Vehicle interaction decision-making method based on unprotected intersection and related device

Abstract

The invention discloses a vehicle interaction decision-making method based on an unprotected intersection and a related device, and the method comprises the steps: obtaining a system state matrix, an own vehicle control matrix and an other vehicle control matrix in linear system state equations of an own vehicle and an other vehicle, first to fourth positive semi-definite matrixes and first and second positive definite matrixes are arranged in the optimization target of the linear quadratic differential game problem of the own vehicle and the other vehicle; taking the first positive semidefinite matrix and the third positive semidefinite matrix as a first intermediate matrix and a second intermediate matrix at the Nth moment respectively; according to the first intermediate matrix, the second intermediate matrix, the first positive definite matrix, the second positive definite matrix, the system state matrix, the self-vehicle control matrix, the other-vehicle control matrix, the second positive definite matrix and the fourth positive definite matrix at the Nth moment, reverse recursion is carried out on an optimal control gain matrix equation set of the two vehicles and a coupling Riccati equation of the first intermediate matrix and the second intermediate matrix at the kth moment; and obtaining an optimal control gain matrix sequence of the vehicle, and controlling the vehicle according to a control quantity sequence determined based on the optimal control gain matrix sequence.

Description

Technical Field

[0001] This application relates to the field of intelligent driving technology, and more specifically, to a vehicle interaction decision-making method and related device based on unprotected intersections. Background Technology

[0002] Unprotected intersections refer to intersections without traffic lights. Their road shapes are often irregular, and they may only have simple stop signs, yield signs, or even no signs at all. Therefore, when vehicles cross the intersection with little or no restraint, the suddenness of the event leaves both oncoming and oncoming vehicles with insufficient time and space to take safe evasive action, greatly increasing the risk of accidents. Therefore, improving vehicle interaction safety at unprotected intersections is a crucial issue that urgently needs to be addressed. Summary of the Invention

[0003] This application provides a vehicle interaction decision-making method and related device based on unprotected intersections, which can automatically calculate the feedback Nash equilibrium solution of the vehicle and other vehicles in the unprotected intersection scenario. This enables the vehicle and other vehicles to strive to optimize their independent and conflicting goals in the continuous game process, thereby avoiding collisions and improving the safety of vehicle interaction in the unprotected intersection scenario.

[0004] The specific technical solution is as follows:

[0005] In a first aspect, embodiments of this application provide a vehicle interaction decision-making method based on unprotected intersections, the method comprising:

[0006] Obtain the system state matrix, the self-vehicle control matrix, and the other-vehicle control matrix from the linear system state equations for the self-vehicle and other vehicles. Also obtain the first semi-positive definite matrix, the second semi-positive definite matrix, and the first positive definite matrix from the optimization objective of the self-vehicle linear quadratic differential game problem in the unprotected intersection scenario. Furthermore, obtain the third semi-positive definite matrix, the fourth semi-positive definite matrix, and the second positive definite matrix from the optimization objective of the other-vehicle linear quadratic differential game problem. The first semi-positive definite matrix represents the coefficients of the linear system state variables at time N in the optimization objective of the self-vehicle linear quadratic differential game problem, and the second semi-positive definite matrix represents the coefficients of the linear system state variables at time k in the optimization objective of the self-vehicle linear quadratic differential game problem. The coefficients of the linear system state variables at time k are given by the following matrix: the first positive definite matrix represents the coefficients of the linear control variables of the self-vehicle at time k in the optimization objective of the linear quadratic differential game problem; the third semi-positive definite matrix represents the coefficients of the linear system state variables of the other-vehicle at time N in the optimization objective of the linear quadratic differential game problem; the fourth semi-positive definite matrix represents the coefficients of the linear system state variables of the other-vehicle at time k in the optimization objective of the linear quadratic differential game problem; and the second positive definite matrix represents the coefficients of the linear control variables of the other-vehicle at time k in the optimization objective of the linear quadratic differential game problem. The Nth time is the last time in a planning and decision-making cycle, and 0 ≤ k. <N;

[0007] The first positive semi-definite matrix and the third positive semi-definite matrix are respectively used as the first intermediate matrix and the second intermediate matrix at time N. The first intermediate matrix is ​​a matrix used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the vehicle and the state of the linear system at the same time. The second intermediate matrix is ​​a matrix used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the other vehicle and the state of the linear system at the same time.

[0008] Based on the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second semi-positive definite matrix, and the fourth semi-positive definite matrix, the equations concerning the optimal control gain matrices of the vehicle and other vehicles, the coupled Riccati equation concerning the first intermediate matrix at time k, and the coupled Riccati equation concerning the second intermediate matrix at time k are solved by reverse recursion to obtain the optimal control gain matrix sequence of the vehicle. The vehicle is then controlled according to the nonlinear optimal control quantity sequence of the vehicle determined based on the optimal control gain matrix sequence of the vehicle. The equations concerning the optimal control gain matrices of the vehicle and other vehicles are expressions for the feedback Nash equilibrium solutions concerning the control gain matrices of the vehicle and other vehicles, obtained by calculating the optimization objectives of the linear quadratic differential game problem of the vehicle and the linear quadratic differential game problem of the other vehicle using the Pontryagin minimum value algorithm. The optimal control gain matrix sequence of the vehicle includes the optimal control gain matrices of the vehicle from time 0 to time N-1.

[0009] In one possible implementation, based on the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second semi-positive definite matrix, and the fourth semi-positive definite matrix, the system of equations concerning the optimal control gain matrices of the vehicle and other vehicles, the coupled Riccati equation concerning the first intermediate matrix at time k, and the coupled Riccati equation concerning the second intermediate matrix at time k are solved recursively in reverse order to obtain the optimal control gain matrix sequence of the vehicle, including:

[0010] By substituting the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, and the other vehicle control matrix into the system of equations concerning the optimal control gain matrices of the vehicle and the other vehicle, the optimal control gain matrix of the vehicle at time N-1 and the optimal control gain matrix of the other vehicle at time N-1 are obtained.

[0011] The first intermediate matrix at time N-1 is obtained by substituting the second semi-positive definite matrix, the optimal control gain matrix of the vehicle at time N-1, the first positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the first intermediate matrix at time N, and the optimal control gain matrix of the other vehicle at time N-1 into the coupled Riccati equation about the first intermediate matrix at time k. The second intermediate matrix at time N-1 is obtained by substituting the fourth semi-positive definite matrix, the optimal control gain matrix of the other vehicle at time N-1, the second positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second intermediate matrix at time N, and the optimal control gain matrix of the vehicle at time N-1 into the coupled Riccati equation about the second intermediate matrix at time k.

[0012] This process continues until the optimal control gain matrix of the vehicle at time 0 and the optimal control gain matrix of the other vehicle at time 0 are obtained. Then, the optimal control gain matrix sequence of the vehicle is constructed based on the optimal control gain matrix of the vehicle from time 0 to time N-1.

[0013] In one possible implementation, controlling the vehicle based on a sequence of nonlinear optimal control quantities determined from the vehicle's optimal control gain matrix sequence includes:

[0014] For each time step in the optimal control gain matrix sequence of the vehicle, the optimal control gain matrix of the vehicle and the linear system state variables at the same time step are used to determine the optimal linear control quantity of the vehicle at each time step.

[0015] Based on the linear system state equation of the vehicle, the nonlinear system state equation of the vehicle, and the linear optimal control quantity of the vehicle at each time step, the nonlinear optimal control quantity of the vehicle from time 0 to time N-1 is determined, and the sequence of nonlinear optimal control quantities of the vehicle is constructed based on the optimal control gain matrix of the vehicle from time 0 to time N-1.

[0016] The vehicle is controlled according to the nonlinear optimal control sequence of the vehicle.

