Distributed Control of Rigid Body Attitude Kinematics

Abstract

Because groups of cooperative vehicles have become more common, the need for multi-agent control techniques has increased. A common technique for controlling agents with linear dynamics is the leader-follower approach, in which an inter-agent consensus dynamic is combined with external control inputs applied to a subset of agents. In this report, we propose a framework that extends this notion of leader-follower control to a nonlinear setting. In particular, we investigate strategies to control the attitude kinematics of a group of rigid bodies in 3 dimensions. Our proposed framework is unique for three reasons: it is intended to be sufficiently flexible to create arbitrary motion, it is based directly on rotation matrices rather than on a parameterization of attitude, and it assumes that follower agents can only measure their relative orientations. We investigate the properties of this framework through several analyses, beginning with an investigation into equilibria and stability. We prove the near-global asymptotic stability of consensus for the 2-agent case, and use numerical tools to indicate that consensus behavior is asymptotically stable for any network which does not contain any loops. We then study controllability and optimal control, and provide a means to compute first-order optimal control inputs via Pontryagin's maximum principle. Finally, we apply our algorithm to the design of a mission to inspect a damaged satellite. We show that by using our framework for leader-follower control, a team of four cubesats can maintain accurate pointing throughout a complex 3-D trajectory with only two of the four agents having external reference information about their position relative to the target.