Human-like driving behaviour emerges from a risk-based driver model

The study addresses whether a single, generalizable principle can explain and generate human-like driving across diverse scenarios, moving beyond task-specific driver models. Building on perceived risk as a unifying construct, the authors hypothesize that drivers act to keep perceived risk below an individual threshold, exhibiting satisficing rather than strict optimization. They introduce the Driver’s Risk Field (DRF) as a representation of the driver’s belief about near-future positional probability (reflecting perception–action uncertainty) and combine it with environmental consequence (cost) to operationalize perceived risk. The purpose is to test if this risk-based cost function, controlled via a risk-threshold policy, can reproduce human driving adaptations in speed and lateral position across multiple road and traffic conditions, thereby offering both scientific insight and practical utility for human-like automated driving.

Prior work has largely produced driver models tailored to specific tasks (e.g., TTC for obstacle approach, THW in car following, two-point steering for lane keeping), lacking a unified account. Early unified theories include Gibson and Crooks’ field of safe travel and motivational theories like risk homeostasis and task-difficulty homeostasis (Wilde; Fuller). These frameworks lack mechanistic specificity and conflict with satisficing behaviour, where drivers aim to remain within acceptable bounds rather than follow exact references. Näätänen and Summala proposed a risk-threshold concept: drivers act when perceived risk exceeds a threshold. However, it has not been quantitatively operationalized across scenarios. In human motor control, cost functions that account for signal-dependent noise unify behaviours across tasks; the authors draw on these ideas to propose an uncertainty-aware perceived-risk cost for driving.

The authors define perceived risk as the product of the driver’s subjective probability of occupying future positions and the consequences associated with those positions. The Driver’s Risk Field (DRF) represents subjective probability and is modeled as a torus with a Gaussian cross-section that follows the vehicle’s predicted path, computed using a kinematic car model assuming constant steering angle and speed over a preview time. Key equations: R_car = L/tan(δ); DRF magnitude z(x,y) = a exp(-((sqrt((x−x_c)^2+(y−y_c)^2)−R_car)^2)/(2σ^2)), where the height a(s) is parabolic in arc length s with parameters p and preview time t_a (a(s)=p(s−v t_a)^2), and the width σ(s) varies linearly with s, with asymmetry for inner (σ1) and outer (σ2) widths: σ_i = (m + k_i δ)s + c, i∈{1,2}. Parameters p, t_a, m, c, k1, k2 define the DRF and depend only on driver state (speed, steering) and not the environment. The environment is encoded as a spatial cost map assigning consequences to scene elements (e.g., ego lane, roadside, parked/moving cars). Quantified perceived risk C is computed by multiplying the DRF field with the cost map and summing over all grid points. A simple risk-threshold controller translates risk into control: the model seeks to achieve a desired speed V_des while maintaining risk below threshold C_th (satisficing). A heading controller δ_{k+1} = δ_k + k_δ (ψ_road − ψ_car) stabilizes steering. At each time step, the algorithm compares current risk C_k to threshold C_t and speed v_k to V_des, resulting in four cases combining acceleration/deceleration and steering. When C_k > C_t and v_k ≥ V_des, it uses a bounded 1D optimization (fminbound) over δ to find δ_opt minimizing C; it applies only the steering needed to bring risk to threshold (not minimum) and adjusts speed accordingly; if steering alone cannot reduce risk sufficiently, it brakes proportional to the residual risk. Parameters were estimated using a human-in-the-loop driving simulator with one volunteer (male, 25 years) driving a virtual track 10 times “normal” and 10 times “sport” to emulate different styles. Grid search identified DRF parameters and driver model parameters; environment costs were set relative to baseline lane costs. The model was then simulated on a composite track covering seven scenarios: curve radii, lane widths, obstacle avoidance, roadside furniture, car-following, overtaking, and oncoming traffic. Model outputs (speed, lateral position) were compared against trends reported in published literature for analogous scenarios.

