Stability analysis of an improved car-following model accounting for the driver’s characteristics and automation

Abstract This study presents an improved car-following model accounting for the driver’s characteristics and automation for longitudinal driving. We attempt to reveal some features of driving behavior, which drivers make decision in consideration with delayed decision and aggressiveness as well as the automated controller. The delayed decision and aggressiveness of drivers are represented via the integral term with kernel function and headway perturbation, and the automated controller consists of proportional–derivative element. Stability analysis is performed both driver’s characteristics and controller gains adopting frequency domain sweeping method. Stability regions of proposed model show the relationships between driver’s characteristics and automated controller. Some numerical examples are given to illustrate the effectiveness of the proposed methods and interpret the relation between driver’s characteristics and automated controller.

[1]  Rajesh Rajamani,et al.  Design and Experimental Implementation of Longitudinal Control for a Platoon of Automated Vehicles , 2000 .

[2]  Zhongke Shi,et al.  An extended car-following model considering vehicular gap fluctuation , 2015 .

[3]  Du Jun,et al.  A compound compensation method for car-following model , 2016, Commun. Nonlinear Sci. Numer. Simul..

[4]  Yunpeng Wang,et al.  An extended car-following model with consideration of the reliability of inter-vehicle communication , 2014 .

[5]  Jianqiang Wang,et al.  Stability and Scalability of Homogeneous Vehicular Platoon: Study on the Influence of Information Flow Topologies , 2016, IEEE Transactions on Intelligent Transportation Systems.

[6]  Hai-Jun Huang,et al.  A new fundamental diagram theory with the individual difference of the driver’s perception ability , 2012 .

[7]  Shaowei Yu,et al.  Full velocity difference and acceleration model for a car-following theory , 2013, Commun. Nonlinear Sci. Numer. Simul..

[8]  Peter Seiler,et al.  Disturbance propagation in vehicle strings , 2004, IEEE Transactions on Automatic Control.

[9]  Davis Lc.  Effect of adaptive cruise control systems on traffic flow. , 2004 .

[10]  Silviu-Iulian Niculescu,et al.  Stability of car following with human memory effects and automatic headway compensation , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[11]  Prabir Barooah,et al.  Stability and robustness of large platoons of vehicles with double‐integrator models and nearest neighbor interaction , 2013 .

[12]  Zhongke Shi,et al.  Impacts analysis of car following models considering variable vehicular gap policies , 2018, Physica A: Statistical Mechanics and its Applications.

[13]  Mark Mulder,et al.  Sharing Control With Haptics , 2012, Hum. Factors.

[14]  Weining Liu,et al.  Linear stability and nonlinear analyses of traffic waves for the general nonlinear car-following model with multi-time delays , 2018, Physica A: Statistical Mechanics and its Applications.

[15]  Wei-Zhen Lu,et al.  Nonlinear analysis of a new car-following model accounting for the optimal velocity changes with memory , 2016, Commun. Nonlinear Sci. Numer. Simul..

[16]  Kentaro Hirata,et al.  Decentralized delayed-feedback control of an optimal velocity traffic model , 2000 .

[17]  Qi Xin,et al.  Relative velocity difference model for the car-following theory , 2018 .

[18]  Dong Chen,et al.  Weakly nonlinear analysis for car-following model with consideration of cooperation and time delays , 2018, Modern Physics Letters B.

[19]  Shaowei Yu,et al.  An improved car-following model considering relative velocity fluctuation , 2016, Commun. Nonlinear Sci. Numer. Simul..

[20]  Dong Ngoduy,et al.  Linear stability of a generalized multi-anticipative car following model with time delays , 2015, Commun. Nonlinear Sci. Numer. Simul..

[21]  L. A. Pipes.  An Operational Analysis of Traffic Dynamics , 1953 .

[22]  Chouki Sentouh,et al.  Automation-driver cooperative driving in presence of undetected obstacles , 2014 .

[23]  Gábor Stépán,et al.  Traffic jams: dynamics and control , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[24]  Jian Zhang,et al.  A speed guidance strategy for multiple signalized intersections based on car-following model , 2018 .

[25]  Roberta Di Pace,et al.  Development and testing of a fully Adaptive Cruise Control system , 2013 .

[26]  Frank Flemisch,et al.  Towards a dynamic balance between humans and automation: authority, ability, responsibility and control in shared and cooperative control situations , 2012, Cognition, Technology & Work.

[27]  Ziyou Gao,et al.  Stabilization strategies of a general nonlinear car-following model with varying reaction-time delay of the drivers. , 2014, ISA transactions.

[28]  Charles A. Desoer,et al.  Control of interconnected nonlinear dynamical systems: the platoon problem , 1992 .

[29]  Tie-Qiao Tang,et al.  An improved car-following model accounting for the preceding car’s taillight , 2018 .

[30]  Meng Wang,et al.  Rolling horizon control framework for driver assistance systems. Part II: Cooperative sensing and cooperative control , 2014 .

[31]  Haijun Huang,et al.  An extended macro traffic flow model accounting for the driver’s bounded rationality and numerical tests , 2017 .

[32]  Philippe Chevrel,et al.  Shared Steering Control Between a Driver and an Automation: Stability in the Presence of Driver Behavior Uncertainty , 2013, IEEE Transactions on Intelligent Transportation Systems.

[33]  Li-Chen Fu,et al.  A Portable Vision-Based Real-Time Lane Departure Warning System: Day and Night , 2009, IEEE Transactions on Vehicular Technology.

[34]  Hui Liu,et al.  Analysis of traffic flow based on car-following theory: a cyber-physical perspective , 2016 .

[35]  Tie-Qiao Tang,et al.  A car-following model accounting for probability distribution , 2018, Physica A: Statistical Mechanics and its Applications.

[36]  Saïd Mammar,et al.  Driver Steering Assistance for Lane-Departure Avoidance Based on Hybrid Automata and Composite Lyapunov Function , 2010, IEEE Transactions on Intelligent Transportation Systems.

[37]  Zhongke Shi,et al.  Dynamics of connected cruise control systems considering velocity changes with memory feedback , 2015 .

[38]  Tie-Qiao Tang,et al.  A car-following model accounting for the driver’s attribution , 2014 .

[39]  Silviu-Iulian Niculescu,et al.  Stability of Traffic Flow Behavior with Distributed Delays Modeling the Memory Effects of the Drivers , 2007, SIAM J. Appl. Math..

[40]  Siuming Lo,et al.  An extended car-following model accounting for the average headway effect in intelligent transportation system , 2017 .