[Paper Review] Intermittent Control Properties of Car Following: Theory and Driving Simulator Experiments

Ihor Lubashevsky, Hiromasa Ando|arXiv (Cornell University)|Sep 7, 2016

Traffic control and management16 references3 citations

TL;DR

This study proposes a four-variable intermittent control model for car-following behavior, treating car jerk (time derivative of acceleration) as a key control variable. Using a TORCS-based driving simulator with eight subjects, it demonstrates that human driving follows noise-driven intermittent control, with distinct driving styles and sharp peaks in jerk distributions indicating probabilistic control activation, challenging traditional Newtonian mechanics-based models.

ABSTRACT

A rather simple car driving simulator was created based on the available open source engine TORCS and used to analyze the basic features of human behavior in car driving within the car-following setups. Eight subjects with different skill in driving real cars participated in these experiments. They were instructed to drive a virtual car without overtaking the lead car driven by computer at a fixed speed and not to lose sight of it. Moreover, these experiments were conducted with four different speed including 60km/h, 80km/h, 100km/h, and 120km/h. Based on the collected data the distribution of the headway, velocity, acceleration, and jerk are constructed and compared with available experimental data collected previously by the analysis of the real traffic flow. A new model for car-following is proposed capture the found properties. As the main results we draw a conclusion that the human behavior in car driving should be categorized as a generalized intermittent control with noise-driven activation of the active phase. Besides, we hypothesize that the extended phase space required for modeling human actions in car driving has to comprise four phase variables, namely, the headway distance, the velocity of car, its acceleration, and the car jerk, i.e., the time derivative of the car acceleration. This time, the time pattern of pedal pushing and the distribution of time derivative of pedal was utilized in addition to previous variables. Moreover, all subjects' driving data were categorized as some styles with their shapes.

Motivation & Objective

• To investigate how human intermittent control manifests in car-following dynamics using a virtual driving environment.
• To isolate and analyze the role of higher-order dynamics, particularly car jerk, in human driving behavior.
• To determine whether control activation is threshold-driven or noise-driven, based on experimental data from a controlled simulator setup.
• To develop a mathematical model of car-following that incorporates headway, velocity, acceleration, and jerk as phase variables.
• To compare simulated results with real traffic flow data and identify driving styles based on pedal dynamics and jerk patterns.

Proposed method

• Developed a custom car-driving simulator using the open-source TORCS engine to replicate realistic car dynamics.
• Conducted experiments with eight drivers under four fixed lead car speeds (60–120 km/h) to collect data on headway, velocity, acceleration, jerk, pedal position, and pedal rate of change.
• Used high-precision Logitech G27 racing wheel and pedal set to ensure accurate data collection on driver inputs.
• Analyzed statistical distributions of control variables, especially focusing on peaks in jerk and pedal derivative distributions.
• Proposed a four-variable phase space model including headway, velocity, acceleration, and jerk, with noise-driven control activation.
• Simulated the model and compared its output with experimental and real-world traffic data.

Experimental results

Research questions

• RQ1 How does human intermittent control in car-following manifest in the statistical distributions of headway, velocity, acceleration, and jerk?
• RQ2 Is control activation in car-following primarily threshold-driven or noise-driven, and what evidence supports this?
• RQ3 What role does car jerk—defined as the time derivative of acceleration—play in human-driven car dynamics?
• RQ4 Can a four-variable phase space model (headway, velocity, acceleration, jerk) accurately represent human driving behavior in car-following?
• RQ5 How do different driving styles emerge from the dynamics of pedal input and jerk distribution?

Key findings

• The distribution of car jerk exhibits a sharp peak at zero, indicating that drivers frequently release or apply the accelerator pedal abruptly, which is a hallmark of intermittent control.
• The time derivative of pedal position (related to jerk) shows a pronounced peak at zero, confirming that jerk is a primary control variable in human driving.
• Driver behavior can be categorized into distinct styles: one where the pedal is pressed and released frequently (high intermittency), and another where it is held pressed most of the time (low intermittency), with intermediate styles showing mesolevel intermittency.
• The data support a noise-driven control activation mechanism rather than a threshold-driven one, as the switching between active and passive phases is probabilistic and reflects human perception uncertainty.
• The four-variable model—incorporating headway, velocity, acceleration, and jerk—successfully reproduces key features of real traffic flow and experimental data, outperforming traditional models.
• The study concludes that car-following cannot be adequately described by Newtonian mechanics alone and requires an extended phase space that includes higher-order derivatives such as jerk.