Tensegrity system dynamics with rigid bars and massive strings

Abstract

This paper provides a single matrix-second-order nonlinear differential equation to simulate the dynamics of tensegrity systems with rigid bars and massive strings. The paper allows one to distribute the string mass into any specified number of point masses along the string while preserving the exact rigid bar dynamics. This formulation also allows modeling of skins and surfaces as a finite set of strings in the tensegrity dynamics. To reduce the complexity of the model, non-minimal coordinates (6 degrees of freedom for each bar instead of 5) were chosen. This is the key to give more accurate results in computer simulations since the mathematical structure of the model is simplified and exploited during numerical computations. A bar length correction algorithm is also provided for both class-1 and class- $k$ tensegrity systems to correct the erroneous change in bar length because of computational errors during numerical integration. We characterize the control variable as the force density in each string. This allows control laws to be developed independently of the material chosen for the structural elements. A nonlinear transformation back to the physical control variables involves the material properties.