, trajectory planning technology has become one of the core technologies for ensuring flight safety and mission efficiency. Existing trajectory planning methods are relatively mature in handling static obstacles, capable of generating geometrically smooth and dynamically feasible local trajectories under known environmental structures. However, in real complex low-altitude environments, planners also need to deal with moving obstacles such as other aircraft, birds, ground-based takeoff targets, and temporary dynamic disturbances. A trajectory that does not geometrically intersect with the current position of an obstacle does not mean that it will remain safe in the future; an obstacle with a large current clearance, if its velocity direction is directly facing the flight corridor, may rapidly evolve into a high-risk conflict target in a short period of time. Therefore, dynamic planning needs to embed relative position, relative velocity, relative acceleration, and potential interaction behaviors into the trajectory and incorporate them into a spatiotemporal joint optimization process.

[0003] In existing technologies, the Time Elastic Band (TEB) method, by jointly optimizing trajectory nodes and time intervals, exhibits good geometric smoothness and dynamic executability in static environments. However, traditional TEB methods have shortcomings when dealing with dynamic obstacle scenarios: First, traditional safety constraints mainly rely on instantaneous distance fields, which are difficult to describe the movement trend of obstacles and future prohibited areas, lacking temporal foresight and easily leading to planning lag or insufficient safety margins; Second, when there are multiple dynamic obstacles or high-density encounters in the scenario, relying solely on a unidirectional prediction model can easily lead to repeated yielding, local deadlocks, and decision oscillations; Third, traditional methods do not incorporate multi-agent interaction behaviors into a unified modeling framework, making it difficult to generate consistent avoidance references in complex encounter scenarios. Summary of the Invention

[0004] To address the aforementioned problems, this invention discloses a time-elastic band trajectory planning method based on a dynamic parabolic control barrier function and game-enhanced theory.

[0005] The specific implementation steps and the collaborative working mechanism of each module are as follows:

[0006] I. Overall Trajectory Planning Process

[0007] The trajectory planning method of this invention mainly includes five core steps: explicit time modeling, dynamic safety cost calculation, game-guided cost calculation, adaptive weight adjustment, and iterative optimization solution.

[0008] Step S1: Receive the initial path, process it through the explicit time modeling module, jointly optimize the trajectory nodes and time intervals to obtain a sequence of trajectory nodes with timestamps;

[0009] Step S2: The above-mentioned trajectory node sequence with timestamps is input into the Dynamic Parabolic Control Barrier Function (DPCBF) module and the game enhancement module, respectively. The DPCBF module calculates the dynamic safety cost based on the relative motion state of the moving body and the dynamic obstacle; the game enhancement module calculates the game guidance cost based on the multi-agent interaction process.

[0010] Step S3: Through the adaptive weight adjustment module, calculate the weight coefficients of static basic items, dynamic security costs, and game guidance costs based on the complexity index of the current environment.

[0011] Step S4: The static basic term, dynamic security cost, and game guidance cost are weighted and summed according to the weight coefficients calculated above to form a unified objective function. This objective function is then fed into the iterative optimizer to solve and output the optimal trajectory.

[0012] II. Functional Modules Involved in This Technical Solution

[0013] 1. Explicit Temporal Modeling Module

[0014] To ensure precise control over the timing of dynamic obstacle avoidance, this scheme uses pose-time as the optimization input and the time interval as an independent variable that can be optimized. This mechanism allows the planner to adjust the UAV's passage speed in a specific area by stretching or compressing local time zones. Simultaneously, to ensure the physical feasibility and logical rationality of the planning, this module sets strict temporal causality constraints to ensure that the time sequence does not reverse, as well as speed boundary constraints corresponding to the maximum and minimum flight speeds to avoid generating speed commands that exceed physical limits.

[0015] 2. Dynamic Parabolic Controlled Barrier Function (DPCBF) Module

[0016] Traditional static distance fields are insufficient to describe obstacle motion trends. This solution constructs a time-varying parabolic safety boundary to generate dynamic safety costs. Specifically:

[0017] Obtain the relative position, relative velocity, and relative acceleration between the moving object and the dynamic obstacle, and calculate the projected distance of the relative position in the direction perpendicular to the relative velocity;

[0018] By combining the shape coefficient, the component of relative acceleration along the relative position direction, and the safety radius, a dynamic parabolic barrier function that incorporates the above kinematic information is constructed.

