As a first step we show, that the exchange of current planned trajectories between vehicles eventually makes these trajectories collision free as long as the vehicles respect the right-of-way rules. In a second step, we analyze the maneuver coordination process and show, that it does not introduce additional safety risks as long as the vehicles follow the rules required by the process. All safety risks presented in this paper already exist without incorporating our protocol and AV s already have to take these risks into account.
Article :. DOI: The DRF model also predicts that curve-cutting is higher in sport setting than in normal setting. Each row represents one scenario and the columns compare two different metrics in that scenario. The DRF model results are compared to the results from literature Supplementary Notes 1—8 in the adjacent subfigures Supplementary Figures 3—6. In the DRF model subfigures, the black and grey markers represent the sport and normal parameter settings, respectively.
The sport setting of DRF cuts the curves more 1a and drives at higher speeds 1c compared to the normal setting. The DRF model 2a can predict this trend. The minimum lateral deviation 3b is calculated from the trajectories in 3a. Subfigure 4c shows the distribution of lateral position of the participants.
The mean lateral deviation 4b and mean speed 4e are calculated from the trajectories in 4a and 4d, respectively.
Speed: Several studies report that the speed at which a curve is taken increases non-linearly with curve radius, in driving simulator 33 , 34 and on-road tests 11 , 33 , The paper from Taragin and Leisch 36 was chosen Fig. The DRF model predicts that the speed increases with curve radius, asymptotically approaching straight road speed for a large radius Fig. The effect of lane width was examined using the standard deviation of lateral position SDLP and speed.
Lateral position: SDLP, which represents the swerving behaviour of a car, is reported to increase with lane width, in a simulator study by Godley et al. They examined the SDLPs of participants on three different lane widths 2. Similar results are reported in other simulator 38 , 39 and on-road studies 40 which are coherent with the predictions of the DRF model Fig.
On a wider road, the DRF model has wider areas of low cost and hence, can use a larger width of the road without steering corrections exhibit satisficing , resulting in higher SDLP. Speed: It is reported that the speed at which drivers negotiate roads increases as the lane width increases, in simulator 37 , 41 , 42 , 43 and on-road studies 40 , The DRF model also showed a similar increase in speed with lane width Fig.
The effect of this temporary narrowing was examined by analysing the lateral deviation and speed of the ego vehicle. We selected the simulator study of Edquist et al. Lateral deviation: Edquist et al. The DRF model yields a similar trend, where the ego car deviates away from the parked car Fig. Speed: A reduction in mean speed was reported in the presence of parked cars Fig. It should be noted that Edquist et al. However, we had only one parked car, which means we can only report the minimum speed.
The DRF model successfully avoided on-road obstacles by steering and braking. Dunning et al. Lateral position: Dunning et al. Speed: Dunning et al. The DRF model also shows similar behaviour where the ego car drove faster in the asymmetric case as compared to the symmetric case.
In the symmetric case, driving on the centreline was not enough to reduce the risk below the threshold and hence the model had to slow down. In both conditions, the sport setting drove faster than the normal setting of the DRF model. The DRF model could react to roadside furniture by steering and braking since the DRF spreads beyond the lane boundaries. We tested three traffic scenarios, namely: car following, overtaking and interaction with oncoming cars. We tested the effect of lead car speed on time headway THW and braking intensity during car following.
THW: THW during car following represents the time available to the driver of the following vehicle to reach the same level of deceleration as the lead vehicle, in case the lead vehicle brakes.
The DRF model, with the current parameter values, behaved more conservatively higher THW pref than the average human driver, as reported by He et al. In addition, the THW pref for the sport parameterization was smaller than that for the normal parameterization of the DRF model. This concurs with the findings in the literature, where sensation-seeking drivers were reported to maintain lower THW pref compared to sensation avoiding individuals 52 , Similar to Fig.
For the DRF model figures, the black and the grey markers represent the sport and normal parameter settings, respectively Supplementary Figs. In 1c, the circular markers indicate the median and the whiskers indicate 25th and 75th percentile. However, the DRF model does not come back to its own lane sufficiently 2a. Subfigures 2e and 2f show that the predictions of the DRF model agree with the results in literature that show the time to collision TTC at the start of the overtake manoeuvre increases, as the speed of the overtaken car increases.
Braking intensity: Another aspect of car following that is widely studied is the braking intensity of the car in response to the separation to the lead car. In a test-track study, Van der Horst 55 reported that the braking intensity deceleration at the onset of braking increased as the approach speed increased Fig. The DRF model also predicts that a sport parameter setting black markers will yield higher deceleration than the normal setting grey markers: Fig.
The DRF model exhibits this behaviour since the lead car encroached the DRF at a higher rate when the approach speed was high and at a lower rate when the approach speed was low. We studied the effect of lead vehicle speed on overtake-distance distance covered during the overtaking manoeuvre and on the TTC at which the overtaking manoeuvre is initiated. Figure 5 -2a illustrates one of the major drawbacks of the DRF model: it overtakes the car but does not return to its own lane after the overtake.
