Planar In-Hand Manipulation Using Primitive Rotations Based on Isometric Transformations

Achieving in-hand manipulation of a grasped object is challenging in robotic communities. This article proposes a planar intrinsic in-hand manipulation approach based on isometric transformation. We demonstrate that the isometric transformation (excluding reflections) can be reduced to rotations with two fixed centers, if more than two rotations around two different centers are performed. Furthermore, this article applies this theory to reposition and reorient a grasped object by performing three or more primitive rotations sequentially. We further analyze the feasible manipulation space, where the desired position and orientation of a grasped object can be attained. The theoretical results have been verified through simulations and experiments. In addition, we performed several real-world tasks using a novel robotic hand with two rotational degrees of freedom at each finger, demonstrating that the proposed in-hand manipulation method can reposition and reorient different grasped objects in $\text{SE}(2)$.