[0019] The barrier condition based on this function is softened into a penalty term. When the trajectory node is inside the safe set, the penalty term is zero. When it enters the dangerous area, the cost increases rapidly, thus forming a dynamic safety cost that drives the trajectory away from the potential conflict area.

[0020] 3. Spatiotemporally Consistent DPCBF Field Construction and Computation Strategy

[0021] To balance computational efficiency and optimized convergence performance, this scheme performs field-based construction and gradient optimization of DPCBF:

[0022] Field Construction and Query: The continuous-time evolution process is approximated using discrete-time sampling, and a soft-min approximation technique is used to achieve fast querying of the spatiotemporal potential field. Simultaneously, a dynamic ROI pruning mechanism is introduced, calculating only dynamic obstacles within the UAV's field of view that pose a potential flight threat, thereby significantly reducing computational complexity.

[0023] Hybrid gradient calculation strategy: When calculating the potential field gradient during trajectory optimization, a hybrid strategy combining analytical and numerical gradients is adopted. The analytical gradient is used to preserve the physical meaning of the potential field direction information, while the numerical gradient is used to compensate for numerical oscillations in non-smooth regions. By dynamically adjusting the fusion weights, the analytical gradient weight is increased when the environment is stable and decreased when obstacles are dense and minimum value switching is frequent, thereby enhancing numerical stability.

[0024] 4. Game Theory Enhancement Module

[0025] In high-density encounter scenarios, this scheme models the multi-agent encounter process as a non-cooperative dynamic game. By constructing a Hamiltonian and solving the Riccati equation, an open-loop Nash equilibrium is obtained, generating feedback control strategies for each participant as reference trajectories. Subsequently, a game guidance term is constructed based on this reference trajectory, serving as the aforementioned game guidance cost. In this module, an adjustment parameter is introduced to control the proportion of the game reference in the overall replanning, providing a consistent avoidance reference without weakening the dynamic feasibility of the original time-elastic band framework.

[0026] 5. Adaptive Weight Adjustment Module

[0027] To avoid introducing excessive redundant constraints in simple scenarios, this solution designs an adaptive dynamic weight adjustment strategy. Based on a normalized complexity index, which includes the number of dynamic obstacles, average relative speed, minimum expected conflict time, and local spatial congestion, the weight coefficients are dynamically adjusted. The weight function adopts a sigmoid form to achieve a smooth transition.

[0028] When the environment complexity is low, the dynamic weights are close to 0, and the system degenerates into a static basic framework to improve efficiency.

[0029] When the environmental complexity is moderate, the weight of dynamic safety constraints increases while the weight of game theory is small, and the system mainly relies on DPCBF to achieve obstacle avoidance.

[0030] When the environment is highly complex, dynamic safety constraints and game-theoretic enhancements are significantly activated. The system focuses on referencing the reference path given by the game outcome to resolve local deadlock and decision oscillation.

[0031] III. System Deployment

[0032] Corresponding to the above method, the present invention also provides a time-elastic band trajectory planning system based on a dynamic parabolic control barrier function and game-enhanced theory, the system comprising:

[0033] The system comprises an explicit time modeling module, a DPCBF module, a game-theoretic enhancement module, an adaptive weight adjustment module, and an optimization module. These modules work collaboratively to perform the data reception, cost calculation, weight allocation, and optimal trajectory solving functions outlined in the above methods, forming a complete closed-loop trajectory planning system.

[0034] The advantages of this invention are:

[0035] 1. Explicit time parameterization mechanism: Time is embedded as an independent optimizable variable into the trajectory planning framework to achieve joint optimization of pose and time, allowing the planner to achieve fine control of dynamic obstacle avoidance timing by adjusting local time bands.

[0036] 2. Dynamic Parabolic Control Barrier Function (DPCBF): By constructing a time-varying parabolic safety boundary that integrates relative position, relative velocity, and relative acceleration, the obstacle motion state is explicitly incorporated into the safety criterion, enabling forward-looking modeling of potential future collision risks and compensating for the lack of time foresight in traditional static distance fields.

[0037] 3. Spatiotemporal consistent DPCBF field construction method: The continuous-time evolution process is transformed into a discrete-time sampling approximation. The soft-min technique is used to realize the fast query of the spatiotemporal potential field. The hybrid strategy of fusion of analytical gradient and numerical gradient is used to ensure optimized convergence performance, taking into account both computational efficiency and numerical stability.

