Topology design of tensegrity structures via mixed integer programming

This paper presents a numerical method for finding a tensegrity structure based on the ground structure method. We first solve a mixed integer programming (MIP) problem which maximizes the number of struts over the self-equilibrium condition of axial forces and the discontinuity condition of struts. Subsequently we solve the minimization problem of the number of cables in order to remove redundant self-equilibrium modes, which is also formulated as an MIP. It is regarded to be advantageous that our method does not require any connectivity information of cables and struts to be known in advance, while the obtained tensegrity structure is guaranteed to satisfy the discontinuity condition of struts rigorously.