WO2021073080A1 - Nash bargaining criterion-based man-car cooperative game control method - Google Patents

Nash bargaining criterion-based man-car cooperative game control method Download PDF

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WO2021073080A1
WO2021073080A1 PCT/CN2020/090243 CN2020090243W WO2021073080A1 WO 2021073080 A1 WO2021073080 A1 WO 2021073080A1 CN 2020090243 W CN2020090243 W CN 2020090243W WO 2021073080 A1 WO2021073080 A1 WO 2021073080A1
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driver
game
car
parties
model
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PCT/CN2020/090243
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赵万忠
张子俊
周小川
郭志强
王安
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南京航空航天大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/20—Design optimisation, verification or simulation

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  • the invention belongs to the technical field of human-vehicle game control, and specifically relates to a human-vehicle cooperative game control method based on Nash negotiation criteria.
  • the active steering control that does not consider the driver's manipulation only focuses on the control performance of the controller and ignores the driver's changeable manipulation, which causes frequent conflicts between the controller and the person, which is not very good. Solve the problem of the human-vehicle game effectively.
  • the active steering technology developed in order to neutralize the driver's manipulation will stimulate the driver's response and enable the driver to improve his steering manipulation to achieve his own control purpose.
  • Model-based control technology uses algorithms such as model predictive control and fuzzy control, but seldom pays attention to the conflict between human-vehicle co-driving.
  • Game-based control technology uses a variety of methods such as Nash equilibrium solution and linear quadratic, but it has not fully studied the influence of the driver's driving experience and steering characteristics.
  • the purpose of the present invention is to provide a human-vehicle cooperative game control method based on the Nash negotiation criteria, which can fully study the human-vehicle interaction process, and control the driver's control
  • the characteristics and driving habits are integrated into the human-vehicle cooperative game control framework to eliminate the manipulation conflict between the two sides of the game and maximize the benefits of the non-zero-sum game.
  • the human-vehicle cooperative game control method based on the Nash negotiation criterion of the present invention includes the following steps:
  • the step 1) specifically includes:
  • m is the mass of the car;
  • u is the speed of the car;
  • a and b are the distances from the center of mass of the car to the front and rear axles;
  • J s and B s are the moment of inertia and steering damping of the steering system, respectively;
  • C f and C r are respectively Front wheel cornering stiffness and rear wheel cornering stiffness of the car;
  • I z is the vertical moment of inertia of the car;
  • i 0 is the standard transmission ratio of the steering system;
  • i m is the reduction ratio of the rear-wheel steering motor;
  • the sixth-order vehicle dynamics model receives the steering wheel torque of the driver's neuromuscular model and the rear wheel angle command of the active rear-wheel steering controller, and outputs the vehicle state quantity;
  • the sampling time is taken as T s , and the driver model is established, including:
  • k represents the pilot's preview point number
  • x d (k) is the state vector at the k-th preview point
  • y d (k) The output vector for the model at the kth preview point
  • the coefficient matrix is:
  • the update process of the pilot preview information can be expressed as:
  • G d (s) also represents the transfer function from the driver's preview input to the driver's torque output; s is the Laplacian operator; K r and B r are the reflection stiffness and reflection damping, respectively; ⁇ r Is the transmission delay; ⁇ r is the cutoff frequency.
  • the driver’s optimal preview model takes road preview information as input, and its output is the optimal steering wheel angle; the driver’s neuromuscular model takes the optimal steering wheel angle as input, and its output is the steering wheel torque.
  • the steering wheel torque is transferred to the sixth-order vehicle dynamics model.
  • the design process of the active rear-wheel steering controller in step 2) is specifically as follows:
  • the three parameters determine the control effect of the algorithm on the stability of the car; choose two Group parameter values (0.82, 0.47, 0.11), (0.63, 0.35, 0.08), the control intensity of the former is slightly higher than the latter, and the oscillation of the two is relatively small.
  • the rear wheel angle command output from the active rear wheel steering controller is transmitted to the sixth-order vehicle dynamics model.
  • the process of identifying the parameters of the driver's neuromuscular model in step 3) is specifically:
  • the transmission delay is reflected in the data stream of MATLAB/Simulink, so it can be omitted in the following formula derivation; the relationship between the input and output of the driver's neuromuscular model is:
  • T d (s) is the driver’s output steering wheel torque
  • the output of the driver's optimal preview model is the driver's expected steering wheel angle
  • the identified parameters of the driver's neuromuscular model are input to the Nash negotiation criteria, which are used to generate the driver's manipulation strategy set to form six combinations of human-vehicle game strategies.
  • the six human-vehicle game strategy combinations in step 4) are specifically:
  • the driver's manipulation strategy set can be expressed as It contains three game strategies:
  • ⁇ the parameter value on the left becomes the value on the right after the game starts.
  • the change in the parameter value represents the different strategies adopted by the driver, K r 0 , B r 0 , They are the identified muscle stiffness, muscle damping and cut-off frequency;
  • the use of the maximum-minimum criterion in the step 5) to calculate the benefits of the two parties in the game is specifically as follows:
  • the driver’s goal is to make the actual lateral displacement Y(k) of the car equal to the lateral displacement Y pa (k) at the road, and to make the actual yaw angle ⁇ (k) of the car equal to the lateral displacement of the road.
  • Swing angle ⁇ pa (k); and the goal of the controller is to make the actual yaw rate ⁇ (k) of the car equal to the desired yaw rate ⁇ * (k), and to make the lateral acceleration u ⁇ (k) of the car as small as possible ; Therefore, the formula for calculating the benefits of both parties can be expressed as:
  • P ij and Q ij respectively represent the strategy combination below, the gains of the driver and the active rear-wheel steering system;
  • g is the local gravity acceleration ;
  • the Nash negotiation solution using the Nash negotiation criterion in the step 6) to solve the human-vehicle game is specifically as follows:
  • the present invention does not place the driver and the advanced driver assistance system in an opposing position, allowing the two to operate independently according to their respective strategies, but applies the concept of non-zero-sum game to humans. -In the car game, solve the problem of manipulation conflict.
  • the present invention identifies some important parameters of the driver’s neuromuscular model, and designs three possible driver’s options based on the identification results.
  • kind of strategy 3.
  • the present invention proposes six game strategy combinations as the basis for solving the game problem.
  • the present invention proposes a profit calculation method for both, which constitutes the profit of both.
  • the present invention uses the Nash negotiation criterion to solve the Nash negotiation solution of the game parties based on the profit. This negotiation solution will eliminate the human-vehicle manipulation conflict to the greatest extent and meet the goals of the game parties.
  • Figure 1 is a block diagram of a human-vehicle cooperative game control method
  • Figure 2 is a schematic diagram of the pilot preview model
  • Figure 3 is a schematic diagram of human-vehicle-road interaction
  • Figure 4 is a schematic diagram of man-vehicle revenue and Nash negotiation set.
  • a human-vehicle cooperative game control method based on Nash negotiation criteria of the present invention is characterized in that it includes the following steps:
  • step 1) specifically includes:
  • m is the mass of the car;
  • u is the speed of the car;
  • a and b are the distances from the center of mass of the car to the front and rear axles;
  • J s and B s are the moment of inertia and steering damping of the steering system, respectively;
  • C f and C r are respectively Front wheel cornering stiffness and rear wheel cornering stiffness of the car;
  • I z is the vertical moment of inertia of the car;
  • i 0 is the standard transmission ratio of the steering system;
  • i m is the reduction ratio of the rear-wheel steering motor;
  • the sampling time is taken as T s , and the driver model is established, including:
  • k represents the pilot's preview point number
  • x d (k) is the state vector at the k-th preview point
  • y d (k) The output vector for the model at the kth preview point
  • the coefficient matrix is:
  • the update process of the pilot preview information can be expressed as:
  • G d (s) represents the transfer function from driver preview input to driver torque output; s is the Laplacian operator; K r and B r are reflection stiffness and reflection damping respectively; ⁇ r is Transmission delay; ⁇ r is the cut-off frequency.
  • the process of interaction between the driver and the car is shown in Figure 3.
  • the driver uses vision to obtain road preview information, uses tactile sense to receive car state feedback information, and calculates the optimal steering wheel angle through the optimal preview model.
  • the optimal steering wheel angle command is executed through the neuromuscular model G d (s), that is, the driver outputs the steering wheel torque T d , and the steering wheel torque is transmitted to the steering system together with the torque fed back from the steering system, and finally produces the actual
  • the steering wheel angle ⁇ sw also acts on the sixth-order dynamics model of the car.
  • the three parameters determine the control effect of the algorithm on the stability of the car; choose two Group parameter values (0.82, 0.47, 0.11), (0.63, 0.35, 0.08), the control intensity of the former is slightly higher than the latter, and the oscillation of the two is relatively small.
