A coupling of discrete and continuous optimization to solve kinodynamic motion planning problems

A new approach to find the fastest trajectory of a robot avoiding obstacles, is presented. This optimal trajectory is the solution of an optimal control problem with kinematic and dynamics constraints. The approach involves a direct method based on the time discretization of the control variable. We mainly focus on the computation of a good initial trajectory. Our method combines discrete and continuous optimization concepts. First, a graph search algorithm is used to determine a list of via points. Then, an optimal control problem of small size is defined to find the fastest trajectory that passes through the vicinity of the via points. The resulting solution is the initial trajectory. Our approach is applied to a single body mobile robot. The numerical results show the quality of the initial trajectory and its low computational cost

A coupling of discrete and continuous optimization to solve kinodynamic motion planning problems

A new approach to find the fastest trajectory of a robot avoiding obstacles, is presented. This optimal trajectory is the solution of an optimal control problem with kinematic and dynamics constraints. The approach involves a direct method based on the time discretization of the control variable. We mainly focus on the computation of a good initial trajectory. Our method combines discrete and continuous optimization concepts. First, a graph search algorithm is used to determine a list of via points. Then, an optimal control problem of small size is defined to find the fastest trajectory that passes through the vicinity of the via points. The resulting solution is the initial trajectory. Our approach is applied to a single body mobile robot. The numerical results show the quality of the initial trajectory and its low computational cost

Task assignment, sequencing and path-planning in robotic welding cells

A workcell composed of a workpiece and several welding robots is considered. We are interested in minimizing the makespan in the workcell. Hence, one needs i) to assign tasks between the robots, ii) to do the sequencing of the tasks for each robot and iii) to compute the fastest collisionfree paths between the tasks. Up to now, task assignment and path-planning were always handled separately, the former being a typical Vehicle Routing Problem whereas the later is modelled using an optimal control problem. In this paper, we present a complete algorithm which combines discrete optimization techniques with collision detection and optimal control problems efficientl

Task assignment, sequencing and path-planning in robotic welding cells

A workcell composed of a workpiece and several welding robots is considered. We are interested in minimizing the makespan in the workcell. Hence, one needs i) to assign tasks between the robots, ii) to do the sequencing of the tasks for each robot and iii) to compute the fastest collision-free paths between the tasks. Up to now, task assignment and path-planning were always handled separately, the former being a typical Vehicle Routing Problem whereas the later is modelled using an optimal control problem. In this paper, we present a complete algorithm which combines discrete optimization techniques with collision detection and optimal control problems efficiently

Exact approaches for designing multifacility buy-at-bulk networks

We study a problem that integrates buy-at-bulk network design into the classical facility location problem. We consider a generalization of the facility location problem where multiple clients may share a capacitated network to connect to open facilities instead of requiring direct links. In this problem, we wish to open facilities, build a routing network by installing access cables of different costs and capacities, and route every client demand to an open facility. We provide a path based formulation and we compare it with the natural compact formulation for this problem. We then design an exact branch-price-and-cut algorithm for solving the path based formulation. We study the effect of two families of valid inequalities. In addition to this, we present three different types of primal heuristics and employ a hybrid approach to effectively combine these heuristics in order to improve the primal bounds. We finally report the results of our approach that were tested on a set of real world instances as well as two sets of benchmark instances and evaluate the effects of our valid inequalities and primal heuristics

The Influence of Different Auditory Stimuli on Attentiveness and Responsiveness in Road Traffic in Simulated Traffic Situations

The use of portable media has become an integral part of our increasingly mobile society. The use of digital audio books is also growing steadily in Germany. The connection between the psychological effect of music of different volumes and rhythms and the change in reaction in road traffic with a corresponding increase in risk behavior, especially when driving, has already been proven in previous studies. Only a few studies are available on the effects of listening to radio plays on reaction behavior and concentration in road traffic as well as on risk behavior among pedestrians and cyclists. In the present study, we have investigated the influences of pop music and a radio play on reaction behavior and thus driving ability during the execution of a traffic psychological test series from the “Wiener Test System”. The central topic deals with the performance of the test subjects in the individual tests. Conclusions are drawn on the reaction behavior and concentration during participation in road traffic and thus the risk of distraction and possible increased risk of accidents. Studies on the influence of auditory stimuli and their effects on concentration and reaction during participation in traffic are of great interest from the point of view of traffic psychology and occupational medicine, since a reduction in the risk of accidents can increase general traffic safety and lead to a decrease in sick leave and therefore fewer absences from work

The influence of different auditory stimuli on attention and responsiveness in road traffic in simulated traffic situations

