Genetic programming is a powerful method for automatically generating computer programs via the process of natural selection (Koza, 1992). However, in its standard form, there is no way to restrict the programs it generates to those where the functions operate on appropriate data types. In the case when the programs manipulate multiple data types and contain functions designed to operate on particular data types, this can lead to unnecessarily large search times and/or unnecessarily poor generalization performance. Strongly typed genetic programming (STGP) is an enhanced version of genetic programming that enforces data-type constraints and whose use of generic functions and generic data types makes it more powerful than other approaches to type-constraint enforcement. After describing its operation, we illustrate its use on problems in two domains, matrix/vector manipulation and list manipulation, which require its generality. The examples are (1) the multidimensional least-squares regression problem, (2) the multidimensional Kalman filter, (3) the list manipulation function NTH, and (4) the list manipulation function MAPCAR.

The kinematics of contact describe the motion of a point of contact over the surfaces of two contacting objects in response to a relative motion of these objects. Using concepts from differential geometry, I derive a set of equations, called the contact equations, that embody this relationship. I employ the contact equations to design the following applications to be executed by an end-effector with tactile sensing capability: ( 1) determining the curvature form of an unknown object at a point of contact; and ( 2) following the surface of an unknown object. The contact equations also serve as a basis for an investigation of the kinematics of grasp. I derive the relation ship between the relative motion of two fingers grasping an object and the motion of the points of contact over the object surface. Based on this analysis, we explore the following applications: ( 1) rolling a sphere between two arbitrarily shaped fingers ; ( 2) fine grip adjustment ( i.e., having two fingers that grasp an unknown object locally optimize their grip for maximum stability).

We distinguish between two types of grasp stability, which we call spatial grasp stability and contact grasp stability. We show via examples that spatial stability cannot capture certain intuitive concepts of grasp stability and hence that any full understanding of grasp stability must include contact stability. We derive a model of how the positions of the points of contact evolve in time on the surface of a grasped object in the absence of any external force or active feedback. From this model, we obtain a general measure of the contact stability of any two-fingered grasp. Finally, we discuss the consequences of this stability measure and a related measure of contact manipulability on strategies for grasp selection.

We distinguish between two types of grasp stability, which we call spatial grasp stability and contact grasp stability. The former is the tendency of the grasped object t o return to an equilibrium location in space; the latter is the tendency of the points of contact to return to an equilibrium position on the object's surface. We show via examples that spatial stability cannot capture certain intuitive concepts of grasp stability and hence that any full understanding of grasp stability must include contact stability. We derive a model of how the positions of the points of contact evolve in time on the surface of the grasped object in the absence of any external force or active feedback. From this model, we obtain a condition which determines whether or not a two-fingered grasp is contact stable.

Previously, general models of the kinematics of multi-fingered manipulation have only treated instantaneous motion (i.e., velocities). However, such models, which ignore the underlying configuration (or state) space, are inherently incapable of capturing certain properties of the fingers-plus-object system important to manipulation. In this paper, we derive a configuration-space description of the kinematics of the fingers-plus-object system. To do this, we first formulate contact kinematics as a "virtual" kinematic chain. Then, the system can be viewed as one large closed kinematic chain composed of smaller chains, one for each finger and one for each contact point. We examine the underlying configuration space and two ways of moving through this space. The first, kinematics-based velocity control, is a generalization of some previous velocity-based approaches. The second, hyperspace jumps, is a purely configuration-space concept. We conclude with a discussion of how these concepts can be used to understand the task of twirling a baton [6].