[0017] In one possible implementation, the set of equations concerning the optimal control gain matrices of the vehicle and other vehicles includes:

[0018]

[0019] Wherein, K1(k) represents the optimal control gain matrix of the vehicle at time k, R1 represents the first positive definite matrix, B1 represents the vehicle control matrix, P1(k+1) represents the first intermediate matrix at time k+1, A represents the system state matrix, B2 represents the other vehicle control matrix, K2(k) represents the optimal control gain matrix of the other vehicle at time k, R2 represents the second positive definite matrix, and P2(k+1) represents the second intermediate matrix at time k+1.

[0020] In one possible implementation, the coupled Riccati equations concerning the first intermediate matrix at time k include:

[0021] P1(k) = Q1 + K1(k) T R1K1(k)+(A+B2K2(k+B1K1(k)) T P1(k+1)(A+B1K1(k)+B2K2(k));

[0022] And / or, the coupled Riccati equations with respect to the second intermediate matrix at time k include:

[0023] P2(k) = Q2 + K2(k) T R2K2(k)+(A+B2K2(k)+B1K1(k)) T P2(k+1)(A+B1K1(k)+B2K2(k));

[0024] Wherein, P1(k) represents the first intermediate matrix at time k, Q1 represents the second positive semi-definite matrix, K1(k) represents the optimal control gain matrix of the vehicle at time k, R1 represents the first positive definite matrix, A represents the system state matrix, B2 represents the control matrix of the other vehicle, K2(k) represents the optimal control gain matrix of the other vehicle at time k, B1 represents the control matrix of the vehicle, P1(k+1) represents the first intermediate matrix at time k+1, P2(k) represents the second intermediate matrix at time k, Q2 represents the fourth positive semi-definite matrix, R2 represents the second positive definite matrix, and P2(k+1) represents the second intermediate matrix at time k+1.

[0025] Secondly, embodiments of this application provide a vehicle interaction decision-making device based on unprotected intersections, the device comprising:

[0026] The acquisition unit is used to acquire the system state matrix, the self-vehicle control matrix, and the other-vehicle control matrix from the linear system state equations of the self-vehicle and other-vehicles; and to acquire the first semi-positive definite matrix, the second semi-positive definite matrix, and the first positive definite matrix from the optimization objective of the self-vehicle linear quadratic differential game problem in the unprotected intersection scenario; and the third semi-positive definite matrix, the fourth semi-positive definite matrix, and the second positive definite matrix from the optimization objective of the other-vehicle linear quadratic differential game problem. The first semi-positive definite matrix represents the coefficients of the linear system state variables at time N in the optimization objective of the self-vehicle linear quadratic differential game problem, and the second semi-positive definite matrix represents the coefficients of the linear system state variables at time N in the optimization objective of the self-vehicle linear quadratic differential game problem. The coefficients of the linear system state variables at time k are given by the first positive definite matrix, which represents the coefficients of the linear control variables of the self-vehicle at time k in the optimization objective of the self-vehicle linear quadratic differential game problem. The third semi-positive definite matrix represents the coefficients of the linear system state variables at time N in the optimization objective of the other-vehicle linear quadratic differential game problem. The fourth semi-positive definite matrix represents the coefficients of the linear system state variables at time k in the optimization objective of the other-vehicle linear quadratic differential game problem. The second positive definite matrix represents the coefficients of the linear control variables of the other-vehicle at time k in the optimization objective of the other-vehicle linear quadratic differential game problem. Time N is the last time in a planning and decision-making cycle, and 0 ≤ k. <N;

[0027] The determining unit is used to take the first positive semi-definite matrix and the third positive semi-definite matrix as the first intermediate matrix and the second intermediate matrix at time N, respectively. The first intermediate matrix is ​​a matrix used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the vehicle and the state of the linear system at the same time. The second intermediate matrix is ​​a matrix used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the other vehicle and the state of the linear system at the same time.

[0028] The solution unit is used to perform reverse recursive solution of the equations concerning the optimal control gain matrices of the vehicle and other vehicles, the coupled Riccati equation concerning the first intermediate matrix at time N, and the coupled Riccati equation concerning the second intermediate matrix at time k, based on the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second semi-positive definite matrix, and the fourth semi-positive definite matrix, to obtain the optimal control gain matrix sequence of the vehicle. The equations concerning the optimal control gain matrices of the vehicle and other vehicles are expressions for the feedback Nash equilibrium solutions concerning the control gain matrices of the vehicle and other vehicles, obtained by calculating the optimization objectives of the linear quadratic differential game problem of the vehicle and the linear quadratic differential game problem of the other vehicle using the Pontryagin minimum algorithm. The optimal control gain matrix sequence of the vehicle includes the optimal control gain matrices of the vehicle from time 0 to time N-1.

[0029] The control unit is used to control the vehicle according to a sequence of nonlinear optimal control quantities determined based on the vehicle's optimal control gain matrix sequence.

[0030] In one possible implementation, the solving unit includes:

[0031] The first calculation module is used to obtain the optimal control gain matrix of the vehicle at time N-1 and the optimal control gain matrix of the other vehicle at time N-1 by substituting the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, and the other vehicle control matrix into the system of equations about the optimal control gain matrices of the vehicle and the other vehicle.

[0032] The second calculation module is used to obtain the first intermediate matrix at time N-1 by substituting the second semi-positive definite matrix, the vehicle's optimal control gain matrix at time N-1, the first positive definite matrix, the system state matrix, the vehicle's control matrix, the other vehicle's control matrix, the first intermediate matrix at time N, and the other vehicle's optimal control gain matrix at time N-1 into the coupled Riccati equation about the first intermediate matrix at time k; and to obtain the second intermediate matrix at time N-1 by substituting the fourth semi-positive definite matrix, the other vehicle's optimal control gain matrix at time N-1, the second positive definite matrix, the system state matrix, the vehicle's control matrix, the other vehicle's control matrix, the second intermediate matrix at time N, and the vehicle's optimal control gain matrix at time N-1 into the coupled Riccati equation about the second intermediate matrix at time k.

[0033] The generation module is used to sequentially obtain the optimal control gain matrix of the vehicle at time 0 and the optimal control gain matrix of the other vehicle at time 0, and then construct the optimal control gain matrix sequence of the vehicle based on the optimal control gain matrix of the vehicle from time 0 to time N-1.

[0034] In one possible implementation, the control unit includes:

[0035] The first determining module is used to determine the vehicle's linear optimal control quantity at each time step, based on the vehicle's optimal control gain matrix at each time step in the optimal control gain matrix sequence of the vehicle and the linear system state quantity at the same time step.

[0036] The second determining module is used to determine the nonlinear optimal control quantity of the vehicle from time 0 to time N-1 based on the linear system state equation of the vehicle, the nonlinear system state equation of the vehicle, and the linear optimal control quantity of the vehicle at each time step, and to construct the sequence of nonlinear optimal control quantities of the vehicle based on the optimal control gain matrix of the vehicle from time 0 to time N-1.

[0037] The control module is used to control the vehicle according to the nonlinear optimal control quantity sequence of the vehicle.

[0038] In one possible implementation, the set of equations concerning the optimal control gain matrices of the vehicle and other vehicles includes:

[0039]

[0040] Wherein, K1(k) represents the optimal control gain matrix of the vehicle at time k, R1 represents the first positive definite matrix, B1 represents the vehicle control matrix, P1(k+1) represents the first intermediate matrix at time k+1, A represents the system state matrix, B2 represents the other vehicle control matrix, K2(k) represents the optimal control gain matrix of the other vehicle at time k, R2 represents the second positive definite matrix, and P2(k+1) represents the second intermediate matrix at time k+1.

