Symbol distance-based safe interaction dynamic game trajectory planning method

Abstract

The invention discloses a safety interaction dynamic game trajectory planning method based on a symbolic distance, and the method comprises the steps: carrying out the dynamic modeling of an intelligent agent and an obstacle based on a vehicle space of a convex polyhedron, and constructing a non-convex safety constraint between the intelligent agent and the obstacle through the combination of the symbolic distance, therefore, the problem of safety redundancy caused by a traditional circular model is avoided, and the feasible solution space of path planning is expanded. And meanwhile, the non-convex security constraint is equivalently converted into the convex security constraint, and the constructed dynamic game trajectory planning optimization problem is solved by adopting an alternating optimization algorithm, so that the solving complexity of the dynamic game problem is remarkably reduced, and the calculation efficiency is effectively improved. Besides, an objective function containing a safe distance item is designed, and efficiency and safety are optimized in a collaborative manner through an adjustment strategy of a weight coefficient and a preset minimum distance. According to the method, the dynamic multi-workshop safety constraint can be accurately modeled, the conservative property of the prior art is overcome, and the track planning requirement of real-time calculation under the game theory framework can be met.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of trajectory planning and control technology, and particularly relates to a safe interaction dynamic game trajectory planning method based on signed distance. BACKGROUND

[0002] In the automatic driving scene of multi-vehicle dynamic interaction, it is a core challenge to plan a trajectory safely and efficiently. The existing trajectory planning method based on dynamic game often uses a circular collision avoidance constraint to simplify safety modeling. However, due to the excessive simplification of the geometric shape, such a method is often too conservative, significantly reducing the feasible solution space of trajectory optimization, 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), which aims to optimize computational efficiency and trajectory quality while ensuring obstacle avoidance safety. The main methods include:

[0004] Elliptical / spherical model: simplifies obstacles to two-dimensional ellipses or three-dimensional spheres. This method is simple and efficient in calculation, easy to calculate distance and obstacle avoidance gradient, and suitable for small-scale scenarios. However, its main drawback is that the shape of the actual obstacle (including vehicles) is complex and diverse, and this simplification cannot accurately describe the true minimum distance, and the obstacle avoidance effect is not good in complex or close interaction scenarios, and there is also a problem of conservatism.

[0005] Safety corridor method: models the free space as a safety corridor of convex polygons (or polyhedrons). This method has good flexibility and can adapt to different scenarios. However, its significant disadvantage is that the cost of constructing a high-quality corridor is highly dependent on the obstacle discretization resolution and expansion step size. Low resolution leads to excessive conservatism, and high resolution results in high computational cost, especially when the trajectory needs to be close to the obstacle, the construction process may become a bottleneck.

[0006] Signed distance combined with bi-convex reconstruction: models obstacles as convex polyhedrons, uses signed distance to accurately represent the distance between the vehicle and the obstacle, and converts non-convex collision avoidance constraints into nonlinear convex constraints through bi-convex reconstruction technology. This method is accurate and can handle complex shapes, and is suitable for various vehicle models. However, the key problem is that the conversion process introduces a large number of equality and inequality constraints, significantly increasing the dimension and complexity of the optimization problem, making it difficult to meet the real-time requirements of dynamic interaction scenarios.

[0007] Linear Programming (LP) collision detection: Transforms the collision detection problem into an efficient linear programming solution. This method is computationally efficient, and only requires a small number of variables as the number of obstacles increases. However, its main limitations are: it is only applicable to convex obstacles and cannot handle common non-convex shapes; and its application is usually limited to being combined with a specific type of trajectory optimization algorithm (such as polynomial-based).

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

[0009] While the above methods have their own application value in single-vehicle obstacle avoidance planning, they have obvious shortcomings when directly applied to dynamic multi-vehicle interaction trajectory planning, especially in game theory-based frameworks:

[0010] Static obstacle assumption invalid: In multi-vehicle interaction, other vehicles themselves are dynamic "obstacles" that change over time, and their behavior is influenced by the decisions of the ego vehicle. Traditional single-vehicle obstacle avoidance methods usually assume that obstacles are static or have known / predictable behavior, and cannot effectively handle this interdependent dynamic interaction.

