Identifying the energy threshold for multistable tensegrity structures using a Mountain Pass algorithm

Abstract

Multistable tensegrity structures are able to switch between equilibrium configurations and maintain these states with no additional energy input; as a result, they have found applications in reconfigurable robotics and deployable structures. However, the actuation strategy for multistable tensegrity structures to transform from one stable state to another remains unknown. In this work, we propose a method to identify a transition route between the known stable states of multistable tensegrity structures. The least-energy threshold and the transformation route formed by a series of deformed position point vectors are obtained. The method is based on the Conjugate Peak Refinement (CPR) method, which is one of the Mountain Pass Algorithms. To capture the fact that cable members could go slack during the transition route, a slack cable model is adapted into the CPR method so that the accurate energy state of the tensegrity structure is derived. The algorithms are successfully applied to examples of 3D multistable tensegrity structures from the literature. The work in this paper provides a minimum energy threshold between stable states, a measure of its shock sensitivity, and a reference actuation strategy to transform between the stable states of multistable tensegrity structures.