Evolutionary trends in rigid body dynamics

Abstract

This paper addresses certain trends in rigid body dynamics evolving from analytical methods into a combination of analytical, computational and measurement methods. It explores implications of these trends in modeling, stability, actuation and control of a single rigid body. These trends are feasible because of recent technical developments in hardware and theory Electronic hardware is currently available for computation, for sensing, and for the combination of the two. Powerful state space methods and large-dimensional system theory have been developed in concept and in software. The availability of modular, efficient and light weight sensors, computer chips and information processors, and the ease of integration of the electrical and mechanical components make the approach presented here more feasible and applicable to a variety of robotic, humanoid, biorobotic and human modeling applications. The approach is based on simultaneous representation of a rigid body in four state spaces. Intelligent choice of one or more of these models at any time is possible. The underlying intelligence can switch the system from one to the other when the system gets close to that representation’s singular points or manifolds. Combinations of two or more such state spaces are possible for having a redundantly formulated system. The paper presents the approach, the state spaces involved, and the Lyapunov stability of the system for a single rigid body.