OPTIMAL ROBOT DESIGN AND DIFFERENTIAL GEOMETRY

In this article we survey some recent developments in optimal robot de sign, and collect some of the differential geometric approaches into a general mathematical framework for robot design. The geometric framew ork permits a set of coordinate-free definitions of robot performance that can be optimized for designing both open- and closed-chain roboti c mechanisms. In particular, workspace volume is precisely defined by regarding the rigid body motions as a Riemannian manifold, and various features of actuators, as well as inertial characteristics of the rob ot, can be captured by the suitable selection of a Riemannian metric i n configuration space. The integral functional of harmonic mapping the ory also provides a simple and elegant global description of dexterity .