This is the drawback of using a cost-threshold-based satisficing controller. Overtake-distance: Crawford 56 reported that the overtake-distance increased with the speed of the overtaken car Fig. In addition, note that the sport setting of the DRF model had larger overtake-distances than the normal setting. The on-road study by Chen et al. In a driving simulator study, Farah 60 reported that young male drivers, generally considered sporty drivers, had smaller TTCs at lane change than adults.
We simulated a narrow rural road with 2-m wide ego and oncoming lanes, without any barrier in between. Lewis-Evans and Charlton 41 reported that on a two-lane rural road, drivers drove more towards the road centre, in the absence of oncoming traffic.
The model shows this behaviour because the paved road to the left i. In addition, it moves even further when the oncoming car is offset towards the lane position of the ego car Fig. Speed: The DRF model slowed down in the presence of oncoming traffic, and slowed down more when the lateral position of the oncoming car was offset towards the ego car Fig. Rasanen 61 Fig. However, Rosey et al. Moreover, they also reported a significant decrease in speed while encountering trucks as compared to cars 62 , which is in line with the predictions of the DRF model.
In this paper, we set out to find the underlying principle that governs human-driving behaviour, implement this into a cost function for an operational driver model, and evaluate the generalizability of the modelled behaviour across different traffic scenarios by comparing it to adaptations in speed and lateral position from available literature of real-world and driving simulator studies.
Without this feature, the DRF model would not slow down on a narrow road wider than car-width. Second, the DRF widens and elongates with increasing speed. Without this, the DRF model would not maintain constant time headways in car following or slow down for curves.
Third, the DRF widens with an increase in steering angle. Without this feature, the DRF model would not slow down more for curves with higher curvature than for curves with lower curvature, and would negotiate all the curves at the same speed.
Without the asymmetric widening, the model would always follow the lane centre. Several models, ranging from tentacle-like algorithms 66 to Rapidly-exploring Random Trees RRT 67 , have been proposed for trajectory and speed planning. The methods that are closest to the cost function proposed in this paper are based on uncertainty propagation Most of these algorithms account for the first two points mentioned in the previous paragraph, namely: widening of the uncertainty with predicted path and speed dependency of uncertainty field.
In addition, these algorithms account for the uncertainty in predicting the future location of the obstacles. This feature needs to be incorporated in the driving scene cost map of future versions of the DRF model Fig.
However, it cannot perceive the risk from oncoming traffic which is currently not in its field of view. Hence, at an intersection, rather than slowing down, it will speed up, since there is larger road-area available, which is contrary to what a human would do. This approach can be extended to other elements such as traffic lights or zebra crossings. However, we can optimise for a vector of steering angles and speed as is done in a Model Predictive Control. This allows for a flexible DRF and better prediction of microscopic trajectories.
However, the risk field extends on all four sides. The bottom image is merely a suggestion, and the shape has not been investigated. However, the motion of dynamic obstacles is less predictable. This uncertainty was ignored in this paper, but will have to be accounted for in future iterations of this model. Implementing a satisficing controller in a potential field has its drawbacks.
The model did not return to its lane after overtaking the lead car because it can sense hazard only from physical objects e. Other tactical risks, such as risks that may occur when approaching an intersection or a red traffic light, are not incorporated in the model either.
In future iterations, a car-dynamic model, a spline instead of a circular arc Fig. Satisficing behaviour becomes important when developing advanced driver assistance systems ADAS that physically interact with the driver, e.
If the HSC tries to follow a reference e. To avoid these undesired torques that can severely hamper the acceptance of the system, we need threshold-based models that can exhibit satisficing behaviour.
An important contribution of this paper is the extensive literature-based validation. Note that, in this paper, we do not compare the trajectories of steering angle, speed and lateral deviation, but assess the behaviour of the model by comparing trends in certain metrics to those reported in the literature. Six out of the seven scenarios were validated using on-road studies or studies from driving simulators backed by on-road studies only simulator studies found for roadside furniture: Supplementary Tables 1 — 8.
In Fig. Despite these limitations, as the results show Figs. Such a generalizable model in which the behaviour emerges from an intrinsically motivated cost does not only provide understanding about human motivations for driving, but also has applications in the design of automated systems.
For example, it could be used to make the automated vehicle drive in a human-like manner, which is reported to be preferred by humans 4 , Our model has been developed for unassisted driving. However, since its behaviour emerges from the underlying motivations for driver adaptation, we hypothesise that it should be able to capture driver adaptations to various driving support systems.