[0041] In one possible implementation, the coupled Riccati equations concerning the first intermediate matrix at time k include:

[0042] P1(k) = Q1 + K1(k) T R1K1(k)+(A+B2K2(k+B1K1(k)) T P1(k+1)(A+B1K1(k)+B2K2(k));

[0043] And / or, the coupled Riccati equations with respect to the second intermediate matrix at time k include:

[0044] P2(k) = Q2 + K2(k) T R2K2(k)+(A+B2K2(k)+B1K1(k)) T P2(k+1)(A+B1K1(k)+B2K2(k));

[0045] Wherein, P1(k) represents the first intermediate matrix at time k, Q1 represents the second positive semi-definite matrix, K1(k) represents the optimal control gain matrix of the vehicle at time k, R1 represents the first positive definite matrix, A represents the system state matrix, B2 represents the control matrix of the other vehicle, K2(k) represents the optimal control gain matrix of the other vehicle at time k, B1 represents the control matrix of the vehicle, P1(k+1) represents the first intermediate matrix at time k+1, P2(k) represents the second intermediate matrix at time k, Q2 represents the fourth positive semi-definite matrix, R2 represents the second positive definite matrix, and P2(k+1) represents the second intermediate matrix at time k+1.

[0046] Thirdly, embodiments of this application provide a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the method as described in any possible implementation of the first aspect.

[0047] Fourthly, embodiments of this application provide an electronic device, which includes:

[0048] One or more processors;

[0049] The processor is coupled to a storage device for storing one or more programs;

[0050] When one or more programs are executed by one or more processors, the electronic device performs the method as described in any possible implementation of the first aspect.

[0051] Fifthly, embodiments of this application provide a vehicle that includes the means as described in any possible implementation of the second aspect, or includes electronic equipment as described in the fourth aspect.

[0052] In a sixth aspect, embodiments of this application provide a computer program product containing instructions that, when executed on a computer or processor, cause the computer or processor to perform the method described in any possible implementation of the first aspect.

[0053] As can be seen from the above scheme, the vehicle interaction decision-making method and related device based on unprotected intersections provided in this application embodiment can pre-calculate the optimization objectives of the linear quadratic differential game problem of the self-vehicle and the other vehicle using the Pontryagin minimum algorithm combined with the linear system state equations of the self-vehicle and the other vehicle, obtaining the equations for the optimal control gain matrices of the self-vehicle and the other vehicle, the coupled Riccati equation for the first intermediate matrix at time k, and the coupled Riccati equation for the second intermediate matrix at time k. Then, when it is necessary to make decisions on vehicle interaction in the unprotected intersection scenario, the system state matrix, the self-vehicle control matrix, and the other vehicle control matrix in the linear system state equations of the self-vehicle and the other vehicle are first obtained, as well as the first positive semi-definite matrix, the second positive semi-definite matrix, and the first positive semi-definite matrix in the optimization objective of the linear quadratic differential game problem of the self-vehicle in the unprotected intersection scenario. The system uses the first and second positive definite matrices in the objective function of the linear quadratic differential game problem involving the vehicle and the other vehicle. Then, it uses these matrices as the first and second intermediate matrices at time N, respectively. Based on these intermediate matrices, the system state matrix, the vehicle's control matrix, the other vehicle's control matrix, the second positive definite matrix, and the fourth positive definite matrix, it performs a reverse recursive solution to the equations concerning the optimal control gain matrices of the vehicle and the other vehicle, the coupled Riccati equation concerning the first intermediate matrix at time k, and the coupled Riccati equation concerning the second intermediate matrix at time k. This yields the optimal control gain matrix sequence for the vehicle. Finally, the vehicle is controlled based on the nonlinear optimal control quantity sequence determined by the optimal control gain matrix sequence. Since the equations relating the optimal control gain matrices of the vehicle and other vehicles are expressions for the feedback Nash equilibrium solutions of the control gain matrices of the vehicle and other vehicles, the calculated optimal control gain matrix sequence of the vehicle is its feedback Nash equilibrium solution. Therefore, the nonlinear optimal control quantity sequence of the vehicle calculated from its optimal control gain matrix sequence is also its feedback Nash equilibrium solution. Similarly, the optimal control gain matrix sequence of other vehicles obtained during the solution process is also their feedback Nash equilibrium solution. This allows the vehicle and other vehicles to strive for optimal independent, conflicting objectives during continuous game play. That is, without either vehicle's intention to change its strategy independently, the game decisions of the interacting vehicles are optimal, thus avoiding collisions and improving the safety of vehicle interaction in unprotected intersection scenarios. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0055] Figure 1 A flowchart illustrating a vehicle interaction decision-making method based on unprotected intersections provided in this application embodiment;

[0056] Figure 2 A block diagram illustrating the composition of a vehicle interaction decision-making device based on an unprotected intersection, provided in an embodiment of this application;

[0057] Figure 3 This is a schematic diagram of the structure of an electronic device or computer device provided in an embodiment of this application. Detailed Implementation

[0058] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0059] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The terms "comprising" and "having," and any variations thereof, in the embodiments and drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices.

[0060] In unprotected intersection interaction scenarios, both the driver and other vehicles need to update their respective action sequences in real time based on observed system state variables, maintaining their independent and conflicting objectives in an optimal state so that neither vehicle wants to change its strategy independently. Therefore, the characteristic of the interaction decision-making problem between drivers and other vehicles in unprotected intersection scenarios is not finding an open-loop Nash equilibrium solution, but rather a feedback Nash equilibrium solution. Based on this, this invention proposes an unprotected intersection interaction decision-making strategy. First, the interaction decision-making problem is modeled as a nonlinear differential game problem between drivers and other vehicles at unprotected intersections. Then, a hierarchical architecture is used to solve this nonlinear differential game problem to obtain the feedback Nash equilibrium solution for both drivers and other vehicles. Specifically, the outer layer uses the augmented Lagrange method to transform the nonlinear differential game problem of the self-vehicle and other vehicles at an unprotected intersection into a linear quadratic differential game problem. The inner layer uses the Pontryagin minimum principle to simplify the solution of the linear quadratic differential game problem into the solution of the coupled Riccati equation problem. Based on the terminal conditions of the coupled Riccati equation, the coupled Riccati equation is solved recursively in reverse. Then, the feedback Nash equilibrium solution of the self-vehicle and other vehicles is obtained through iterative calculations of the outer and inner layers. The process is described in detail below:

[0061] Figure 1 This is a flowchart illustrating a vehicle interaction decision-making method based on unprotected intersections. This method can be applied to various road scenarios, such as autonomous valet parking, memory parking, and other autonomous driving scenarios. It can be applied to electronic devices or computer equipment, specifically vehicles or servers, and includes the following steps:

[0062] S110: Obtain the system state matrix, the control matrix of the self-vehicle, and the control matrix of the other vehicle in the linear system state equations for the self-vehicle and the other vehicle, as well as the first semi-positive definite matrix, the second semi-positive definite matrix, and the first positive definite matrix in the optimization objective of the linear quadratic differential game problem of the self-vehicle in the scenario of an unprotected intersection, and the third semi-positive definite matrix, the fourth semi-positive definite matrix, and the second positive definite matrix in the optimization objective of the linear quadratic differential game problem of the other vehicle.

[0063] Among them, the first positive semi - definite matrix is the coefficient of the linear system state quantity at the N - th moment in the optimization objective of the ego - vehicle linear - quadratic differential game problem, the second positive semi - definite matrix is the coefficient of the linear system state quantity at the k - th moment in the optimization objective of the ego - vehicle linear - quadratic differential game problem, the first positive definite matrix is the coefficient of the ego - vehicle linear control quantity at the k - th moment in the optimization objective of the ego - vehicle linear - quadratic differential game problem, the third positive semi - definite matrix is the coefficient of the linear system state quantity at the N - th moment in the optimization objective of the other - vehicle linear - quadratic differential game problem, the fourth positive semi - definite matrix is the coefficient of the linear system state quantity at the k - th moment in the optimization objective of the other - vehicle linear - quadratic differential game problem, the second positive definite matrix is the coefficient of the other - vehicle linear control quantity at the k - th moment in the optimization objective of the other - vehicle linear - quadratic differential game problem. The N - th moment is the last moment in a planning decision cycle, and 0 ≤ k < N. The linear system state equation is a linear equation for determining the linear system state quantity at the second moment based on the linear system state quantity at the first moment, the system state matrix, the ego - vehicle linear control quantity at the first moment, the ego - vehicle control matrix, the other - vehicle linear control quantity at the first moment, and the other - vehicle control matrix. The second moment is the next moment adjacent to the first moment.