  • step 3 The process of identifying the parameters of the driver's neuromuscular model in step 3) is specifically as follows:
  • the transmission delay is reflected in the data stream of MATLAB/Simulink, so it can be omitted in the following formula derivation; the relationship between the input and output of the driver's neuromuscular model is:
  • T d (s) is the driver’s output steering wheel torque
  • the output of the driver's optimal preview model is the driver's expected steering wheel angle
  • the six human-vehicle game strategy combinations in the step 4) are specifically:
  • the driver’s manipulation strategy set is expressed as It contains three game strategies:
  • ⁇ the parameter value on the left becomes the value on the right after the game starts.
  • the change in the parameter value represents the different strategies adopted by the driver, K r 0 , B r 0 , They are the identified muscle stiffness, muscle damping and cut-off frequency;
  • the driver’s goal is to make the actual lateral displacement Y(k) of the car equal to the lateral displacement Y pa (k) at the road, and to make the actual yaw angle ⁇ (k) of the car equal to the lateral displacement of the road.
  • Swing angle ⁇ pa (k); and the goal of the controller is to make the actual yaw rate ⁇ (k) of the car equal to the desired yaw rate ⁇ * (k), and to make the lateral acceleration u ⁇ (k) of the car as small as possible ;
  • the income calculation formula of both parties is expressed as:
  • P ij and Q ij respectively represent the strategy combination below, the gains of the driver and the active rear-wheel steering system;
  • g is the local gravity acceleration ;
  • the Nash negotiation solution using the Nash negotiation criterion to solve the human-car game in the step 6) is specifically:

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Abstract

A nash bargaining criterion-based man-car cooperative smart steering game control method, comprising: establishing a sixth-order automobile dynamic model, a driver optimal preview model, and a driver neuromuscular model; identifying some important parameters in the driver neuromuscular model, and designing an active rear wheel steering controller by using a sliding mode variable structure algorithm; reasonably assuming manipulation strategies of the driver and the active rear wheel steering controller, to propose six strategy combinations of a man-car game; and calculating, by using a maximum-minimum criterion, benefits of the game parties under various policy combinations, and solving a nash bargaining solution by using a nash bargaining criterion. The man-car cooperative game control method can effectively solve a game problem and maintain a good balance between two game parties by enabling the two game parties to pre-negotiate a strategy combination.

Description

一种基于纳什谈判准则的人-车合作型博弈控制方法A Human-Vehicle Cooperative Game Control Method Based on Nash Negotiation Criterion 技术领域Technical field
本发明属于人-车博弈控制技术领域，具体涉及一种基于纳什谈判准则的人-车合作型博弈控制方法。The invention belongs to the technical field of human-vehicle game control, and specifically relates to a human-vehicle cooperative game control method based on Nash negotiation criteria.
背景技术Background technique
当前在人-车博弈领域涌现了多种控制方法，包括不考虑驾驶员操纵的主动前轮转向技术、中和驾驶员操纵的主动转向技术、基于模型的控制技术和基于博弈的控制技术等。At present, a variety of control methods have emerged in the field of human-vehicle games, including active front-wheel steering technology that does not consider driver manipulation, active steering technology that neutralizes driver manipulation, model-based control technology, and game-based control technology.
与基于博弈的控制技术相比，不考虑驾驶员操纵的主动转向控制由于只注重控制器的控制性能，忽略了驾驶员的多变操纵，而使得控制器与人发生频繁的冲突，不能很好地解决人-车博弈的问题。为了中和驾驶员操纵而开发的主动转向技术将刺激到驾驶员的反应，使驾驶员提升自己的转向操纵以实现自身的控制目的。基于模型的控制技术使用了模型预测控制、模糊控制等算法，但很少关注到人-车共驾的冲突本身。基于博弈的控制技术使用了纳什平衡解、线性二次型等多种方法，但没有充分研究驾驶员的驾驶经验和转向特征的影响。Compared with the game-based control technology, the active steering control that does not consider the driver's manipulation only focuses on the control performance of the controller and ignores the driver's changeable manipulation, which causes frequent conflicts between the controller and the person, which is not very good. Solve the problem of the human-vehicle game effectively. The active steering technology developed in order to neutralize the driver's manipulation will stimulate the driver's response and enable the driver to improve his steering manipulation to achieve his own control purpose. Model-based control technology uses algorithms such as model predictive control and fuzzy control, but seldom pays attention to the conflict between human-vehicle co-driving. Game-based control technology uses a variety of methods such as Nash equilibrium solution and linear quadratic, but it has not fully studied the influence of the driver's driving experience and steering characteristics.
为了解决以上问题，需要认识到在人-车博弈的本质是驾驶员的个人操纵特征与控制器的控制规则之间的矛盾，博弈双方因有不同的目标而争夺控制权。为了解决这一冲突，需要研究人-车交互过程，并将驾驶员的驾驶习惯纳入博弈策略的设计中。In order to solve the above problems, it is necessary to realize that the essence of the human-vehicle game is the contradiction between the driver's personal manipulation characteristics and the control rules of the controller. The two sides of the game compete for control due to different goals. In order to resolve this conflict, it is necessary to study the human-vehicle interaction process and incorporate the driver's driving habits into the design of game strategies.
发明内容Summary of the invention
针对于上述现有技术的不足，本发明的目的在于提供一种基于纳什谈判准则的人-车合作型博弈控制方法，其可以在充分研究人-车交互过程的基础上，将驾驶员的操纵特征和驾驶习惯融入到人-车合作型博弈控制框架中，消除博弈双方的操纵冲突，将非零和博弈的收益最大化。In view of the above-mentioned shortcomings of the prior art, the purpose of the present invention is to provide a human-vehicle cooperative game control method based on the Nash negotiation criteria, which can fully study the human-vehicle interaction process, and control the driver's control The characteristics and driving habits are integrated into the human-vehicle cooperative game control framework to eliminate the manipulation conflict between the two sides of the game and maximize the benefits of the non-zero-sum game.
为达到上述目的，本发明采用的技术方案如下：In order to achieve the above objectives, the technical solutions adopted by the present invention are as follows:
本发明的一种基于纳什谈判准则的人-车合作型博弈控制方法，包括步骤如下：The human-vehicle cooperative game control method based on the Nash negotiation criterion of the present invention includes the following steps:
1)建立六阶汽车动力学模型及驾驶员模型；1) Establish a sixth-order vehicle dynamics model and driver model;
2)利用滑模变结构算法设计主动后轮转向控制器；2) Design of active rear-wheel steering controller using sliding mode variable structure algorithm;
3)辨识驾驶员模型中的驾驶员神经肌肉模型参数；3) Identify the driver neuromuscular model parameters in the driver model;
4)提出六种人-车博弈策略组合；4) Propose six combinations of human-car game strategy;
5)利用最大-最小准则计算博弈双方的收益；5) Use the maximum-minimum criterion to calculate the benefits of both parties in the game;
6)利用纳什谈判准则求解人-车博弈的纳什谈判解。6) Use the Nash negotiation criterion to solve the Nash negotiation solution of the man-car game.
