Driver Assisting by Inverse Time to Collision

Copyright - World Aut om at ion Congress ( WAC) 2006, July 24- 26, Budapest , Hungary DRIVER ASSISTING BY INVERSE TIME TO COLLISION VALENTINA E. BALAS, MARIUS M. BALAS “AUREL VLAICU” UNIVERSITY OF ARAD, ROMANIA balas@inext.ro ABSTRACT The paper is proposing a specific indicator, the inverse time to collision TTC-1, useful when analyzing the highway traffic. The advantage of TTC-1 vs. TTC is a direct and continuous dependence with the collision risk. TTC-1 could be used as an input in car following algorithms. Because the automate driving is yet in a research stage, a feasible application for TTC-1 would be rather assisting the driver of the following car at the choice of the distance gap towards the first car. KEYWORDS: Time to collision, Time to collision trajectory, Inverse time to collision. 1. INTRODUCTION The field of automate driving is developing very fast, by different methods as the Autonomous Intelligent Cruise Control (AICC) or the Collision Avoidance Systems (CAS) [1], [2]. A set of facilities with different degrees of implication in the driving action is introduced by the Advance Driver Assistance Systems (ADAS) [3], etc. Yet, despite the safety benefits: enhanced driving performance and minimization of crash risks, reduced driver stress and fatigue, reduced conflicts and variance in behavior, etc. the effective put in practice of these developments will have to wait. The causes are economic, namely the high costs demanded by the infrastructure and the equipment installed on each car, but also technical. Automate driving is likely to produce at its turn safety risks by the driver distraction and reduced situation awareness, causing in time the reducing of the driving skill. But above all, any automate intervention into the car’s operation can cause instinctive and inopportune reactions of the driver. That is why automate driving applications will probably face a transition period. A common sense approach assumes a gradual introduction of the automate features and the abortion of the automate mode at the slightest human intervention. A productive approach is to use of the automate features in the sense of assisting and advising the driver [4]. In the car following case, several indicators were introduced in order to measure the characteristics of the traffic flow: the time-to-collision (TTC), the time-to-accident (TTA), the post-encroachment-time (PET), the deceleration-to-safety-time (DTS), the number of shockwaves, etc. TTC is the time that it takes before the following Car2 collide with the previous Car1, assuming unchanged speeds of both vehicles during this approach [3]. The paper intends to introduce a slightly different analyze tool in this issue: TTC-1, the inverse TTC. A case study is illustrating the utility of TTC-1: a linguistic decision making assistant concerning the distance gap between following cars. 2. THE TIME TO COLLISION TRAJECTORIES We will consider TTC as TTC = d v 2 − v1 (1) where v1 and v2 are the speeds of Car1 and Car2 and d is the distance gap between the cars. The time evolution of TTC is offering valuable information about traffic’s safety. Small positive TTCs mean that d is decreasing and a collision is imminent while negative TTCs mean that d is increasing. A simulation with the following data will exemplify TTC: - Car 1 and Car 2 are identical; they are weighting 1200kg; - The highest driving and braking force involved are equal to ±3kN; - The distance controller that is controlling Car 2 is slightly distorted in order to obtain a diversified and illustrative behavior of the system. The evolution of the two cars is presented in fig. 1. V2 150 V1 & V2 V1 100 50 0 0 20 40 60 0 20 40 60 80 100 120 140 80 100 120 140 30 25 d [m] 20 15 10 5 0 t [s] Figure 1. A car following simulation TTC’s time evolution is shown in fig. 2. Because of the discontinuity caused by the denominator when v1 - v2 = 0, TTC is presenting a totally inadequate behavior for on-line automate manipulation: frequent commutations between ±∞. The TTC values were artificially bounded at ±40s, still significant TTC information is not