A Geometric Variable-Strain Approach for Static Modeling of Soft Manipulators with Tendon and Fluidic Actuation

We propose a novel variable-strain parametrization for soft manipulators, which discretizes the continuous Cosserat rod model onto a finite set of strain basis functions. This approach generalizes the recently proposed piecewise-constant strain method to the case of non-constant strain sections. As for its predecessor, the discrete model is based on the relative pose between consecutive cross-sections and is provided in its minimal matrix form (Lagrangian-like). The novel variable-strain model is applied to the static equilibrium of tendon and/or fluidic actuated soft manipulators. It is shown that, for a specific choice of strain basis, exploiting the actuator geometry, the system is trivialized, providing useful tools for control and actuator routing design. Comparisons with the full continuous Cosserat model demonstrate the feasibility of the approach.