I. Motivation and Introduction
The Advanced Driver Assistance Systems (ADAS) are designed to assist drivers and enhance safety and driving comfort [1], [2]. A class of ADAS which attracted considerable interest and reached the deployment and commercialization stage is adaptive cruise control (ACC) which provides automatic vehicle following capabilities in the longitudinal direction. The goal of ACC is to match the speed of a leading vehicle while keeping safe distance and within certain acceleration constraints for driver comfort. The inter-vehicle spacing is often measured in units of time and is referred to as time headway. It is defined as the time it takes for the vehicle to cover the distance between the two vehicles. Different time headway policies have been proposed by researchers for automatic vehicle following and cruising applications [3]–[12]. In [9], [10] variable time headway (VTH) is proposed. In VTH policies, the time headway increases with the speed of the lead vehicle. A time headway policy based upon traffic flow is used in [11], [12]. These time headway policies are designed for the case of an ego vehicle following a lead vehicle on a straight road. The ego vehicle travelling on a curved path or transitioning from straight road to a sharp curve, needs special attention. There is a need to design a safe vehicle following and cruising system for all road geometric constraints such as curvature, slope, superelevation and lane-width. All automatic vehicle following, and cruising systems rely on on-board sensors for the effective detection and tracking of objects in their environment. Currently, none of the existing sensors based on forward looking beams and vision can tell what is around the curve that is outside the view of the vehicle no matter how accurate they are. So collision avoidance with potential in-path objects not visible by on-board sensors under all possible road geometry characteristics and traffic conditions needs to be addressed. For sharp turns, various methods are proposed to avoid false alarms from objects from the adjacent lanes [13]–[15]. For sharp turns, researchers have focused upon identifying objects in ego vehicle’s path [13]–[15] and limiting lateral acceleration [16], [17]. Little if any research has been done to address the problem of avoiding collision with potentially invisible objects on sharp curves.