A new data-driven approach could help automated cars take rural curves in ways that feel more natural to human passengers. Researchers in Germany have converted thousands of real-world cornering maneuvers into a catalog of likely driving trajectories, using spatial “keypoints,” machine-learning clustering and graph theory to describe how vehicles enter, negotiate and leave a bend. The method is designed to give automated lateral-control systems more than a single mathematically optimal path: it offers a menu of human-inspired alternatives that could eventually be selected according to road geometry, vehicle type, traffic and passenger expectations.
The work addresses a major road-safety problem. Although most injury crashes in Germany occur in urban areas, rural roads are responsible for a disproportionate share of deaths. In 2024, country roads excluding motorways accounted for 23.69 percent of injury crashes but 56.71 percent of road fatalities, according to national statistics cited by the researchers. Leaving the road was the most common injury-crash category on these roads, representing 28.74 percent of cases. Curves are particularly demanding because the vehicle must continuously regulate its lateral position while speed, visibility, road curvature and the presence of oncoming traffic change the driver’s available safety margin.
Advanced driver-assistance systems can reduce unintended lane departures, but their safety benefits depend on whether people are willing to leave them switched on. Steering that feels abrupt, overly cautious or difficult to understand can make drivers uncomfortable, and previous research has shown that users often deactivate assistance functions that do not match their expectations. For highly automated driving at SAE Level 3 or above, this issue becomes more important: the system, rather than the driver, is responsible for choosing and following a trajectory, so the vehicle’s behavior must be both technically safe and psychologically acceptable.
To learn how people actually drive curves, the team analyzed data from eight instrumented vehicles operated during a field campaign covering approximately 250,000 kilometers. The fleet included two Volkswagen Golf 7s, four Volkswagen Passat B8s, a Volkswagen Tiguan III and a Volkswagen Atlas, providing a mixture of compact, midsize and sport-utility vehicle geometries. The vehicles recorded data at 100 hertz, or 100 measurements per second, from vehicle-dynamics sensors, steering and pedal inputs, GPS, radar and a forward-facing camera. The campaign involved 128 participants aged 20 to 43, although the sample was predominantly male and therefore does not represent the entire driving population.
The researchers focused on country-road curves with radii of 450, 600 and 900 meters, driven at speeds between 60 and 110 kilometers per hour. Curve radius is a measure of how sharply a road bends: a smaller radius means greater curvature and stronger steering demands. The team estimated radius from vehicle speed and yaw rate, the rate at which the car rotates around its vertical axis, using the relationship ρ = v/|ψ̇|. The sign of yaw rate distinguished left-hand from right-hand bends. A detection algorithm then isolated sustained curves, rejecting short transients and complex combinations such as tightly connected S-bends. A candidate segment had to cover more than 150 meters and remain within 75 meters of its target radius.
Because the analysis depended on the vehicle’s position inside the lane, the researchers also developed a quality-control system for camera-based lane detection. The camera supplied distances to the left and right lane markings, but worn paint, missing markings and sudden detection errors could create false lateral movements. When one boundary disappeared temporarily, the system estimated it using the recent average lane width, provided the remaining boundary was detected with high confidence. The vehicle’s lateral deviation was then calculated relative to the lane center and normalized by lane width, allowing trajectories from roads with different physical dimensions to be compared. Only curve segments with a lane-quality score of at least 0.8 were retained, meaning that reliable lane information was available for at least 80 percent of the maneuver.
More than 2,800 valid curve segments survived the filtering process. Each curve was reduced to three spatial keypoints: the entry, the apex and the exit. The apex is the central portion of the bend, where the vehicle is typically most deeply engaged with the curve. At each keypoint, the team measured normalized lateral deviation, which indicates whether the car was positioned toward the center, inner side or outer side of the lane. This compression transformed every continuous maneuver into three representative observations while preserving the most important phases of cornering. The curves were also labeled according to direction and whether oncoming traffic was present, producing separate groups for left and right bends under traffic and free-driving conditions.
