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