• Across seven scenarios, the DRF model reproduced human-like trends in speed and lateral position found in on-road and simulator studies.
• Curve radius: The model exhibited curve-cutting that decreased as radius increased (consistent with Xu et al.), and speed in curves increased nonlinearly with radius, asymptotically approaching straight-road speed (consistent with Taragin & Leisch). Sport setting produced more curve-cutting and higher speeds than normal.
• Lane width: Standard deviation of lateral position (SDLP) increased with lane width (as in Godley et al.), reflecting satisficing use of wider lanes; speeds increased with lane width (consistent with Liu et al. and others).
• On-road obstacles (parked car encroaching lane): The model steered away from the obstacle and reduced speed in its presence, aligning with Edquist et al.
• Roadside furniture: In asymmetric risk (e.g., higher risk on one side), lateral position shifted toward the safer side; in symmetric risk, it stayed centered. Speeds were higher in asymmetric than symmetric conditions (concordant with Dunning et al.).
• Car following: Preferred time headway (THW_pref) was approximately constant above 10 m/s lead speeds, matching literature; the model was somewhat more conservative (larger THW) than on-road medians. Braking intensity at onset increased with approach speed, consistent with Van der Horst.
• Overtaking: Overtake distance increased with overtaken vehicle speed (Crawford). Time-to-collision (TTC) at overtake initiation increased with the speed of the overtaken car (Chen et al.); sport setting maintained lower TTCs and larger overtake distances than normal, consistent with sensation-seeking driver tendencies.
• Oncoming traffic: The model biased toward the road center when no oncoming traffic; with oncoming vehicles, it shifted laterally away from them and reduced speed, with greater reductions for closer lateral offsets. Human data show similar lateral shifts; some studies observed smaller speed changes.
• Emergent satisficing and uncertainty-awareness: Human-like behaviours (e.g., curvature-dependent speeds, curve-cutting, constant THW) arose from DRF features: speed- and steering-dependent widening/elongation, predicted-path coupling, and asymmetric widening.
• Parameterization: A single set of DRF parameters, combined with different driver model parameters for “normal” vs “sport,” captured style-dependent differences in speed, headway, and risk-taking tendencies.
• Noted drawback: In overtaking without oncoming traffic, the satisficing controller did not reliably return to the original lane due to absence of tactical costs.

Findings support the central hypothesis that perceived risk, quantified as the product of an uncertainty-based DRF and environmental consequences, under a risk-threshold control policy, can generate human-like driving across diverse scenarios. The model explains key adaptations—slowing in curves and narrow lanes, curve-cutting, constant headway in following, lateral shifts away from hazards—via four uncertainty-aware DRF properties: (1) widening along the predicted path, (2) speed-dependent widening/elongation, (3) steering-angle-dependent widening consistent with signal-dependent noise, and (4) asymmetric widening enabling curve-cutting. Compared with robotics motion planning, the approach aligns with uncertainty propagation but uniquely incorporates steering-dependent and asymmetric uncertainty, important for human-like behaviours seldom modelled in robotics. The results highlight practical implications: a unified, interpretable cost function can inform automated driving to behave more human-like (potentially improving trust and acceptance) and serve as a feature in learning-from-demonstration. It also provides a framework to predict how assistance (e.g., haptic shared control) affects behaviour by effectively narrowing the DRF (reduced uncertainty), leading to higher comfortable speeds. The literature-based validation across seven scenarios underscores generalizability, despite dynamic scenario complexities and metric selection challenges.

The paper introduces and operationalizes a generalizable, uncertainty-aware perceived-risk metric for driving: the Driver’s Risk Field (DRF) multiplied by environmental consequence. Coupled with a risk-threshold, satisficing controller, the model produces human-like behaviour across seven road and traffic scenarios without task-specific switching. Key contributions include: (1) formalizing the risk-threshold theory for driving, (2) deriving DRF features grounded in sensorimotor noise, and (3) extensive literature-based validation showing alignment with human trends in speed and lateral control. Future research directions include incorporating tactical costs (e.g., intersections, lane-discipline), richer predicted paths (e.g., MPC/splines) and full vehicle dynamics, a surround DRF to handle rear and lateral hazards, explicit uncertainty for dynamic obstacles, broader empirical validation and personalization, and integration with driver-assistance systems and automated driving for human-like control.

• Tactical risk omissions: The model perceives only physical/object-based risk within view and lacks tactical costs (e.g., risk of staying in oncoming lane after overtaking, intersections, traffic lights), leading to unrealistic behaviours like not returning to lane post-overtake.
• Prediction simplifications: Predicted path assumes constant steering and speed with a circular arc; no model predictive control or spline optimization is used.
• Vehicle model: Kinematic model only; no full vehicle dynamics.
• DRF extent: DRF extends only forward; no surround field to capture rear/lateral threats (e.g., being followed or overtaken).
• Dynamic obstacle uncertainty: Ignores uncertainty in other actors’ future motion.
• Parameterization and validation: Environment costs simplified and partly assumed; parameters estimated using one participant (n=1) and a grid search; validation relies on matching trends from literature rather than extensive new multi-participant experiments.
• Controller artefacts: Satisficing controller can produce ‘bouncing’ without heading stabilization and may not perform accelerative overtakes due to V_des limitation.