Motion Primitives for Stabiluization and Control of Underactuated Vehicle

Francesco Bullo, Caltech, Control & Dynamical Systems

In this talk we present controllability tests and motion algorithms for a class of underactuated systems that include planar vehicles, spacecrafts and submersibles. The vehicles are modelled as mechanical systems on Lie groups, with the Lagrangian equal to kinetic energy and with body-fixed forces. We characterize the set of reachable velocities and configurations via the operations of Lie bracket and symmetric product. Perturbation theory is then applied to compute approximate solutions for the system under small-amplitude forcing. Based on these analyses, we design two motion primitives that perform the basic tasks of changing and maintaining velocity. These primitives can then be used for a variety of low velocity maneuvers, such as exponential point stabilization and static interpolation. We evaluate our algorithms and investigate the advantage of planning motions along relative equilibria.