[0064] The linear system state quantity refers to the system state quantity in the optimization objective of the ego - vehicle linear - quadratic differential game problem, the optimization objective of the other - vehicle linear - quadratic differential game problem, or the linear system state equation. The ego - vehicle linear control quantity refers to the ego - vehicle control quantity in the optimization objective of the ego - vehicle linear - quadratic differential game problem, the optimization objective of the other - vehicle linear - quadratic differential game problem, or the linear system state equation. The other - vehicle linear control quantity refers to the other - vehicle control quantity in the optimization objective of the ego - vehicle linear - quadratic differential game problem, the optimization objective of the other - vehicle linear - quadratic differential game problem, or the linear system state equation. The system state quantity includes the state of the ego - vehicle and the state of the other - vehicle, specifically including state quantities such as the longitudinal position, longitudinal velocity, and longitudinal acceleration of the ego - vehicle and the other - vehicle; the ego - vehicle control quantity includes control quantities such as the longitudinal acceleration of the ego - vehicle; the other - vehicle control quantity includes control quantities such as the longitudinal acceleration of the other - vehicle.

[0065] The non - linear system state equation of the ego - vehicle and the other - vehicle is

[0066] X(k + 1)=f(X(k), U1(k), U2(k))(1)

[0067] In the formula, X(k) is the non - linear system state quantity of the ego - vehicle and the other - vehicle at the k - th moment; U1(k) is the non - linear control quantity of the ego - vehicle at the k - th moment; U2(k) is the non - linear control quantity of the other - vehicle at the k - th moment, and X(k + 1) is the non - linear system state quantity of the ego - vehicle and the other - vehicle at the k + 1 - th moment.

[0068] Considering the collision constraints, target - point constraints, and control - quantity constraints of the ego - vehicle and the other - vehicle comprehensively, the optimization objective of the non - linear differential game problem of the ego - vehicle and the other - vehicle in the unprotected intersection scenario is

[0069]

[0070] In the formula, when i=1, it represents the vehicle itself; when i=2, it represents another vehicle. L1 and L2 represent the first and third positive semi-definite matrices, respectively; Q1 and Q2 represent the second and fourth positive semi-definite matrices, respectively; R1 and R2 represent the first and second positive definite matrices, respectively; J... i Let X(N) represent the optimization objective of the nonlinear differential game problem, and let X(N) be the nonlinear system state variables of the vehicle and the other vehicle at time N.

[0071] The state variables of a nonlinear system refer to the optimization objectives of the nonlinear differential game problem of the vehicle itself, the optimization objectives of the nonlinear differential game problem of the other vehicle, or the system state variables in the state equation of the nonlinear system. The nonlinear control variables of the vehicle itself refer to the optimization objectives of the nonlinear differential game problem of the vehicle itself, the optimization objectives of the nonlinear differential game problem of the other vehicle, or the control variables of the vehicle itself in the state equation of the nonlinear system. The nonlinear control variables of the other vehicle refer to the optimization objectives of the nonlinear differential game problem of the other vehicle, the optimization objectives of the nonlinear differential game problem of the other vehicle, or the control variables of the other vehicle in the state equation of the nonlinear system.

[0072] The augmented Lagrangian method is used to transform the state equations of the nonlinear system into those of the linear system.

[0073] x(k+1)=Ax(k)+B1u1(k)+B2u2(k)(3)

[0074] Where x(k+1) is the linear system state variable of the vehicle and other vehicles at time k+1; x(k) is the linear system state variable of the vehicle and other vehicles at time k+1; u1(k) is the linear control variable of the vehicle at time k; u2(k) is the linear control variable of other vehicles at time k; A is the system state matrix; B1 is the vehicle control matrix; and B2 is the other vehicle control matrix.

[0075] The augmented Lagrange method is used to transform the optimization objective of the nonlinear differential game problem into the optimization objective of the linear quadratic differential game problem:

[0076]

[0077] In the formula, when i = 1, it represents the vehicle itself; when i = 2, it represents another vehicle. L1 and L2 represent the first and third positive semi-definite matrices, respectively; Q1 and Q2 represent the second and fourth positive semi-definite matrices, respectively; R1 and R2 represent the first and second positive definite matrices, respectively; j i Let x(N) represent the optimization objective of the linear quadratic differential game problem, and let x(N) be the linear system state variables of the vehicle and the other vehicle at time N.

[0078] It should be added that the system state matrix, the self-vehicle control matrix, the other vehicle control matrix, the first semi-positive definite matrix, the second semi-positive definite matrix, the first positive definite matrix, the third semi-positive definite matrix, the fourth semi-positive definite matrix, and the second positive definite matrix are all fixed matrices that can be determined based on practical experience.

[0079] S120: Use the first and third positive semi-definite matrices as the first intermediate matrix and the second intermediate matrix at time N, respectively.

[0080] The first intermediate matrix is ​​used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the vehicle and the state of the linear system at the same time, and the second intermediate matrix is ​​used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the other vehicle and the state of the linear system at the same time.

[0081] The control variable for the other vehicle is a known state feedback control variable, which can be expressed as:

[0082] u2(k)=K2(k)x(k)(5)

[0083] Where K2(k) represents the gain matrix of the optimal control law for the other vehicle at time k.

[0084] Substituting equation (5) into equation (3), the updated state equation of the linear system is:

[0085] x(k+1)=(A+B2K2(k))x(k)+B1u1(k)=A cl,2 x(k)+B1u1(k)(6)

[0086] In equation (6), A satisfies cl,2 =A+B2K2(k).

[0087] In solving equation (4) using the Pontryagin minimum algorithm, the discrete Hamiltonian function h1(k) of the vehicle is defined as follows:

[0088]

[0089] Based on equation (7), the costate equation and the transverse condition are constructed as follows:

[0090]

[0091] That is, λ1(k) can be expressed as the costate of the discrete Hamiltonian function of the vehicle at time k, λ1(N) can be expressed as the costate of the discrete Hamiltonian function of the vehicle at time N, and λ1(N)=L1x(N) represents the transverse condition.

[0092] Based on the control equations, the control quantity of the vehicle is obtained as follows:

[0093]

[0094] Substituting equation (9) into equation (6), we obtain the discrete two-point boundary value problem as follows:

[0095]

[0096] Where x0 is the system state variable at time k, solve the discrete two-point boundary value problem described by equation (10), and obtain the... Substituting into equation (9), the optimal control quantity of the vehicle can be obtained. If the solution to the discrete two-point boundary value problem described by equation (10) has the following form...

[0097] λ1(k)=x(k) T P1(k)(11)

[0098] From the fourth term in equation (10), we know that P1(N) = L1, that is, the first intermediate matrix at time N is the first positive semi-definite matrix. Similarly, we can obtain that P2(N) = L2, that is, the second intermediate matrix at time N is the second positive semi-definite matrix.

[0099] S130: Based on the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second semi-positive definite matrix, and the fourth semi-positive definite matrix, the equations concerning the optimal control gain matrices of the vehicle and the other vehicle, the coupled Riccati equation concerning the first intermediate matrix at time k, and the coupled Riccati equation concerning the second intermediate matrix at time k are solved in reverse recursion to obtain the optimal control gain matrix sequence of the vehicle. The vehicle is then controlled based on the nonlinear optimal control quantity sequence of the vehicle determined by the optimal control gain matrix sequence of the vehicle.

[0100] Among them, the equations concerning the optimal control gain matrices of the vehicle and other vehicles are expressions for the feedback Nash equilibrium solutions of the control gain matrices of the vehicle and other vehicles, obtained by calculating the optimization objectives of the linear quadratic differential game problem of the vehicle and the linear quadratic differential game problem of other vehicles using the Pontryagin minimum value algorithm. The optimal control gain matrix sequence of the vehicle includes the optimal control gain matrix of the vehicle from time 0 to time N-1.

