Enhanced intelligent driver model to access the impact of driving strategies… — Volkswagen Transp

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With an increasing of vehicles equipped with cruise control (ACC), the of such vehicles on the collective of traffic flow becomes By means of simulation, we investigate the of variable percentages of ACC vehicles on flow characteristics. For simulating the ACC we propose a new car-following model also serves as the basis of an ACC in real cars. The model is on the intelligent driver model and inherits its intuitive behavioural desired velocity, acceleration, deceleration and desired minimum headway. It eliminates, however, the unrealistic behaviour of the IDM in cut-in with ensuing small that regularly are caused by changes of other vehicles in or congested traffic. We simulate the of different ACC strategies on the maximum before breakdown and the (dynamic) capacity after breakdown. a suitable strategy, we find of the order of 0.3, i.e. 1 per more ACC vehicles will to an increase in the capacities by about 0.3 per This sensitivity multiplies considering travel times at breakdowns.

1. Introduction

Efficient systems are essential to the functioning and of modern, industrialized societies. are therefore seeking solutions to the of how the capacity of the road network be used more efficiently and how can be improved by way of intelligent transportation Achieving this efficiency automated vehicle control is the vision in transport telematics. the recent advent of advanced assistance systems, at least automated driving is already for basic driving tasks as accelerating and braking by means of cruise control (ACC) An ACC system extends earlier control to situations with traffic in which driving at speed is not possible. The driver can not adjust the desired velocity but set a certain safe time gap the distance to the leading car when slower vehicles.

Although developed to delineate human behaviour, car-following models can be used to describe or even ACC systems. A radar sensor the car ahead to measure the net distance and the approaching rate, which (in addition to the car’s own speed) as quantities just as in many car-following models. Then, the ACC calculates the appropriate acceleration for the speed and the safety gap to the leader. analogy is scientifically interesting a ‘good’ car-following model serve as the basis for a control of a real-world ACC system. On the one hand, the implementation would allow the of the car-following model under to be judged, which is a further promising) approach towards the plethora of car-following models. question has recently been with different methods in the (Brockfeld et al. 2004 ; Ossen 2005 ; Panwai Dia 2005 ; Simonelli 2005 ; Kesting 2008 a ). On the other hand, the direct driving experience, one may new insights for the (better) description of drivers through adequate models, which is still an challenge in traffic science 2001 ; Kerner 2004 ; et al. 2006 a ; Ossen et al. 2007 ).

Furthermore, one may raise the interesting of how the collective traffic dynamics be influenced in the future by an increasing of vehicles equipped with ACC Microscopic traffic simulations are the methodology for this, since approach allows us to treat units’ individually and in interaction. The however, may significantly depend on the modelling assumptions. In the literature, as well as negative effects of ACC have been reported et al. 2001 ; VanderWerf et al. 2002 ; Ioannou 2003 ; Davis ; Ioannou Stefanovic 2005 ; van et al. 2006 ; Kesting et al. 2008 ). puzzling fact points to the when investigating mixed consisting of human drivers and controlled vehicles: how to describe and automated driving and their appropriately?

The intelligent driver (IDM) (Treiber et al. 2000) to be a good basis for the development of an ACC The IDM shows a crash-free collective exhibits controllable stability (Helbing et al. 2009 ) and implements an braking strategy with transitions between acceleration and behaviour. Moreover, it has only six with a concrete meaning, makes them measurable. the IDM was originally developed as a simple model for one-lane situations. to lane changes (‘cut-in’ the input quantities change in a way, in which the new distance to the can drop significantly below the equilibrium distance, particularly if is dense or congested traffic, the change is mandatory or if drivers different conceptions of safe This may lead to strong manoeuvres of the IDM, which not be acceptable (nor possible) in a ACC system.

In this paper, we therefore the IDM by a new constant-acceleration heuristic (CAH), implements a more relaxed to cut-in manoeuvres without the mandatory model property of essentially crash free. model extension has already implemented (with some confidential extensions) in real cars (Kranke et al. 2006 ; Poppe 2008 ). The ‘ACC presented can be considered as an abstraction of the of physical ACC vehicles. It eliminates all the details (physical layer), but the overall properties regarding and capacity. Large-scale simulations the proposed model will lead to relevant and valid regarding the impact of recently ACC vehicles on traffic flow. In the part of this contribution, we the enhanced IDM to multi-lane traffic in which we study the collective of mixed traffic flows of human drivers and ACC systems. The equipped with ACC systems a recently proposed traffic-adaptive strategy (Kesting et al. 2008 ), is realized by a situation-dependent parameter for each vehicle.

Our paper is as follows. In §2, we will present an heuristic of the IDM particularly suited for simulations. Section 3 presents driving strategies for ACC systems. The of temporarily changed model on the relevant traffic capacities in traffic flows will be evaluated by simulations in §4. Finally, we conclude with a discussion in §5.

2. A for ACC vehicles

In this section, we develop the model equations of the IDM. To do this, we will present the relevant aspects of the IDM (Treiber et al. 2000 ) in §2 a . in most situations, the IDM describes and decelerations in a satisfactory way, it can to unrealistic driving behaviour if the vehicle gap is significantly lower the desired gap and, simultaneously, the can be considered as only mildly

Therefore, in §2 b . we develop an limit of a safe acceleration on the more optimistic CAH, in drivers assume that the vehicle will not change its for the next few seconds. This is applicable precisely in these where the IDM reacts too strongly. c . we combine the IDM and CAH accelerations to specify the function of the final model for ACC (‘ACC model’) such the well-tested IDM is applied whenever it to a plausible behaviour, using the a CAH − a IDM as an indicator for plausibility. Finally, the of the new model are tested by computer in §2 d .

