Analyzing physical system interaction

Abstract

Achieving stable manipulation in robots requires understanding of the consequences of physical contact and interaction. This thesis considers the problem of contact instability and provides a framework to analyze physical system interaction and provides the first step in building a design synthesis method, i.e. finding a stability criterion. By posing interaction in terms of interconnected port functions such as impedances and admittances, stability analysis can be treated as an input;'output analysis of a feedback system. Previous researchers have already used this framework to show how this method can be of use in showing a form of Lyapunov stability for interacting systems. The systems previously studied were purely passive in nature. No system was capable of power generation, and no power could enter through command inputs or external perturbations. As such, the stability results have a narrow range of applications. Even though passive systems may be commonplace, the inability to actively control the interaction limits their practicality. Analyzing interaction accounting for inputs is shown to be non-trivial within this thesis. The non-nodic behavior common to many physical systems constrains the structure of the feedback interconnections such that most existing 1/0 results are inapplicable. This non-nodic behavior is studied in order to form a representative model of a robot interacting with an unknown environment. Using a technique based on topologically separating the input/output space, we show that robust stability solutions can be obtained for such systems with unknown but passive environments. In addition, frameworks for analyzing active interactions are analyzed and discsed.