Die Nutzung portabler Medienabspielgeräte liegt besonders bei jugendlichen Verkehrsteilnehmern im Trend. Die portablen Medien lassen sich zu jeder Zeit in den Alltag integrieren. Mit ihrer Nutzung gehen jedoch eine gewisse Isolierung von der Umwelt und entsprechende psychologische Effekte einher. Beim Hören im Fahrzeug ist der Verkehrsteilnehmer durch die Karosserie akustisch von der Umgebung abgeschirmt. Als Fußgänger oder Fahrradfahrer erfolgt die Abschirmung durch die Nutzung von Kopfhörern. Der Zusammenhang zwischen der psychischen Wirkung verschiedenartig lauter und rhythmischer Musik und der Veränderung der Reaktion im Straßenverkehr mit entsprechend gesteigertem Risikoverhalten speziell beim Autofahren konnte bereits in vorausgegangenen Studien belegt werden. Über die Auswirkungen des Hörens von Hörspielen auf das Reaktionsverhalten und die Konzentration im Straßenverkehrsowie das Risikoverhalten bei Fußgängern und Fahrradfahrern existieren jedoch bislang nur wenige Untersuchungen. In der vorliegenden Arbeit wurden die Einflüsse von Popmusik und eines Hörspielkrimis auf das Reaktionsverhalten und somit die Fahrtauglichkeit während der Durchführung einer verkehrspsychologischen Testreihe aus dem Wiener Testsystem analysiert. Der zentrale Untersuchungsgegenstand ist das Abschneiden der Probandenin den einzelnen Tests. Es werden Rückschlüsse auf das Reaktionsverhalten und die Konzentration während der Teilnahme am Straßenverkehr und somit das Risiko der Ablenkung und der möglichen gesteigerten Unfallgefährdung gezogen. Das Abschneiden in den durchgeführten Tests zeigte in der vorliegenden Studie keine signifikanten Unterschiede zwischen den Probandengruppen.Jedoch konnten Abweichungen im subjektiven Stressempfinden sowie im Abschneiden in den Tests mit zunehmender Testdauer sowie Testschwierigkeit gefunden werden. In der Zusammenschau der Ergebnisse ist eine Erhöhung der Verkehrssicherheit letztlich nur dann zu konstatieren, wenn während der Teilnahme am Straßenverkehr jegliche akustischen Einflüsse über Kopfhörer, egal welcher Art, weggelassen werden. Nur so ist eine ausreichende Konzentration für die Verkehrsteilnahme gegeben. Zukünftige Studien mit größeren Probandenkollektiven sollten sich detaillierter mit der Verarbeitung von Sprachinhalten während der gleichzeitigen Durchführung einer Konzentration erfordernden Aufgabe befassen, da die vorliegende Studie nicht alle individuellen Faktoren, die einen zusätzlichen Einfluss auf das Abschneiden in den Tests haben können, erfassen konnte.The use of portable media players is especially popular among young road users. Download portals for music and audio books are recording continuously rising numbers. It is possible to integrate portable media into our everyday lives at any time. While listening in a car, the road user is acoustically shielded from the environment by the car body. As a pedestrian or cyclist, the acoustic shielding is achieved by the use of headphones. The connection between the psychological effect of different kinds of loud and rhythmic music and the change of the reaction in traffic with an accordingly higher risk behaviour, especially when driving a car, has already been confirmed in previous studies. Until now, few studies on the effect of the reactive behaviour and concentration in road traffic, as well as on the risk behaviour of pedestrians while listening to radio plays have been available. In the present study, we have examined the impacts of pop music and a radio thriller on the reactive behaviour and therefore the driving ability during a series of traffic psychology tests from the “Wiener Testsystem”. The central question dealt with the possible differences in the performance of the test groups in each specific test. Conclusions could be drawn from the reactive behaviour and concentration while taking part in road traffic and therefore the risk of distraction and the potential increased risk of accidents. The test results of our study showed no significant differences between the test groups. Nevertheless, differences could be found in the subjective stress perception as well as in the test performances with increasing test duration and difficulty. Summarizing all the results, a rise in road safety can only be assured by foregoing all acoustic influences by headphones, regardless what kind, while taking part in road traffic. This is the only way to ensure sufficient concentration for the participation in road traffic. Not all individual factors that could have an impact on the test results could be examined in detail. Future studies with bigger groups of test individuals should continue to consider the processing of speech during the performance of a concentration demanding task at the same time, because we could only touch scratch the surface of such complex processes in our present study. The studies on the influence of auditory stimuli and the effects on concentration and responsiveness while taking part in road traffic are of huge interest in traffic psychology and occupational medicine, because a decrease in accident risks leads to an increase of general road safety and therefore to lower health care costs and fewer work-related accidents

Farbbestimiuungen bei patnologischanatomischen Untersuchungen.

