Symbolic distance-based safe interactive dynamic game trajectory planning method

Abstract

The application discloses a kind of based on symbol distance's safe interaction dynamic game trajectory planning method, comprising: based on the spatial vehicle of convex polyhedron is dynamically modeled for agent and obstacle, combine symbol distance and construct the non-convex safety constraint between the agent and the obstacle, to avoid the safety redundancy problem caused by traditional circular model, expand the feasible solution space of path planning.Simultaneously, the non-convex safety constraint is equivalently converted into convex safety constraint, for the dynamic game trajectory planning optimization problem constructed, alternating optimization algorithm is used to solve, significantly reduce the solution complexity of dynamic game problem, effectively improve the calculation efficiency.In addition, the target function including safety distance term is also designed, through the adjustment strategy of weight coefficient and preset minimum distance, collaborative optimization efficiency and safety.The application can not only accurately model dynamic safety constraint between multiple vehicles, overcome the conservativeness of prior art, but also meet the real-time calculation requirements of trajectory planning under the framework of game theory.

Description

Technical Field

[0001] This invention relates to the field of trajectory planning and control technology, and in particular to a secure interactive dynamic game trajectory planning method based on symbolic distance. Background Technology

[0002] In autonomous driving scenarios involving dynamic multi-vehicle interactions, safe and efficient trajectory planning is a core challenge. Existing trajectory planning methods based on dynamic game theory often employ circular collision avoidance constraints to simplify safety modeling. However, due to their oversimplification of geometry, these methods are often too conservative, significantly reducing the feasible solution space for trajectory optimization and leading to rigid vehicle behavior (such as the "frozen robot problem") or low traffic efficiency.

[0003] It is worth learning from the various obstacle modeling techniques developed in the field of single-vehicle trajectory planning (usually based on model predictive control), whose core objective is to optimize computational efficiency and trajectory quality while ensuring obstacle avoidance safety. The main methods include:

[0004] Elliptical / Sphere Model: This method simplifies obstacles into two-dimensional ellipses or three-dimensional spheres. It is computationally simple and efficient, easily calculating distances and obstacle avoidance gradients, and is suitable for small-scale scenarios. However, its main drawback is that real-world obstacles (including vehicles) have complex and diverse shapes, making this simplification unable to accurately describe the true minimum distance. This results in poor obstacle avoidance performance in complex or closely interacting scenarios, and it also suffers from conservatism.

[0005] The safe corridor method models free space as a safe passageway using convex polygons (or polyhedra). This method offers good flexibility and can adapt to different scenarios. However, its significant drawback is that the cost of constructing a high-quality corridor is highly dependent on the obstacle discretization resolution and the expansion step size. Low resolution leads to over-conservatism, while high resolution results in high computational costs, especially when the trajectory needs to closely follow obstacles, where the construction process may become a bottleneck.

[0006] The method combines signed distance with biconvex reconstruction. Obstacles are modeled as convex polyhedra, and the distance between the vehicle and obstacles is accurately represented using signed distance. Biconvex reconstruction technology transforms non-convex collision avoidance constraints into nonlinear convex constraints. This method offers high accuracy, can handle complex shapes, and is applicable to various vehicle models. However, its key challenge lies in the fact that the transformation process introduces numerous equality and inequality constraints, significantly increasing the dimensionality and solution complexity of the optimization problem, making it difficult to meet the real-time requirements of dynamic interactive scenarios.

[0007] Linear Programming (LP) Collision Detection: This method transforms the collision detection problem into an efficient linear programming solution. It is computationally efficient and requires only a small number of variables to be introduced as the number of obstacles increases. However, its main limitations are: it only works for convex obstacles and cannot handle common non-convex shapes; and its application is often limited to combining with specific types of trajectory optimization algorithms (such as polynomial-based algorithms).

[0008] Potential field methods (such as ESDF, risk field, SDF Any-Shape): These methods drive away obstacles by constructing a virtual potential field (e.g., based on an extended symbolic distance field). These methods perform well in handling continuity. Methods like SDF Any-Shape offer improvements in efficiency and accuracy. However, common issues include the need to balance field resolution with computation time / memory consumption; in particular, methods like SDF Any-Shape require the trajectory to be differentiable with respect to time, limiting their application in complex scenarios involving discontinuities or emergency maneuvers.

