Matthew Hampsey's Talk on Nonlinear trajectory tracking on homogeneous spaces

Title: Nonlinear trajectory tracking on homogeneous spaces

Time, Date, Location: 11:00, Friday, 14 April, 2023, Brian Anderson Building Seminar Room

Abstract: Accurate tracking of planned trajectories in the presence of perturbations is a fundamental problem in control and robotics. A powerful set of tracking control algorithms have been developed over the last half-century, however, these tools often rely on local coordinates or extrinsic features of the system state space. Initial work in equivariant systems theory has begun addressing these shortcomings for systems with transitive symmetries. Symmetry is a fundamental mathematical feature of many dynamical systems and allows for intrinsic formulations of much of the structure required for these control tools. In this thesis proposal review, I present a recent conference paper of ours which formulates a geometrically motivated linear tracking controller for input-affine systems on homogeneous spaces. Additionally, I present my plans for future work in the area of geometric control for equivariant systems.