[0101] The specific implementation of obtaining the optimal control gain matrix sequence of the vehicle by recursively solving the system of equations concerning the optimal control gain matrices of the vehicle and other vehicles, the coupled Riccati equation concerning the first intermediate matrix at time k, and the coupled Riccati equation concerning the second intermediate matrix at time k can include: substituting the first intermediate matrix, the second intermediate matrix, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, and the other vehicle control matrix into the system of equations concerning the optimal control gain matrices of the vehicle and other vehicles to obtain the optimal control gain matrix of the vehicle at time N-1 and the optimal control gain matrix of the other vehicle at time N-1; and obtaining the optimal control gain matrix of the vehicle at time N-1 by substituting the second semi-positive definite matrix, the optimal control gain matrix of the vehicle at time N-1, the first positive definite matrix, the system state matrix, the vehicle control matrix, and the other vehicle control matrix... Substituting the first intermediate matrix at time N and the optimal control gain matrix of the other vehicle at time N-1 into the coupled Riccati equation about the first intermediate matrix at time k, we obtain the first intermediate matrix at time N-1. Similarly, by substituting the fourth semi-positive definite matrix, the optimal control gain matrix of the other vehicle at time N-1, the second positive definite matrix, the system state matrix, the vehicle's control matrix, the other vehicle's control matrix, the second intermediate matrix at time N, and the optimal control gain matrix of the vehicle at time N-1 into the coupled Riccati equation about the second intermediate matrix at time k, we obtain the second intermediate matrix at time N-1. This process continues until the optimal control gain matrix of the vehicle at time 0 and the optimal control gain matrix of the other vehicle at time 0 are obtained. Based on the optimal control gain matrices of the vehicle from time 0 to time N-1, we construct the optimal control gain matrix sequence of the vehicle.

[0102] Following formula (11), the derivation process of obtaining the system of equations for the optimal control gain matrix of the vehicle and other vehicles, the coupled Riccati equation for the first intermediate matrix at time k, and the coupled Riccati equation for the second intermediate matrix at time k will be explained below:

[0103] Substituting equation (11) into the first term of equation (10), we get

[0104]

[0105] Further simplification of equation (12) yields:

[0106]

[0107] Substituting equation (11) into the second term of equation (10), we get

[0108]

[0109] Substituting equation (13) into equation (14), we get

[0110]

[0111] For equation (15) to hold for any x(k), matrix P1(k) must satisfy the following Riccati equation.

[0112]

[0113] If the conjecture described by equation (11) is true, the matrix P1(k) must satisfy the Riccati equation described by equation (16).

[0114] Using matrix operation identities (U -1 +VZ -1 W) -1 =U-UV(Z+WUV) -1 WU will factor in equation (16)

[0115] Become

[0116]

[0117] Substituting equation (17) into equation (16), we get

[0118]

[0119] Combining equation (18), P1(k) can be determined by reverse recursion using P1(N) = L1.

[0120] like It exists, and can be solved from the second term in equation (10).

[0121]

[0122] Substituting equation (19) into equation (9), we obtain the optimal control quantity for the vehicle as follows:

[0123]

[0124] Substituting equation (16) into equation (20), we get

[0125]

[0126] From equation (21), we can obtain

[0127]

[0128] Further rearranging equation (22), we can obtain

[0129] K1(k) T R1K1(k)+(B1K1(k)) T P1(k+1)(A+B1K1(k)+B2K2(k))=0(23)

[0130] Substituting equation (22) into equation (18), we get

[0131]

[0132] A cl,2 Substituting A + B2K2(k) into equation (24), we can obtain

[0133]

[0134] Substituting equation (23) into equation (25), we get

[0135]

[0136] Symmetrically, the optimal control expression for the other vehicle can be obtained using the above derivation process. Therefore, given matrices P1(k+1) and P2(k+1), the Nash equilibrium solution to the differential game problem between the driver and the other vehicle is:

[0137]

[0138] In the formula, A cl,1 =A+B1K1(k), and matrices P1(k+1) and P2(k+1) are obtained by reverse recursion calculation using the coupled Riccati equation described by equation (28).

[0139]

[0140] In summary, given P1(N) = L1 and P2(N) = L2, the optimal control gain matrices K1(N-1) and K2(N-1) of the vehicle and other vehicles can be obtained using equation (27). Substituting K1(N-1) and K2(N-1) into equation (28), we can obtain P1(N-1) and P2(N-1). Continuing in this way, we can obtain the optimal control gain matrix sequence K1(k), K2(k), k = 0, ..., N-1 of the vehicle and other vehicles.

[0141] In one possible implementation, after obtaining the optimal control gain matrix sequence of the vehicle, the specific method for controlling the vehicle based on the nonlinear optimal control quantity sequence determined by the optimal control gain matrix sequence of the vehicle may include: determining the vehicle's linear optimal control quantity at each time step for the optimal control gain matrix of the vehicle at each time step and the linear system state quantity at the same time step; determining the vehicle's nonlinear optimal control quantity from time 0 to time N-1 based on the vehicle's linear system state equation, the vehicle's nonlinear system state equation, and the vehicle's linear optimal control quantity at each time step; constructing the vehicle's nonlinear optimal control quantity sequence based on the optimal control gain matrix of the vehicle from time 0 to time N-1; and controlling the vehicle based on the vehicle's nonlinear optimal control quantity sequence.

[0142] After obtaining K2(k), K2(k) and x(k) can be substituted into the formula u2(k)=K2(k)x(k) to obtain the vehicle's linear optimal control quantity u2(k) at time k. Then, according to the inverse process of the algorithm for obtaining the vehicle's linear system state equation based on the vehicle's nonlinear system state equation, the vehicle's nonlinear optimal control quantity U2(k) is obtained from u2(k). The vehicle's nonlinear optimal control quantity sequence is constructed based on the vehicle's optimal control gain matrix from time 0 to time N-1. Finally, the vehicle is controlled based on the vehicle's nonlinear optimal control quantity sequence constructed from the vehicle's nonlinear optimal control quantity from time 0 to time N-1.

[0143] The vehicle interaction decision-making method based on unprotected intersections provided in the application embodiments can pre-calculate the optimization objectives of the linear quadratic differential game problem for the self-vehicle and the other vehicle using the Pontryagin minimum algorithm combined with the linear system state equations of the self-vehicle and other vehicles. This yields a set of equations for the optimal control gain matrices of the self-vehicle and other vehicles, a coupled Riccati equation for the first intermediate matrix at time k, and a coupled Riccati equation for the second intermediate matrix at time k. Then, when making decisions on vehicle interaction in the unprotected intersection scenario, it first obtains the system state matrix, the self-vehicle control matrix, and the other vehicle control matrix from the linear system state equations of the self-vehicle and other vehicles, as well as the first positive semi-definite matrix, the second positive semi-definite matrix, and the first positive definite matrix from the optimization objective of the self-vehicle linear quadratic differential game problem in the unprotected intersection scenario, and the other vehicle... In the optimization objective of the linear quadratic differential game problem, the third, fourth, and second positive definite matrices are used. The first and third positive definite matrices are then used as the first and second intermediate matrices at time N, respectively. Based on the first and second intermediate matrices at time N, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second and fourth positive definite matrices, the equations concerning the optimal control gain matrices of the vehicle and the other vehicle, the coupled Riccati equation concerning the first intermediate matrix at time k, and the coupled Riccati equation concerning the second intermediate matrix at time k are solved in reverse recursion to obtain the optimal control gain matrix sequence of the vehicle. Finally, the vehicle is controlled based on the nonlinear optimal control quantity sequence of the vehicle determined by the optimal control gain matrix sequence of the vehicle. Since the equations relating the optimal control gain matrices of the vehicle and other vehicles are expressions for the feedback Nash equilibrium solutions of the control gain matrices of the vehicle and other vehicles, the calculated optimal control gain matrix sequence of the vehicle is its feedback Nash equilibrium solution. Therefore, the nonlinear optimal control quantity sequence of the vehicle calculated from its optimal control gain matrix sequence is also its feedback Nash equilibrium solution. Similarly, the optimal control gain matrix sequence of other vehicles obtained during the solution process is also their feedback Nash equilibrium solution. This allows the vehicle and other vehicles to strive for optimal independent, conflicting objectives during continuous game play. That is, without either vehicle's intention to change its strategy independently, the game decisions of the interacting vehicles are optimal, thus avoiding collisions and improving the safety of vehicle interaction in unprotected intersection scenarios.

