A Foresighted Driver Model derived from Integral Expected Risk

Abstract

Current efforts in Advanced Driver Assistant Systems and Autonomous Driving research target at making the vehicles more intelligent, in terms of understanding what is going on and selecting the most appropriate behaviors. A crucial element of this research is the prediction of the evolution of the current driving situation with microscopic driver models. In this paper we present a microscopic driver model with a gradientlike, simple behavior generation that is fully and concisely derived from mathematical risk theory. Following this model, drivers act by estimating the expected, integral future risks and benefits and by seeking the best instantaneous tradeoff between these quantities, choosing the immediate action that reduces the hypothetical risks in the most efficient way. We show how this model is able to incorporate different risk types and situation parameters, allowing an extension and generalization to variable scenarios.

Time-Course Sensitive Collision Probability Model for Risk Estimation

“…( 9) to calculate the integral probabilities and risk contributions (see e.g. [15]) involved in a planned, predicted ego-vehicle trajectory, simply by adding over all the event contributions (e.g. all other vehicles which might collide) future time,…”

“…This becomes clear observing that the relevant quantity for calculating the collision probability is not the total probability within the collision area (15), but instead the amount of probability that moves into the collision area over time when the scenario evolves, given by the probability density flow into the collision area, i.e., the inbound flux of p d,ij (d ij ) over the collision area boundary dΩ ij . The flux originates by both p d,ij (d ij ) and Ω ij changing over time, the first because of e.g.…”

“…The interesting point is that in several previous approaches [15], [16], P ov,ij (t) was used directly (without truncation) to calculate the collision probability, which leads to effects which are inconsistent with real driving behavior, because colliding states survive for the next risk calculations. The question is now, how can we use (16) with truncation to derive fast and analytic approaches to calculate an improved estimate for collision risk probability.…”

“…The truncated pdf is then used as input pdf p d,ij (d ij ) for the next truncation. To calculate the P ov,ij for (15), we multiply all overlap collision probabilities P ov (eq. ( 19)) gained from the different truncation processes, where we use both finite borders α + and α − for parallel collision area edges.…”

“…To address this, the Survival Theory, described in [14], provides a probabilistic model for the time-course-sensitive probability reduction along the prediction time. This was used in [15], [16] for the construction of a simple integral risk-based motion planner capable of handling a range of parallel lane scenarios with multiple vehicles based on incremental utility, risk and comfort terms. Other works incorporate the prediction time-course by the incremental extraction of already collided parts of a distribution.…”