Adaptive control to prevent transfer between bistable configurations of a tensegrity

Abstract

The adaptive control capability of tensegrities is investigated in terms of preventing the transfer between bistable configurations due to load-induced structural instability. In contrast to conventional structures, the structural geometry and internal force of tensegrities can be changed synchronously by member length actuation, thus achieving the adjustment of the structural elastic and geometric stiffnesses. The concept of the domain of attraction (DOA) is introduced to intuitively demonstrate the ability of a tensegrity to remain stable at the current configuration, and a method is suggested to estimate the DOA for a given load. Based on the quasistatic assumption, the analytical relationship between the eigenvalues of the structural tangent stiffness matrix and the member length actuations is derived. Further combining it with the structural equilibrium relationship, the equation that can be employed to simultaneously correct both the eigenvalues of the tangent stiffness matrix and the structural geometry is established. An adaptive control strategy is thus proposed to prevent the buckling of a loaded bistable tensegrity by specifying a threshold for the eigenvalues of the tangent stiffness matrix. A 6-bar 24-cable bistable tensegrity is employed as an illustrative example to verify the validity of the proposed adaptive control strategy by preventing mutual transfers between its bistable configurations. The results show that the load resistance of the tensegrity can be significantly improved by adaptive control without loss of the structural stability, and both the elastic stiffness and the geometrical stiffness provide comparable contributions to the adjustment of the eigenvalues of its tangent stiffness matrix.