[0009] While the methods described above each have their own applications in single-vehicle obstacle avoidance planning, they have significant shortcomings when directly applied to trajectory planning for dynamic multi-vehicle interactions (especially within a game theory framework):

[0010] The static obstacle assumption fails: In multi-vehicle interactions, other vehicles are themselves dynamically changing "obstacles," and their behavior interacts with the vehicle's decisions. Traditional single-vehicle obstacle avoidance methods typically assume that obstacles are static or that their behavior is known / predictable, which cannot effectively handle such interdependent dynamic interactions.

[0011] Contradiction between conservatism and efficiency: The conservatism problem is exacerbated in dynamic multi-vehicle scenarios by circular / elliptical models and safe corridor methods, resulting in overly cautious interaction behaviors (such as unnecessary parking and detours), which seriously reduces traffic efficiency and system smoothness.

[0012] Computational complexity challenge: While the symbolic distance method (biconvex reconstruction) boasts high accuracy, its high computational complexity makes it difficult to apply in dynamic games requiring rapid responses (involving multiple optimization agents and real-time decision-making). The LP method is also limited by the convex shape assumption.

[0013] Lack of interaction model: Existing methods mainly focus on how a bicycle avoids (static or dynamic) obstacles, lacking explicit modeling of the interaction decision-making process (such as competition, cooperation, and concession), which is the core value of game theory applied to trajectory planning.

[0014] The potential and limitations of the signed distance method:

[0015] Among geometric modeling methods, the symbolic distance method shows significant potential in multi-vehicle interaction safety constraint modeling due to its ability to accurately describe the minimum distance between objects of arbitrary shapes. It not only accurately characterizes vehicle-to-vehicle or vehicle-to-obstacle distances but also captures complex relative motion relationships between vehicles, which is crucial for ensuring safety in dynamic games. The introduction of biconvex reconstruction technology further enhances its feasibility. However, as mentioned earlier, its core bottleneck—the computational complexity caused by numerous constraints—becomes particularly prominent in dynamic game planning with an increasing number of interactive vehicles and a dramatic increase in the dimensionality of the state space, limiting its practical application effectiveness.

[0016] Therefore, there is an urgent need to develop a new trajectory planning method that can accurately model dynamic multi-workshop safety constraints (overcoming the conservatism caused by geometric simplification) and meet the real-time computation requirements under the game theory framework. Summary of the Invention

[0017] This invention provides a secure interactive dynamic game trajectory planning method based on symbolic distance, aiming to effectively solve the above-mentioned technical problems.

[0018] According to a first aspect of the present invention, the present invention provides a method for planning the trajectory of a secure interactive dynamic game based on symbolic distance, characterized by comprising the following steps:

[0019] Vehicle space based on convex polyhedra is used for dynamic modeling of intelligent agents and obstacles;

[0020] Construct non-convex safety constraints between the agent and the obstacle based on symbolic distance, and convert the non-convex safety constraints into equivalent convex safety constraints.

[0021] Construct a dynamic game trajectory planning optimization problem that includes an objective function and the convex safety constraints, wherein the objective function includes a safety distance term;

[0022] Solve the trajectory planning and optimization problem to output a safe trajectory that meets real-time requirements.

[0023] Furthermore, the spatial dynamics of the intelligent agent are described as follows:

[0024] at the same time

[0025] In the formula, A = G[R(x k )] -1 b = g + G[R(x) k )] -1 t(x k ), R(x k ) is the rotation matrix, t(x) k ) is the translation vector. Let the intelligent agent be a convex polyhedron in the coordinate system, defined as G and g are intelligent agents;

[0026] The spatial dynamics of the obstacle are described as follows:

[0027]

[0028] In the formula, Let A represent the set of real numbers, indicating that y belongs to the two-dimensional real number space, that is, y is a two-dimensional vector, where each component of the vector is a real number, m represents the m-th obstacle, M represents the total number of obstacles, and A ( m) and b ( m) represent the spatial representation of the m-th obstacle.