[0144] Based on the above method embodiments, another embodiment of this application provides a vehicle interaction decision-making device based on unprotected intersections, such as... Figure 2 As shown, the device includes:

[0145] The acquisition unit 210 is used to acquire the system state matrix, the self-vehicle control matrix, and the other-vehicle control matrix in the linear system state equations concerning the self-vehicle and other-vehicles; and to acquire the first semi-positive definite matrix, the second semi-positive definite matrix, and the first positive definite matrix in the optimization objective of the self-vehicle linear quadratic differential game problem in the unprotected intersection scenario; and the third semi-positive definite matrix, the fourth semi-positive definite matrix, and the second positive definite matrix in the optimization objective of the other-vehicle linear quadratic differential game problem. The first semi-positive definite matrix represents the coefficients of the linear system state variables at time N in the optimization objective of the self-vehicle linear quadratic differential game problem, and the second semi-positive definite matrix represents the coefficients of the linear system state variables at time N in the optimization objective of the self-vehicle linear quadratic differential game problem. The coefficients of the linear system state variables at time k in the table are defined as follows: the first positive definite matrix represents the coefficients of the linear control variables of the self-vehicle at time k in the optimization objective of the self-vehicle linear quadratic differential game problem; the third semi-positive definite matrix represents the coefficients of the linear system state variables at time N in the optimization objective of the other-vehicle linear quadratic differential game problem; the fourth semi-positive definite matrix represents the coefficients of the linear system state variables at time k in the optimization objective of the other-vehicle linear quadratic differential game problem; and the second positive definite matrix represents the coefficients of the linear control variables of the other-vehicle at time k in the optimization objective of the other-vehicle linear quadratic differential game problem. Time N is the last time in a planning and decision-making cycle, and 0 ≤ k. <N;

[0146] The determining unit 220 is used to take the first positive semi-definite matrix and the third positive semi-definite matrix as the first intermediate matrix and the second intermediate matrix at time N, respectively. The first intermediate matrix is ​​a matrix used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the vehicle and the state of the linear system at the same time. The second intermediate matrix is ​​a matrix used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the other vehicle and the state of the linear system at the same time.

[0147] The solution unit 230 is used to solve the equations concerning the optimal control gain matrices of the vehicle and other vehicles, the coupled Riccati equation concerning the first intermediate matrix at time N, and the coupled Riccati equation concerning the second intermediate matrix at time k, based on the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second semi-positive definite matrix, and the fourth semi-positive definite matrix, by reverse recursion to obtain the optimal control gain matrix sequence of the vehicle. The equations concerning the optimal control gain matrices of the vehicle and other vehicles are expressions for the feedback Nash equilibrium solutions concerning the control gain matrices of the vehicle and other vehicles, obtained by calculating the optimization objectives of the linear quadratic differential game problem of the vehicle and the linear quadratic differential game problem of the other vehicle using the Pontryagin minimum algorithm. The optimal control gain matrix sequence of the vehicle includes the optimal control gain matrices of the vehicle from time 0 to time N-1.

[0148] The control unit 240 is used to control the vehicle according to a sequence of nonlinear optimal control quantities determined based on the vehicle's optimal control gain matrix sequence.

[0149] In one possible implementation, the solving unit 230 includes:

[0150] The first calculation module is used to obtain the optimal control gain matrix of the vehicle at time N-1 and the optimal control gain matrix of the other vehicle at time N-1 by substituting the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, and the other vehicle control matrix into the system of equations about the optimal control gain matrices of the vehicle and the other vehicle.

[0151] The second calculation module is used to obtain the first intermediate matrix at time N-1 by substituting the second semi-positive definite matrix, the vehicle's optimal control gain matrix at time N-1, the first positive definite matrix, the system state matrix, the vehicle's control matrix, the other vehicle's control matrix, the first intermediate matrix at time N, and the other vehicle's optimal control gain matrix at time N-1 into the coupled Riccati equation about the first intermediate matrix at time k; and to obtain the second intermediate matrix at time N-1 by substituting the fourth semi-positive definite matrix, the other vehicle's optimal control gain matrix at time N-1, the second positive definite matrix, the system state matrix, the vehicle's control matrix, the other vehicle's control matrix, the second intermediate matrix at time N, and the vehicle's optimal control gain matrix at time N-1 into the coupled Riccati equation about the second intermediate matrix at time k.

[0152] The generation module is used to sequentially obtain the optimal control gain matrix of the vehicle at time 0 and the optimal control gain matrix of the other vehicle at time 0, and then construct the optimal control gain matrix sequence of the vehicle based on the optimal control gain matrix of the vehicle from time 0 to time N-1.

[0153] In one possible implementation, the control unit 240 includes:

[0154] The first determining module is used to determine the vehicle's linear optimal control quantity at each time step, based on the vehicle's optimal control gain matrix at each time step in the optimal control gain matrix sequence of the vehicle and the linear system state quantity at the same time step.

[0155] The second determining module is used to determine the nonlinear optimal control quantity of the vehicle from time 0 to time N-1 based on the linear system state equation of the vehicle, the nonlinear system state equation of the vehicle, and the linear optimal control quantity of the vehicle at each time step, and to construct the sequence of nonlinear optimal control quantities of the vehicle based on the optimal control gain matrix of the vehicle from time 0 to time N-1.

[0156] The control module is used to control the vehicle according to the nonlinear optimal control quantity sequence of the vehicle.

[0157] In one possible implementation, the set of equations concerning the optimal control gain matrices of the vehicle and other vehicles includes:

[0158]

[0159] Wherein, K1(k) represents the optimal control gain matrix of the vehicle at time k, R1 represents the first positive definite matrix, B1 represents the vehicle control matrix, P1(k+1) represents the first intermediate matrix at time k+1, A represents the system state matrix, B2 represents the other vehicle control matrix, K2(k) represents the optimal control gain matrix of the other vehicle at time k, R2 represents the second positive definite matrix, and P2(k+1) represents the second intermediate matrix at time k+1.

[0160] In one possible implementation, the coupled Riccati equations concerning the first intermediate matrix at time k include:

[0161] P1(k) = Q1 + K1(k) T R1K1(k)+(A+B2K2(k+B1K1(k)) T P1(k+1)(A+B1K1(k)+B2K2(k));

[0162] And / or, the coupled Riccati equations with respect to the second intermediate matrix at time k include:

[0163] P2(k) = Q2 + K2(k) T R2K2(k)+(A+B2K2(k)+B1K1(k)) T P2(k+1)(A+B1K1(k)+B2K2(k));

[0164] Wherein, P1(k) represents the first intermediate matrix at time k, Q1 represents the second positive semi-definite matrix, K1(k) represents the optimal control gain matrix of the vehicle at time k, R1 represents the first positive definite matrix, A represents the system state matrix, B2 represents the control matrix of the other vehicle, K2(k) represents the optimal control gain matrix of the other vehicle at time k, B1 represents the control matrix of the vehicle, P1(k+1) represents the first intermediate matrix at time k+1, P2(k) represents the second intermediate matrix at time k, Q2 represents the fourth positive semi-definite matrix, R2 represents the second positive definite matrix, and P2(k+1) represents the second intermediate matrix at time k+1.

