Kinematic restriction method for tensegrity structures

The use of tensegrity structures in robotics has been studied in recent years thanks to their properties of light weight, efficient distribution of forces and the possibility of applying control methods for the active shape reconfiguration, with crawling and rolling as examples. The structural composition of tensegrities, particularly the use of tensile elements, results in the presence of infinitesimal mechanisms. These affine motions have been considered for the development of control strategies that follow the manifold of stable positions described by these mechanisms. However, in robotic applications, the presence of rigid body motions can cause undesired effects, such as tensegrity structures flipping over. The form finding methods available in literature consider only the statics of tensegrities and most dynamic models work assume free-standing structures, while few consider fixed structures but do not deepen into the process of removing the rigid body motions. In this paper, the formulation of the equilibrium equations of tensegrity structures is reviewed, to describe the presence of the affine motions in the vector spaces of the equilibrium matrix. A simplified method for removing rigid body motions from the equilibrium equations is detailed, and the effect on the set of affine motions is explained. To verify the validity of this process, two numerical examples are given, including a single unit and a two stage tensegrity structures.