Form-finding of Tensegrity Structures Utilizing a Nonlinear Fletcher-Reeves Conjugate Gradient Method

In the domain of soft tensegrity robot, the self-equilibrium tensegrity structure is vital for the further analysis of robot's locomotion. Furthermore, form-finding is an important step for finding a self-equilibrium tensegrity structure. In this paper, a conjugate gradient form-finding (CGFF) algorithm is developed and investigated for the form-finding problems of tensegrity systems. Besides, a Fletcher-Reeves conjugate gradient method is employed to solve the nonlinear unconstrained optimization problems which transformed from the form-finding problems. Moreover, the initial conditions of the tensegrity structure such as the axial stiffness and rest lengths of the element have been utilized to explore the configuration details of the self-equilibrium tensegrity system. Eventually, several numerical simulations are provided to verify the accuracy and high-efficiency of the CGFF form-finding algorithm.