Recognition of Topological Invariants by Iterative Arrays

A study is made of the recognition and transformation of figures by iterative arrays of finite state automata. A figure is a finite rectangular two-dimensional array of symbols. The iterative arrays considered are also finite, rectangular, and two-dimensional. The automata comprising any given array are called cells and are assumed to be isomorphic and to operate synchronously with the state of a cell at time t+1 being a function of the states of it and its four nearest neighbors at time t. At time t=0 each cell is placed in one of a fixed number of initial states. The pattern of initial states thus introduced represents the figure to be processed. The resulting sequence of array states represents a computation based on the input figure. If one waits for a specially designated cell to indicate acceptance or rejection of the figure, the array is said to be working on a recognition problem. If one waits for the array to come to a stable configuration representing an output figure, the array is said to be working on a transformation problem.

The Synthesis of Stable Force-Closure Grasps

This thesis addresses the problem of synthesizing grasps that are force-closure and stable. The synthesis of force-closure grasps constructs independent regions of contact for the fingertips, such that the motion of the grasped object is totally constrained. The synthesis of stable grasps constructs virtual springs at the contacts, such that the grasped object is stable, and has a desired stiffness matrix about its stable equilibrium. A grasp on an object is force-closure if and only if we can exert, through the set of contacts, arbitrary forces and moments on the object. So force-closure implies equilibrium exists because zero forces and moment is spanned. In the reverse direction, we prove that a non-marginal equilibrium grasp is also a force-closure grasp, if it has at least two point contacts with friction in 2D, or two soft-finger contacts or three hard-finger contacts in 3D. Next, we prove that all force-closure grasps can be made stable, by using either active or passive springs at the contacts. The thesis develops a simple relation between the stability and stiffness of the grasp and the spatial configuration of the virtual springs at the contacts. The stiffness of the grasp depends also on whether the points of contact stick, or slide without friction on straight or curved surfaces of the object. The thesis presents fast and simple algorithms for directly constructing stable fore-closure grasps based on the shape of the grasped object. The formal framework of force-closure and stable grasps provides a partial explanation to why we stably grasp objects to easily, and to why our fingers are better soft than hard.

The Synthesis of Stable Grasps in the Plane

This paper addresses the problem of synthesizing stable grasps on arbitrary planar polygons. Each finger is a virtual spring whose stiffnes and compression can be programmed. The contacts between the finger tips and the object are point contacts without friction. We prove that all force-closure grasps can be made stable, and it costs 0(n) time to synthesize a set of n virtual springs such that a given force closure grasp is stable. We can also choose the compliance center and the stiffness matrix of the grasp, and so choose the compliant behavior of the grasped object about its equilibrium. The planning and execution of grasps and assembly operations become easier and less sensitive to errors.

Stable Mixing of Complete and Incomplete Information

An increasing number of parameter estimation tasks involve the use of at least two information sources, one complete but limited, the other abundant but incomplete. Standard algorithms such as EM (or em) used in this context are unfortunately not stable in the sense that they can lead to a dramatic loss of accuracy with the inclusion of incomplete observations. We provide a more controlled solution to this problem through differential equations that govern the evolution of locally optimal solutions (fixed points) as a function of the source weighting. This approach permits us to explicitly identify any critical (bifurcation) points leading to choices unsupported by the available complete data. The approach readily applies to any graphical model in O(n^3) time where n is the number of parameters. We use the naive Bayes model to illustrate these ideas and demonstrate the effectiveness of our approach in the context of text classification problems.

The Grasping Problem: Toward Task-Level Programming for an Articulated Hand

This report presents a system for generating a stable, feasible, and reachable grasp of a polyhedral object. A set of contact points on the object is found that can result in a stable grasp; a feasible grasp is found in which the robot contacts the object at those contact points; and a path is constructed from the initial configuration of the robot to the stable, feasible final grasp configuration. The algorithm described in the report is designed for the Salisbury hand mounted on a Puma 560 arm, but a similar approach could be used to develop grasping systems for other robots.

Dynamically Stable Legged Locomotion (September 1985-Septembers1989)

This report documents our work in exploring active balance for dynamic legged systems for the period from September 1985 through September 1989. The purpose of this research is to build a foundation of knowledge that can lead both to the construction of useful legged vehicles and to a better understanding of animal locomotion. In this report we focus on the control of biped locomotion, the use of terrain footholds, running at high speed, biped gymnastics, symmetry in running, and the mechanical design of articulated legs.