For example, drivers drove faster when their vehicle was equipped with lane-keeping assistance based on HSC than in a car without this assistance This thought experiment illustrates that a generalizable model in which behaviour emerges from underlying cost functions, not only predicts unassisted driver behaviour but also the effect of automated and assistive technologies on driver behaviour. This paper focuses on validating the DRF the dynamic field. However, to generate model predictions on human-driving behaviour, the risk metric calculated using the DRF needs to be connected to a controller that converts the risk metric into control actions.
We chose a simple control algorithm over more complex ones for two reasons. Second, we wanted to avoid unnecessary complexity in formalising the optimisation problem. However, since the environment is represented as a discretized grid cost map, the risk metric needs to be calculated numerically. Moreover, we need a controller that maintains the cost below a certain threshold and not one that minimises it. Hence, formulating the optimisation problem with the necessary constraints would itself be a separate study and is beyond the scope of this paper.
The basic control structure Fig. The inner workings of the driver model block are shown in Fig. The DRF is multiplied with the cost map of the driving scene, and summed over all points to provide us with the quantified perceived risk cost. This cost is then used by the driver model algorithm, which is based on the risk-threshold theory, to generate the control actions.
A simple driver model that utilises the estimated risk metric to generate control actions is shown. The DRF is multiplied with the cost map of the driving scene and summed over all grid points to generate the quantified perceived risk cost function. The DRF model algorithm is based on the risk-threshold theory and compares quantified perceived risk C with risk threshold C t.
The DRF can be individualised based on DRF parameters while the driver model parameters determine how the cost perceived risk is converted to control actions speed and steering. This results in four distinct cases of inequality. V des is the speed at which the driver wants to drive on an open straight road, uninhibited. In accordance to the risk-threshold theory, the model tries to maintain the risk C below the risk threshold C t , and hence does not provide a specific trajectory, but rather a range of safe trajectories satisficing.
The gain of the heading controller is k h. The driver model algorithm Fig. We do not consider the equality relations e. The parameter k v specific for each driver represents how aggressively the model accelerates. In this case, we first check if the steering alone can help the model reduce the risk below the threshold. Hence the model tries to apply a steering that is just enough to reduce the risk C k and get it below the threshold C t.
This is done so that we do not slow down more than what is required. The implementation of the track in a fixed base driving simulator is shown in the Supplementary Video 1. Simulations of the DRF model in normal and sport parameter settings are shown in Supplementary Videos 2 and 3.
The parameters can be segregated into three types: first, the DRF parameters that determine the shape of DRF, and are specific to each person. Second, the driver model parameters that connect the risk estimated by the DRF to the control inputs of the vehicle. Third, the environment parameters that describe the consequences of being in a particular state position, velocity, etc.
Parameter c , which represents the initial width of the DRF can be directly calculated from the width of the ego car 2. The remaining five parameters were estimated using the grid search algorithm. Driver model parameters Table 2 : The driver model parameters include the speed controller gains k vc , k v , the risk threshold C t , and the desired speed V des.
Environment parameters Table 3 : The environment parameters define the consequence of being in a particular state restricted to position, in this study. These parameters are independent of the driver and hence are the same for everyone.
Personalised driving behaviour is obtained by changing the parameters of the DRF and the driver model. The costs of all other objects in the environment were identified relative to C env.
Different objects have different costs; for example, a car in traffic may be assigned a cost of , and a roadside tree may be assigned a cost of However, since the focus of this paper is to demonstrate the working of the model, and not identifying the costs of different obstacles, all the obstacles in our simulation were identical: a sedan 1.
In all these scenarios, the same cost C obs was assigned to the car, as identified using the grid search algorithm.
All the signals were a function of the distance travelled along the lane centre. It has to be noted that, to personalise the DRF model to an individual, only seven parameters need to be estimated p , t la , m , c , k 1 , k 2 , k vc and C t. Further information on research design is available in the Nature Research Reporting Summary linked to this article. Statistics of New York pedestrian and bicyclist crashes show that left turns are twice more fatal than right turns.
Pedestrians and bicyclists are severely injured by a left-turning vehicle at over three times the rate of pedestrians and bicyclists adversely affected by a right-turning car. Left turns are also dangerous to motorcyclists because their smaller vehicles can go unobserved by a driver. Inattention, distraction, blind spots, and even psychology can be blamed for accidents; a driver looking for cars sees merely the absence of cars, not the presence of a motorcycle. When turning left, the driver needs to cross completely one lane of traffic after waiting for traffic from both the left and the right.
This maneuver requires quick and serious decisions. The driver must judge the speed and distance of the oncoming vehicles and make sure they have enough time to turn. To further complicate this maneuver, it is possible that pedestrians will be crossing the street into which the driver is attempting to turn.
Read more about the dangers of Miami left turns in our faq Why are left turns bad in Florida? Various solutions have been proposed by transportation experts to solve the problem of left-hand crashes.
One solution suggests a greater offset of the left turn lane of oncoming traffic to the right, allowing a better view of the oncoming traffic. Another proposed solution is to give left-turning vehicles their own turning phase.
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