available all the time. That is why TTC is usually replaced by another meaningful trajectory: the d(v1 - v2), presented in fig. 3. However d(v1 - v2) is not very suggesting when evaluating the collision risk. That is why it worth introducing the Inverse Time to Collision TTC-1. The derived TTC-1 is presented in fig. 4. This time TTC-1 is proportional to the collision risk: the higher is TTC-1 the higher is the risk. Negative TTC-1s have the same significance as negative TTCs. The zone close to TTC-1 = 0 is corresponding to the TTC’s saturation so it is not sensitive. The TTC-1(v1 - v2) trajectory may also be used, as in fig. 5. 40 30 20 TTC [s] 10 0 -1 0 -2 0 -3 0 -4 0 0 20 40 60 80 100 120 140 t [s ] Fig. 2. The time evolution of TTC 30 25 d [m] 20 15 10 5 0 -8 -6 -4 -2 0 V 2 -V 1 [km /h] Fig. 3. The d(v2 – v1) trajectory 2 4 0.1 1 / TTC [1/s] 0.05 0 -0.05 -0.1 0 20 40 60 80 100 120 140 t [s] Fig. 4. The time evolution of TTC-1 H IG H E S T D A N G E R 0.1 1 / TTC [1/s] 0.05 0 -0.05 -0.1 -4 -2 0 2 4 V 2 -V 1 [km /h] Figure 5. The TTC-1(v2 – v1) trajectory 6 8 3. USING TTC-1 IN SAFETY DRIVING SYSTEMS Since the significance of TTC-1 is clear, this index can be used as an input variable in more comprehensive decision-making systems dedicated to the improvement of the traffic safety. The TTC-1 universe of discourse can be classified in four significant zones, with implications for the driver’s attitude: - Negative: any action is permitted; - Zero: preserving the trend is recommended, no interdictions; - Positive small: easy braking is recommended; - Positive great: hard braking is compulsory. These regimes may be attached to specific colors, in order to provide the advices to the driver in a very friendly and simple manner: - Negative: blue; - Zero: green; - Positive small: yellow; - Positive great: red. The four linguistic labels may be non-fuzzy or fuzzy, according to the conception of the application. The simulations and the experimental tests are leading to the correct settings. In figure 6 the definition of the four fuzzy linguistic labels is based on the TTC-1(v2 – v1) trajectory. The positive great TTC-1 is not including the values that are reached during oscillatory regimes that can occur at low speeds because of the distorted controller. Positive small Zero 0.1 0.05 1 / TTC [1/s] Positive great 0 -0.05 Negative -0.1 -4 -2 0 2 V2-V1 [km/h] Figure 6. A TTC-1 fuzzy partition TTC-1 is fully compatible to the adaptive cruise control concept [6]. 4 6 8 4. CONCLUSIONS The inverse time to collision TTC-1 presents a useful feature when comparing it to TTC: a direct and continuous dependence with the collision risk. Using TTC-1 when analyzing the highway traffic could produce more transparent conclusions. The control rules including TTC-1 are equally very simple. Because the automate driving is yet in a research stage, the most immediate and feasible application for TTC-1 could be its inclusion in decision making systems dedicated to the assisting and advising of the drivers. 5. REFERENCES [1] K.M. Passino, “Intelligent Control for Autonomous Systems”, IEEE Spectrum, June 1995, pp. 55-62. [2] A.R. Girard, J. Borges de Sousa, J.A. Misener and J. K. Hendrick, “A Control Architecture for Integrated Cooperative Cruise Control and Collision Warning Systems”, http://path.berkeley. edu/ ~anouck/papers/cdc01inv3102.pdf [3] M.M. Minderhoud and S.P. Hoogendoorn, “Extended Time-to-Collision Safety Measures for ADAS Safety Assessment”, 5th International Conference on Technology, Policy and Innovation, Delft, Netherlands, 26-29 June, 2001, C3-2. [4] P. Protzel, R. Holve, J. Bernach, K. Naab, “Fuzzy Distance Control for Intelligent Vehicle guidance”, http://citeseer.ist.psu.edu/318524.html. [5] B. Riley, G. Kuo, B. Schwartz, J. Zumberge, “Development of a Controlled Braking Strategy for Vehicle Adaptive Cruise Control”, Proc. of SAE 2000 World Congress, Detroit, U.S.A., 6-9 March, 2000, Reprinted in Brake Technology: ABS/TCS Systems, NVH, and Foundation Brakes, pp. 1-6. [6] P. Clarke, “Adaptive Cruise Control Takes to the Highway”, EE Times, 28 Oct, 1998, http://www.eetimes.com/story/OEG19981020S0007.