[0029] Furthermore, the safety constraints between the intelligent agent and the obstacle are represented as follows:

[0030]

[0031] Construct non-convex safety constraints between the agent and the obstacle based on symbolic distance:

[0032]

[0033] In the formula, Let it be a distance function. The osmotic function,

[0034] Introducing dual variables transforms the non-convex security constraint into a dual form:

[0035] satisfy:

[0036]

[0037] For the non-convex form ||A in the above equation T λ||=1, using a convex relaxation algorithm, the above constraint is simplified to a convex form:

[0038] satisfy:

[0039]

[0040] The convex security constraints between the agents are then represented as follows:

[0041] satisfy:

[0042]

[0043] Furthermore, the distance function is defined as:

[0044]

[0045] The permeability function is defined as:

[0046]

[0047] Furthermore, the objective function is expressed as follows:

[0048]

[0049] In the formula, w is the weighting coefficient. This refers to the safe distance item.

[0050] Furthermore, the objective function adopts a fusion weighting mechanism of safety distance term and weight coefficient. The influence of safety constraint is controlled by a collaborative adjustment strategy of weight coefficient and preset minimum distance safety constraint. Specifically, when the preset minimum distance increases, the weight coefficient increases accordingly to strengthen the optimization of safety distance and ensure the conservatism of behavior under higher safety requirements.

[0051] Furthermore, an alternating optimization algorithm is used to alternately optimize the dual variables and the trajectory variables, thereby solving the trajectory planning optimization problem. The process is as follows:

[0052] The original updates for the dual variables λ,μ,d,s and the trajectory variables x,u are as follows:

[0053]

[0054] Alternate optimization is performed on the dual variables:

[0055]

[0056] In the formula, p represents the p-th iteration, and the problem is a convex problem subject only to linear constraints.

[0057] With the dual variable fixed, the trajectory variable is optimized alternately:

[0058]

[0059] In the formula, NE represents solving for Nash equilibrium, which is a game problem that removes security constraints and is only subject to state transition constraints and linear constraints.

[0060] Furthermore, the IPOPT solver is used to solve the convex optimization problem of the dual variables, and the ALGAMES solver is used to solve the Nash equilibrium problem of the trajectory variables.

[0061] According to a second aspect of the present invention, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement any of the steps of the above-described secure interactive dynamic game trajectory planning method based on symbolic distance.

[0062] According to a third aspect of the invention, the invention also provides a storage medium storing a plurality of instructions adapted for loading by a processor to execute the steps of any of the symbol distance-based secure interactive dynamic game trajectory planning methods described above.

[0063] Through one or more embodiments of the above embodiments of the present invention, at least the following technical effects can be achieved: The safe interactive dynamic game trajectory planning method of the present invention, based on symbolic distance, uses convex polyhedra to describe the vehicle space and combines symbolic distance to accurately calculate the minimum safe distance. Therefore, it completely avoids the redundancy problem of the safe area in the traditional circular / elliptical model, expands the feasible solution space of the trajectory, and reduces excessively conservative behavior (such as unnecessary detours or deceleration) from the root. At the same time, it transforms non-convex safety constraints into convex forms and designs an alternating optimization algorithm to solve the game problem, significantly reducing the solution complexity of the dynamic game problem and substantially improving the computational efficiency, making real-time trajectory planning in multi-vehicle interaction scenarios possible. In addition, a weighted fusion mechanism of the safe distance term is designed for the objective function. The weight coefficient and the minimum distance are used to jointly optimize efficiency and safety. Under the premise of satisfying the convex safety constraints, the optimization algorithm can actively find trajectories that maintain a greater distance from obstacles, thereby generating smoother and safer avoidance behavior in game interaction, effectively alleviating the "frozen robot problem," and enabling vehicles to exhibit natural and flexible intelligent interactive behavior in complex scenarios (such as unprotected left turns and narrow road encounters). Attached Figure Description

[0064] The technical solution and other beneficial effects of the present invention will become apparent from the following detailed description of specific embodiments of the invention, in conjunction with the accompanying drawings.

[0065] Figure 1 This is a schematic diagram of existing obstacle modeling methods;

[0066] Figure 2 This is a schematic diagram showing how conservative safety constraints in the traditional obstacle avoidance circular model lead to a reduction in the feasible solution space for path planning.

