Motion Actuation Optimization And Structural Stability Control Of Morphing Tensegrities

Morphing tensegrities generally deform with the length actuation of active elements(cables and/or struts)whose rest lengths can be adjusted,and they have been studied in multidisciplinary fields.In this paper,the theoretical problems of motion actuation optimization and structural stability control on the kinematic path of the morphing tensegrity are investigated from the perspective of morphological analysis of pin-jointed bar assemblies under quasi-static assumptions.The main work and contributions of this paper are as follows:(1)The effectiveness of the element length actuations is substantially determined by the sensitivity matrix of the node displacements to the element elongations,and each column in the sensitivity matrix is contributed by the corresponding active element.It is pointed out that the displacement of the tensegrity induced by the length actuations of active elements must be located in the column space of the sensitivity matrix.It is proven that even if all the elements are active,the tensegrity may not achieve the target configuration accurately,and the displacement closest to the target motion direction can be calculated with any basis for the column space of the sensitivity matrix.(2)A novel method for active element selection of the morphing tensegrities is proposed in this paper based on constructing the basis by converting the passive elements to active elements one by one according to a proposed criterion.A stepwise active element selection and path-tracing strategy is given if the tensegrity implements a large deformation.The results of numerical examples show that the proposed method can effectively solve the optimal arrangement of active elements and can greatly improve the computational efficiency when compared with the genetic algorithm.(3)The eigenvalues of the stiffness matrix for morphing tensegrities can be described as a function of the element rest lengths if the element axial stiffnesses are assumed to be constant.Based on the chain rule of composite functions,the partial derivative of any eigenvalue to the rest length of the element is derived in this paper,and a sensitivity matrix between the increment of eigenvalues and the element elongations is constructed,which is applicable to all kinds of pin-jointed bar assemblies.(4)The basic kinematic equation for morphing tensegrities which can keep any eigenvalue of the tangent stiffness matrix constant,is derived in this paper,and the displacement closest to the target motion direction when considering the structural stability control can be calculated.Based on the derived correction equation that can simultaneously eliminate nodal forces and eigenvalue residuals,a nonlinear kinematic analysis method for morphing tensegrities considering structural stability control is proposed using the Newton-Raphson method.Finally,the validity of the proposed stability control theory and strategy is verified by two numerical examples.