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Tensegrity structures are a class of mechanical structures which are highly controllable. These smart structures have a large number of potential applications, for the benefit of systems which need, for instance, a small transportation or storage volume, tunable stiffness properties, active vibration damping and deployment or configuration control. We model tensegrity structures as mechanical trusses made of bars and strings. The bars, assumed to be rigid rods, are held in stable equilibrium by a continuous network of strings in tension. The dynamic equations of motion for rigid rods are differentialalgebraic equations of motion, derived on a non-minimal coordinate system with an associated dynamic algebraic constraint. The use of differential-algebraic equations of motion simplifies the system description but introduce some challenges for control design. This paper introduces and compares two different Lyapunov based control design methodologies for tensegrity structures. The theory is developed and illustrated on the simplest possible example of a three-dimensional controlled tensegrity system, a pinned bar actuated by three strings.

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