Slender structures, widely found from natural environments (e.g., tendrils) to engineering applications (e.g., flexible electronics), frequently experience geometrically nonlinear deformations and substantial topological changes when exposed to simple boundary conditions or modest external stimuli. On one hand, the nonlinear dynamics of slender structures present considerable challenges for the automated manipulation of these structures by robots. On the other hand, the automated interactions between robots and such structures also open up opportunities to enhance our understanding of the mechanics governing slender structures.This dissertation focuses on the synergy between computational mechanics and robotics for the manipulation and study of slender structures. Specifically, it delves into discrete differential geometry (DDG)-based simulations, an emerging field in computational mechanics, to develop a comprehensive sim2Real manipulation framework for generating task-oriented deformable manipulation strategies. Moreover, we conduct automated experiments to gain valuable insights into the behavior of slender structures. Our contributions can be categorized into three main areas:

First, we develop a penalty-energy-based method and combine it with Kirchoff rod's theory to simulate rod assemblies with frictional contact responses. Our simulation method is validated, demonstrating its robustness, accuracy, and efficiency across diverse scenarios. These scenarios include modeling flagella bundling, a significant biological phenomenon for bacterial navigation, as well as tying knots. These numerical validations underscore the potential of our approach as a significant step toward the ultimate goal of a computational framework for sim2real manipulation tasks. We then combine our numerical framework with desktop experiments to investigate the mechanics of various types of knots.

Second, we combine DDG-based simulations, scaling analysis, and machine learning to develop a sim2Real framework for various deformable manipulation tasks, including paper folding and the deployment of deformable linear objects onto rigid substrates. Our sim2Real framework harnesses the precision of physical simulations, the rapid inference capabilities of neural networks, and the enhanced adaptability conferred by scaling analysis. This synergy yields robust, accurate, and efficient solutions for these manipulation tasks. In the paper folding task, a physics-informed model is learned using scaled simulation data, enabling the creation of a model predictive control system for precise paper folding. We validate the effectiveness of this physics-based approach through extensive robotic experiments. In addition, we construct a physics-informed manipulation policy within the same framework for the deployment task. This policy proves to be robust, accurate, and efficient in controlling the shape of various deformable linear objects during deployments. Furthermore, we demonstrate the potential of this deployment scheme in various engineering applications including cable management and knot tying.

Finally, we delve into the application of automation science to explore the nonlinear mechanics of slender structures. Traditional experimental platforms (e.g., optical platforms) struggle to systematically capture the numerous boundary conditions and corresponding equilibriums of slender structures. To address this challenge, we've designed a robotic system for automated experiments. This system allows us to investigate one of the fundamental problems in solid mechanics: the buckling of an elastic rod with a helical centerline. We answer this problem with a combination of theoretical analysis, numerical simulation, and automated robotic experiments. Then, significant advances are made in understanding this phenomenon, uncovering different buckling types within this system, including continuous buckling and snap buckling. Given the distinct behaviors of these two types of buckling, our exploration is particularly meaningful in demonstrating how various buckling can be triggered within a single system. Our automated robotic experiments highlight the potential of robotic technology in advancing our understanding of mechanics through intelligent interactions with the physical world.