Research Colloquium: Lectures by Professor Anton Tkachuk and Professor Valter Böhm

As part of the research colloquium, we cordially invite you to two lectures on the fascinating and aesthetic tensegrity structures:

Prof. Dr.-Ing. Anton Tkachuk (Karlstad University, Sweden):

Form-finding of tensegrity structures via rank minimization formulations: relaxations, examples and limitations

and

Prof. Dr.-Ing. Valter Böhm (OTH Regensburg):

A contribution to possibilities of realizing multistable tensegrity structures in connection with compliant robotic systems and shape-adaptive structures

Tuesday, 16.07.2024, at 17.00 in room 3516 (Mönchebergstr. 7)

We look forward to seeing you there and are looking forward to an interesting scientific exchange!

Prof. Dr.-Ing. Anton Tkachuk : Form-finding of tensegrity structures via rank minimization formulations: relaxations, examples and limitations
The form-finding process for tensegrity structures with a given topology seeks a distribution of force densities that primarily satisfy stability and equilibrium conditions. A new idea for form-finding that utilizes a rank minimization problem regarding the force density matrix can yield feasible distributions of force densities. The rank minimization problem is solved via proper relaxations or heuristics. In a recent contribution, Wang et al. propose to use the trace heuristic for form-finding of tensegrity structures. Like any other heuristic, the trace heuristic does not guarantee recovery of the globally minimal rank. Insufficient rank deficiency makes recovery of proper geometry of tensegrity impossible, i.e. it leads to a degenerated geometry of the tensegrity. The latter form-finding approach is extended to the log-det heuristic initially proposed for other applications. Additionally, the robustness of the form-finding procedure for tensegrities using trace and log-det heuristics is compared. The robustness of the form-finding procedure is understood here as the ability to recover at least one feasible tensegrity design. Several examples show that the robustness is mainly influenced by the topology of the structure, constraints on force densities, and the admissible set for force densities. Furthermore, several ways to reduce computational costs are highlighted. Considered examples are implemented in the open-source Matlab package for disciplined convex programming CVX paired with two open-source semi-define program solvers: SDPT3 and SeDuMi.

Prof. Dr.-Ing. Valter Böhm: A contribution to the possibilities of realizing multistable tensegrity structures in connection with compliant robot systems and shape-adaptive structures
The lecture presents various possibilities of realizing tensegrity structures with several stable equilibrium configurations. Furthermore, possibilities for form finding as well as inspirations for the realization of shape-adaptive structures and compliant robot systems based on these structures are shown by means of examples.