[0038] 4. Game-theoretic Enhanced Reference Trajectory Generation Mechanism: Differential game theory is introduced into high-interaction encounter scenarios to establish a multi-agent non-cooperative dynamic game model. A consistent avoidance reference is generated by solving the open-loop Nash equilibrium and embedded as a guiding term into the TEB objective function, which effectively alleviates the problems of repeated yielding, local deadlock and decision oscillation in dense encounters of multiple agents.

[0039] 5. Adaptive weight dynamic adjustment strategy: Based on environmental complexity indicators (including the number of dynamic obstacles, average relative speed, minimum expected conflict time, local space congestion, etc.), the weight coefficients of dynamic safety constraints and game enhancement terms are dynamically adjusted to achieve a smooth transition from a static basic framework to a complete dynamic game framework. Attached Figure Description

[0040] Figure 1 The flowchart shows the overall implementation process of constructing a spatiotemporally consistent DPCBF field and coupling it with the TEB planner in this invention. Detailed Implementation

[0041] 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. 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.

[0042] The trajectory planning method provided by this invention includes the following technical modules: explicit time modeling module, dynamic parabolic control barrier function (DPCBF) module, spatiotemporal consistent DPCBF field construction module, game enhancement module, and adaptive weight adjustment module.

[0043] The data flow relationship between the modules is as follows: the input initialization path is processed by the explicit time modeling module to obtain a sequence of trajectory nodes with timestamps; this sequence is simultaneously input into the DPCBF module and the game enhancement module to calculate the dynamic security cost and the game guidance cost, respectively; the adaptive weight adjustment module calculates the weight coefficient of each cost term according to the environmental complexity index; finally, the unified objective function is composed of the weighted sum of the static basic term, the DPCBF cost term, and the game enhancement cost term, and is sent to the iterative optimizer to solve for the optimal trajectory.

[0044] In dynamic obstacle avoidance scenarios, the safety of trajectory points depends not only on their spatial location but also, more importantly, on their positioning in the time coordinate system. Therefore, the input for optimization should be expanded to pose-time:

[0045]

[0046] in, For the first The position of each trajectory point This is the absolute moment when the drone arrives at that point.

[0047] If time interval As optimization variables, we have:

[0048]

[0049] This parameterization approach makes time an explicit variable that can be optimized, allowing the planner to adjust the drone's speed in a specific area by stretching or compressing local time bands, thereby avoiding high-speed obstacles.

[0050] To ensure temporal causality, the following must be true:

[0051]

[0052] At the same time, time stretching and compression must be subject to strict boundary constraints to avoid generating speed commands that exceed physical limits:

[0053]

[0054] in, The minimum time interval corresponds to the maximum flight speed of the drone; The maximum time interval corresponds to the minimum flight speed of the drone. The overall cost function is:

[0055]

[0056] in, The objective is to optimize the static trajectory, including a smoothing term. Safety corridor constraints Dynamic constraints and time regularization terms ; For dynamic safety constraints; This is an enhancement for multi-agent interaction; and This is a weighting function that adaptively adjusts based on environmental complexity.

[0057] The Control Barrier Function (CBF) is an application of barrier functions in control systems to ensure system safety. Its basic idea is to construct a scalar function to describe the safe set in the system's state space, and to use the Lyapunov forward invariance condition to ensure that once the system trajectory enters this set, it will not leave.

[0058] For a general affine system, it can be written as:

[0059]

[0060] in, Indicates the system status. For designable control inputs, and It is a locally continuous Lipschitz function.

[0061] The security requirements of a system can typically be defined by a security set. Characterization:

[0062] in, It is a continuously differentiable function.

[0063] Traditional barrier functions typically use Euclidean distance as their core, reflecting only the static geometric relationship between the flying object and the obstacle at the current moment, making it difficult to accurately characterize the potential threat posed by dynamic obstacles to the system. To address this issue, this invention reconstructs the Dynamic Parabolic Safety Function (DPCBF) into a time-varying control barrier function.

[0064] Let the relative positions between the moving body and the dynamic obstacle be . The relative speed is The relative acceleration is .set up Let the relative velocity direction be a unit vector, then the projected distance of the relative position in the direction perpendicular to the relative velocity direction is denoted as:

[0065]

[0066] Under the deterministic assumption, the obstacle is defined by a dynamic parabolic barrier function in the future time t_{la}:

[0067]

[0068] in, This is a shape coefficient used to adjust the safety envelope width of the parabola; This represents the component of relative acceleration along the direction of relative position. The safety radius is determined by comprehensively considering the aircraft size, obstacle radius, and additional safety margin.

