Abstract: Automation and autonomy becomes more and more important in many robotics applications, especially for mobile robots, which move automatically in a production site, for automated cars, which move in the traffic, or in space robotics. These mobile robots typically do not just follow a precomputed reference path, but they need to be able to update their trajectories in order to react on changing environments. This typically requires a feedback control strategy, which takes into account the current state of the robot and the environment. To this end we employ a model-predictive control (MPC) strategy, which requires to solve (discretized) optimal control problems repeatedly. We discuss suitable optimal control methods and address issues like real-time capability. Based on these methods we suggest two path planning approaches for the control of interacting systems. The first approach uses generalized Nash equilibrium problems, which allow to model the coordination of automated agents without using pre-defined priorities. The second approach couples scheduling tasks with optimal control and leads to a bi-level optimization problem. Numerical experiments and case studies will be presented to illustrate the methods.
Bio: Prof. Dr. Matthias Gerdts studied Mathematics with minor Computer Science at the University of Technology Clausthal, Germany, and graduated in 1997. He received his doctoral degree in 2001 and his Habilitation in 2006 from the University of Bayreuth, Germany. In 2003 he was a visiting professor at the University of California, San Diego. From 2004 to 2007 he held a junior professorship for numerical optimal control at the Department of Mathematics of the University of Hamburg, Germany, and moved to a lecturer position for mathematical optimization at the University of Birmingham, U.K., from 2007 to 2009. From 2009 to 2010 he was an associate professor for optimal control at the University of Wurzburg, Germany. Since 2010 he is a full professor for engineering mathematics at the Department of Aerospace Engineering of the Bundeswehr University Munich, Germany. His primary research interests are optimal control, optimization techniques, model-predictive control, differential algebraic equations, and sensitivity analysis with applications in automotive systems, robotics, and aerospace engineering. Prof. Gerdts served as a principal investigator in various projects funded by national and international science organizations and industry. He is author of more than 80 publications in journals, book chapters, and proceedings. Moreover, he authored two textbooks, one on Optimal Control of ODEs and DAEs and the other one on Mathematical Optimization Methods of Operatios Research (in German, co-authored by Frank Lempio), both being published by DeGruyter in 2011. He is a member of the editorial boards of Optimization - A Journal of Mathematical Programming and Operations Research" (Taylor & Francis) and Differential-Algebraic Equations Forum" (Springer).
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