优选地，所述步骤1)具体包括：Preferably, the step 1) specifically includes:
所述六阶汽车动力学模型：The sixth-order vehicle dynamics model:
Figure PCTCN2020090243-appb-000001
Figure PCTCN2020090243-appb-000001
式中，
Figure PCTCN2020090243-appb-000002
为状态向量；θ sw为转向盘转角；
Figure PCTCN2020090243-appb-000003
为转向盘转角速度；v为汽车侧向速度；γ为汽车横摆角速度；Y为汽车侧向位移；ψ为汽车横摆角；T d为驾驶员转矩输入；
Figure PCTCN2020090243-appb-000004
为后轮转向电机转角输入；w为施加于前轮转向系统的转向阻力矩；y c为模型输出向量；系数矩阵为： Where
Figure PCTCN2020090243-appb-000002
Is the state vector; θ sw is the steering wheel angle;
Figure PCTCN2020090243-appb-000003
Is the steering wheel angular velocity; v is the lateral velocity of the vehicle; γ is the yaw angular velocity of the vehicle; Y is the lateral displacement of the vehicle; ψ is the yaw angle of the vehicle; T d is the driver's torque input;
Figure PCTCN2020090243-appb-000004
Is the input of the rotation angle of the rear-wheel steering motor; w is the steering resistance torque applied to the front-wheel steering system; y c is the model output vector; the coefficient matrix is:
Figure PCTCN2020090243-appb-000005
Figure PCTCN2020090243-appb-000005
式中，m为汽车质量；u为车速；a和b分别为汽车质心到前轴和后轴的距离；J s和B s分别为转向系统转动惯量和转向阻尼；C f和C r分别为汽车前轮侧偏刚度和后轮侧偏刚度；I z为汽车垂向转动惯量；i 0为转向系统标准传动比；i m为后轮转向电机减速比； Where m is the mass of the car; u is the speed of the car; a and b are the distances from the center of mass of the car to the front and rear axles; J s and B s are the moment of inertia and steering damping of the steering system, respectively; C f and C r are respectively Front wheel cornering stiffness and rear wheel cornering stiffness of the car; I z is the vertical moment of inertia of the car; i 0 is the standard transmission ratio of the steering system; i m is the reduction ratio of the rear-wheel steering motor;
所述六阶汽车动力学模型接收驾驶员神经肌肉模型的转向盘转矩量和主动后轮转向控制器的后轮转角指令，并输出汽车状态量；The sixth-order vehicle dynamics model receives the steering wheel torque of the driver's neuromuscular model and the rear wheel angle command of the active rear-wheel steering controller, and outputs the vehicle state quantity;
根据驾驶员实际操作情况，取采样时间为T s，建立驾驶员模型，包括： According to the actual operating conditions of the driver, the sampling time is taken as T s , and the driver model is established, including:
驾驶员预瞄模型：Pilot preview model:
Figure PCTCN2020090243-appb-000006
Figure PCTCN2020090243-appb-000006
式中，k表示驾驶员的预瞄点编号；x d(k)为第k个预瞄点处的状态向量；为第k个预瞄点处的驾驶员转矩输入；y d(k)为第k个预瞄点处的模型输出向量；系数矩阵为： In the formula, k represents the pilot's preview point number; x d (k) is the state vector at the k-th preview point; is the driver torque input at the k-th preview point; y d (k) The output vector for the model at the kth preview point; the coefficient matrix is:
Figure PCTCN2020090243-appb-000007
Figure PCTCN2020090243-appb-000007
通过使用一个移位寄存器，驾驶员预瞄信息的更新过程可表示为：By using a shift register, the update process of the pilot preview information can be expressed as:
Figure PCTCN2020090243-appb-000008
Figure PCTCN2020090243-appb-000008
式中，Y pa(k)和ψ pa(k)分别为汽车在第k个预瞄点处的侧向位移和横摆角；预瞄点个数n＝T p/T s；T p为预瞄时间； In the formula, Y pa (k) and ψ pa (k) are respectively the lateral displacement and yaw angle of the car at the k-th preview point; the number of preview points n=T p /T s ; T p is Preview time
驾驶员神经肌肉模型：Driver neuromuscular model:
Figure PCTCN2020090243-appb-000009
Figure PCTCN2020090243-appb-000009
式中，G d(s)也表示从驾驶员预瞄输入到驾驶员转矩输出的传递函数；s为拉普拉斯算子；K r和B r分别为反射刚度和反射阻尼；τ r为传输延迟；ω r为截至频率。 In the formula, G d (s) also represents the transfer function from the driver's preview input to the driver's torque output; s is the Laplacian operator; K r and B r are the reflection stiffness and reflection damping, respectively; τ r Is the transmission delay; ω r is the cutoff frequency.
驾驶员最优预瞄模型以道路预瞄信息作为输入，其输出量为最优转向盘转角；驾驶员神经肌肉模型以最优转向盘转角作为输入，其输出量为转向盘转矩，并将转向盘转矩传给六阶汽车动力学模型。The driver’s optimal preview model takes road preview information as input, and its output is the optimal steering wheel angle; the driver’s neuromuscular model takes the optimal steering wheel angle as input, and its output is the steering wheel torque. The steering wheel torque is transferred to the sixth-order vehicle dynamics model.
优选地，所述步骤2)中的主动后轮转向控制器设计过程具体为：Preferably, the design process of the active rear-wheel steering controller in step 2) is specifically as follows:
为了使汽车横摆角速度准确跟踪参考值，使用滑模变结构算法设计主动后轮转向控制器，取误差指标为e＝γ *-γ，开关函数为
Figure PCTCN2020090243-appb-000010
控制率为
Figure PCTCN2020090243-appb-000011
其中，γ *和γ分别为期望横摆角速度和实际横摆角速度；c为开关系数，α为误差系数，β为误差率系数，三个参数决定了算法对汽车稳定性的控制效果；挑选两组参数值(0.82,0.47,0.11)、(0.63,0.35,0.08)，前者的控制强度略高于后者，两者的振荡都比较小。 In order to make the vehicle yaw rate accurately track the reference value, the sliding mode variable structure algorithm is used to design the active rear-wheel steering controller, and the error index is e=γ * -γ, and the switching function is
Figure PCTCN2020090243-appb-000010
Control rate
Figure PCTCN2020090243-appb-000011
Among them, γ * and γ are the expected yaw rate and actual yaw rate respectively; c is the switching coefficient, α is the error coefficient, and β is the error rate coefficient. The three parameters determine the control effect of the algorithm on the stability of the car; choose two Group parameter values (0.82, 0.47, 0.11), (0.63, 0.35, 0.08), the control intensity of the former is slightly higher than the latter, and the oscillation of the two is relatively small.
主动后轮转向控制器的输出的后轮转角指令传给六阶汽车动力学模型。The rear wheel angle command output from the active rear wheel steering controller is transmitted to the sixth-order vehicle dynamics model.
优选地，所述步骤3)中的驾驶员神经肌肉模型参数的辨识过程具体为：Preferably, the process of identifying the parameters of the driver's neuromuscular model in step 3) is specifically:
面对相同的行驶工况，不同驾驶员通过调节K r、B r和ω r而展现出不同的转向特征即采取不同的操纵策略；实际上，传输延迟在不同驾驶员之间变化很小，可取为τ r＝0.04s，本发明中，传输延迟体现在MATLAB/Simulink的数据流中，因此在下面的公式推导中可省略；驾驶员神经肌肉模型的输入-输出量之间的关系为： Facing the same driving conditions, different drivers exhibit different steering characteristics by adjusting K r , B r and ω r , that is, adopt different steering strategies; in fact, the transmission delay varies little between different drivers. It can be taken as τ r =0.04s. In the present invention, the transmission delay is reflected in the data stream of MATLAB/Simulink, so it can be omitted in the following formula derivation; the relationship between the input and output of the driver's neuromuscular model is:
Figure PCTCN2020090243-appb-000012
Figure PCTCN2020090243-appb-000012
式中，T d(s)为驾驶员输出转向盘转矩，
Figure PCTCN2020090243-appb-000013
为驾驶员最优预瞄模型的输出即驾驶员期望转向盘转角； In the formula, T d (s) is the driver’s output steering wheel torque,
Figure PCTCN2020090243-appb-000013
The output of the driver's optimal preview model is the driver's expected steering wheel angle;
将上述驾驶员神经肌肉模型带入驾驶员输入-输出量关系表达式，得到：Incorporating the above driver neuromuscular model into the driver input-output relationship expression, we get:
Figure PCTCN2020090243-appb-000014
Figure PCTCN2020090243-appb-000014
Figure PCTCN2020090243-appb-000015
Figure PCTCN2020090243-appb-000015
式中，a i(i＝1,2,3)为待辨识的参数。 In the formula, a i (i=1, 2, 3) is the parameter to be identified.
辨识出的驾驶员神经肌肉模型参数输入到纳什谈判准则，用于产生驾驶员操纵策略集，形成六种人-车博弈策略组合。The identified parameters of the driver's neuromuscular model are input to the Nash negotiation criteria, which are used to generate the driver's manipulation strategy set to form six combinations of human-vehicle game strategies.
优选地，所述步骤4)中的六种人-车博弈策略组合具体为：Preferably, the six human-vehicle game strategy combinations in step 4) are specifically:
根据对驾驶员神经肌肉模型的辨识结果，可将驾驶员的操纵策略集表示为
Figure PCTCN2020090243-appb-000016
其中包含三个博弈策略： According to the identification result of the driver's neuromuscular model, the driver's manipulation strategy set can be expressed as
Figure PCTCN2020090243-appb-000016
It contains three game strategies:
Figure PCTCN2020090243-appb-000017
Figure PCTCN2020090243-appb-000017
式中，→左边的参数值在博弈开始后变为右边的值，以这种参数值的上的变化表征驾驶员采取的不同策略，K r 0、B r 0、
Figure PCTCN2020090243-appb-000018
分别为辨识出的肌肉刚度、肌肉阻尼和截至频率； In the formula, → the parameter value on the left becomes the value on the right after the game starts. The change in the parameter value represents the different strategies adopted by the driver, K r 0 , B r 0 ,
Figure PCTCN2020090243-appb-000018
They are the identified muscle stiffness, muscle damping and cut-off frequency;
同时，主动后轮转向控制器可选择强干涉策略
Figure PCTCN2020090243-appb-000019
即控制器参数取(c,α,β)＝(0.82,0.47,0.11)，或弱干涉策略
Figure PCTCN2020090243-appb-000020
即控制器参数取(c,α,β)＝(0.63,0.35,0.08)，其策略集为
Figure PCTCN2020090243-appb-000021
At the same time, the active rear-wheel steering controller can choose a strong interference strategy
Figure PCTCN2020090243-appb-000019
That is, the controller parameters take (c, α, β) = (0.82, 0.47, 0.11), or weak interference strategy
Figure PCTCN2020090243-appb-000020
That is, the controller parameters take (c, α, β) = (0.63, 0.35, 0.08), and its strategy set is
Figure PCTCN2020090243-appb-000021
因此，博弈双方一共有六种策略组合
Figure PCTCN2020090243-appb-000022
i＝1,2,3，j＝1,2。 Therefore, there are a total of six strategy combinations for both parties in the game
Figure PCTCN2020090243-appb-000022
i=1, 2, 3, j=1, 2.
