This paper presents an algorithm for overapproximating the drivable area of road vehicles in the presence of time-varying obstacles. The drivable area can be used to detect whether a feasible trajectory exists and in which area one can limit the search of drivable trajectories. For this purpose we abstract the considered road vehicle by a point mass with bounded velocity and acceleration. Our algorithm calculates the reachable occupancy at discrete time steps. At each time step the set is represented by a union of finitely many sets which are each the Cartesian product of two 2-dimensional convex polytopes. We demonstrate our method with three examples: i) a traffic situation with identical dynamic constraints in x-and y-direction, ii) a highway scenario with different lateral and longitudinal constraints of the dynamics and iii) a highway scenario with different traffic predictions. The examples demonstrate, that we can compute the drivable area quickly enough to deploy our approach in real vehicles.

The hybrid nature of optoacoustic imaging might impose limitations on concurrent placement of optical and ultrasonic detection components, especially in high resolution microscopic applications that require dense arrangements and miniaturization of components. This hinders optimal deployment of the optical excitation and ultrasonic detection paths, leading to reduction of imaging speed and spatial resolution performance. We suggest a compact coaxial design for optoacoustic microscopy that allows optimizing both the light illumination and ultrasonic detection parameters of the imaging system. System performance is showcased in phantoms and in vivo imaging of microvasculature, achieving real time operation in two dimensions and penetration of 6 mm into optically dense human tissues.

Collision mitigation and collision avoidance systems in intelligent vehicles reduce the severity and number of accidents. To determine the optimal point in time at which such systems should intervene, time-based criticality metrics such as the Time-To-React (TTR) are commonly used. The TTR describes the last point in time along the current trajectory at which an evasive trajectory exists. In this paper, we present a novel approach to determine the point in time after which it is guaranteed that no evasive maneuver exists, i.e., by using reachable sets, we over-approximate the TTR. Our deterministic upper bound of the TTR can be used to trigger a collision mitigation system or to find a feasible emergency maneuver which avoids the collision. We demonstrate the efficient computation of the tight over-approximated TTR in different urban and rural traffic scenarios, and compare our results to an estimated TTR using an optimization-based trajectory planner.

Motion planning in dynamic traffic scenes is a challenging problem. In particular, since it is unknown during planning whether a certain decision, such as passing another traffic participant on the left or right, will result in a safe and comfortable motion. Exhaustive exploration of all principle driving paths is computationally expensive, so that one typically reverts to heuristics-this, however can be unsatisfactory in situations when the heuristics fail to find a solution although it exists. We address this problem by computing the union of all possible motions for a sequence of high-level decisions (e.g. overtake vehicle on the left and then another one on the right), which we refer to as a driving corridor. Our proposed algorithm is over-approximative, i.e. the union of driving corridors provably encloses all possible motions. Thus, if the set of reachable positions within a driving corridor becomes empty, the corresponding sequence of high-level decisions is infeasible and can be discarded by the motion planner. Driving corridors also facilitate selecting high-level plans: Large driving corridors should be preferred since they provide more opportunities for optimizing motions and are more robust towards unpredicted changes. Numerical examples demonstrate the usefulness of our approach.