A novel port-Hamiltonian framework for clustered tensegrity systems

Clustered tensegrity systems (CTSs) are lightweight, energy-efficient, and modular, making them ideal for engineering applications. The port-Hamiltonian (pH) framework is well-suited for their design and analysis due to its effectiveness in modeling dynamic systems. However, when CTSs are modeled within the pH framework, several challenges arise: (1) Current spatial discretization methods for pH systems are complex and inefficient for CTSs, and cannot directly represent strong nonlinear coupling. (2) Current symplectic time discretization methods for pH systems are inefficient and unstable when solving stiff equations. First, a spatial discretization method based on positional finite element method (PFEM) is proposed. It can accurately capture strong nonlinear coupling from large-scale rotations and deformations without relying on rotation matrices. Then, a stiff problem modification based on symplectic time discretization is proposed. Combined with a Quasi-Newton strategy, it significantly improves computational efficiency with few losses of precision. Numerical simulations show that discrete pH systems based on PFEM can efficiently and accurately capture the energy and dynamic behavior of CTSs. The proposed modification effectively improves stiff problem and significantly enhances computational efficiency.