Closed-Loop Control of Tensegrity Structures
In this chapter we address the problem of designing closed loop control algorithms for tensegrity structures. In the literature, most closed-loop control algorithms for tensegrity structures have been developed for planar structures. This is understandable, since dynamic models for planar structures can be obtained using a minimal set of coordinates and ordinary differential equations (see [ASKD03, AS03]). In three dimensions, as shown in Chapter 5, one has to deal with differential-algebraic equations. No minimal ordinary differential equation model is possible. The options are to deal with singularities of the mass matrix, or to describe the system in a non-minimal set of coordinates without singularities, as done in Chapter 5. An additional nontrivial difficulty is to correctly model the strings, which are elements that cannot take compression. This can be thought of as a type of control saturation, which significantly complicates control design. In this chapter we present a control strategy for three-dimensional tensegrity structures that can address both of these issues.
KeywordsLyapunov Function Control Input Control Design Lyapunov Stability Force Density
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