Dynamics of Continuum and Soft Robots: A Strain Parameterization Based Approach

In this article, we propose a new dynamic model of Cosserat beams in view of its application to continuum and soft robotics manipulation and locomotion. In contrast to usual approaches, it is based on the nonlinear parameterization of the beam shape by its strain fields and their reduction on a functional basis of strain modes. While remaining geometrically exact, the approach provides us with a minimal set of ordinary differential equations in the usual Lagrange matrix form that can be exploited for analysis and control design. Inspired from rigid robotics, the calculation of the matrices of this Lagrangian model is performed with a new reduced inverse Newton-Euler algorithm. To assess the approach, this Lagrangian model is compared against a well-validated finite element method through several benches of nonlinear structural statics and dynamics.