Pose tracking using a Lorentzian approximation to rigid-motion

Abstract Geometric formulations of rigid-body dynamics, pose determination and control are conventionally defined on the Special Euclidean Group of motions. In this paper a rigid-motion is defined on a group with Lorentzian structure and is shown to approximate the classical equations of a rigid-body for non-relativistic velocities. A tracking control law is developed using Lyapunov functions and is proved to almost globally asymptotically stablize the error dynamics and kinematics. This demonstrates the advantage of using a Lorentzian structure, in contrast to the Special Euclidean Group, as it is endowed with a non-degenerate trace form that is used to define simple Lyapunov functions for control design and stability proofs.