[0067] Figure 3 This is a schematic diagram illustrating the accurate calculation of the minimum safe distance based on symbolic distance provided in an embodiment of the present invention;

[0068] Figure 4 This is a flowchart illustrating the secure interactive dynamic game trajectory planning method based on symbolic distance provided in this embodiment of the invention.

[0069] Figure 5 This is a schematic diagram illustrating the space occupied by a vehicle according to an embodiment of the present invention;

[0070] Figure 6 In Experiment 1 provided in this embodiment of the invention, the weighting coefficient w = 0.05, d min A schematic diagram of the dynamic interaction process at 0.001m.

[0071] Figure 7 These are schematic diagrams of the two closest frames in the planning results of the 40th time step in Experiment 1 provided in this embodiment of the invention;

[0072] Figure 8 In Experiment 1 provided in this embodiment of the invention, the weighting coefficient w = 0.05, d min A schematic diagram of the dynamic interaction process at 0.2m.

[0073] Figure 9 This is a schematic diagram of global trajectory planning and the nearest distance frame in the planning process in Experiment 1 provided by the embodiments of the present invention;

[0074] Figure 10 This is a schematic diagram of the dynamic interactive game process for safe vehicle passing on a narrow road in Experiment 2 provided in this embodiment of the invention;

[0075] Figure 11 This is a schematic diagram of the distance curves between the two vehicles in Experiment 2 provided in this embodiment of the invention. Detailed Implementation

[0076] 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. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0077] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the term "and / or" in this document is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Furthermore, the character " / " in this document, unless otherwise specified, generally indicates that the preceding and following related objects have an "or" relationship.

[0078] In complex dynamic scenarios involving multiple vehicles, non-convex safety constraints pose a significant challenge to trajectory planning algorithms. On one hand, non-convex safety constraints increase the algorithm's complexity. While traditional obstacle avoidance models with elliptical or spherical shapes are easy to implement, their simplification often fails to accurately reflect the true geometry of obstacles and the dynamic characteristics of vehicles or dynamic obstacles. This simplification leads to redundant safety regions, directly impacting the feasible solution space for trajectory optimization (e.g., ...). Figure 2 As shown in the diagram, this makes it more difficult to find a solution for the optimization algorithm, and may even prevent the finding of a reasonable solution, thus affecting the solution performance. On the other hand, overly conservative safety constraints lead to unreasonable driving strategies. In complex interaction scenarios, overly conservative avoidance behavior can cause unnecessary detours or decelerations, reducing driving efficiency. Especially in multi-vehicle interactions, conservative behavior may lead to traffic congestion or a decrease in system efficiency. In addition, non-convex constraints are difficult to solve directly, and existing symbolic distance methods require the introduction of a large number of constraints, which is difficult to meet the real-time requirements of dynamic game theory.

[0079] To address the aforementioned technical problems, this invention remodels the safety issues between vehicles based on dynamic game trajectory planning. Specifically, obstacles are modeled as convex polyhedrons, and the distance between vehicles and obstacles is represented by symbolic distance, such as... Figure 3 As shown in the attached diagram. This method can accurately calculate the minimum distance between vehicles and incorporate it into the trajectory optimization process, thereby avoiding redundant safety zones and making trajectory planning more accurate. The method will be introduced below with reference to the attached diagram.

[0080] like Figure 4 As shown, the trajectory planning method for secure interactive dynamic game based on symbolic distance in this embodiment includes the following steps:

[0081] Step S1: Dynamically model the intelligent agent and obstacles based on the vehicle space of the convex polyhedron.

[0082] In this embodiment of the application, the space is defined when the agent is at the origin and its orientation is 0 rad:

[0083]

[0084] For autonomous vehicles, the space occupied by G and g is described as follows: Figure 5 As shown.

[0085] Next, define the rotation matrix R(x) k Translation vector t(x) k )

[0086]

[0087] The space occupied by the intelligent agent can be described as follows:

[0088] at the same time

[0089] in,

[0090] A = G[R(x) k )] -1 (2.4)

[0091] b = g + G[R(x) k )] -1 t(x k (2.5)

[0092] For static obstacles in the scene, the space they occupy is described as follows:

[0093]

[0094] In the formula, Let A represent the set of real numbers, indicating that y belongs to the two-dimensional real number space, that is, y is a two-dimensional vector, where each component of the vector is a real number, m represents the m-th obstacle, M represents the total number of obstacles, and A ( m) and b ( m) represent the spatial representation of the m-th obstacle.