[0069] The physical meanings of each component of this function are as follows:

[0070] The item describes the degree of lateral deviation in the direction of relative velocity: when the lateral distance is large enough, even if the relative velocity is high, it may not necessarily constitute a direct collision; The term characterizes the trend of safety margin contraction as relative velocity increases, making the system more inclined to avoid risks in advance; This reflects future maneuvering trends; as obstacles continue to accelerate and approach, the safety boundary will be further compressed. The term provides the minimum safety envelope.

[0071] The safe set is defined as:

[0072]

[0073] To maintain consistency with the TEB objective function form, this invention softens the barrier condition into a penalty term:

[0074]

[0075] The dynamic barrier cost term is defined as:

[0076]

[0077] in, The number of dynamic obstacles included in the current planning window.

[0078] This definition satisfies: if a node is inside a safe set, then If the cost is zero, the cost increases rapidly in a quadratic form if the area is entered, thus driving the trajectory away from potential conflict areas during optimization.

[0079] DPCBF exhibits spatiotemporal consistency. Unlike static safety boundaries, the protected area constructed by DPCBF evolves over time, forming a dynamically expanding parabolic safety envelope. This envelope considers the current relative velocity and estimates the future motion trend of the obstacle through an acceleration term, thus achieving predictive modeling of potential future collision risks.

[0080] To optimize the adaptation of the TEB framework to DPCBF, it is not feasible to perform long-term continuous integration over all obstacles at each node update. This invention proposes a spatiotemporally consistent DPCBF field, which combines safety constraints with the time dimension to achieve more accurate trajectory planning.

[0081] Let the first three-dimensional space be the first... A dynamic obstacle, whose geometric shape is approximately sphere, with a radius of... Then at time... The original net distance is defined as:

[0082]

[0083] Further, a safety margin is introduced. The spacetime barrier function:

[0084]

[0085] when "Time" indicates the moment. It is in a safe state; otherwise, there is a risk of intrusion.

[0086] Define the minimum time interval as:

[0087]

[0088] Considering the computational requirements for potential field construction and online querying, this invention employs discrete-time sampling to approximate a continuous-time evolution process, transforming the continuous optimization problem into a minimum problem on a finite candidate set. To maintain the continuity and stability of the optimization process, a soft-min approximation is further used:

[0089]

[0090] in, The smoothing parameter is used to adjust the accuracy of the soft-min approximation. These are discrete-time sampling points.

[0091] Therefore, real-time calculated DPCBF queries can be uniformly transformed into directly accessible spatiotemporal secure fields. This applies to grid point locations. Its potential field can be expressed as:

[0092]

[0093] This field further utilizes a broadcast mechanism to achieve vectorized computation, thereby enabling parallel processing of multiple grid points and their time-sampled values:

[0094]

[0095] Here, ROI is the effective computation set, containing only dynamic obstacles within the UAV's field of view that may pose a potential flight threat. This dynamic pruning mechanism reduces the number of objects involved in the computation, thereby decreasing the overall computational complexity of the DPCBF field. Down to .

[0096] During trajectory optimization, the potential field gradient directly determines the update direction of the trajectory away from the potential collision region. This invention employs a hybrid strategy that combines analytical gradients and numerical gradients.

[0097] First, consider the single barrier potential function in continuous form:

[0098]

[0099] when When, its gradient can be written as:

[0100]

[0101] in, For the time corresponding to the minimum distance, we further have:

[0102]

[0103] Analytical gradients preserve the physical meaning of the potential field direction information, i.e., they always point away from obstacles. However, in actual calculations, since the minimum distance time is obtained by discrete-time sampling, and the minimum operator may introduce non-differentiable points when switching between multiple candidate time points, directly using analytical gradients can easily lead to optimization oscillations.

[0104] Therefore, this invention further introduces a numerical gradient for correction. For discrete potential fields... Central difference calculation can be used:

[0105]

[0106] Finally, the two types of gradients are fused according to their weights:

[0107]

[0108] in, For fusion weights. A larger weight is chosen when the environment is stable and the analytical model is reliable. When obstacles are dense and minimum value switching is frequent, appropriately reduce the value. To enhance numerical stability.

[0109] When there are only a few dynamic obstacles in the scene, forward-looking safety constraints based on obstacle avoidance (CBF) are usually sufficient to avoid collisions. However, in high-density dynamic scenes, other UAVs or cooperative / non-cooperative aircraft also have autonomous maneuvering capabilities. In this case, dynamic obstacle avoidance is no longer an optimal control problem for a single agent facing environmental disturbances, but evolves into a coupled decision-making problem under the mutual influence of multiple decision-makers.

