Lagrangian and QuasiLagrangian Models for Noninertial Pneumatic Soft Cylindrical Robots

Abstract

Current Lagrangian models for soft cylindrical robots (SCRs) have been developed under rigid body considerations, and therefore, body deformation properties have not been fully incorporated into these models. Thus, key deformation properties such as density variation, variable CoM, and timevarying inertia tensor are missing. In addition, the highly nonlinear dynamical couplings arising from deformation are also missing in deformable bodybased formulations. In this paper, Lagrangian and quasiLagrangian models of a noninertial soft robot are developed under the essential modeling assumption that distance among particles varies. Such nonrigid body assumption introduces deformation properties that lead to a clear description of freemotion deformation dynamics subject to reaction forces. Altogether, our proposal gives rise to sound qualitative mathematical models that incorporate deformation phenomena, with wellposed structural properties. To exemplify quantitatively the usefulness of the proposed models, two simulation scenarios are presented and discussed. In the first one, the soft robot is fixed to the ground, while the second scenario, a soft robot is attached to a threedimensional freeflying rigid frame.