  This letter considers model predictive control of a tandem-rotor helicopter.
The error is formulated using the matrix Lie group $SE_2(3)$. A reference
trajectory to a target is calculated using a quartic guidance law, leveraging
the differentially flat properties of the system, and refined using a
finite-horizon linear quadratic regulator. The nonlinear system is linearized
about the reference trajectory enabling the formulation of a quadratic program
with control input, attitude keep-in zone, and attitude error constraints. A
non-uniformly spaced prediction horizon is leveraged to capture the
multi-timescale dynamics while keeping the problem size tractable. Monte-Carlo
simulations demonstrate robustness of the proposed control structure to initial
conditions, model uncertainty, and environmental disturbances.