优选地，所述步骤5)中的利用最大-最小准则计算博弈双方的收益具体为：Preferably, the use of the maximum-minimum criterion in the step 5) to calculate the benefits of the two parties in the game is specifically as follows:
在博弈中双方的目标不同，驾驶员的目标是使汽车实际侧向位移Y(k)等于道路处的侧向位移Y pa(k)，并且使汽车实际横摆角ψ(k)等于道路横摆角ψ pa(k)；而控制器的目标是使汽车实际横摆角速度γ(k)等于期望横摆角速度γ *(k)，并且使汽车侧向加速度u·γ(k)尽可能小；因此双方的收益计算公式可表示为： In the game, the goals of the two parties are different. The driver’s goal is to make the actual lateral displacement Y(k) of the car equal to the lateral displacement Y pa (k) at the road, and to make the actual yaw angle ψ(k) of the car equal to the lateral displacement of the road. Swing angle ψ pa (k); and the goal of the controller is to make the actual yaw rate γ (k) of the car equal to the desired yaw rate γ * (k), and to make the lateral acceleration u·γ (k) of the car as small as possible ; Therefore, the formula for calculating the benefits of both parties can be expressed as:
Figure PCTCN2020090243-appb-000023
Figure PCTCN2020090243-appb-000023
式中，P ij和Q ij分别代表策略组合
Figure PCTCN2020090243-appb-000024
下，驾驶员和主动后轮转向系统的收益；ω l为收益指标的权重，其中，l＝1,2,3,4，旨在使收益指标归一化以便作比较；g为当地重力加速度； In the formula, P ij and Q ij respectively represent the strategy combination
Figure PCTCN2020090243-appb-000024
Below, the gains of the driver and the active rear-wheel steering system; ω l is the weight of the gain index, where l=1, 2, 3, 4, which aims to normalize the gain index for comparison; g is the local gravity acceleration ；
让驾驶员和主动后轮转向控制器采取某一组固定的策略，采集汽车在双移线工况下的行驶数据后便可以根据收益计算公式求出双方的收益；经试验测量，在策略组合
Figure PCTCN2020090243-appb-000025
下，双方收益为P ij＝1.6341,Q ij＝4.0049，在策略组合
Figure PCTCN2020090243-appb-000026
下，双方收益为P ij＝2.1679,Q ij＝1.9022，在策略组合
Figure PCTCN2020090243-appb-000027
下，双方收益为P ij＝3.0004,Q ij＝8.1775，在策略组合
Figure PCTCN2020090243-appb-000028
下，双方收益为P ij＝3.7883,Q ij＝3.2357，在策略组合
Figure PCTCN2020090243-appb-000029
下，双方收益为P ij＝2.2804,Q ij＝6.3381，在策略组合
Figure PCTCN2020090243-appb-000030
下，双方收益为P ij＝2.9147,Q ij＝2.5386； Let the driver and the active rear-wheel steering controller adopt a certain set of fixed strategies. After collecting the driving data of the car in the double shifting condition, the profit of both parties can be calculated according to the profit calculation formula; after test and measurement, in the strategy combination
Figure PCTCN2020090243-appb-000025
Under the circumstance, the gains of both parties are P ij =1.6341 and Q ij =4.0049. In the strategy combination
Figure PCTCN2020090243-appb-000026
Under the strategy combination, the gains of both parties are P ij = 2.1679 and Q ij = 1.9022.
Figure PCTCN2020090243-appb-000027
Under the circumstance, the gains of both parties are P ij =3.0004 and Q ij =8.1775. In the strategy combination
Figure PCTCN2020090243-appb-000028
Under the circumstance, the gains of both parties are P ij =3.7883 and Q ij =3.2357. In the strategy combination
Figure PCTCN2020090243-appb-000029
Under the circumstance, the gains of both parties are P ij =2.2804 and Q ij =6.3381. In the strategy combination
Figure PCTCN2020090243-appb-000030
In the next step, the income of both parties is P ij =2.9147,Q ij =2.5386;
接着利用最大-最小准则，求出博弈双方的最大-最小值：Then use the maximum-minimum criterion to find the maximum-minimum value of both parties in the game:
Figure PCTCN2020090243-appb-000031
Figure PCTCN2020090243-appb-000031
优选地，所述步骤6)中的利用纳什谈判准则求解人-车博弈的纳什谈判解具体为：Preferably, the Nash negotiation solution using the Nash negotiation criterion in the step 6) to solve the human-vehicle game is specifically as follows:
先将博弈双方的收益绘制在二维平面上，其中横轴为驾驶员的收益，纵轴为主动后轮转向系统的收益；First draw the benefits of both parties in the game on a two-dimensional plane, where the horizontal axis is the driver's revenue, and the vertical axis is the revenue of the active rear-wheel steering system;
再将双方的最大-最小值绘制出来，由此确定出纳什谈判集{(p,q)|q＝-6.2721p+26.9964,3.0004≤p≤3.6657}，则纳什谈判解(p *,q *)必定存在于纳什谈判集中； Then draw the maximum-minimum value of the two parties to determine the Nash negotiation set {(p,q)|q=-6.2721p+26.9964,3.0004≤p≤3.6657}, then the Nash negotiation solution (p * ,q * ) Must exist in the Nash negotiation center;
接着通过在纳什谈判集中寻找使整体收益I n＝(p-v D)(q-v AD)最大的点，求出纳什谈判解(p *,q *)。 Then find the point that maximizes the overall income I n =(pv D )(qv AD ) in the Nash negotiation center, and find the Nash negotiation solution (p * , q * ).
本发明的有益效果：The beneficial effects of the present invention:
1、本发明与其他博弈控制方法相比，不是将驾驶员和先进驾驶员辅助系统置于对立的地位，让两者按照各自的策略独立操纵，而是将非零和博弈的概念应用到人-车博弈中，解决操纵冲突的问题。1. Compared with other game control methods, the present invention does not place the driver and the advanced driver assistance system in an opposing position, allowing the two to operate independently according to their respective strategies, but applies the concept of non-zero-sum game to humans. -In the car game, solve the problem of manipulation conflict.
2、本发明为了将驾驶员的个人驾驶习惯和操纵特征融入到博弈控制策略的设计中，对驾驶员神经肌肉模型的部分重要参数进行了辨识，并根据辨识结果设计了驾驶员可能采取的三种策略。2. In order to integrate the driver’s personal driving habits and manipulation characteristics into the design of the game control strategy, the present invention identifies some important parameters of the driver’s neuromuscular model, and designs three possible driver’s options based on the identification results. Kind of strategy.
3、本发明通过分析驾驶员和主动后轮转向系统的可行策略，提出了六种博弈策略组合，作为解决博弈问题的基础。3. By analyzing the feasible strategies of the driver and the active rear-wheel steering system, the present invention proposes six game strategy combinations as the basis for solving the game problem.
4、本发明通过分析驾驶员和主动后轮转向系统的控制目标，提出了两者的收益计算方法，构成了两者的收益。4. By analyzing the control targets of the driver and the active rear-wheel steering system, the present invention proposes a profit calculation method for both, which constitutes the profit of both.
5、本发明利用纳什谈判准则，基于收益求解出博弈双方的纳什谈判解，这一谈判解将最大程度地消除人-车操纵冲突，满足博弈双方的目标。5. The present invention uses the Nash negotiation criterion to solve the Nash negotiation solution of the game parties based on the profit. This negotiation solution will eliminate the human-vehicle manipulation conflict to the greatest extent and meet the goals of the game parties.
附图说明Description of the drawings
图1为人-车合作型博弈控制方法框图；Figure 1 is a block diagram of a human-vehicle cooperative game control method;
图2为驾驶员预瞄模型示意图；Figure 2 is a schematic diagram of the pilot preview model;
图3为人-车-路交互示意图；Figure 3 is a schematic diagram of human-vehicle-road interaction;
图4为人-车收益和纳什谈判集示意图。Figure 4 is a schematic diagram of man-vehicle revenue and Nash negotiation set.
