125 years after Bertha Benz completed the first overland journey in automotive history, the Mercedes Benz S-Class S 500 INTELLIGENT DRIVE followed the same route from Mannheim to Pforzheim, Germany, in fully autonomous manner. The autonomous vehicle was equipped with close-toproduction sensor hardware and relied solely on vision and radar sensors in combination with accurate digital maps to obtain a comprehensive understanding of complex traffic situations. The historic Bertha Benz Memorial Route is particularly challenging for autonomous driving. The course taken by the autonomous vehicle had a length of 103 km and covered rural roads, 23 small villages and major cities (e.g. downtown Mannheim and Heidelberg). The route posed a large variety of difficult traffic scenarios including intersections with and without traffic lights, roundabouts, and narrow passages with oncoming traffic. This paper gives an overview of the autonomous vehicle and presents details on vision and radar-based perception, digital road maps and video-based self-localization, as well as motion planning in complex urban scenarios.

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Abstract-Active safety systems hold great potential to reduce the accident frequency and severity, by warning the driver and/or exerting automatic vehicle control ahead of crashes. This paper presents a novel active pedestrian safety system, which combines sensing, situation analysis, decision making and vehicle control. The sensing component is based on stereo vision; it fuses two complementary approaches for added robustness: motion-based object detection and pedestrian recognition. The highlight of the system is the ability to decide within a split second whether to perform automatic braking or evasive steering, and to execute this maneuver reliably, at relatively high vehicle speeds (up to 50 km/h).We performed extensive pre-crash experiments with the system on the test track (22 scenarios with real pedestrians and a dummy). We obtained a significant benefit in detection performance and improved lateral velocity estimation by the fusion of motion-based object detection and pedestrian recognition. On a fully reproducible scenario subset, involving the dummy entering laterally into the vehicle path from behind an occlusion, the system executed in over 40 trials the intended vehicle action: automatic braking (if a full stop is still possible) or else, automatic evasive steering.

In this paper we discuss novel numerical schemes for the computation of the curve shortening and mean curvature flows that are based on special reparametrizations. The main idea is to use special solutions to the harmonic map heat flow in order to reparametrize the equations of motion. This idea is widely known from the Ricci flow as the DeTurck trick. By introducing a variable time scale for the harmonic map heat flow, we obtain families of numerical schemes for the reparametrized flows. For the curve shortening flow this family unveils a surprising geometric connection between the numerical schemes in [5] and [9]. For the mean curvature flow we obtain families of schemes with good mesh properties similar to those in [3]. We prove error estimates for the semi-discrete scheme of the curve shortening flow. The behaviour of the fully-discrete schemes with respect to the redistribution of mesh points is studied in numerical experiments. We also discuss possible generalizations of our ideas to other extrinsic flows.

In this paper we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is suitable for the study of deformations of cell membranes induced by the cytoskeleton. We describe the deformation of the surface as a graph over the undeformed surface. A new Lagrangian and the associated Euler-Lagrange equations for the height function of the graph are derived. This is the natural generalisation of the well known linearisation in the Monge gauge for initially flat surfaces. We discuss energy perturbations of point constraints and point forces acting on the surface. We establish existence and uniqueness results for weak solutions on spheres and on tori. Algorithms for the computation of numerical solutions in the general setting are provided. We present numerical examples which highlight the behaviour of the surface deformations in different settings at the end of the paper.