A mixed 0-1 programing approach to topology-finding of tensegrity structures

Abstract

In this paper we propose an optimization-based approach to finding a tensegrity structure based on the ground structure method. We first solve a problem which maximizes the number of struts over the self-equilibrium condition 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. The optimization problem at each step can be formulated as a mixed integer programming (MIP) problem. The 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.