[0011] Conservatism vs. efficiency contradiction: The circular / elliptical model and safety corridor method exacerbate the conservatism problem in dynamic multi-vehicle scenarios, leading to overly cautious interaction behavior (such as unnecessary stopping and detours), which severely reduces traffic efficiency and system fluidity.

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

[0013] Interaction model missing: Existing methods mainly focus on how a single vehicle avoids (static or dynamic) obstacles, and lack explicit modeling of the interaction decision-making process (such as competition, cooperation, and yielding), which is the core value of applying game theory to trajectory planning.

[0014] Potential and limitations of signed distance methods:

[0015] In the geometric modeling method, the signed distance method shows significant potential in the modeling of multi-vehicle interaction safety constraints due to its ability to accurately describe the minimum distance between any shaped objects. It not only accurately depicts the car-car or car-obstacle distance, but also captures the complex relative motion relationship between vehicles, which is crucial to ensure safety in dynamic games. The introduction of double convex reconstruction technology further improves the feasibility of processing. However, as mentioned earlier, the core bottleneck: the computational complexity problem caused by a large number of constraints becomes particularly prominent in dynamic game planning with an increasing number of interacting vehicles and a dramatic increase in state space dimension, limiting its practical application performance.

[0016] Therefore, it is urgent to develop a new trajectory planning method that can accurately model safety constraints between dynamic multi-vehicles (overcome the conservatism caused by geometric simplification) and meet the real-time computing requirements under the game theory framework. SUMMARY

[0017] The present application provides a safety interaction dynamic game trajectory planning method based on signed distance, which aims to effectively solve the above technical problems.

[0018] According to the first aspect of the present application, the present application provides a safety interaction dynamic game trajectory planning method based on signed distance, characterized in that it comprises the following steps:

[0019] The vehicle space based on convex polyhedron is dynamically modeled for agents and obstacles;

[0020] Non-convex safety constraints between the agents and the obstacles are constructed based on signed distance, and the non-convex safety constraints are equivalently converted into convex safety constraints;

[0021] A dynamic game trajectory planning optimization problem containing a target function and the convex safety constraints is constructed, and the target function contains a safety distance term;

[0022] The trajectory planning optimization problem is solved, thereby outputting a safety trajectory that meets the real-time requirement.

[0023] Further, the spatial dynamic description of the agent is:

[0024] Meanwhile

[0025] In the formula, A=G[R(x k )] -1 , b=g+G[R(x k )] -1 t(x k ), R(x k ) is a rotation matrix, t(x k ) is a translation vector, For the convex polyhedron of the agent in the coordinate system, it is defined as

[0026] G and g are agents;

[0027] The spatial dynamic description of the obstacle is:

[0028]

[0029] In the formula, Indicates a set of real numbers, represents that y belongs to a two-dimensional real number space, that is, y is a two-dimensional vector, and each component of the vector is a real number, m represents the mth obstacle, M represents the total number of obstacles, A ( m) and b ( m) respectively represent the spatial representation of the mth obstacle.

[0030] Further, the safety constraint between the agent and the obstacle is represented as follows:

[0031]

[0032] Based on the symbolic distance, the non-convex safety constraint between the agent and the obstacle is constructed:

[0033]

[0034] In the formula, is a distance function, is a penetration function,

[0035] The non-convex safety constraint is converted into a dual form by introducing a dual variable:

[0036] Satisfies:

[0037]

[0038] For the non-convex form ||A T λ||=1, using the convex relaxation algorithm, the above constraint is simplified to a convex form:

[0039] Satisfies:

[0040]

[0041] Then the convex safety constraint between the agents is represented as follows:

[0042] Satisfies:

[0043]

[0044] Further, the distance function is defined as:

[0045]

[0046] The penetration function is defined as:

[0047]

[0048] Further, the objective function is represented as:

[0049]

[0050] where w is a weight coefficient, is a safety distance term.

