Compound Ellipsotopes for Control

In order to represent autonomous cyber-physical systems (such as autonomous vehicles, robots, etc.), these need to be modeled using a geometric set representation amenable to numeric computations, for instance to compute/predict the trajectory of the system. Several such representations exist in the literature, such as polytopes, zonotopes, ellipsoids, etc. Ellipsotopes are a relatively recent kind of representation, that can be seen as an intermediate between zonotopes and ellipsoids (they are defined in the same fashion as zonotopes, but can have curved facets). In this study, we propose to analyze compound ellipsotopes, which can be seen as the sum of basic ellipsotopes. This has applications in reachability analysis and trajectory planning, as set computations in those areas often rely on adding two sets together, an operation that until now could only be performed in an approximative manner, which compound ellipsotopes aim to avoid.

The topic of this thesis sits at the intersection between numerical methods, optimization theory, complexity theory, logic, and some programming in MATLAB will be expected. Proficiency in all aspects is not necessary, but the applicant should bring some solid knowledge in linear algebra.

For more information, please reach out to adrian.kulmburg@kit.edu.