[0110] This invention introduces differential game theory to model complex encounter processes as non-cooperative dynamic games, and generates a consistent interaction trajectory reference by solving Nash equilibrium.

[0111] Assume there are a total of The first intelligent agent, the... The state of each agent is: The control input is The overall system state is denoted as:

[0112] The system dynamics are expressed as:

[0113]

[0114] In a non-cooperative game framework, each agent aims to minimize its own cost function. This function considers its own flight cost, flight safety, and interactions with other participants. For the ... An agent, whose cost is defined as:

[0115]

[0116] To align with the form of the trajectory optimization problem, the discrete time window is... It can be written as:

[0117]

[0118] in:

[0119] The objective term is used to encourage the agent to approach its own objective and to measure the degree of deviation from the trajectory.

[0120] This is a control term used to suppress excessively large input amplitudes to ensure trajectory smoothness.

[0121] This is an interaction risk item used to avoid getting too close to other intelligent agents.

[0122] Because of the existence of interaction terms, each participant's optimal control will explicitly depend on the behavior of other participants, thus forming a typical game-coupling structure.

[0123] This invention employs Open-Loop Nash Equilibrium (OLNE) as the fundamental concept for solving multi-agent policies. When a set of control sequences... When an open-loop Nash equilibrium is formed, for any participant i and any feasible control sequence satisfy:

[0124]

[0125] This equilibrium state corresponds to a stable strategy configuration among the participants: under Nash equilibrium, no participant can obtain a higher return by unilaterally changing their strategy.

[0126] For linear quadratic differential games, the open-loop Nash equilibrium problem can be transformed into a problem of solving the corresponding partial differential equations by constructing the Hamilton-Jacobi-Bellman (HJB) equation.

[0127] First, construct the Hamiltonian, and construct the discrete-time Hamiltonian for each participant i:

[0128] When the optimal control input satisfies The optimal control law can be obtained at this time:

[0129]

[0130] in, The input matrix is ​​used for the system.

[0131] To achieve system closed-loop operation, the relationship between co-state variables and state variables needs to be established. Based on the adjoint equation structure in optimal control theory, it is assumed that the co-state variables can be represented as affine functions of the state:

[0132]

[0133] in, This represents the overall system state vector. It is a symmetric matrix. This is the bias vector.

[0134] Substituting the optimal control law into the system dynamics and costate equations yields the Riccati equation:

[0135] in, The system's overall state transition matrix. Input matrix to the system, The weight matrix is ​​controlled by all participants. The block diagonal matrix formed For the first Each participant at time The Ricardi matrix, By all participants The block diagonal matrix formed.

[0136] After solving the Riccati equation, participants can be defined. Feedback gain matrix:

[0137]

[0138] Ultimately, the open-loop Nash equilibrium control strategies of all participants can be uniformly represented in the form of state feedback:

[0139]

[0140] The encounter strategies obtained from differential game theory can provide a consistent avoidance reference for multi-agent interactions. However, if they are directly used to replace the local trajectory optimizer, it can easily weaken the continuous optimization capabilities of the original TEB framework in terms of dynamic feasibility and time allocation. Based on this, this invention does not regard the game module as an independent planner, but rather embeds it as a reference generator in the EGE-TEB optimization framework under high-interaction scenarios.

[0141] Let the reference trajectory obtained by the game theory solution be... Therefore, the game-leading term can be constructed based on this:

[0142]

[0143] Among them, the introduction This is used to adjust the proportion of game references in the overall replanning. When the interaction density increases and local channel competition intensifies, this weight can be appropriately increased to strengthen consistent avoidance behavior; when the scene is open or there are no significant dynamic conflicts, this weight should be decreased to make the planner revert to the standard dynamic optimization mode dominated by spatiotemporal safety constraints.

[0144] To avoid introducing too many redundant constraints in simple scenarios, this invention does not employ discrete switching, but instead defines a switching method based on environment state. The adaptive weighting function.

[0145] set up Normalized complexity metric:

[0146]

[0147] in: The number of dynamic obstacles; The average relative velocity; Minimum expected conflict time; Local space congestion level; These are the weighting coefficients. The weighting function uses the Sigmoid form:

[0148]

[0149]

[0150] in, For the Sigmoid function, This indicates the activation threshold for CBF and Game, and is usually... The activation threshold is higher.

