Application of Open-Loop Stackelberg Equilibrium to Modeling a Driver's Interaction with Vehicle Active Steering Control in Obstacle Avoidance

Na, Xiaoxiang; Cole, David J.

doi:10.1109/thms.2017.2700541

Cited by 52 publications

(21 citation statements)

References 19 publications

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“…Remark 1. To clearly show the game process, a two-dimensional evolution diagram is constructed based on the ideas of [21]. As shown in Figure 5, the discrete control system develops as the game proceeds.…”

Section: Division Of Control Modesmentioning

confidence: 99%

“…where the constraint in Equation (23) is the equation of game progression at time step k; it has the same form as the error state in Equation (14). This is a standard optimal problem and the Lagrange multiplier method is used to solve it [12,21]. The augmented cost function of the follower is constructed as follows:…”

Section: Stackelberg Game-based Controllermentioning

confidence: 99%

“…The leader has priority in making decisions, and knows the cost function mapping of the follower, while the follower does not know the cost function mapping of the leader [11]. However, the follower knows the decisions of the leader and the follower's control strategies are restricted by the leader's decisions [21]. In addition, the leader has the option to declare his/her strategy in advance, and then the follower formulates strategies by obeying the leader's decision.…”

mentioning

confidence: 99%

“…The main contributions of this study are threefold: First, inspired by [21], a leader-follower-based interactive control strategy between AFWS and DYC is proposed to deal with their unequal control authority based on dynamic game theory. Different from [21], this work mainly focuses on machine-machine cooperative control to properly determine the variable control authority between the two subsystems. Second, the tire forces the control allocation problem to the lower-level controller, which is tailored to a series of highly efficient quadratic Energies 2019, 12, 3339 3 of 21 programming subproblems by the sequential quadratic programming (SQP) method.…”

mentioning

confidence: 99%

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Game-Based Hierarchical Cooperative Control for Electric Vehicle Lateral Stability via Active Four-Wheel Steering and Direct Yaw-Moment Control

Zhao

Zhang

2019

Energies

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A Stackelberg game-based cooperative control strategy is proposed for enhancing the lateral stability of a four-wheel independently driving electric vehicle (FWID-EV). An upper-lower double-layer hierarchical control structure is adopted for the design of a stability control strategy. The leader-follower-based Stackelberg game theory (SGT) is introduced to model the interaction between two unequal active chassis control subsystems in the upper layer. In this model, the direct yaw-moment control (DYC) and the active four-wheel steering (AFWS) are treated as the leader and the follower, respectively, based on their natural characteristics. Then, in order to guarantee the efficiency and convergence of the proposed control strategy, a sequential quadratic programming (SQP) algorithm is employed to solve the task allocation problem among the distributed actuators in the lower layer. Also, a double-mode adaptive weight (DMAW)-adjusting mechanism is designed, considering the negative effect of DYC. The results of cosimulation with CarSim and Matlab/Simulink demonstrate that the proposed control strategy can effectively improve the lateral stability by properly coordinating the actions of AFWS and DYC.Energies 2019, 12, 3339 2 of 21 approaches the adhesion limit [9], whereas DYC could play an effective role under these extreme conditions. This phenomenon reflects the variable control effects of AFS and DYC under changing vehicle states, and some research may not sufficiently consider the dynamic characteristics of the vehicle subsystems. Game theory is an effective method for dealing with the interaction of multiple agents, which provides a system control framework for this kind of cooperative control problem [10]. Since the AFS and DYC-based stability controller generally operate in an interactive manner as the vehicle travels ahead in a road tracking scenario, dynamic game theory should be applied.Dynamic game theory is an optimal approach based on the decision theory and the rules of dynamic game, as defined by Cruz [11] and Basar [12]. There exist three core principles in the dynamic game theory [13]: (1) Each player's attitude towards his own as well as others' interests. (2) Each player's strategy adopted for pursuing their goal. (3) Each player's knowledge received about the state of the system during the game process. Based on these principles, different kinds of game rules are formed, such as for a noncooperative game and a cooperative game. (Due to limited space, for more details about game theory we refer readers to [13] and [14].) Assume that each subsystem aims to achieve individual rationality and to maximize the vehicle stability in its own way. Thus, this work mainly focuses on noncooperative game theory.Noncooperative game theory has been widely studied to solve problems involving multiple individuals where their welfare is interactional [15]. It is an effective approach to address the problem of control authority allocation for multiple players [12]. Tamaddoni et al. [16,17] designed a vehicle lateral s...

