Exploiting Different Symmetries for Trajectory Tracking Control with Application to Quadrotors*

High performance trajectory tracking control of quadrotor vehicles is an important challenge in aerial robotics. Symmetry a fundamental property physical systems and offers the potential to provide tool design high-performance algorithms. We propose methodology that takes any given symmetry, linearises associated error single set coordinates, uses LQR obtain high control; approach we term Equivariant Regulator design. show admit several different symmetries: direct product extended pose symmetry velocity each can be used define global error. compare linearised via simulation find symmetries outperform presence large disturbances. This suggests choices equivariant group affine have improved linearisation