Integrated control/structure design for planar tensegrity models

A tensegrity structure is built using compressive members (bars) and tensile members (tendons). We discuss how an optimal and integrated design of tendon length control and topology/geometry of the structure can improve the stiffness and stiffness-to-mass properties of tensegrity systems. To illustrate our approach we apply it on a tensegrity system build up from several elementary stages that form a planar beam structure. The computations are done with a nonlinear programming approach and most design aspects (decentralized co-located control, static equilibrium, yield and buckling limits, force directionality, etc., both for the unloaded and loaded cases) are incorporated. Due to the way the control coefficients are constrained, this approach also delivers information for a proper choice of actuator or sensor locations: there is no need to control or sense the lengths of all tendons. From this work it becomes clear that certain actuator/sensor locations and certain topologies are clearly advantageous. For the minimal compliance objective in a planar tensegrity beam structure, proper tendons for control are those that are perpendicular to the disturbance force direction, close to the support, and relatively long, while good topologies are the ones that combine different nodal configurations in a tensegrity topology that is akin to a framed beam, but, when control is used, can be quite different from a classical truss structure.