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Section: Division Of Control Modesmentioning

confidence: 99%

Section: Stackelberg Game-based Controllermentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Game-Based Hierarchical Cooperative Control for Electric Vehicle Lateral Stability via Active Four-Wheel Steering and Direct Yaw-Moment Control

Zhao

Zhang

2019

Energies

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“…Li et al [20] proposed a driving style estimation method based on maneuver transition probability to promote the optimization of man-computer cooperation, considering multiple vehicle maneuver states (e.g., free driving, approaching, near following, and constrained left and right lane changes). Na and Cole [21] explored the relationship between driving behavior and vehicle front wheel steering using the Stackelberg equilibrium theory. ey also explored the control strategy of driver and active front wheel steering by applying a linear quadratic dynamic optimization algorithm and a distributed model predictive control method, respectively.…”

Section: Introductionmentioning

confidence: 99%

The Relationship between Bus Drivers’ Improper Driving Behaviors and Abnormal Vehicle States Based on Advanced Driver Assistance Systems in Naturalistic Driving

Wang

Chen

Yan

et al. 2020

Mathematical Problems in Engineering

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In order to improve the adaptation of driver to the advanced driver assistance system (ADAS) and optimize the active safety control technology of vehicle under man-computer cooperative driving, this paper investigated the correlation between driver’s improper driving behaviors and abnormal vehicle states under the ADAS. Based on the warning data collected from the driver’s assistance warning system equipped on buses, the interaction between improper behaviors, between abnormal vehicle states, and between improper behaviors and abnormal vehicle states were quantitatively analyzed through the hierarchical clustering method and improved Apriori algorithm. The results showed that eye closure and yawn were high in concurrency (probability: 0.888) and interaction (average probability: 0.946); the interaction among lane departure, rapid acceleration, and rapid deceleration are frequent (average probability: 0.7224); eye closure (average probability: 0.452) and yawn (average probability: 0.444) are likely to induce abnormal vehicle states such as rapid acceleration and rapid deceleration. Some suggestions proposed based on the results are as follows. First, it is suggested that the ADAS should combine the warning modes of eye closure and yawn; second, when the driver closes eyes or yawns, the control of the ADAS over the lateral and longitudinal performance of vehicle should be enhanced; third, the extent of control by the ADAS should be determined according to the relationship probability; finally, the lateral control over the vehicle by the ADAS should be strengthened when there is a forward collision warning.

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Global stability of road vehicle motion with driver control

et al. 2023

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The paper contributes to unveil how drivers—either human or not—may lose control of road vehicles after a disturbance. First, a simple vehicle-and-driver model is considered: Its motion is characterized by the existence of limit cycles whose amplitude depend on vehicle forward velocity (both oversteering and understeering vehicles may exibit this property). Such limit cycles are originated by a Hopf bifurcation occurring at a relatively high vehicle forward velocity. A mathematical proof of the existence of Hopf bifurcations is given. The existence of Hopf bifurcations and saddle limit cycles is confirmed by experimental tests performed by a dynamic driving simulator with a complex vehicle model and human in the loop. By a Zubov method, a Lyapunov function is derived to compute the region of asymptotic stability for the simple vehicle-and-driver model. A necessary and sufficient condition is derived for global asymptotic stability. Such a condition refers to the variation of the kinetic energy which must vanish at the end of the disturbed motion. This occurrence has been detected at the driving simulator too. Just a single stable equilibrium has been found inside the domain of attraction in all of the examined cases.

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Application of Open-Loop Stackelberg Equilibrium to Modeling a Driver's Interaction with Vehicle Active Steering Control in Obstacle Avoidance

Cited by 52 publications

References 19 publications

Game-Based Hierarchical Cooperative Control for Electric Vehicle Lateral Stability via Active Four-Wheel Steering and Direct Yaw-Moment Control

Game-Based Hierarchical Cooperative Control for Electric Vehicle Lateral Stability via Active Four-Wheel Steering and Direct Yaw-Moment Control

The Relationship between Bus Drivers’ Improper Driving Behaviors and Abnormal Vehicle States Based on Advanced Driver Assistance Systems in Naturalistic Driving

Global stability of road vehicle motion with driver control

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