[0165] The vehicle interaction decision-making device based on unprotected intersections provided in the application embodiment can pre-calculate the optimization objectives of the linear quadratic differential game problem for the self-vehicle and the other vehicle using the Pontryagin minimum algorithm combined with the linear system state equations of the self-vehicle and other vehicles. This yields a set of equations concerning the optimal control gain matrices of the self-vehicle and other vehicles, a coupled Riccati equation concerning the first intermediate matrix at time k, and a coupled Riccati equation concerning the second intermediate matrix at time k. Then, when a decision needs to be made regarding vehicle interaction in an unprotected intersection scenario, it first obtains the system state matrix, the self-vehicle control matrix, and the other vehicle control matrix from the linear system state equations of the self-vehicle and other vehicles, as well as the first positive semi-definite matrix, the second positive semi-definite matrix, and the first positive definite matrix from the optimization objective of the self-vehicle linear quadratic differential game problem in the unprotected intersection scenario, and the other vehicle... In the optimization objective of the linear quadratic differential game problem, the third, fourth, and second positive definite matrices are used. The first and third positive definite matrices are then used as the first and second intermediate matrices at time N, respectively. Based on the first and second intermediate matrices at time N, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second and fourth positive definite matrices, the equations concerning the optimal control gain matrices of the vehicle and the other vehicle, the coupled Riccati equation concerning the first intermediate matrix at time k, and the coupled Riccati equation concerning the second intermediate matrix at time k are solved in reverse recursion to obtain the optimal control gain matrix sequence of the vehicle. Finally, the vehicle is controlled based on the nonlinear optimal control quantity sequence of the vehicle determined by the optimal control gain matrix sequence of the vehicle. Since the equations relating the optimal control gain matrices of the vehicle and other vehicles are expressions for the feedback Nash equilibrium solutions of the control gain matrices of the vehicle and other vehicles, the calculated optimal control gain matrix sequence of the vehicle is its feedback Nash equilibrium solution. Therefore, the nonlinear optimal control quantity sequence of the vehicle calculated from its optimal control gain matrix sequence is also its feedback Nash equilibrium solution. Similarly, the optimal control gain matrix sequence of other vehicles obtained during the solution process is also their feedback Nash equilibrium solution. This allows the vehicle and other vehicles to strive for optimal independent, conflicting objectives during continuous game play. That is, without either vehicle's intention to change its strategy independently, the game decisions of the interacting vehicles are optimal, thus avoiding collisions and improving the safety of vehicle interaction in unprotected intersection scenarios.

[0166] Based on the above method embodiments, another embodiment of this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method as described in any of the above embodiments.

[0167] Based on the above method embodiments, another embodiment of this application provides an electronic device or computer device, such as... Figure 3 As shown, it includes:

[0168] One or more processors 310;

[0169] The processor 310 is coupled to a storage device 320, the storage device 320 being used to store one or more programs;

[0170] When the one or more programs are executed by the one or more processors 310, the electronic device or computer device performs the method as described in any of the above embodiments.

[0171] Based on the above method embodiments, another embodiment of this application provides a vehicle that includes the apparatus as described in any of the above embodiments, or includes electronic devices as described above.

[0172] Based on the above embodiments, another embodiment of this application provides a computer program product, which includes instructions that, when executed on a computer or processor, cause the computer or processor to perform the method described in any of the above embodiments.

[0173] The above-described apparatus embodiments correspond to the method embodiments and have the same technical effects. For detailed descriptions, please refer to the method embodiments. The apparatus embodiments are derived from the method embodiments; detailed descriptions can be found in the method embodiments section, and will not be repeated here. Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing this application.

[0174] Those skilled in the art will understand that the modules in the apparatus of the embodiments can be distributed in the apparatus of the embodiments as described in the embodiments, or they can be located in one or more devices different from this embodiment with corresponding changes. The modules of the above embodiments can be combined into one module, or they can be further divided into multiple sub-modules.

[0175] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A vehicle interaction decision-making method based on unprotected intersections, characterized in that, The method includes: Obtain the system state matrix, the self-vehicle control matrix, and the other-vehicle control matrix from the linear system state equations for the self-vehicle and other vehicles. Also obtain the first semi-positive definite matrix, the second semi-positive definite matrix, and the first positive definite matrix from the optimization objective of the self-vehicle linear quadratic differential game problem in the unprotected intersection scenario. Furthermore, obtain the third semi-positive definite matrix, the fourth semi-positive definite matrix, and the second positive definite matrix from the optimization objective of the other-vehicle linear quadratic differential game problem. The first semi-positive definite matrix represents the coefficients of the linear system state variables at time N in the optimization objective of the self-vehicle linear quadratic differential game problem, and the second semi-positive definite matrix represents the coefficients of the linear system state variables at time k in the optimization objective of the self-vehicle linear quadratic differential game problem. The coefficients of the linear system state variables at time k are given by the following matrix: the first positive definite matrix represents the coefficients of the linear control variables of the self-vehicle at time k in the optimization objective of the linear quadratic differential game problem; the third semi-positive definite matrix represents the coefficients of the linear system state variables of the other-vehicle at time N in the optimization objective of the linear quadratic differential game problem; the fourth semi-positive definite matrix represents the coefficients of the linear system state variables of the other-vehicle at time k in the optimization objective of the linear quadratic differential game problem; and the second positive definite matrix represents the coefficients of the linear control variables of the other-vehicle at time k in the optimization objective of the linear quadratic differential game problem. The Nth time is the last time in a planning and decision-making cycle, and 0 ≤ k. <N; The first positive semi-definite matrix and the third positive semi-definite matrix are respectively used as the first intermediate matrix and the second intermediate matrix at time N. The first intermediate matrix is ​​a matrix used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the vehicle and the state of the linear system at the same time. The second intermediate matrix is ​​a matrix used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the other vehicle and the state of the linear system at the same time. Based on the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second semi-positive definite matrix, and the fourth semi-positive definite matrix, the equations concerning the optimal control gain matrices of the vehicle and other vehicles, the coupled Riccati equation concerning the first intermediate matrix at time k, and the coupled Riccati equation concerning the second intermediate matrix at time k are solved by reverse recursion to obtain the optimal control gain matrix sequence of the vehicle. The vehicle is then controlled according to the nonlinear optimal control quantity sequence of the vehicle determined based on the optimal control gain matrix sequence of the vehicle. The equations concerning the optimal control gain matrices of the vehicle and other vehicles are expressions for the feedback Nash equilibrium solutions concerning the control gain matrices of the vehicle and other vehicles, obtained by calculating the optimization objectives of the linear quadratic differential game problem of the vehicle and the linear quadratic differential game problem of the other vehicle using the Pontryagin minimum value algorithm. The optimal control gain matrix sequence of the vehicle includes the optimal control gain matrices of the vehicle from time 0 to time N-1.

2. The method according to claim 1, characterized in that, Based on the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second semi-positive definite matrix, and the fourth semi-positive definite matrix, the equations concerning the optimal control gain matrices of the vehicle and other vehicles, the coupled Riccati equation concerning the first intermediate matrix at time k, and the coupled Riccati equation concerning the second intermediate matrix at time k are solved recursively in reverse order to obtain the optimal control gain matrix sequence of the vehicle, including: By substituting the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, and the other vehicle control matrix into the system of equations concerning the optimal control gain matrices of the vehicle and the other vehicle, the optimal control gain matrix of the vehicle at time N-1 and the optimal control gain matrix of the other vehicle at time N-1 are obtained. The first intermediate matrix at time N-1 is obtained by substituting the second semi-positive definite matrix, the optimal control gain matrix of the vehicle at time N-1, the first positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the first intermediate matrix at time N, and the optimal control gain matrix of the other vehicle at time N-1 into the coupled Riccati equation about the first intermediate matrix at time k. The second intermediate matrix at time N-1 is obtained by substituting the fourth semi-positive definite matrix, the optimal control gain matrix of the other vehicle at time N-1, the second positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second intermediate matrix at time N, and the optimal control gain matrix of the vehicle at time N-1 into the coupled Riccati equation about the second intermediate matrix at time k. This process continues until the optimal control gain matrix of the vehicle at time 0 and the optimal control gain matrix of the other vehicle at time 0 are obtained. Then, the optimal control gain matrix sequence of the vehicle is constructed based on the optimal control gain matrix of the vehicle from time 0 to time N-1.

