Attitude control via structural vibration : an application of compliant robotics

Abstract

We review and present techniques for effecting and controlling the reorientation of structures "floating" in angular-momentum-conserving environments, applicable to both space robotics and small satellite attitude control. Conventional orientation control methods require either the usage of continuously rotating structures (e.g. momentum wheels) or the jettisoning of system mass (e.g. hydrazine thrusters). However, the systems proposed herein require neither rotating structures nor mass ejection; instead, orientation is controlled by the imposition of a bounded cyclic shape change-the canonical example of such a system is a cat righting herself while falling, thereby always landing on her feet-coupled with the conservation of angular momentum, which acts analogously to a nonholonomic constraint on the system dynamics. Further, by considering the reduced system dynamics, we extend the concept to consider the class of structures where the requisite cyclic shape change is attainable via dynamical effects, such as the normal modes of structural vibration for structures with finite stiffness. This is the central novel result of this thesis and has implications for the design of space structures where the attitude control hardware is integrated directly into the preexisting structure, the development of orientation control techniques for soft robots in space and underwater, and the design of MEMS attitude control actuators for very tiny satellites. We apply mathematical tools drawn from differential geometry and geometric mechanics, which can be intimidating but which provide a comprehensive and powerful framework for understanding a wide range of locomotion problems fundamental to robotics and control theory. These tools allow us to make succinct statements regarding gait design, controllability, and optimality that would be otherwise inaccessible.