具体实施方式Detailed ways
为了便于本领域技术人员的理解，下面结合实施例与附图对本发明作进一步的说明，实施方式提及的内容并非对本发明的限定。In order to facilitate the understanding of those skilled in the art, the present invention will be further described below in conjunction with the embodiments and the drawings, and the content mentioned in the embodiments does not limit the present invention.
参照图1所示，本发明的一种基于纳什谈判准则的人-车合作型博弈控制方法，其特征在于，包括步骤如下：Referring to Figure 1, a human-vehicle cooperative game control method based on Nash negotiation criteria of the present invention is characterized in that it includes the following steps:
1)建立六阶汽车动力学模型及驾驶员模型；1) Establish a sixth-order vehicle dynamics model and driver model;
2)利用滑模变结构算法设计主动后轮转向控制器；2) Design of active rear-wheel steering controller using sliding mode variable structure algorithm;
3)辨识驾驶员模型中的驾驶员神经肌肉模型参数；3) Identify the driver neuromuscular model parameters in the driver model;
4)提出六种人-车博弈策略组合；4) Propose six combinations of human-car game strategy;
5)利用最大-最小准则计算博弈双方的收益；5) Use the maximum-minimum criterion to calculate the benefits of both parties in the game;
6)利用纳什谈判准则求解人-车博弈的纳什谈判解。6) Use the Nash negotiation criterion to solve the Nash negotiation solution of the man-car game.
其中，所述步骤1)具体包括：Wherein, the step 1) specifically includes:
所述六阶汽车动力学模型：The sixth-order vehicle dynamics model:
Figure PCTCN2020090243-appb-000032
Figure PCTCN2020090243-appb-000032
式中，
Figure PCTCN2020090243-appb-000033
为状态向量；θ sw为转向盘转角；
Figure PCTCN2020090243-appb-000034
为转向盘转角速度；v为汽车侧向速度；γ为汽车横摆角速度；Y为汽车侧向位移；ψ为汽车横摆角；T d为驾驶员转矩输入；
Figure PCTCN2020090243-appb-000035
为后轮转向电机转角输入；w为施加于前轮转向系统的转向阻力矩；y c为模型输出向量；系数矩阵为： Where
Figure PCTCN2020090243-appb-000033
Is the state vector; θ sw is the steering wheel angle;
Figure PCTCN2020090243-appb-000034
Is the steering wheel angular velocity; v is the lateral velocity of the vehicle; γ is the yaw angular velocity of the vehicle; Y is the lateral displacement of the vehicle; ψ is the yaw angle of the vehicle; T d is the driver's torque input;
Figure PCTCN2020090243-appb-000035
Is the input of the rotation angle of the rear-wheel steering motor; w is the steering resistance torque applied to the front-wheel steering system; y c is the model output vector; the coefficient matrix is:
Figure PCTCN2020090243-appb-000036
Figure PCTCN2020090243-appb-000036
式中，m为汽车质量；u为车速；a和b分别为汽车质心到前轴和后轴的距离；J s和B s分别为转向系统转动惯量和转向阻尼；C f和C r分别为汽车前轮侧偏刚度和后轮侧偏刚度；I z为汽车垂向转动惯量；i 0为转向系统标准传动比；i m为后轮转向电机减速比； Where m is the mass of the car; u is the speed of the car; a and b are the distances from the center of mass of the car to the front and rear axles; J s and B s are the moment of inertia and steering damping of the steering system, respectively; C f and C r are respectively Front wheel cornering stiffness and rear wheel cornering stiffness of the car; I z is the vertical moment of inertia of the car; i 0 is the standard transmission ratio of the steering system; i m is the reduction ratio of the rear-wheel steering motor;
根据驾驶员实际操作情况，取采样时间为T s，建立驾驶员模型，包括： According to the actual operating conditions of the driver, the sampling time is taken as T s , and the driver model is established, including:
(1)驾驶员预瞄模型，如图2所示：(1) Pilot preview model, as shown in Figure 2:
Figure PCTCN2020090243-appb-000037
Figure PCTCN2020090243-appb-000037
式中，k表示驾驶员的预瞄点编号；x d(k)为第k个预瞄点处的状态向量；为第k个预瞄点处的驾驶员转矩输入；y d(k)为第k个预瞄点处的模型输出向量；系数矩阵为： In the formula, k represents the pilot's preview point number; x d (k) is the state vector at the k-th preview point; is the driver torque input at the k-th preview point; y d (k) The output vector for the model at the kth preview point; the coefficient matrix is:
Figure PCTCN2020090243-appb-000038
Figure PCTCN2020090243-appb-000038
通过使用一个移位寄存器，驾驶员预瞄信息的更新过程可表示为：By using a shift register, the update process of the pilot preview information can be expressed as:
Figure PCTCN2020090243-appb-000039
Figure PCTCN2020090243-appb-000039
式中，Y pa(k)和ψ pa(k)分别为汽车在第k个预瞄点处的侧向位移和横摆角；预瞄点个数n＝T p/T s；T p为预瞄时间； In the formula, Y pa (k) and ψ pa (k) are respectively the lateral displacement and yaw angle of the car at the k-th preview point; the number of preview points n=T p /T s ; T p is Preview time
(2)驾驶员神经肌肉模型：(2) Driver neuromuscular model:
Figure PCTCN2020090243-appb-000040
Figure PCTCN2020090243-appb-000040
式中，G d(s)表示从驾驶员预瞄输入到驾驶员转矩输出的传递函数；s为拉普拉斯算子；K r和B r分别为反射刚度和反射阻尼；τ r为传输延迟；ω r为截至频率。 In the formula, G d (s) represents the transfer function from driver preview input to driver torque output; s is the Laplacian operator; K r and B r are reflection stiffness and reflection damping respectively; τ r is Transmission delay; ω r is the cut-off frequency.
驾驶员与汽车交互的过程如图3所示，驾驶员利用视觉获取道路预瞄信息，利用触觉接收汽车状态反馈信息，经过最优预瞄模型计算出最优转向盘转角
Figure PCTCN2020090243-appb-000041
然后经过神经肌肉模型G d(s)执行最优转向盘转角指令，即驾驶员输出转向盘转矩T d，转向盘转矩与从转向系统反馈的力矩一起传递到转向系统，最终产生实际的转向盘转角θ sw并作用于汽车六阶动力学模型。 The process of interaction between the driver and the car is shown in Figure 3. The driver uses vision to obtain road preview information, uses tactile sense to receive car state feedback information, and calculates the optimal steering wheel angle through the optimal preview model.
Figure PCTCN2020090243-appb-000041
Then the optimal steering wheel angle command is executed through the neuromuscular model G d (s), that is, the driver outputs the steering wheel torque T d , and the steering wheel torque is transmitted to the steering system together with the torque fed back from the steering system, and finally produces the actual The steering wheel angle θ sw also acts on the sixth-order dynamics model of the car.
其中，所述步骤2)具体包括：使用滑模变结构算法设计主动后轮转向控制器，取误差指标为e＝γ *-γ，开关函数为
Figure PCTCN2020090243-appb-000042
控制率为
Figure PCTCN2020090243-appb-000043
其中，γ *和γ分别为期望横摆角速度和实际横摆角速度；c为开关系数，α为误差系数，β为误差率系数，三个参数决定了算法对汽车稳定性的控制效果；挑选两组参数值(0.82,0.47,0.11)、(0.63,0.35,0.08)，前者的控制强度略高于后者，两者的振荡均比较小。 Wherein, the step 2) specifically includes: using a sliding mode variable structure algorithm to design an active rear wheel steering controller, taking the error index as e = γ * -γ, and the switching function as
Figure PCTCN2020090243-appb-000042
Control rate
Figure PCTCN2020090243-appb-000043
Among them, γ * and γ are the expected yaw rate and actual yaw rate respectively; c is the switching coefficient, α is the error coefficient, and β is the error rate coefficient. The three parameters determine the control effect of the algorithm on the stability of the car; choose two Group parameter values (0.82, 0.47, 0.11), (0.63, 0.35, 0.08), the control intensity of the former is slightly higher than the latter, and the oscillation of the two is relatively small.