3. The method according to claim 1, characterized in that, The vehicle is controlled based on a sequence of nonlinear optimal control quantities determined from the optimal control gain matrix sequence of the vehicle, including: For each time step in the optimal control gain matrix sequence of the vehicle, the optimal control gain matrix of the vehicle and the linear system state variables at the same time step are used to determine the optimal linear control quantity of the vehicle at each time step. Based on the linear system state equation of the vehicle, the nonlinear system state equation of the vehicle, and the linear optimal control quantity of the vehicle at each time step, the nonlinear optimal control quantity of the vehicle from time 0 to time N-1 is determined, and the sequence of nonlinear optimal control quantities of the vehicle is constructed based on the optimal control gain matrix of the vehicle from time 0 to time N-1. The vehicle is controlled according to the nonlinear optimal control sequence of the vehicle.

4. The method according to claim 1, characterized in that, The set of equations concerning the optimal control gain matrices for the vehicle and other vehicles includes: Wherein, K1(k) represents the optimal control gain matrix of the vehicle at time k, R1 represents the first positive definite matrix, B1 represents the vehicle control matrix, P1(k+1) represents the first intermediate matrix at time k+1, A represents the system state matrix, B2 represents the other vehicle control matrix, K2(k) represents the optimal control gain matrix of the other vehicle at time k, R2 represents the second positive definite matrix, and P2(k+1) represents the second intermediate matrix at time k+1.

5. The method according to any one of claims 1-4, characterized in that, The coupled Riccati equations concerning the first intermediate matrix at time k include: P1(k)=Q1+K1(k) T R1K1(k)+(A+B2K2(k)+B1K1(k)) T P1(k+1)(A+B1K1(k)+B2K2(k)); And / or, the coupled Riccati equations with respect to the second intermediate matrix at time k include: P2(k)=Q2+K2(k) T R2K2(k)+(A+B2K2(k)+B1K1(k)) T P2(k+1)(A+B1K1(k)+B2K2(k)); Wherein, P1(k) represents the first intermediate matrix at time k, Q1 represents the second positive semi-definite matrix, K1(k) represents the optimal control gain matrix of the vehicle at time k, R1 represents the first positive definite matrix, A represents the system state matrix, B2 represents the control matrix of the other vehicle, K2(k) represents the optimal control gain matrix of the other vehicle at time k, B1 represents the control matrix of the vehicle, P1(k+1) represents the first intermediate matrix at time k+1, P2(k) represents the second intermediate matrix at time k, Q2 represents the fourth positive semi-definite matrix, R2 represents the second positive definite matrix, and P2(k+1) represents the second intermediate matrix at time k+1.

6. A vehicle interaction decision-making device based on unprotected intersections, characterized in that, The device includes: The acquisition unit is used to acquire the system state matrix, the self-vehicle control matrix, and the other-vehicle control matrix from the linear system state equations of the self-vehicle and other-vehicles; and to acquire the first semi-positive definite matrix, the second semi-positive definite matrix, and the first positive definite matrix from the optimization objective of the self-vehicle linear quadratic differential game problem in the unprotected intersection scenario; and the third semi-positive definite matrix, the fourth semi-positive definite matrix, and the second positive definite matrix from the optimization objective of the other-vehicle linear quadratic differential game problem. The first semi-positive definite matrix represents the coefficients of the linear system state variables at time N in the optimization objective of the self-vehicle linear quadratic differential game problem, and the second semi-positive definite matrix represents the coefficients of the linear system state variables at time N in the optimization objective of the self-vehicle linear quadratic differential game problem. The coefficients of the linear system state variables at time k are given by the first positive definite matrix, which represents the coefficients of the linear control variables of the self-vehicle at time k in the optimization objective of the self-vehicle linear quadratic differential game problem. The third semi-positive definite matrix represents the coefficients of the linear system state variables at time N in the optimization objective of the other-vehicle linear quadratic differential game problem. The fourth semi-positive definite matrix represents the coefficients of the linear system state variables at time k in the optimization objective of the other-vehicle linear quadratic differential game problem. The second positive definite matrix represents the coefficients of the linear control variables of the other-vehicle at time k in the optimization objective of the other-vehicle linear quadratic differential game problem. Time N is the last time in a planning and decision-making cycle, and 0 ≤ k. <N; The determining unit is used to take the first positive semi-definite matrix and the third positive semi-definite matrix as the first intermediate matrix and the second intermediate matrix at time N, respectively. The first intermediate matrix is ​​a matrix used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the vehicle and the state of the linear system at the same time. The second intermediate matrix is ​​a matrix used to describe the mapping relationship between the costate of the discrete Hamiltonian function of the other vehicle and the state of the linear system at the same time. The solution unit is used to perform reverse recursive solution of the equations concerning the optimal control gain matrices of the vehicle and other vehicles, the coupled Riccati equation concerning the first intermediate matrix at time N, and the coupled Riccati equation concerning the second intermediate matrix at time k, based on the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, the other vehicle control matrix, the second semi-positive definite matrix, and the fourth semi-positive definite matrix, to obtain the optimal control gain matrix sequence of the vehicle. The equations concerning the optimal control gain matrices of the vehicle and other vehicles are expressions for the feedback Nash equilibrium solutions concerning the control gain matrices of the vehicle and other vehicles, obtained by calculating the optimization objectives of the linear quadratic differential game problem of the vehicle and the linear quadratic differential game problem of the other vehicle using the Pontryagin minimum algorithm. The optimal control gain matrix sequence of the vehicle includes the optimal control gain matrices of the vehicle from time 0 to time N-1. The control unit is used to control the vehicle according to a sequence of nonlinear optimal control quantities determined based on the vehicle's optimal control gain matrix sequence.

7. The apparatus according to claim 6, characterized in that, The solution unit includes: The first calculation module is used to obtain the optimal control gain matrix of the vehicle at time N-1 and the optimal control gain matrix of the other vehicle at time N-1 by substituting the first intermediate matrix at time N, the second intermediate matrix at time N, the first positive definite matrix, the second positive definite matrix, the system state matrix, the vehicle control matrix, and the other vehicle control matrix into the system of equations about the optimal control gain matrices of the vehicle and the other vehicle. The second calculation module is used to obtain the first intermediate matrix at time N-1 by substituting the second semi-positive definite matrix, the vehicle's optimal control gain matrix at time N-1, the first positive definite matrix, the system state matrix, the vehicle's control matrix, the other vehicle's control matrix, the first intermediate matrix at time N, and the other vehicle's optimal control gain matrix at time N-1 into the coupled Riccati equation about the first intermediate matrix at time k; and to obtain the second intermediate matrix at time N-1 by substituting the fourth semi-positive definite matrix, the other vehicle's optimal control gain matrix at time N-1, the second positive definite matrix, the system state matrix, the vehicle's control matrix, the other vehicle's control matrix, the second intermediate matrix at time N, and the vehicle's optimal control gain matrix at time N-1 into the coupled Riccati equation about the second intermediate matrix at time k. The generation module is used to sequentially obtain the optimal control gain matrix of the vehicle at time 0 and the optimal control gain matrix of the other vehicle at time 0, and then construct the optimal control gain matrix sequence of the vehicle based on the optimal control gain matrix of the vehicle from time 0 to time N-1.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-5.

9. An electronic device, characterized in that, The electronic device includes: One or more processors; The processor is coupled to a storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the electronic device performs the method as described in any one of claims 1-5.

10. A vehicle, characterized in that, The vehicle includes the device as described in any one of claims 6-7, or the electronic device as described in claim 9.

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