Single rigid body representation, control and stability for robotic applications

In this paper, a novel formulation of the dynamics, control and stability of a single rigid body is presented. Effects of gravity, and visco-elastic coupling to an inertial frame of reference at a single point of contact are included. This formulation is very convenient, and analytically tractable for animation and computer simulation of human, animal, robotic and humanoid movements, for studies of performance assessment and enhancement in natural and man-made systems, and in other studies of systems of connected rigid bodies. The representation includes simple and general linear and nonlinear position and velocity, i.e., state feedback structures that guarantee asymptotic stability of the system in the sense of Lyapunov. The Lyapunov function is simply the physical energy stored in the system, namely, a quadratic in the state space of the system: the sum of kinetic, elastic and potential energies of the system The approach is extended to a rigid body coupled to an inertial frame of reference. Digital computer simulation of the behavior of the system under disturbance are presented.