URN to cite this document: urn:nbn:de:bvb:703-epub-5054-7
Title data
Riedl, Wolfgang ; Baier, Robert ; Gerdts, Matthias:
Optimization-based subdivision algorithm for reachable sets.
Mathematisches Institut, Universität Bayreuth, Institut für Mathematik und Rechneranwendung, Universität der Bundeswehr in Neubiberg/München
Bayreuth
,
2020
. - 38 S.
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Project information
Project title: |
Project's official title Project's id European Union's Seventh Framework Programme 338508 |
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Project financing: |
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union |
Abstract
Reachable sets for nonlinear control systems can be computed via the use of solvers for optimal control problems. The paper presents a new improved variant which applies adaptive concepts similar to the framework of known subdivision techniques by Dellnitz/Hohmann. Using set properties of the nearest point projection, the convergence and rigorousness of the algorithm can be proved without the assumption of diffeomorphism on a nonlinear mapping. The adaptive method is demonstrated by two nonlinear academic examples and for a more complex robot model with box constraints for four states, two controls and five boundary conditions. In these examples adaptive and non-adaptive techniques as well as various discretization methods and optimization solvers are compared. The method also offers interesting features, like zooming into details of the reachable set, self-determination of the needed bounding box, easy parallelization and the use of different grid geometries. With the calculation of a 3d funnel in one of the examples, it is shown that the algorithm can also be used to approximate higher dimensional reachable sets and the resulting box collection may serve as a starting point for more sophisticated visualizations or algorithms.
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Optimization-based subdivision algorithm for reachable sets. (deposited 30 Jan 2017 07:33)
- Optimization-based subdivision algorithm for reachable sets. (deposited 15 Sep 2020 06:31) [Currently Displayed]