Robotic Manipulation of a Rotating Chain

Abstract

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 a complex multi-solutions behavior typical of nonlinear systems. We prove that the configuration space of the uniformly rotating chain is homeomorphic to a two-dimensional surface embedded in 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 circularly towed aerial systems, elastic rods or concentric tubes.

Arm Manipulation Planning of Tethered Tools with the Help of a Tool Balancer

“…On the other hand, robot motion planning involving cable-like objects has presented many challenges, these objects are difficult to manipulate, with often unpredictable deformations and, in the case of cables, they can get entangled around the robot or its surroundings. Several work centered around manipulation planning have tackled different problems associated with deformable objects like cables, chains and hoses [8,5,13,1,14]. In particular, deformable object manipulation has been explored in different work: In [22] a framework for cable shapes manipulation using a deformation model was shown.…”

Rotational modes of a double conical pendulum

“…Equation (8) can be solved for any given value of θ 2 by iteration of θ 1 . That is, θ 1 can be varied in a systematic manner until it is found to satisfy equation (8). Alternatively, if θ 1 and θ 2 are both small, then a simple analytical solution is…”

Manipulation of Flexible Objects

“…The optimal paths are the ones that minimize the object potential energy. Pham and Pham (2018) consider robotic manipulation of a chain that is rotating at constant angular speed around a fixed axis. Having proved that the chain's configuration space is homeomorphic to a two-dimensional surface embedded in IR 3 , the authors devise a strategy for transiting between different rotation modes in a stable and controlled manner.…”