Abstract
This paper derives a mathematical model of motion of a pair of multi-DOF fingers grasping a 3D-object with rolling contacts under the gravity effect. Even if the instantaneous axis of rotation of the object is time-varying and spinning around the opposition axis stops (this induces another non-holonomic constraint), it is shown that Lagrange's equation of motion of the overall fingers-object system can be expressed with an explicit form of contact and rolling constraint force terms. The overall system equation is accompanied with the non-holonomic constraint expressed as a linear differential equation of an orthogonal matrix belonging to SO(3) without violating causality. A simple control signal constructed from finger-thumb opposition for precision prehension is proposed and shown to realize stable grasping in a dynamic sense under the gravity effect without using object information or external sensing (this is called “blind grasping” in this paper). A sketch of the proof of stability of the closed-loop dynamics is presented together with some results of numerical simulation.
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