[0151] When the environmental complexity is low, When all values ​​are close to 0, the system degenerates into a static basic framework; when the environmental complexity is moderate, Increase The system is still relatively small, and mainly relies on dynamic safety constraints to achieve obstacle avoidance; however, when the environment becomes more complex, and All are significantly activated, and the system will focus on the reference path given by the game result.

[0152] The above description is only a preferred embodiment of the present invention and is not intended to limit the ideas of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A time-elastic band trajectory planning method based on a dynamic parabolic control barrier function and game-enhancing techniques, characterized in that, Includes the following steps: S1: Receive the initial path, and jointly optimize the trajectory nodes and time intervals through the explicit time modeling module to obtain a sequence of trajectory nodes with timestamps; S2: Input the time-stamped trajectory node sequence into the dynamic parabolic control barrier function module to calculate the dynamic safety cost based on the relative motion state of the moving body and the dynamic obstacle; simultaneously input it into the game enhancement module to calculate the game guidance cost of multi-agent interaction; S3: The adaptive weight adjustment module calculates the weight coefficients of static basic items, dynamic security costs, and game guidance costs based on the environmental complexity index; S4: The static basic terms, dynamic security costs, and game-guided costs are weighted and summed to form a unified objective function, which is then input into the iterative optimizer to solve for the optimal trajectory.

2. The method according to claim 1, characterized in that, The explicit time modeling module takes pose-time as the optimization input. If the time interval is used as the optimization variable, the speed can be adjusted by stretching or compressing the local time band. It also satisfies the time causality constraint and the speed boundary constraint corresponding to the maximum and minimum flight speed.

3. The method according to claim 1, characterized in that, The process of constructing a time-varying parabolic safety boundary by the dynamic parabolic control barrier function module includes: obtaining the relative position, relative velocity, and relative acceleration between the moving body and the dynamic obstacle; calculating the projected distance of the relative position in the direction perpendicular to the relative velocity; constructing a dynamic parabolic barrier function by combining the shape coefficient, the component of the relative acceleration along the relative position direction, and the safety radius; and softening the barrier condition into a penalty term to form the dynamic safety cost.

4. The method according to claim 3, characterized in that, By constructing a spatiotemporally consistent DPCBF field, the time dimension is combined with security constraints: the continuous-time evolution process is approximated by discrete-time sampling, and the soft-min approximation technique is used to achieve fast query of the spatiotemporal potential field; at the same time, the ROI dynamic pruning mechanism is used to calculate only dynamic obstacles within the field of view that pose a potential flight threat, so as to reduce computational complexity.

5. The method according to claim 4, characterized in that, When calculating the potential field gradient during trajectory optimization, a hybrid strategy of fusion of analytical gradient and numerical gradient is adopted. When the environment is stable, the fusion weight of analytical gradient is increased, and when obstacles are dense and the minimum value changes frequently, the fusion weight of analytical gradient is decreased to enhance numerical stability.

6. The method according to claim 1, characterized in that, The game enhancement module models the multi-agent encounter process as a non-cooperative dynamic game. It solves the open-loop Nash equilibrium by constructing the Hamiltonian and the Riccati equation, and generates the feedback control strategies of each participant as reference trajectories. Based on the reference trajectories, it constructs game guidance terms as game guidance costs, and introduces adjustment parameters to control the proportion of game references in the overall replanning.

7. The method according to claim 1, characterized in that, The adaptive weight adjustment module dynamically adjusts the weight coefficients based on a normalized complexity index, which includes the number of dynamic obstacles, average relative speed, minimum expected conflict time, and local spatial congestion. The weighting function adopts the Sigmoid form. When the environmental complexity is low, the system degenerates into a static basic framework. When the complexity is medium, it mainly relies on dynamic security constraints. When the complexity is high, the weight of the reference path of the game result is strengthened.

8. A time-elastic band trajectory planning system based on a dynamic parabolic control barrier function and game-theoretic enhancement, characterized in that, include: The explicit time modeling module is used to jointly optimize trajectory nodes and time intervals, and output a sequence of trajectory nodes with timestamps. The DPCBF module is used to receive the trajectory node sequence and calculate the dynamic safety cost based on the time-varying parabolic safety boundary that integrates relative motion information. The game enhancement module is used to receive the trajectory node sequence and calculate the game guidance cost based on the Nash equilibrium solution of the non-cooperative dynamic game. The adaptive weight adjustment module is used to calculate the weight coefficients of each cost item based on the environmental complexity index. The optimization module is used to sum the static basic items, dynamic security costs, and game guidance costs according to the weight coefficients to form an objective function, and solve for and output the optimal trajectory.

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