所述步骤3)中的驾驶员神经肌肉模型参数的辨识过程具体为：The process of identifying the parameters of the driver's neuromuscular model in step 3) is specifically as follows:
面对相同的行驶工况，不同驾驶员通过调节K r、B r和ω r而展现出不同的转向特征即采取不同的操纵策略；实际上，传输延迟在不同驾驶员之间变化很小，可取为τ r＝0.04s，本发明中，传输延迟体现在MATLAB/Simulink的数据流中，因此在下面的公式推导中可省略；驾驶员神经肌肉模型的输入-输出量之间的关系为： Facing the same driving conditions, different drivers exhibit different steering characteristics by adjusting K r , B r and ω r , that is, adopt different steering strategies; in fact, the transmission delay varies little between different drivers. It can be taken as τ r =0.04s. In the present invention, the transmission delay is reflected in the data stream of MATLAB/Simulink, so it can be omitted in the following formula derivation; the relationship between the input and output of the driver's neuromuscular model is:
Figure PCTCN2020090243-appb-000044
Figure PCTCN2020090243-appb-000044
式中，T d(s)为驾驶员输出转向盘转矩，
Figure PCTCN2020090243-appb-000045
为驾驶员最优预瞄模型的输出即驾驶员期望转向盘转角； In the formula, T d (s) is the driver’s output steering wheel torque,
Figure PCTCN2020090243-appb-000045
The output of the driver's optimal preview model is the driver's expected steering wheel angle;
将上述驾驶员神经肌肉模型带入驾驶员输入-输出量关系表达式，得到：Incorporating the above driver neuromuscular model into the driver input-output relationship expression, we get:
Figure PCTCN2020090243-appb-000046
Figure PCTCN2020090243-appb-000046
Figure PCTCN2020090243-appb-000047
Figure PCTCN2020090243-appb-000047
式中，a i为待辨识的参数，i＝1,2,3。 In the formula, a i is the parameter to be identified, i=1, 2, 3.
所述步骤4)中的六种人-车博弈策略组合具体为：The six human-vehicle game strategy combinations in the step 4) are specifically:
根据对驾驶员神经肌肉模型的辨识结果，将驾驶员的操纵策略集表示为
Figure PCTCN2020090243-appb-000048
其中包含三个博弈策略： According to the identification results of the driver’s neuromuscular model, the driver’s manipulation strategy set is expressed as
Figure PCTCN2020090243-appb-000048
It contains three game strategies:
Figure PCTCN2020090243-appb-000049
Figure PCTCN2020090243-appb-000049
式中，→左边的参数值在博弈开始后变为右边的值，以这种参数值的上的变化表征驾驶员采取的不同策略，K r 0、B r 0、
Figure PCTCN2020090243-appb-000050
分别为辨识出的肌肉刚度、肌肉阻尼和截至频率； In the formula, → the parameter value on the left becomes the value on the right after the game starts. The change in the parameter value represents the different strategies adopted by the driver, K r 0 , B r 0 ,
Figure PCTCN2020090243-appb-000050
They are the identified muscle stiffness, muscle damping and cut-off frequency;
同时，主动后轮转向控制器可选择强干涉策略
Figure PCTCN2020090243-appb-000051
即控制器参数取(c,α,β)＝(0.82,0.47,0.11)，或弱干涉策略
Figure PCTCN2020090243-appb-000052
即控制器参数取(c,α,β)＝(0.63,0.35,0.08)，其策略集为
Figure PCTCN2020090243-appb-000053
At the same time, the active rear-wheel steering controller can choose a strong interference strategy
Figure PCTCN2020090243-appb-000051
That is, the controller parameters take (c, α, β) = (0.82, 0.47, 0.11), or weak interference strategy
Figure PCTCN2020090243-appb-000052
That is, the controller parameters take (c, α, β) = (0.63, 0.35, 0.08), and its strategy set is
Figure PCTCN2020090243-appb-000053
博弈双方一共有六种策略组合
Figure PCTCN2020090243-appb-000054
i＝1,2,3，j＝1,2。 There are a total of six strategy combinations for both sides of the game
Figure PCTCN2020090243-appb-000054
i=1, 2, 3, j=1, 2.
所述步骤5)中的利用最大-最小准则计算博弈双方的收益具体为：The use of the maximum-minimum criterion in the step 5) to calculate the benefits of both parties in the game is specifically:
在博弈中双方的目标不同，驾驶员的目标是使汽车实际侧向位移Y(k)等于道路处的侧向位移Y pa(k)，并且使汽车实际横摆角ψ(k)等于道路横摆角ψ pa(k)；而控制器的目标是使汽车实际横摆角速度γ(k)等于期望横摆角速度γ *(k)，并且使汽车侧向加速度u·γ(k)尽可能小；双方的收益计算公式表示为： In the game, the goals of the two parties are different. The driver’s goal is to make the actual lateral displacement Y(k) of the car equal to the lateral displacement Y pa (k) at the road, and to make the actual yaw angle ψ(k) of the car equal to the lateral displacement of the road. Swing angle ψ pa (k); and the goal of the controller is to make the actual yaw rate γ (k) of the car equal to the desired yaw rate γ * (k), and to make the lateral acceleration u·γ (k) of the car as small as possible ; The income calculation formula of both parties is expressed as:
Figure PCTCN2020090243-appb-000055
Figure PCTCN2020090243-appb-000055
式中，P ij和Q ij分别代表策略组合
Figure PCTCN2020090243-appb-000056
下，驾驶员和主动后轮转向系统的收益；ω l为收益指标的权重，其中，l＝1,2,3,4，旨在使收益指标归一化以便作比较；g为当地重力加速度； In the formula, P ij and Q ij respectively represent the strategy combination
Figure PCTCN2020090243-appb-000056
Below, the gains of the driver and the active rear-wheel steering system; ω l is the weight of the gain index, where l=1, 2, 3, 4, which aims to normalize the gain index for comparison; g is the local gravity acceleration ；
让驾驶员和主动后轮转向控制器采取某一组固定的策略，采集汽车在双移线工况下的行驶数据后根据收益计算公式求出双方的收益；经试验测量，在策略组合
Figure PCTCN2020090243-appb-000057
下，双方收益为P ij＝1.6341,Q ij＝4.0049，在策略组合
Figure PCTCN2020090243-appb-000058
下，双方收益为P ij＝2.1679,Q ij＝1.9022，在策略组合
Figure PCTCN2020090243-appb-000059
下，双方收益为P ij＝3.0004,Q ij＝8.1775，在策略组合
Figure PCTCN2020090243-appb-000060
下，双方收益为P ij＝3.7883,Q ij＝3.2357，在策略组合
Figure PCTCN2020090243-appb-000061
下，双方收益为P ij＝2.2804,Q ij＝6.3381，在策略组合
Figure PCTCN2020090243-appb-000062
下，双方收益为P ij＝2.9147,Q ij＝2.5386； Let the driver and the active rear-wheel steering controller adopt a certain set of fixed strategies, collect the driving data of the car under the double-line shifting condition, and calculate the revenue of both parties according to the revenue calculation formula; after testing and measurement, in the strategy combination
Figure PCTCN2020090243-appb-000057
Under the circumstance, the gains of both parties are P ij =1.6341 and Q ij =4.0049. In the strategy combination
Figure PCTCN2020090243-appb-000058
Under the strategy combination, the gains of both parties are P ij = 2.1679 and Q ij = 1.9022.
Figure PCTCN2020090243-appb-000059
Under the circumstance, the gains of both parties are P ij =3.0004 and Q ij =8.1775. In the strategy combination
Figure PCTCN2020090243-appb-000060
Under the circumstance, the gains of both parties are P ij =3.7883 and Q ij =3.2357. In the strategy combination
Figure PCTCN2020090243-appb-000061
Under the circumstance, the gains of both parties are P ij =2.2804 and Q ij =6.3381. In the strategy combination
Figure PCTCN2020090243-appb-000062
In the next step, the income of both parties is P ij =2.9147,Q ij =2.5386;
接着利用最大-最小准则，求出博弈双方的最大-最小值：Then use the maximum-minimum criterion to find the maximum-minimum value of both parties in the game:
Figure PCTCN2020090243-appb-000063
Figure PCTCN2020090243-appb-000063
参照图4所示，所述步骤6)中的利用纳什谈判准则求解人-车博弈的纳什谈判解具体为：Referring to Fig. 4, the Nash negotiation solution using the Nash negotiation criterion to solve the human-car game in the step 6) is specifically:
先将博弈双方的收益绘制在二维平面上，其中横轴为驾驶员的收益，纵轴为主动后轮转向系统的收益；First draw the benefits of both parties in the game on a two-dimensional plane, where the horizontal axis is the driver's revenue, and the vertical axis is the revenue of the active rear-wheel steering system;
再将双方的最大-最小值绘制出来，由此确定出纳什谈判集{(p,q)|q＝-6.2721p+26.9964,3.0004≤p≤3.6657}，则纳什谈判解(p *,q *)必定存在于纳什谈判集中； Then draw the maximum-minimum value of the two parties to determine the Nash negotiation set {(p,q)|q=-6.2721p+26.9964,3.0004≤p≤3.6657}, then the Nash negotiation solution (p * ,q * ) Must exist in the Nash negotiation center;
接着通过在纳什谈判集中寻找使整体收益I n＝(p-v D)(q-v AD)最大的点，求出纳什谈判解(p *,q *)，(p *,q *)＝(3.3330,6.0912)。 Then find the point that maximizes the overall income I n = (pv D )(qv AD ) in the Nash negotiation center, and find the Nash negotiation solution (p * , q * ), (p * , q * ) = (3.3330, 6.0912) ).