(a) Intelligent driver model

The IDM is a continuous function incorporating driving modes for all velocities in traffic as well as city Besides the (bumper-to-bumper) distance s to the vehicle and the actual speed v . the IDM takes into account the difference (approaching rate) Δv = v − v l the leading vehicle. The IDM acceleration is given by 2.1 and 2.2 This expression the free-road acceleration strategy a deceleration strategy that relevant when the gap to the leading is not significantly larger than the ‘desired (safe) gap’ s *( v , Δv ). The acceleration is characterized by the desired v 0 . the maximum acceleration a and the exponent δ how the acceleration decreases with ( δ =1 corresponds to a linear decrease denotes a constant acceleration). The minimum gap s * is composed of the minimum s 0 (which is relevant for low velocities the velocity-dependent distance vT . which to following the leading vehicle a constant desired time gap T . and a contribution, which is only in non-stationary traffic corresponding to in which Δv ≠0. This last implements an ‘intelligent’ driving that, in normal situations, braking decelerations to the comfortable b . In critical situations, however, the IDM becomes significantly higher, the IDM collision free (Treiber et al. ). The IDM parameters v 0 . T . s 0 . a and b (table 1 ) have a interpretation, are known to be relevant, are measurable and have realistic (Kesting Treiber 2008 a ).

(b) Constant-acceleration heuristic

The braking of the IDM is developed such that are avoided even in the worst . where the driver of the leading suddenly brakes with the possible deceleration b max ≫ b to a complete Since the IDM does not include reaction times, it is even when the time headway T is set to zero. 1

However, there are characterized by comparatively low-velocity and gaps that are significantly than the desired gaps, this worst-case heuristic to over-reactions. In fact, human simply rely on the fact the drivers of preceding vehicles not suddenly initiate full-stop brakings without any reason therefore, consider such as only mildly critical. this judgement is correct. the frequent observations of accident-free at time headways significantly 1 s, i.e. below the time of even an attentive would not be observed so frequently et al. 2006 b ). Moreover, drivers may for their delayed reaction by (Treiber et al. 2006 a ).

In order to this more optimistic of drivers, let us investigate the implications of the CAH on acceleration. The CAH is based on the following

— The accelerations of the vehicle consideration and the leading vehicle not change in the relevant future a few seconds).

— No safe headway or minimum distance is at any moment.

— Drivers react delay (zero reaction

When calculating the maximum for which the situation remains free, one needs to distinguish the velocity of the leading vehicle is or non-zero at the time when the gap (i.e. s =0) is reached. For given values of the gap s . velocity v . velocity v l of the vehicle, and its acceleration a l . the maximum a CAH leading to no crashes is given by 2.3 the effective acceleration has been to avoid artefacts that may be by leading vehicles with acceleration capabilities. The condition v l ( v − v l )= v l Δv ≤−2 sa l is if the vehicles have stopped at the the minimum gap s =0 is reached. Otherwise, approaching rates do not make to the CAH and are therefore eliminated by the Heaviside function Θ .

In figure 1 b . the CAH acceleration (2.3 ) has been for a leading vehicle driving at a velocity. A comparison with a clearly shows that, for values of the gap s . the CAH acceleration is significantly (i.e. less negative) that for the IDM.

Dropped and customize vw velocity golf

Acceleration ( a ) of the IDM, ( b ) resulting from the CAH and ( c ) of the proposed ACC model as a function of the gap s and the difference (approaching rate) Δv the leading vehicle. The velocity of the vehicle and its acceleration a l are given by v l = −1 and a l =0, respectively.

(c) The ACC model

For the situations the IDM leads to unnecessarily strong reactions, the CAH acceleration is significantly corresponding to a more relaxed This heuristic, however, on the other side and therefore is not to directly model the accelerations of ACC Specifically, the CAH leads to zero for some cases that require at least a moderate reaction. This includes a car-following situation ( Δv =0, a l =0), a CAH =0 for arbitrary values of the gap s and velocity v b ). Moreover, since the CAH does not minimum time headways or an to a desired velocity, it does not in a complete model.

For the actual of a model for ACC vehicles, we will use the CAH only as an indicator to determine the IDM will lead to unrealistically decelerations, or not. Specifically, the ACC model is based on the following

— The ACC acceleration is never than that of the IDM. is motivated by the circumstance that the IDM lead to crash-free vehicle for all simulated situations.

— If the IDM and the CAH produce the same acceleration, the ACC is the same as well.

— If the IDM extreme decelerations, while the CAH accelerations in the comfortable range than − b ), the situation is considered to be critical at most, and the ACC acceleration above the CAH acceleration minus the deceleration.

— If both the IDM and the CAH result in significantly below − b . the situation is critical and the ACC acceleration must not be than the maximum of the IDM and CAH accelerations.

ACC acceleration should be a continuous and function of the IDM and CAH accelerations.

Probably, the simple functional form these criteria is given by ) 2.4 This acceleration equation of the ACC is the main model-related result of paper. Figure 1 shows the conditions listed above are Notably, the ACC model leads to relaxed reactions in situations in the IDM behaves too conservatively. In contrast to the the acceleration depends not only on the gap to and the of the leading vehicle, but (through a CAH ) on the acceleration a l of this vehicle as This leads to a more driving behaviour when congested traffic (reaction to lights’), but also to a more behaviour in typical cut-in where a slower vehicle to the fast lane (e.g. in to overtake a truck) while vehicle in the fast lane is from behind.

Compared the IDM parameters, the ACC model contains one additional model parameter c . can be interpreted as a coolness factor . For c =0, the reverts to the IDM, while for c =1 the with respect to changes in the gap in situations with small and no velocity difference. This that the behaviour would be too In this paper, we have c =0.99 (see table 1 ).

(d) the properties of the ACC model


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