[0051] Further, the objective function adopts a fusion weighting mechanism of the safety distance term and the weight coefficient, and controls the influence degree of the safety constraint through a synergistic adjustment strategy of the weight coefficient and the safety constraint of the preset minimum distance, and the synergistic adjustment strategy is specifically that when the preset minimum distance increases, the weight coefficient correspondingly increases, so as to strengthen the optimization strength of the safety distance, and ensure the behavior conservatism under higher safety requirements.

[0052] Further, an alternating optimization algorithm is adopted to alternately optimize the dual variables and the trajectory variables, so as to solve the trajectory planning optimization problem, and the process is as follows:

[0053] The original update of the dual variables λ, μ, d, s and the trajectory variables x, u is:

[0054]

[0055] The dual variables are alternately optimized:

[0056]

[0057] where p represents the pth iteration, and the problem is a convex problem only subject to linear constraints,

[0058] The trajectory variables are alternately optimized by fixing the dual variables:

[0059]

[0060] where NE represents solving the Nash equilibrium, and the problem is a game problem only subject to state transition constraints and linear constraints by eliminating the safety constraint.

[0061] Further, the convex optimization problem of the dual variables is solved by using an IPOPT solver, and the Nash equilibrium problem of the trajectory variables is solved by using an ALGAMES solver.

[0062] According to a second aspect of the present application, the present application further provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any of the above symbol distance based safe interaction dynamic game trajectory planning methods when executing the program.

[0063] According to a third aspect of the present application, the present application further provides a storage medium, wherein a plurality of instructions are stored in the storage medium, and the instructions are adapted to be loaded by a processor to execute the steps of any of the above symbol distance based safe interaction dynamic game trajectory planning methods.

[0064] By one or more of the above embodiments of the present application, at least the following technical effects can be achieved: the symbol distance based safe interaction dynamic game trajectory planning method of the present application, since the convex polyhedron is used to describe the vehicle space and the minimum safe distance is accurately calculated in combination with the symbol distance, the safety area redundancy problem of the traditional circular / elliptical model is completely avoided, the trajectory feasible solution space is expanded, and the over-conservative behavior (such as unnecessary detour or deceleration) is reduced from the root. At the same time, the non-convex safety constraint is converted into a convex form, and an alternating optimization algorithm is designed to solve the game problem, which significantly reduces the solution complexity of the dynamic game problem, substantially improves the calculation efficiency, and makes real-time trajectory planning of multi-vehicle interaction scenarios possible. In addition, a weighting fusion mechanism of the safety distance term is designed for the objective function, the weight coefficient is used to optimize the efficiency and safety in cooperation with the minimum distance, under the premise of meeting the convex safety constraint, the optimization algorithm can actively find a trajectory that keeps a larger distance from the obstacle, thereby producing a smoother and safer avoidance behavior in the game interaction, effectively alleviating the “frozen robot problem”, and enabling the vehicle to exhibit natural and flexible intelligent interaction behavior in complex scenarios (such as unprotected left turn and narrow lane meeting). BRIEF DESCRIPTION OF DRAWINGS

[0065] The technical solutions and other beneficial effects of the present application will become apparent from the following detailed description of specific embodiments of the present application, combined with the accompanying drawings.

[0066] Figure 1 is a schematic diagram of an existing obstacle modeling method;

[0067] Figure 2 is a schematic diagram of a conservative safety constraint of a traditional obstacle avoidance circular model leading to a reduction in the path planning feasible solution space;

[0068] Figure 3 is a schematic diagram of the present application for accurately calculating the minimum safe distance based on the symbol distance;

[0069] Figure 4is a flowchart of a symbol distance-based safe interaction dynamic game trajectory planning method provided by an embodiment of the present application;

[0070] Figure 5 is a vehicle space description diagram provided by an embodiment of the present application;

[0071] Figure 6 is a dynamic interaction process diagram under the condition of setting a weight coefficient w = 0.05 and d min = 0.001 m in experiment 1 provided by an embodiment of the present application;

[0072] Figure 7 is a diagram of the two closest frames in the planning result of the 40th time step in experiment 1 provided by an embodiment of the present application;

