Dynamics and Nonlinear Coordination Control of Multifingered Mechanical Hands

Abstract

This paper presents a study of the dynamics and nonlinear coordination control of multifingered mechanical hands. Considering the dynamics of the object and the fingers, the equations of motion are derived in the finger joint space resulting in a set of differential equations with some algebraic constraints. Using dynamic extension, the equations are converted to the state space form, which results in a nonlinear system affine in control. For the purpose of control, certain output equations are defined. Using the tools of differential geometric control theory, some important properties of the system are shown. Using these properties, a nonlinear input-output linearizing controller is synthesized which yields a decoupled linear system. The poles of the resulting linearized system are then placed appropriately to render desirable features to the system. The theory is validated with an example of a three-fingered spatial hand manipulating a cuboidal object.