Robotic manipulation of a rotating chain

This paper considers the problem of manipulating a uniformly rotating chain: the chain is rotated at a constant angular speed around a fixed axis using a robotic manipulator. Manipulation is quasi-static in the sense that transitions are slow enough for the chain to be always in "rotational" equilibrium. The curve traced by the chain in a rotating plane -- its shape function -- can be determined by a simple force analysis, yet it possesses complex multi-solutions behavior typical of non-linear systems. We prove that the configuration space of the uniformly rotating chain is homeomorphic to a two-dimensional surface embedded in $\mathbb{R}^3$. Using that representation, we devise a manipulation strategy for transiting between different rotation modes in a stable and controlled manner. We demonstrate the strategy on a physical robotic arm manipulating a rotating chain. Finally, we discuss how the ideas developed here might find fruitful applications in the study of other flexible objects, such as elastic rods or concentric tubes.Comment: 12 pages, 9 figure

Robotic manipulation planning for shaping deformable linear objects with environmental contacts

Humans use contacts in the environment to modify the shape of deformable objects. Yet, few papers have studied the use of contacts in robotic manipulation. In this paper, we investigate the problem of robotic manipulation of cables with environmental contacts. Instead of avoiding contacts, we propose a framework that allows the robot to use them for shaping the cable. We introduce an index to quantify the contact mobility of a cable with a circular contact. Based on this index, we present a planner to plan robot motions. The planner is aided by a vision-based contact detector. The framework is validated with robot experiments on different desired cable configurations

On the Statics, Dynamics, and Stability of Continuum Robots: Model Formulations and Efficient Computational Schemes

This dissertation presents advances in continuum-robotic mathematical-modeling techniques. Specifically, problems of statics, dynamics, and stability are studied for robots with slender elastic links. The general procedure within each topic is to develop a continuous theory describing robot behavior, develop a discretization strategy to enable simulation and control, and to validate simulation predictions against experimental results.Chapter 1 introduces the basic concept of continuum robotics and reviews progress in the field. It also introduces the mathematical modeling used to describe continuum robots and explains some notation used throughout the dissertation.The derivation of Cosserat rod statics, the coupling of rods to form a parallel continuum robot (PCR), and solution of the kinematics problem are reviewed in Chapter 2. With this foundation, soft real-time teleoperation of a PCR is demonstrated and a miniature prototype robot with a grasper is controlled.Chapter 3 reviews the derivation of Cosserat rod dynamics and presents a discretization strategy having several desirable features, such as generality, accuracy, and potential for good computational efficiency. The discretized rod model is validated experimentally using high speed camera footage of a cantilevered rod. The discretization strategy is then applied to simulate continuum robot dynamics for several classes of robot, including PCRs, tendon-driven robots, fluidic actuators, and concentric tube robots.In Chapter 4, the stability of a PCR is analyzed using optimal control theory. Conditions of stability are gradually developed starting from a single planar rod and finally arriving at a stability test for parallel continuum robots. The approach is experimentally validated using a camera tracking system.Chapter 5 provides closing discussion and proposes potential future work