A General Framework for Rigid Body Dynamics, Stability, and Control

Abstract

Augmented state spaces for the representation of systems that include rigid bodies, actuators, controllers, and integrate mechanical, electrical, sensory, and computational subsystems, are proposed here. The formulation is based on the Newton-Euler point of view, and has many advantages in stability, control, simulation, and computational considerations. The formulation is developed here for a one- and two-link three-dimensional rigid body system. Three simulations are presented to study stability of the system and to demonstrate feasibility and application of the formulation. The formulation affords an embedding of the system in a larger state space. The rigid body system can be stabilized, in the sense of Lyapunov, in this larger space with very general and minimally restricted feedback structures. The formulation is modular to implementation and is computationally efficient. The method offers alternative states that are easier to control and measure than Euler angles. Thus, the formulation offers advantages from a sensory and instrumentation point of view. The formulation is versatile, and yields conveniently to applications in studies of human neuro-musculo-skeletal systems, robotic systems, marionettes and humanoids for animation and simulation of crash and other injury prone maneuvers and sports. It offers a methodical and systematic procedure for formulation of large systems of interconnected rigid bodies.