Motion and Shape Control of Soft Robots

Unlike conventional robots, soft robots are designed to have higher number of degrees of freedom to provide higher degree of flexibility, have lower weight, and provide safe interactions with the environments. In this thesis, a new continuum-based approach for simultaneously controlling the motion and shape of soft robots and materials (SRM) is proposed based on the absolute nodal coordinate formulation. This approach allows for computing the actuation forces for arbitrary desired SRM motion and geometry. A new hybrid-actuation system for near-elimination of the small oscillations of articulated flexible-robot systems is proposed based on the floating frame of reference. This thesis discusses fundamental issues relevant to the motion and shape control of articulated robots that consist of components made of soft materials. These issues include joint formulation, geometric and material nonlinearities, and definition of torsional strains. Because in articulated systems very flexible bodies are often connected with other bodies, which have different degrees of flexibility; it is necessary to develop an efficient joint formulation. A new simple formulation of the orientation constraints for flexible bodies using two position-gradient vectors is introduced. This thesis demonstrates that, in more general beam formulations, higher stiffness can be attributed to geometric nonlinearities as result of cross-section deformations, not properly captured by the analytical or less general FE beam formulations. The effect of using different constitutive models on the stiff behavior of beams is investigated. It is demonstrated that the stiff behavior resulting from the geometric stiffening due to the coupling between the cross-section deformations and beam vibrations in more general beam formulations cannot always be interpreted as locking. This thesis introduces a new geometrically consistent plane strain and stress constitutive models for the nonlinear large-displacement analysis of soft materials using position-gradient constraints. The position gradients are used to define strain and stress constraints that enter into the formulation of the deformation tensor, strain-energy density function, and new constitutive models. The linear and nonlinear torsion-kinematic equations are also developed in this thesis using the position-gradient vectors. This thesis presents a new gradient interpretation of the linear torsion formulation, develops its governing equations, and sheds light on its assumptions.