[0073] Figure 8 is a dynamic interaction process diagram under the condition of setting a weight coefficient w = 0.05 and d min = 0.2 m in experiment 1 provided by an embodiment of the present application;

[0074] Figure 9 is a diagram of global trajectory planning and the closest frame in planning in experiment 1 provided by an embodiment of the present application;

[0075] Figure 10 is a process diagram of a narrow road meeting safe interaction dynamic game in experiment 2 provided by an embodiment of the present application;

[0076] Figure 11 is a two-vehicle distance curve diagram in experiment 2 provided by an embodiment of the present application. DETAILED DESCRIPTION

[0077] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0078] In the description of the present application, it should be noted that, unless otherwise explicitly specified and limited, the term “and / or” in this paper is only to describe the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B can represent the three cases of A alone, A and B together, and B alone. In addition, the character “ / ” in this paper generally represents an “or” relationship between the front and rear associated objects without special explanation.

[0079] 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.

[0080] 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.

[0081] 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:

[0082] Step S1: Dynamically model the intelligent agent and obstacles based on the vehicle space of the convex polyhedron.

[0083] In this embodiment of the application, the space is defined when the agent is at the origin and its orientation is 0 rad:

[0084]

[0085] For autonomous vehicles, the space occupied by G and g is described as follows: Figure 5 As shown.

[0086] Next, define the rotation matrix R(x) k Translation vector t(x) k )

[0087]

[0088] The space occupied by the intelligent agent can be described as follows:

[0089] at the same time

[0090] in,

[0091] A = G[R(x) k )] -1 (2.4)

[0092] b = g + G[R(x) k )] -1 t(x k (2.5)

[0093] For static obstacles in the scene, the space they occupy is described as follows:

[0094]

[0095] 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.

[0096] 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.

[0097] In this step, the safety constraints between the agent and static obstacles can be defined as:

[0098]

[0099] 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.

[0100]

[0101] in, Let the distance function be defined as:

[0102]

[0103] The osmotic function is defined as:

[0104]

[0105] The above security constraints are transformed into dual form by introducing additional dual variables, as shown in the following formula:

[0106] satisfy:

[0107]

[0108] 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:

[0109] satisfy:

[0110]

[0111] Regarding security constraints between agents, let's note: Let i be the space occupied by the i-th agent. Then we have...

[0112]

[0113] 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 ).

[0114] Security constraints between agents can be represented as:

[0115] satisfy:

[0116]

[0117] 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.

[0118] Step S3: Construct a dynamic game trajectory planning optimization problem that includes an objective function and convex safety constraints.

[0119] In this step, we first convert formula (2.13) into an equality constraint:

[0120]

[0121] remember

[0122] remember

[0123] remember

[0124] Then, a game theory problem is constructed: for agent i, each agent hopes to optimize its objective function while satisfying the constraints.

[0125]

[0126] stx0 = x S

[0127]

[0128] x min ≤x≤x max

[0129]

[0130] 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.

[0131] The augmented Lagrangian function of the above objective function is:

[0132]

[0133] Step S4: Solve the trajectory planning optimization problem to output a safe trajectory that meets real-time requirements.

[0134] 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:

[0135] The original updates for the dual variables λ,μ,d,s and the trajectory variables x,u are as follows:

[0136]

[0137] 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...

[0138] Solve using solvers such as IPOPT.

[0139]

[0140] 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.

[0141] 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:

[0142]

[0143] Table 1

[0144] For all experimental vehicles in their initial pose Perform initialization and preset the path endpoint. Real-time iteration is set to occur 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 $.

[0145] Experiment 1: Dynamic Interactive Verification of Open Roads

[0146] Experimental scenario: Two-way, two-lane open road

[0147] Interactive vehicles: Two autonomous vehicles of the same size (length × width = 2m × 1m).

[0148] The results of Experiment 1, performed based on the above parameters and algorithm flow, are as follows:

[0149] 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 frames closest to each other in the planning results at the 40th time step are shown.

[0150] 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%.

