Modelling and Control of Tensegrity Structures

This thesis contains new results with respect to several aspects within tensegrity research. Tensegrity structures are prestressable mechanical truss structures with simple dedicated elements, that is rods in compression and strings in tension. The study of tensegrity structures is a new field of research at the Norwegian University of Science and Technology (NTNU), and our alliance with the strong research community on tensegrity structures at the University of California at San Diego (UCSD) has been necessary to make the scientific progress presented in this thesis. Our motivation for starting tensegrity research was initially the need for new structural concepts within aquaculture having the potential of being wave compliant. Also the potential benefits from controlling geometry of large and/or interconnected structures with respect to environmental loading and fish welfare were foreseen. When initiating research on this relatively young discipline we discovered several aspects that deserved closer examination. In order to evaluate the potential of these structures in our engineering applications, we entered into modelling and control, and found several interesting and challenging topics for research. To date, most contributions with respect to control of tensegrity structures have used a minimal number of system coordinates and ordinary differential equations (ODEs) of motion. These equations have some inherent drawbacks, such as singularities in the coordinate representation, and recent developments therefore used a non-minimal number of system coordinates and differential-algebraic equations (DAEs) of motion to avoid this problem. This work presents two general formulations, both DAEs and ODEs, which have the ability to choose the position on rods the translational coordinates should point to, and further constrain some, or all of these coordinates depending on how the structural system should appear. The DAE formulation deduced for tensegrity structures has been extended in order to simulate the dynamics of relatively long and heavy cables. A rigid bar cable (RBC) model is created by interconnecting a finite number of inextensible thin rods into a chain system. The main contribution lies in the mathemati-

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