Motion Planning for Object Manipulation by Edge-Rolling

Abstract

A common way to manipulate heavy objects is to maintain at least one point of the object in contact with the environment during the manipulation. When the object has a cylindrical shape or, in general, a curved edge, not only sliding and pivoting motions but also rolling the object along the edge can effectively satisfy this condition. Edge-rolling offers several advantages in terms of efficiency and maneuverability. This paper aims to develop a novel approach for approximating the prehensile edge-rolling motion on any path by a sequence of constant screw displacements, leveraging the principles of screw theory. Based on this approach, we proposed an algorithmic method for task-space-based path generation of object manipulation between two given configurations using a sequence of rolling and pivoting motions. The method is based on an optimization algorithm that takes into account the joint limitations of the robot. To validate our approach, we conducted experiments to manipulate a cylinder along linear and curved paths using the Franka Emika Panda manipulator.

Figures (13)

• Figure 1: Schematic sketch for the manipulation of a cylinder through a sequence of pivoting and rolling motions, transitioning it from an initial configuration $\mathcal{C}_O$ to a final configuration $\mathcal{C}_F$.
• Figure 2: A cylindrical-shape object being rolled by $n$ manipulators.
• Figure 3: Moving from configuration $\mathcal{C}_1$ to configuration $\mathcal{C}_2$ of an element $\mathrm{d}x$ using an intermediate configuration $\mathcal{C}_I$ and two screw displacements, (a) demonstration on a 2D circle, (b) demonstration on a 3D cylinder.
• Figure 4: ScLERP between two given configurations $\mathcal{C}_1$ and $\mathcal{C}_2$ of a cylinder.
• Figure 5: Edge-rolling of a cylinder on a discretized curved path. The screw axes $\mathcal{S}_1^i$ and $\mathcal{S}_2^i$ correspond to the constant screw displacements to roll the cylinder along the segment $dx_i$ and the screw axis $\mathcal{S}_3^i$ corresponds to a pivoting motion to align the cylinder with the next segment.