本发明具体应用途径很多，以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以作出若干改进，这些改 进也应视为本发明的保护范围。There are many specific applications of the present invention. The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements can be made. These Improvements should also be regarded as the protection scope of the present invention.

Claims (7)

  1. 一种基于纳什谈判准则的人-车合作型博弈控制方法，其特征在于，包括步骤如下：A human-vehicle cooperative game control method based on Nash negotiation criteria, which is characterized in that it includes the following steps:
    1)建立六阶汽车动力学模型及驾驶员模型；1) Establish a sixth-order vehicle dynamics model and driver model;
    2)利用滑模变结构算法设计主动后轮转向控制器；2) Design of active rear-wheel steering controller using sliding mode variable structure algorithm;
    3)辨识驾驶员模型中的驾驶员神经肌肉模型参数；3) Identify the driver neuromuscular model parameters in the driver model;
    4)提出六种人-车博弈策略组合；4) Propose six combinations of human-car game strategy;
    5)利用最大-最小准则计算博弈双方的收益；5) Use the maximum-minimum criterion to calculate the benefits of both parties in the game;
    6)利用纳什谈判准则求解人-车博弈的纳什谈判解。6) Use the Nash negotiation criterion to solve the Nash negotiation solution of the man-car game.
  2. 根据权利要求1所述的基于纳什谈判准则的人-车合作型博弈控制方法，其特征在于，所述步骤1)具体包括：The human-vehicle cooperative game control method based on Nash negotiation criteria according to claim 1, wherein said step 1) specifically comprises:
    所述六阶汽车动力学模型：The sixth-order vehicle dynamics model:
    Figure PCTCN2020090243-appb-100001
    Figure PCTCN2020090243-appb-100001
    式中，
    Figure PCTCN2020090243-appb-100002
    为状态向量；θ sw为转向盘转角；
    Figure PCTCN2020090243-appb-100003
    为转向盘转角速度；v为汽车侧向速度；γ为汽车横摆角速度；Y为汽车侧向位移；ψ为汽车横摆角；T d为驾驶员转矩输入；
    Figure PCTCN2020090243-appb-100004
    为后轮转向电机转角输入；w为施加于前轮转向系统的转向阻力矩；y c为模型输出向量；系数矩阵为：     Where
    Figure PCTCN2020090243-appb-100002
    Is the state vector; θ sw is the steering wheel angle;
    Figure PCTCN2020090243-appb-100003
    Is the steering wheel angular velocity; v is the lateral velocity of the vehicle; γ is the yaw angular velocity of the vehicle; Y is the lateral displacement of the vehicle; ψ is the yaw angle of the vehicle; T d is the driver's torque input;
    Figure PCTCN2020090243-appb-100004
    Is the input of the rotation angle of the rear-wheel steering motor; w is the steering resistance torque applied to the front-wheel steering system; y c is the model output vector; the coefficient matrix is:
    Figure PCTCN2020090243-appb-100005
    Figure PCTCN2020090243-appb-100005
    式中，m为汽车质量；u为车速；a和b分别为汽车质心到前轴和后轴的距离；J s和B s分别为转向系统转动惯量和转向阻尼；C f和C r分别为汽车前轮侧偏刚度和后轮侧偏刚度；I z为汽车垂向转动惯量；i 0为转向系统标准传动比；i m为后轮转向电机减速比； Where m is the mass of the car; u is the speed of the car; a and b are the distances from the center of mass of the car to the front and rear axles; J s and B s are the moment of inertia and steering damping of the steering system, respectively; C f and C r are respectively Front wheel cornering stiffness and rear wheel cornering stiffness of the car; I z is the vertical moment of inertia of the car; i 0 is the standard transmission ratio of the steering system; i m is the reduction ratio of the rear-wheel steering motor;
    根据驾驶员实际操作情况，取采样时间为T s，建立驾驶员模型，包括： According to the actual operating conditions of the driver, the sampling time is taken as T s , and the driver model is established, including:
    (1)驾驶员预瞄模型：(1) Pilot preview model:
    Figure PCTCN2020090243-appb-100006
    Figure PCTCN2020090243-appb-100006
    式中，k表示驾驶员的预瞄点编号；x d(k)为第k个预瞄点处的状态向量；为第k个预瞄点处的驾驶员转矩输入；y d(k)为第k个预瞄点处的模型输出向量；系数矩阵为： In the formula, k represents the pilot's preview point number; x d (k) is the state vector at the k-th preview point; is the driver torque input at the k-th preview point; y d (k) The output vector for the model at the kth preview point; the coefficient matrix is:
    Figure PCTCN2020090243-appb-100007
    Figure PCTCN2020090243-appb-100007
    通过使用一个移位寄存器，驾驶员预瞄信息的更新过程可表示为：By using a shift register, the update process of the pilot preview information can be expressed as:
    Figure PCTCN2020090243-appb-100008
    Figure PCTCN2020090243-appb-100008
    式中，Y pa(k)和ψ pa(k)分别为汽车在第k个预瞄点处的侧向位移和横摆角；预瞄点个数n＝T p/T s；T p为预瞄时间； In the formula, Y pa (k) and ψ pa (k) are respectively the lateral displacement and yaw angle of the car at the k-th preview point; the number of preview points n=T p /T s ; T p is Preview time
    (2)驾驶员神经肌肉模型：(2) Driver neuromuscular model:
    Figure PCTCN2020090243-appb-100009
    Figure PCTCN2020090243-appb-100009
    式中，G d(s)表示从驾驶员预瞄输入到驾驶员转矩输出的传递函数；s为拉普拉斯算子；K r和B r分别为反射刚度和反射阻尼；τ r为传输延迟；ω r为截至频率。 In the formula, G d (s) represents the transfer function from driver preview input to driver torque output; s is the Laplacian operator; K r and B r are reflection stiffness and reflection damping respectively; τ r is Transmission delay; ω r is the cut-off frequency.
  3. 根据权利要求2所述的基于纳什谈判准则的人-车合作型博弈控制方法，其特征在于，所述步骤2)中的主动后轮转向控制器设计过程具体为：The human-vehicle cooperative game control method based on Nash negotiation criteria according to claim 2, wherein the design process of the active rear-wheel steering controller in step 2) is specifically:
    使用滑模变结构算法设计主动后轮转向控制器，取误差指标为e＝γ *-γ，开关函数为
    Figure PCTCN2020090243-appb-100010
    控制率为
    Figure PCTCN2020090243-appb-100011
    其中，γ *和γ分别为期望横摆角速度和实际横摆角速度；c为开关系数，α为误差系数，β为误差率系数，三个参数决定了算法对汽车稳定性的控制效果；挑选两组参数值(0.82,0.47,0.11)、(0.63,0.35,0.08)，前者的控制强度略高于后者，两者的振荡均比较小。     Use the sliding mode variable structure algorithm to design the active rear wheel steering controller, take the error index as e = γ * -γ, and the switch function as
    Figure PCTCN2020090243-appb-100010
    Control rate
    Figure PCTCN2020090243-appb-100011
    Among them, γ * and γ are the expected yaw rate and actual yaw rate respectively; c is the switching coefficient, α is the error coefficient, and β is the error rate coefficient. The three parameters determine the control effect of the algorithm on the stability of the car; choose two Group parameter values (0.82, 0.47, 0.11), (0.63, 0.35, 0.08), the control intensity of the former is slightly higher than the latter, and the oscillation of the two is relatively small.
  4. 根据权利要求3所述的基于纳什谈判准则的人-车合作型博弈控制方法，其特征在于， 所述步骤3)中的驾驶员神经肌肉模型参数的辨识过程具体为：The human-vehicle cooperative game control method based on Nash negotiation criteria according to claim 3, wherein the process of identifying the parameters of the driver's neuromuscular model in step 3) is specifically:
    面对相同的行驶工况，不同驾驶员通过调节K r、B r和ω r而展现出不同的转向特征即采取不同的操纵策略；驾驶员神经肌肉模型的输入-输出量之间的关系为： Facing the same driving conditions, different drivers exhibit different steering characteristics by adjusting K r , B r and ω r , that is, adopt different steering strategies; the relationship between the input and output of the driver's neuromuscular model is :
    Figure PCTCN2020090243-appb-100012
    Figure PCTCN2020090243-appb-100012
    式中，T d(s)为驾驶员输出转向盘转矩，
    Figure PCTCN2020090243-appb-100013
    为驾驶员最优预瞄模型的输出即驾驶员期望转向盘转角；     In the formula, T d (s) is the driver’s output steering wheel torque,
    Figure PCTCN2020090243-appb-100013
    The output of the driver's optimal preview model is the driver's expected steering wheel angle;
    将上述驾驶员神经肌肉模型带入驾驶员输入-输出量关系表达式，得到：Incorporating the above driver neuromuscular model into the driver input-output relationship expression, we get:
    Figure PCTCN2020090243-appb-100014
    Figure PCTCN2020090243-appb-100014
    Figure PCTCN2020090243-appb-100015
    Figure PCTCN2020090243-appb-100015
    式中，a i为待辨识的参数，i＝1,2,3。 In the formula, a i is the parameter to be identified, i=1, 2, 3.