[0095] Step S2: Construct non-convex safety constraints between the agent and obstacles based on symbolic distance, and convert the non-convex safety constraints into equivalent convex safety constraints.

[0096] In this step, the safety constraints between the agent and static obstacles can be defined as:

[0097]

[0098] The distance between the agent and obstacles is represented by symbolic distance to accurately calculate the minimum distance between vehicles, thus avoiding redundant safety zones. The aforementioned safety constraint is a nonlinear and non-convex problem; this embodiment uses symbolic distance to analyze this problem.

[0099]

[0100] in, Let the distance function be defined as:

[0101]

[0102] The osmotic function is defined as:

[0103]

[0104] The above security constraints are transformed into dual form by introducing additional dual variables, as shown in the following formula:

[0105] satisfy:

[0106]

[0107] In the above formula, ||A T λ||=1 is still a non-convex form. By setting the distance to always be positive, for example, using a robust initial trajectory, the constraint can be simplified to a convex form, as follows:

[0108] satisfy:

[0109]

[0110] Regarding security constraints between agents, let's note: Let i be the space occupied by the i-th agent. Then we have...

[0111]

[0112] Among them, A i =G i [R i (x k )] -1 ,b i =g i +G i [R i (x k )] -1 t i (x k ).

[0113] Security constraints between agents can be represented as:

[0114] satisfy:

[0115]

[0116] Thus, the embodiments of this application have completed the theoretical derivation of the safety constraints between the intelligent agent and static obstacles, as well as between the intelligent agent and the static obstacles.

[0117] Step S3: Construct a dynamic game trajectory planning optimization problem that includes an objective function and convex safety constraints.

[0118] In this step, we first convert formula (2.13) into an equality constraint:

[0119]

[0120] remember

[0121] remember

[0122] remember

[0123] Then, a game theory problem is constructed: for agent i, each agent hopes to optimize its objective function while satisfying the constraints.

[0124]

[0125] stx0 = x S

[0126]

[0127] x min ≤x≤x max

[0128]

[0129] The objective function in this embodiment employs a weighted mechanism that combines a safety distance term and weighting coefficients, by using the weighting coefficient w and a preset minimum distance d. min The safety constraint coordination and adjustment strategy controls the degree of influence of safety constraints.

[0130] The augmented Lagrangian function of the above objective function is:

[0131]

[0132] Step S4: Solve the trajectory planning optimization problem to output a safe trajectory that meets real-time requirements.

[0133] This embodiment of the application employs an alternating optimization algorithm to solve the trajectory planning optimization problem, which alternately optimizes the dual variables and trajectory variables. The specific process is as follows:

[0134] The original updates for the dual variables λ,μ,d,s and the trajectory variables x,u are as follows:

[0135]

[0136] In the formula, p represents the p-th iteration. This problem is a convex problem subject only to linear constraints and can be solved using...

[0137] Solve using solvers such as IPOPT.

[0138]

[0139] In the formula, NE represents solving for Nash equilibrium. This problem is a game problem that removes security constraints and is only subject to state transition constraints and linear constraints. It can be solved quickly using ALGAMES or other dynamic game solving algorithms.

[0140] To verify the effectiveness of the secure interactive dynamic game trajectory planning method based on symbolic distance provided in this application, experiments were conducted in different scenarios, with parameter configurations as shown in Table 1 below:

[0141]

[0142] Table 1

[0143] For all experimental vehicles in their initial pose Perform initialization and preset the path endpoint. Real-time iteration is performed every Δt = 0.1s. Based on Formula 2.12 in this embodiment, convex polyhedra of the vehicle and other vehicles are constructed to perform dynamic spatial description of the vehicle. The dual variable λ in Equation 2.15 is solved using IPOPT. k ,μ k ,d k ,s k During alternating optimization, the dual variable is fixed, and ALGAMES is used to solve for the Nash equilibrium trajectory x in Equation 2.16. k+1 ,u k+1 The final output control command is $u k =[a k ,δ k ] T $.

