Stochastic hybrid models for predicting the behavior of drivers facing the yellow-light-dilemma

We address the problem of predicting whether a driver facing the yellow-light-dilemma will cross the intersection with the red light. Based on driving simulator data, we propose a stochastic hybrid system model for driver behavior. Using this model combined with Gaussian process estimation and Monte Carlo simulations, we obtain an upper bound for the probability of crossing with the red light. This upper bound has a prescribed confidence level and can be calculated quickly on-line in a recursive fashion as more data become available. Calculating also a lower bound we can show that the upper bound is on average less than 3% higher than the true probability. Moreover, tests on driving simulator data show that 99% of the actual red light violations, are predicted to cross on red with probability greater than 0.95 while less than 5% of the compliant trajectories are predicted to have an equally high probability of crossing. Determining the probability of crossing with the red light will be important for the development of warning systems that prevent red light violations

Design of Driver-Assist Systems Under Probabilistic Safety Specifications Near Stop Signs

In this paper, we consider the problem of designing in-vehicle driver-assist systems that warn or override the driver to prevent collisions with a guaranteed probability. The probabilistic nature of the problem naturally arises from many sources of uncertainty, among which the behavior of the surrounding vehicles and the response of the driver to on-board warnings. We formulate this problem as a control problem for uncertain systems under probabilistic safety specifications and leverage the structure of the application domain to reach computationally efficient implementations. Simulations using a naturalistic data set show that the empirical probability of safety is always within 5% of the theoretical value in the case of direct driver override. In the case of on-board warnings, the empirical value is more conservative due primarily to drivers decelerating more strongly than requested. However, the empirical value is greater than or equal to the theoretical value, demonstrating a clear safety benefit

Controller design under safety specifications for a class of bounded hybrid automata

Motivated by driver-assist systems that warn the driver before taking control action, we study the safety problem for a class of bounded hybrid automata. We show that for this class there exists a least restrictive safe feedback controller that has a simple structure and can be computed efficiently online. The theoretical results are then used to design driver-assist systems for rear-end and merging collision scenarios.National Science Foundation (U.S.). Cyber-Physical Systems (Award number 1239182

Safety control of a class of stochastic order preserving systems with application to collision avoidance near stop signs

In this paper, we consider the problem of keeping the state of a system outside of an undesired set of states with probability at least P. We focus on a class of order preserving systems with a constant input disturbance that is extracted from a known probability distribution. Leveraging the structure of the system, we construct an explicit supervisor that guarantees the system state to be kept outside the undesired set with at least probability P. We apply this supervisor to a collision avoidance problem, where a semi-autonomous vehicle is engaged in preventing a rear-end collision with a preceding human-driven vehicle, while stopping at a stop sign. We apply the designed supervisor in simulations in which the preceding vehicle trajectories are taken from a test data set. Using this data, we demonstrate experimentally that the probability of preventing a rear-end collision while stopping at the stop sign is at least P, as expected from theory. The simulation results further show that this probability is very close to P, indicating that the supervisor is not conservative.National Science Foundation (U.S.) (award #1161893