Analysis and Control of Robot Manipulators with Kinematic Redundancy

A closed-form solution formula for the kinematic control of manipulators with redundancy is derived, using the Lagrangian multiplier method. Differential relationship equivalent to the Resolved Motion Method has been also derived. The proposed method is proved to provide with the exact equilibrium state for the Resolved Motion Method. This exactness in the proposed method fixes the repeatability problem in the Resolved Motion Method, and establishes a fixed transformation from workspace to the joint space. Also the method, owing to the exactness, is demonstrated to give more accurate trajectories than the Resolved Motion Method. In addition, a new performance measure for redundancy control has been developed. This measure, if used with kinematic control methods, helps achieve dexterous movements including singularity avoidance. Compared to other measures such as the manipulability measure and the condition number, this measure tends to give superior performances in terms of preserving the repeatability property and providing with smoother joint velocity trajectories. Using the fixed transformation property, Taylor's Bounded Deviation Paths Algorithm has been extended to the redundant manipulators.

The Architect's Collaborator: Toward Intelligent Tools for Conceptual Design

In early stages of architectural design, as in other design domains, the language used is often very abstract. In architectural design, for example, architects and their clients use experiential terms such as "private" or "open" to describe spaces. If we are to build programs that can help designers during this early-stage design, we must give those programs the capability to deal with concepts on the level of such abstractions. The work reported in this thesis sought to do that, focusing on two key questions: How are abstract terms such as "private" and "open" translated into physical form? How might one build a tool to assist designers with this process? The Architect's Collaborator (TAC) was built to explore these issues. It is a design assistant that supports iterative design refinement, and that represents and reasons about how experiential qualities are manifested in physical form. Given a starting design and a set of design goals, TAC explores the space of possible designs in search of solutions that satisfy the goals. It employs a strategy we've called dependency-directed redesign: it evaluates a design with respect to a set of goals, then uses an explanation of the evaluation to guide proposal and refinement of repair suggestions; it then carries out the repair suggestions to create new designs. A series of experiments was run to study TAC's behavior. Issues of control structure, goal set size, goal order, and modification operator capabilities were explored. In addition, TAC's use as a design assistant was studied in an experiment using a house in the process of being redesigned. TAC's use as an analysis tool was studied in an experiment using Frank Lloyd Wright's Prairie houses.

Convergence Rates of Approximation by Translates

In this paper we consider the problem of approximating a function belonging to some funtion space Φ by a linear comination of n translates of a given function G. Ussing a lemma by Jones (1990) and Barron (1991) we show that it is possible to define function spaces and functions G for which the rate of convergence to zero of the erro is 0(1/n) in any number of dimensions. The apparent avoidance of the "curse of dimensionality" is due to the fact that these function spaces are more and more constrained as the dimension increases. Examples include spaces of the Sobolev tpe, in which the number of weak derivatives is required to be larger than the number of dimensions. We give results both for approximation in the L2 norm and in the Lc norm. The interesting feature of these results is that, thanks to the constructive nature of Jones" and Barron"s lemma, an iterative procedure is defined that can achieve this rate.