Stability on a manifold: Concurrent control for secure grasp and manipulation of a rigid object by dual robot fingers

It is well known that three frictionless fingers suffice to immobilize any 2D object with triangular shape but four fingers are necessary for a parallelepiped. However, it has been recently shown that only two fingers are enough to realize secure grasp of a rigid object with parallel flat surfaces in a dynamic sense if finger ends have a hemispherical shape with appropriate radius and thereby rollings are induced between finger ends and object surfaces. This paper focuses on the two problems: 1) realization of secure grasp of rigid objects with non-parallel flat surfaces (including triangular objects) by dual muIti-degrees-of-freedom rigid fingers with hemispherical ends and 2) concurrent realization of secure grasp and orientation control of polygonal objects under the effect of gravity. It is shown that stable grasp is realized by a sensory feedback constructed on the basis of measurements of finger joint angles and angles of the object surfaces relative to finger links without knowing object kinematics and mass center. Further, it is shown that there exists an additional sensory feedback that can regulate orientation angle of the object simultaneously.