[0144] Experiment 1: Dynamic Interactive Verification of Open Roads

[0145] Experimental scenario: Two-way, two-lane open road

[0146] Interactive vehicles: Two autonomous vehicles of the same size (length × width = 2m × 1m).

[0147] The results of Experiment 1, performed based on the above parameters and algorithm flow, are as follows:

[0148] Figure 6 The diagram shows the setting of weight coefficient w = 0.05, d min The dynamic interaction process at 0.001m, such as Figure 6 As shown, the feasible trajectory set is expanded, enabling close overtaking (see...). Figure 6 (See the lower left figure), the minimum set distance is 0.002m. There are no collisions at the discrete time step, but there is a risk of collisions at continuous time, such as... Figure 7 The two closest frames in the planning results at the 40th time step are shown.

[0149] Figure 8 The weighting coefficient w = 0.05, d is shown. min =0.2m dynamic interaction process, such as Figure 8 As shown, the risk of collision over continuous time is eliminated, and the minimum distance throughout the entire process is >0.2m (see...). Figure 9 (The closest frame in the plan) is compared. Figure 6 and Figure 8 It can be seen that the traffic efficiency remains unchanged, while the trajectory smoothness loss is less than 5%.

[0150] Experiment 2: Verification of passing on narrow roads

[0151] Experimental scenario: A 2.5m wide one-way lane with a 1m x 1m obstacle in the center (see...). Figure 10 )

[0152] Interactive vehicles: Two vehicles, each 5m long and 2m wide, traveling in opposite directions.

[0153] Dynamically model the two vehicles using convex polyhedra to ensure their contours closely match their actual shapes. Figure 10 It can be seen that the vehicle safely navigated the narrow road without incident, and as... Figure 11 As shown, the minimum distance between vehicles was >0m and there were zero collisions throughout the entire process.

[0154] Based on the above embodiments and experimental verification, it can be seen that the safe interactive dynamic game trajectory planning method based on symbolic distance in this application uses convex polyhedra to describe vehicle space and combines symbolic distance to accurately calculate the minimum safe distance, fundamentally solving the problem of overly conservative behavior and achieving accurate modeling of safety constraints in dynamic multi-vehicle interactions. By transforming non-convex safety constraints into convex forms through duality theory and designing an alternating solution algorithm, the complexity of solving dynamic game problems is significantly reduced, and computational efficiency is improved. To ensure higher smoothness in dynamic interaction, a weighted fusion mechanism for the safety distance term is designed for the objective function. Weight coefficients and minimum distance are used to collaboratively optimize efficiency and safety. Under the premise of satisfying convex safety constraints, the optimization algorithm can actively seek trajectories that maintain a greater distance from obstacles, thereby generating smoother and safer avoidance behavior in game interaction, effectively alleviating the "frozen robot problem," and enabling vehicles to exhibit natural and flexible intelligent interactive behavior in complex scenarios (such as unprotected left turns and narrow road encounters).

[0155] In summary, the dynamic game-theoretic trajectory planning method of this application also has the following derivative benefits: Technically, it provides a reliable solution for high-density dynamic traffic scenarios, promoting the implementation of autonomous driving technology. Economically, it reduces ineffective travel caused by conservative driving and lowers system energy consumption. Furthermore, in terms of safety, the use of precise symbolic distance constraints fundamentally avoids collision risks, providing a strong guarantee for safe and intelligent driving.

[0156] In another embodiment of this application, for cases where the accuracy requirements of the safety area are not high, the safety constraint of the safety area can also adopt a simplified scheme, that is, use multiple overlapping circles to approximate the contour of the vehicle's convex polyhedron, thereby reducing the complexity of geometric modeling.

[0157] In other embodiments of this application, for cases requiring high local trajectory accuracy, trajectory optimization can also employ a hierarchical optimization scheme. Specifically, the first stage uses traditional methods (such as safety corridors) to generate a coarse trajectory, while the second stage uses refined symbolic distance constraints locally. This scheme is compatible with existing planning frameworks and reduces computational complexity.

