Matthias Knauer

Fast and save container cranes as bilevel optimal control problems

For the use of container cranes in high rack warehouses, reference trajectories can be obtained from optimal control problems in order to control the swinging of the crane system during the fast movement and in order to reach an equilibrium position at the end of the trajectory. Safety requirements extend these problems to bilevel optimal control problems, where the existence of alternative stop trajectories has to be guaranteed. A method as to how these complex problems can be reduced to conventional optimal control problems, even under control and state constraints, is presented together with numerical examples.

Optimal Guidance and Control of Lunar Landers with Non-throttable Main Engine

Autonomous soft, safe and precise landing on celestial bodies like the Moon, planets and asteroids is still a challenging task for future exploration missions. To achieve a maximum of payload mass landed on the target body the trajectories of landing vehicles need to be (fuel) optimized. In order to allow an adjustability of the trajectory and a compensation of disturbances for all vehicles so far a thrust modulation is required. The drawback is that currently no main engine is available which allows the needed thrust modulation for an efficient, robust and safe landing on a celestial body like the Moon. The technology of the Apollo missions is not available anymore.Most planned lunar missions rely on the modulation capability of multiple engines where in some cases the thrust of the auxiliary engines for modulation is in the order of main engine thrust. This approach requires a large number of smaller engines to achieve the needed thrust modulation adding complexity and increasing the probability of failure.

Hybrid Solution Methods for Bilevel Optimal Control Problems with Time Dependent Coupling

To operate crane systems in high rack warehouses, reference trajectories have to ensure that the swinging of the crane is under control during the fast movement and disappears at the final point. These trajectories can be obtained solving optimal control problems.

Optimization of Satellite Constellations

Constellations of satellites are used for a steady and efficient monitoring of selected regions of the Earth.

Bilevel Optimization of Container Cranes

Bilevel optimal control problems are presented as an extension of classical optimal control problems. Hereby, additional constraints are considered for the primary problem, which depend on the optimal solutions of secondary optimal control problems.

Optimal routing of pipes in a virtual environment using nonlinear programming

Abstract Nowadays the routing of pipes inside or outside of structural components is usually done with CAD tools like CATIA. Up to now it is the task of design-engineers to manually find a connection between two points in which on one hand respects all design directives and on the other hand minimises the weight of the pipe. As in general the number of feasible routings is very high, if not infinite, it is almost impossible to find an optimal solution without a powerful algorithm and an immense amount of development time. This paper presents a mathematical framework which allows the designer to automatically generate the optimal routing. To do so, the aforementioned problem is treated as an optimisation problem. With the mass of the pipe as the cost function to be minimised and the design directives handled as equality and inequality constraints, this leads to a nonlinear problem (NLP) which is solved by WORHP – a large-scale sparse NLP solver. A series of practically relevant scenarios like routings close to structural components, routings with standard bending angles as well as network routings for metallic and non-metallic pipes are investigated. First tests with real assemblies reveal that a significant reduction of the total mass is achieved by optimising the existing routing.