Diss. Berlin.OPLADEN-RUG0

Roboter-Tourenplanung mit hohen Explorationskosten : Routing unter Unsicherheit

In der Automobilindustrie spielt die Computerisierung eine immer größer werdende Rolle. Deshalb und aus Kostengründen ist es vorteilhaft, die auftretenden Prozesse mit mathematischen Methoden zu optimieren. Nur so kann auch automatisch sofort auf Änderungen des Produktionsprozesses reagiert werden. In der vorliegenden Arbeit wird hierzu ein Beitrag geleistet, indem sogenannte Schweißzellen studiert werden, in denen mehrere Roboterarme gleichzeitig Schweißpunkte an demselben Werkstück vornehmen. Dabei sind die Touren dieser Schweißroboter so zu planen, dass die notwendigen Schweißpunkte in möglichst kurzer Zeit abgefahren werden, ohne dass es zu Kollisionen zwischen den Robotern kommt. Wissenschaftlich gesehen besteht diese Optimierungsaufgabe, das "Welding Cell Problem", aus Aspekten zweier klassischer Bereiche der Mathematik: Es hat auf der einen Seite Ähnlichkeiten mit dem berühmten "Problem des Handlungsreisenden", in dem eine optimale kollisionsfreie Reihenfolge der Punkte bestimmt werden muss. Auf der anderen Seite enthält es auch klassische Elemente der Bewegungsplanung und -optimierung der Robotik. Im ersten Teil der Arbeit werden die eher praktischen Probleme des Welding Cell Problems untersucht. In diesem Zusammenhang stellen wir einen Algorithmus vor, der die beiden Teile dieses Problems kombiniert, indem die kontinuierliche Bewegungsplanung direkt in den branch-and-price-Prozess des diskreten Teils integriert wird. Da die Trajektorienberechnung rechnerisch viel aufwändiger ist als die diskrete Optimierung, wurde bei diesem Ansatz besonderer Wert darauf gelegt, unnötige Pfadberechnungen zu vermeiden. Dieser Ansatz führt auch zu der wichtigen theoretischen Frage, wie viele dieser Berechnungen im Minimum erforderlich sind um eine optimale Lösung garantieren zu können. Diese Frage wird im zweiten Teil genauer analysiert. Dazu werden einige klassische kombinatorische Probleme (kürzeste Wege, minimal spannende Bäume und das Problem des Handlungsreisenden) in diesem sogenannten Uncertainty-Szenario betrachtet. Am Ende ist es so möglich einen Approximationsalgorithmus für das TSP mit Unsicherheiten anzugeben, der in Erwartung nur O(n) solcher exakter Distanzberechnungen benötigt. Dieses Problem ähnelt dem "U-Bahn-Problem", bei dem das gesamte U-Bahnnetz einer Großstadt in möglichst kurzer Zeit durchfahren werden muss. Im letzten Kapitel beschrieben wir deshalb einen branch-and-cut Algorithmus, der durch das Hinzufügen von Kurzzyklusungleichungen in der Lage ist, eine optimale Lösung des U-Bahn-Problems für eine Metropole - hier am Beispiel von Berlin - in weniger als einer Sekunde zu berechnen.The automotive industry of today is characterized by an increasing importance of computerization and robotic automation. In order to adapt to the highly flexible production as fast as possible, it is crucial to optimize these processes with mathematical methods. In this thesis we study one particular optimization problem as it occurs for welding cells. In these cells several robots perform spot welding tasks on the same component within the cycle time. Given the data of the workpiece, the task is to find a feasible sequence of weld points as well as to arrange the trajectory planning for all robots such that the robot arms do not collide with each other. As for many real-world problems, it is hard to represent this Welding Cell Problem in its entirety by one "scientific" field of research alone. The Welding Cell Problem, on the one hand, has similarities to the famous travelling salesman problem, as it is necessary to determine the best order in which the welding tasks should be processed. On the other hand, it also contains traditional elements of robot motion planning and optimization. In the first part of the thesis the practical aspects of the Welding Cell Problem are discussed. In this context we propose a constraint integer programming formulation that efficiently integrates the robot motion planning into a branch-and-price approach for the underlying routing problem. As the exact trajectory calculations are usually computationally much more expensive, this algorithm focuses on reducing the number of exact trajectory computations required for a feasible solution. Aside from this combination, especially the computational performance of the underlying combinatorial pricing problem is discussed. This integrated approach leads to the important theoretical problem to minimize the number of exact distance queries while, at the same time, the optimality of the solution needs to be maintained. This question is discussed in the second part. We explore several of the most famous combinatorial optimization problems (shortest paths, minimum spanning tree and the Travelling Salesman Problem) within this particular uncertainty setting to combine them into an algorithm that is guaranteed to find an approximation algorithm for the TSP under uncertainty that only requires O(n) edge updates in expectation. This problem relates to the the famous rapid transit challenge, where the entire subway network of a metropolitan area needs to be traversed as fast as possible. Here, techniques that were originally developed in the context of a preprocessing strategy for the Welding Cell Problem can be used for a branch-and-cut approach that uses subtour elimination constraints to compute the optimal tour for the Berlin subway challenge in less than a second