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In this paper, we study the problem of determining a mathematical description of the surface defined by the shape of a membrane based on an image o fit and present an algorithm for reconstructing the surface when the membrane is deformed by unknown external elements. The given data are the projection on an image plane of markings on the surface of the membrane, the undeformed configuration of the membrane, and a model for the membrane mechanics. The method of reconstruction is based on the principle that the shape assumed by the membrane will minimize the elastic energy stored in the membrane subject to the constraints implied by the measurements. Energy minimization leads to a set of nonlinear partial differential equations. An approximate solution is found using linearization. The initial motivation, and our first application of these ideas, comes from tactile sensing. Experimental results affirm that this approach can be very effective in this context. [ABSTRACT FROM AUTHOR]

In this article we develop a mathematical theory for optimizing the kinematic dexterity of robotic mechanisms and obtain a collection of analytical tools for robot design. The performance criteria we consider are workspace volume and dexterity; by the latter we mean the ability to move and apply forces in arbitrary directions as easily as possible. Clearly, dexterity and workspace volume are intrinsic to a mechanism, so that any mathematical formulation of these properties must necessarily be independent of the particular coordinate representation of the kinematics. By regarding the forward kinematics of a mechanism as defining a mapping between Riemannian manifolds, we apply the coordinate-free language of differential geometry to define natural measures of kinematic dexterity and workspace volume. This approach takes into account the geometric and topological structures of the joint and workspaces. We show that the functional associated with harmonic mapping theory provides a natural measure of the kinematic dexterity of a mechanism. Optimal designs among the basic classes of mechanisms are determined as extreme of this measure. We also examine the qualitative connections between kinematic dexterity and workspace volume. [ABSTRACT FROM AUTHOR]