Rigid Body Vehicle Modeling Using Geometric Mechanics and Multi-vehicle Consensus Control

Abstract

Geometric mechanics is useful in developing a compact description of the motion of a rigid body in three-dimensional space which is singularity-free, unique, does not limit the motion to small angles, and enables a single control law to be obtained even in the presence of translational/rotational coupling. Such a description, which is based on the Lie group SE(3) and its corresponding "exponential coordinates", is especially useful for spacecraft and other types of autonomous vehicles undergoing fast rotations and tumbling motions. This talk will explore various coordinates for rigid body attitude along with their pros and cons (including the phenomenon of unwinding when using a quaternion attitude description) as well as the use of the SE(3) framework in multi-vehicle consensus control design in which it is desired to achieve leader-follower formations along with attitude synchronization. The case of four formation flying spacecraft in a Molniya orbit will serve as an illustrative example.