Geometric MPC Techniques for Reduced Attitude Control on Quadrotors with Bidirectional Thrust

We present two novel nonlinear MPC formulations for reduced attitude tracking on quadrotors with bidirectional thrust capabilities. Reduced attitude tracking is relevant to recovery from partial thrust loss, which can occur due to the failure of one or more motors. The first formulation builds on a linearization of the quadrotor attitude dynamics on
$S(2)$
to achieve simultaneous tracking of reduced attitude and total thrust targets. The second formulation, meanwhile, accomplishes the same goal using a linearization of the dynamics on the Lie algebra of
$SO(3)$
and a proposed method for projecting Lie algebra errors onto reduced attitude errors. Both methods achieve global tracking on
$S(2)$
without requiring the use of computationally expensive sequential quadratic program solvers. Through simulations, we show that the second approach generally tracks aggressive attitude references better, while the first controller offers more reliable regulation.