[0151] Experiment 2: Verification of passing on narrow roads

[0152] Experimental scenario: A 2.5m wide one-way lane with a 1m x 1m obstacle in the center (see...). Figure 10 )

[0153] Interactive vehicles: Two vehicles, each 5m long and 2m wide, traveling in opposite directions.

[0154] 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.

[0155] 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).

[0156] 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.

[0157] 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.

[0158] 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.

[0159] 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.

[0160] 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.

[0161] 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.

[0162] 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.

[0163] 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.

[0164] 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.

[0165] 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.

[0166] 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 safe interactive dynamic game trajectory planning based on signed distance, characterized in that, The method comprises the following steps: a space of a vehicle is dynamically modeled for an agent and an obstacle based on a convex polyhedron; a non-convex safety constraint between the agent and the obstacle is constructed based on a signed distance, and the non-convex safety constraint is equivalently converted into a convex safety constraint; a dynamic game trajectory planning optimization problem containing an objective function and the convex safety constraint is constructed, and the objective function contains a safety distance term; the trajectory planning optimization problem is solved, so that a safety trajectory meeting a real-time requirement is output.

2. The method of claim 1, wherein, a space dynamic description of the agent is as follows: at the same time where A = G[R(x k )] -1 , b = g + G[R(x k )] -1 t(x k ), R(x k ) is a rotation matrix, t(x k ) is a translation vector, is the convex polyhedron of the agent in the coordinate system, defined as G and g are the agents; a space dynamic description of the obstacle is as follows: wherein denotes a set of real numbers, represents that y belongs to a two-dimensional real number space, that is, y is a two-dimensional vector, each component of the vector is a real number, m represents the mth obstacle, M represents the total number of obstacles, A ( m) and b ( m) respectively represent the spatial representation of the mth obstacle.

3. The method of claim 2, wherein, a safety constraint between the agent and the obstacle is represented as follows: a non-convex safety constraint between the agent and the obstacle is constructed based on a signed distance: wherein is a distance function, is a penetration function, a dual variable is introduced to convert the non-convex safety constraint into a dual form: satisfies: For the non-convex form ||A T λ|| = 1, the above constraint is simplified to a convex form using the convex relaxation algorithm: satisfies: a convex safety constraint between the agents is represented as follows: satisfies:

4. The method of claim 3, wherein, the distance function is defined as: the penetration function is defined as:

5. The method of claim 1, wherein, the objective function is represented as follows: In the formula, w is a weight coefficient, is a safety distance term.

6. The method of claim 1, wherein, The objective function adopts a fusion and weighting mechanism of a safety distance term and a weight coefficient, and controls the influence degree of the safety constraint through a cooperative regulation strategy of the weight coefficient and a preset minimum distance safety constraint, and the cooperative regulation strategy is specifically that when the preset minimum distance increases, the weight coefficient correspondingly increases, so as to strengthen the optimization strength of the safety distance, and ensure the behavior conservatism under a higher safety requirement.

7. The symbol distance based safe interactive dynamic game of trajectories planning method according to claim 1, wherein, An alternating optimization algorithm is adopted to alternately optimize the dual variable and the trajectory variable, so as to solve the trajectory planning optimization problem, and the process is as follows: original updates of the dual variable λ, μ, d, s and the trajectory variable x, u are as follows: the dual variable is alternately optimized: wherein, p represents the pth iteration, the problem is a convex problem only subjected to linear constraints, the dual variable is fixed, and the trajectory variable is alternately optimized: wherein, NE represents solving a Nash equilibrium, the problem is a game problem only subjected to state transition constraints and linear constraints.

8. The method of claim 7, wherein, The IPOPT solver is adopted to solve the convex optimization problem of the dual variable, and the ALGAMES solver is adopted to solve the Nash equilibrium problem of the trajectory variable. 9.An electronic device comprising a memory and a processor, the memory storing a computer program, wherein, The processor executes the computer program to realize the steps of the method in any one of claims 1 to 8.

10. A storage medium, characterized by The storage medium stores a plurality of instructions, and the instructions are suitable for being loaded by the processor to execute the steps of the method in any one of claims 1 to 8.

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