[0158] Furthermore, for non-dynamic scenarios or situations with abundant prior environmental information, the extended symbolic distance field (ESDF) can be pre-calculated, and online queries can replace real-time symbolic distance calculations, thereby effectively improving computation speed.

[0159] Based on any of the above embodiments, another embodiment of the present invention provides an electronic device, which may include: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor may invoke logical instructions in the memory to execute the above method.

[0160] Furthermore, when the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0161] On the other hand, embodiments of the present invention also provide a storage medium storing a plurality of instructions, which are adapted to be loaded by a processor to execute the secure interactive dynamic game trajectory planning method based on symbolic distance provided in the above embodiments.

[0162] On the other hand, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0163] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0164] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of various embodiments or some parts of embodiments.

[0165] In summary, although the present invention has been disclosed above with reference to preferred embodiments, the above preferred embodiments are not intended to limit the present invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the scope defined in the claims.

Claims

1. A method for trajectory planning in a secure interactive dynamic game based on symbolic distance, characterized in that, Includes the following steps: Vehicle space based on convex polyhedra is used for dynamic modeling of intelligent agents and obstacles; Construct non-convex safety constraints between the agent and the obstacle based on symbolic distance, and convert the non-convex safety constraints into equivalent convex safety constraints. A dynamic game trajectory planning optimization problem is constructed, which includes an objective function and the convex safety constraints. The objective function includes a safety distance term, expressed as follows: ； In the formula, These are the weighting coefficients. For the safe distance item, The objective function employs a fusion weighting mechanism of safety distance term and weight coefficient. The influence of safety constraints is controlled by a collaborative adjustment strategy between the weight coefficient and the safety constraint of the preset minimum distance. Specifically, when the preset minimum distance increases, the weight coefficient increases accordingly to strengthen the optimization of safety distance and ensure the conservatism of behavior under higher safety requirements. Solve the trajectory planning and optimization problem to output a safe trajectory that meets real-time requirements. The safety constraints between the intelligent agent and the obstacle are represented as follows: ， Construct non-convex safety constraints between the agent and the obstacle based on symbolic distance: ； In the formula, Let be the distance function. The osmotic function, Introducing dual variables transforms the non-convex security constraint into a dual form: ； ； For the non-convex form in the above equation The above constraints are simplified into a convex form using a convex relaxation algorithm: ； ； The convex security constraints between the agents are then represented as follows: ； 。 2. The secure interactive dynamic game trajectory planning method based on symbolic distance according to claim 1, characterized in that, The spatial dynamics of the agent are described as follows: ,at the same time , In the formula, , , For rotation matrix, It is a translation vector. Let the intelligent agent be a convex polyhedron in the coordinate system, defined as , and For intelligent agents; The spatial dynamics of the obstacle are described as follows: ； In the formula, Represents the set of real numbers, representing It belongs to the two-dimensional real number space, that is It is a two-dimensional vector, where each component is a real number. Indicates the first An obstacle, Indicates the total number of obstacles. and They represent the first Spatial representation of an obstacle.

3. The secure interactive dynamic game trajectory planning method based on symbolic distance according to claim 1, characterized in that, The distance function is defined as: ； The permeability function is defined as: 。 4. The secure interactive dynamic game trajectory planning method based on symbolic distance according to claim 1, characterized in that, The alternating optimization algorithm is used to alternately optimize the dual variables and the trajectory variables, thereby solving the trajectory planning optimization problem. The process is as follows: Dual variables With trajectory variables The original update was: ； Alternate optimization is performed on the dual variables: ； In the formula, Indicates the first In the next iteration, the problem becomes a convex problem subject only to linear constraints. With the dual variable fixed, the trajectory variable is optimized alternately: ； In the formula, This indicates the search for Nash equilibrium, a game problem that removes security constraints and is only subject to state transition constraints and linear constraints.

5. The secure interactive dynamic game trajectory planning method based on symbolic distance according to claim 4, characterized in that, The convex optimization problem of the dual variables is solved using the IPOPT solver, and the Nash equilibrium problem of the trajectory variables is solved using the ALGAMES solver.

6. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 5.

7. A storage medium, characterized in that, The storage medium stores a plurality of instructions adapted for loading by a processor to perform the steps of the method according to any one of claims 1 to 5.

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