Geometric soft robotics: a finite element approach

Enabling remote semi-autonomous operations in hazardous environments is a challenging technological problem, given the difficulty to access in confined and constrained spaces using classical robotic systems. Inspired by biological trunks and tentacles, soft continuum robots constitute a possible solution to this problem, for their ability to traverse confined spaces, manipulate objects in complex environments, and conform their shape to nonlinear curvilinear paths. The need of reaching difficult-to-access industrial sites for maintenance and inspection procedures or anatomical sites for less invasive robotic surgery mainly motivates the current research. Despite the recent advances in the design and fabrication of soft robots, the community still suffers for the lack of a consolidate modeling framework for simulating their mechanical behavior. Such a modeling framework is the necessary condition for developing new physical design and control strategies, as well as path planning algorithms. Indeed, despite their appreciable features, soft robots usually generate undesired vibrations during normal procedures. This is one of the main reasons which still limits their potentially wide use in real scenario. Realistic modeling frameworks might leverage the development of model-based predictive controllers to compensate for the undesired vibrations, as well as design concepts and optimized trajectories to avoid the excitation of the vibration modes of the mechanical structure. The main objective of the thesis is to develop a unified mathematical framework for simulating the mechanical behavior of soft continuum robotic manipulators, which can also accommodate the dynamic simulation of classical rigid robots. The computer implementation of this theoretical framework leads to the development of SimSOFT, a physics engine for soft robots. The formulation has been validated through literature benchmark and some applications are presented. One of the major strengths of the framework is that it can accommodate the realistic simulation of kinematic trees or loops constituted either by rigid or soft arms connected by rigid or flexible joints.The simulation of hybrid mechanisms, composed by classical rigid kinematic chains and soft continuum manipulators, which can be used to have larger dexterity in smaller workspaces, as they are easily to miniaturize, is thus possible. To the best of the author's knowledge, the mathematical models developed in the thesis constitute the first attempt in the robotics community towards a unified framework for the dynamics of soft continuum multibody systems.