The researchers used the unsupervised machine-learning method k-means to identify three characteristic lateral positions at each keypoint. K-means groups observations by minimizing the squared distance between individual measurements and their assigned cluster center. An elbow analysis showed that the improvement in fit was substantial up to three clusters but became much smaller when additional clusters were added. The resulting groups broadly represented near-center driving, moderate lateral bias and stronger movement toward the inner or outer edge. In one example involving a 450-meter left curve without oncoming traffic, the inner-biased group at the apex corresponded to classic “corner cutting,” in which the driver moves toward the inside of the bend rather than tracing the lane center precisely.
Clustering alone, however, does not describe a complete trajectory. A driver may enter a curve near the center, move inward at the apex and return outward at the exit, while another may maintain a relatively constant offset throughout. To model these possibilities, the team arranged the three clusters at the entry, apex and exit into layers of a directed graph. A path through the graph represents one full trajectory variant. With three choices at each of three points, there are 27 possible combinations, such as 1-1-1 for a consistent position or 1-2-3 for a progressive shift across the curve. The researchers then restricted the combinations to transitions actually supported by the measurements and assigned probabilities using a first-order Markov model: the probability of an apex position depends on the entry position, and the exit position depends on the apex position. This preserves sequential behavior rather than treating the three points as statistically independent.
The most probable trajectories were reconstructed between the keypoints using a shape-preserving piecewise cubic Hermite interpolation, or PCHIP. Unlike an unconstrained smooth curve, this interpolation is designed to avoid artificial overshoots between measured anchor values, producing a continuous lateral path that is more suitable for vehicle-control calculations. When the graph-based probabilities were compared with the combinations directly observed in the field data, the dominant patterns showed strong agreement. In the example 450-meter left curve, the 2-2-2 path was the most common in both analyses. The model was less accurate in ranking rarer strategies, suggesting that the compact graph captures the main structure of human behavior but does not reproduce every individual decision.
The results challenge the simplistic idea that human drivers normally remain exactly at the geometric center of their lane. In the 450-meter left-curve example, the most common 2-2-2 trajectory had normalized offsets of 0.071 at entry, 0.095 at the apex and 0.091 at exit. On a 3.5-meter-wide lane, those values correspond to approximately 0.25, 0.33 and 0.32 meters from the lane center. Such shifts are small enough to appear stable but large enough to matter for automated steering. In some 600-meter left curves without oncoming traffic, observed offsets reached 0.209, or roughly 0.7 meters on a 3.5-meter lane. For a compact car about 2 meters wide, that positioning can bring the vehicle’s outer edge close to the lane marking.
Oncoming traffic generally pushed the trajectory catalog toward more conservative, centered behavior, consistent with drivers anticipating reduced clearance and greater perceived risk. The dominant cluster combination was usually labeled 2-2-2, although this label describes the middle cluster within each scenario and does not necessarily mean the vehicle occupied the exact lane center. In one case—900-meter right curves with oncoming traffic—the most common pattern was labeled 3-3-3, a change in cluster numbering that reflected the local data distribution rather than a wholly different driving philosophy. The absence of a single universal strategy underscores why automated vehicles may need context-sensitive trajectory selection instead of one fixed curve-following rule.
The study does not yet show that any of the generated trajectories are safer, more comfortable or more trusted by passengers. Those questions are reserved for future experiments in a Dynamic Vehicle Road Simulator and in test vehicles on real roads. The current dataset also has important limits: it covers only three radius classes, comes from vehicles made by one manufacturer, depends on reliable lane markings and reflects a relatively young, mostly male driver group. Nevertheless, by converting continuous human behavior into interpretable graph paths with measurable probabilities, the research provides a practical bridge between naturalistic driving data and automated-control software. The next generation of systems could use such catalogs to choose not only a path that keeps a car within its lane, but one that behaves in a way passengers recognize as deliberate, cautious and human.
