Control algorithms using affine connections on principal fiber bundles

In this paper, we develop tools for studying the control of underactuated mechanical systems that evolve on a configuration space with a principal fiber bundle structure. We utilize the affine connection to describe the equations of motion and study the controllability of such systems. The invariance of the system with respect to the action of a Lie group leads to a reduced form of the affine connection. This connection, and its corresponding symmetric product, are then used to develop constructive, cyclic control inputs to steer the mechanical system. We explore the development of the equations, based on the original formulation by Bullo, and its application to the steering of a blimp-like vehicle with directional thrusters. Copyright (C) 2000 IFAC.