Path Planning and Open-Loop Shape Control of Modular Tensegrity Structures

Abstract

We characterize the planned path for a shape change in a tensegrity structure as a path from one equilibrium to another. For tensegrity structures, this means that in every desired configuration the structure has to satisfy tensegrity conditions. Required trajectories are feasible, and changes in potential energy are not required to follow these trajectories. This is a benefit over normal control paths that require strain-energy changes because such energy must be supplied by the control system. For the class of modular tensegrity structures defined, configurations that satisfy tensegrity conditions can be parameterized in terms of only a few parameters that can meaningfully be related to the overall desired shape of the structures. Equilibrium rest lengths of string elements are defined first. An open-loop rest-length control is defined by slowly varying desired geometric parameters, which causes the structure to track trajectories defined by the time-dependent geometric parameters. Examples with simulation results show different reconfiguration scenarios of tensegrity plates and class-2 tensegrity towers.