  5. 根据权利要求4所述的基于纳什谈判准则的人-车合作型博弈控制方法，其特征在于，所述步骤4)中的六种人-车博弈策略组合具体为：The human-vehicle cooperative game control method based on Nash negotiation criteria according to claim 4, wherein the six human-vehicle game strategy combinations in step 4) are specifically:
    根据对驾驶员神经肌肉模型的辨识结果，将驾驶员的操纵策略集表示为
    Figure PCTCN2020090243-appb-100016
    其中包含三个博弈策略：     According to the identification results of the driver’s neuromuscular model, the driver’s manipulation strategy set is expressed as
    Figure PCTCN2020090243-appb-100016
    It contains three game strategies:
    Figure PCTCN2020090243-appb-100017
    Figure PCTCN2020090243-appb-100017
    式中，→左边的参数值在博弈开始后变为右边的值，以这种参数值的上的变化表征驾驶员采取的不同策略，K r 0、B r 0、
    Figure PCTCN2020090243-appb-100018
    分别为辨识出的肌肉刚度、肌肉阻尼和截至频率；     In the formula, → the parameter value on the left becomes the value on the right after the game starts. The change in the parameter value represents the different strategies adopted by the driver, K r 0 , B r 0 ,
    Figure PCTCN2020090243-appb-100018
    They are the identified muscle stiffness, muscle damping and cut-off frequency;
    同时，主动后轮转向控制器可选择强干涉策略
    Figure PCTCN2020090243-appb-100019
    即控制器参数取(c,α,β)＝(0.82,0.47,0.11)，或弱干涉策略
    Figure PCTCN2020090243-appb-100020
    即控制器参数取(c,α,β)＝(0.63,0.35,0.08)，其策略集为
    Figure PCTCN2020090243-appb-100021
    At the same time, the active rear-wheel steering controller can choose a strong interference strategy
    Figure PCTCN2020090243-appb-100019
    That is, the controller parameters take (c, α, β) = (0.82, 0.47, 0.11), or weak interference strategy
    Figure PCTCN2020090243-appb-100020
    That is, the controller parameters take (c, α, β) = (0.63, 0.35, 0.08), and its strategy set is
    Figure PCTCN2020090243-appb-100021
    博弈双方一共有六种策略组合
    Figure PCTCN2020090243-appb-100022
    There are a total of six strategy combinations for both sides of the game
    Figure PCTCN2020090243-appb-100022
  6. 根据权利要求5所述的基于纳什谈判准则的人-车合作型博弈控制方法，其特征在于，所述步骤5)中的利用最大-最小准则计算博弈双方的收益具体为：The human-vehicle cooperative game control method based on the Nash negotiation criterion according to claim 5, characterized in that, in the step 5), using the maximum-minimum criterion to calculate the benefits of the two parties in the game is specifically:
    在博弈中双方的目标不同，驾驶员的目标是使汽车实际侧向位移Y(k)等于道路处的侧向位移Y pa(k)，并且使汽车实际横摆角ψ(k)等于道路横摆角ψ pa(k)；而控制器的目标是使汽车实际横摆角速度γ(k)等于期望横摆角速度γ *(k)，并且使汽车侧向加速度u·γ(k)尽可能小；双方的收益计算公式表示为： In the game, the goals of the two parties are different. The driver’s goal is to make the actual lateral displacement Y(k) of the car equal to the lateral displacement Y pa (k) at the road, and to make the actual yaw angle ψ(k) of the car equal to the lateral displacement of the road. Swing angle ψ pa (k); and the goal of the controller is to make the actual yaw rate γ (k) of the car equal to the desired yaw rate γ * (k), and to make the lateral acceleration u·γ (k) of the car as small as possible ; The income calculation formula of both parties is expressed as:
    Figure PCTCN2020090243-appb-100023
    Figure PCTCN2020090243-appb-100023
    式中，P ij和Q ij分别代表策略组合
    Figure PCTCN2020090243-appb-100024
    下，驾驶员和主动后轮转向系统的收益；ω l为收益指标的权重，其中，l＝1,2,3,4，旨在使收益指标归一化以便作比较；g为当地重力加速度；     In the formula, P ij and Q ij respectively represent strategy combination
    Figure PCTCN2020090243-appb-100024
    Below, the gains of the driver and the active rear-wheel steering system; ω l is the weight of the gain index, where l=1, 2, 3, 4, which aims to normalize the gain index for comparison; g is the local gravity acceleration ；
    让驾驶员和主动后轮转向控制器采取某一组固定的策略，采集汽车在双移线工况下的行驶数据后根据收益计算公式求出双方的收益；经试验测量，在策略组合
    Figure PCTCN2020090243-appb-100025
    下，双方收益为P ij＝1.6341,Q ij＝4.0049，在策略组合
    Figure PCTCN2020090243-appb-100026
    下，双方收益为P ij＝2.1679,Q ij＝1.9022，在策略组合
    Figure PCTCN2020090243-appb-100027
    下，双方收益为P ij＝3.0004,Q ij＝8.1775，在策略组合
    Figure PCTCN2020090243-appb-100028
    下，双方收益为P ij＝3.7883,Q ij＝3.2357，在策略组合
    Figure PCTCN2020090243-appb-100029
    下，双方收益为P ij＝2.2804,Q ij＝6.3381，在策略组合
    Figure PCTCN2020090243-appb-100030
    下，双方收益为P ij＝2.9147,Q ij＝2.5386；     Let the driver and the active rear-wheel steering controller adopt a certain set of fixed strategies, collect the driving data of the car under the double-line shifting condition, and calculate the revenue of both parties according to the revenue calculation formula; after testing and measurement, in the strategy combination
    Figure PCTCN2020090243-appb-100025
    Under the circumstance, the gains of both parties are P ij =1.6341 and Q ij =4.0049. In the strategy combination
    Figure PCTCN2020090243-appb-100026
    Under the strategy combination, the gains of both parties are P ij = 2.1679 and Q ij = 1.9022.
    Figure PCTCN2020090243-appb-100027
    Under the circumstance, the gains of both parties are P ij =3.0004 and Q ij =8.1775. In the strategy combination
    Figure PCTCN2020090243-appb-100028
    Under the circumstance, the gains of both parties are P ij =3.7883 and Q ij =3.2357. In the strategy combination
    Figure PCTCN2020090243-appb-100029
    Under the circumstance, the gains of both parties are P ij =2.2804 and Q ij =6.3381. In the strategy combination
    Figure PCTCN2020090243-appb-100030
    In the next step, the income of both parties is P ij =2.9147,Q ij =2.5386;
    接着利用最大-最小准则，求出博弈双方的最大-最小值：Then use the maximum-minimum criterion to find the maximum-minimum value of both parties in the game:
    Figure PCTCN2020090243-appb-100031
    Figure PCTCN2020090243-appb-100031
  7. 根据权利要求6所述的基于纳什谈判准则的人-车合作型博弈控制方法，其特征在于，所述步骤6)中的利用纳什谈判准则求解人-车博弈的纳什谈判解具体为：The human-vehicle cooperative game control method based on the Nash negotiation criterion according to claim 6, wherein the Nash negotiation solution of the human-vehicle game using the Nash negotiation criterion in the step 6) is specifically:
    先将博弈双方的收益绘制在二维平面上，其中横轴为驾驶员的收益，纵轴为主动后轮转向系统的收益；First draw the benefits of both parties in the game on a two-dimensional plane, where the horizontal axis is the driver's revenue, and the vertical axis is the revenue of the active rear-wheel steering system;
    再将双方的最大-最小值绘制出来，由此确定出纳什谈判集{(p,q)|q＝-6.2721p+26.9964,3.0004≤p≤3.6657}，则纳什谈判解(p *,q *)必定存在于纳什谈 判集中； Then draw the maximum-minimum value of the two parties to determine the Nash negotiation set {(p,q)|q=-6.2721p+26.9964,3.0004≤p≤3.6657}, then the Nash negotiation solution (p * ,q * ) Must exist in the Nash negotiation center;
    接着通过在纳什谈判集中寻找使整体收益I n＝(p-v D)(q-v AD)最大的点，求出纳什谈判解(p *,q *)。 Then find the point that maximizes the overall income I n =(pv D )(qv AD ) in the Nash negotiation center, and find the Nash negotiation solution (p * , q * ).
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