Executing precise and agile flight maneuvers is important for the ongoing commoditization of unmanned aerial vehicles (UAVs), in applications such as drone delivery, rescue and search, and urban air mobility. In particular, accurately following arbitrary trajectories with quadrotors is among the most notable challenges to precise flight control for the following reasons. First, quadrotor dynamics are highly nonlinear and underactuated, and often hard to model due to unknown system parameters (e.g., motor characteristics) and uncertain environments (e.g., complex aerodynamics from unknown wind gusts). Second, aggressive trajectories demand operating at the limits of system performance, requiring awareness and proper handling of actuation constraints, especially for quadrotors with small thrust-to-weight ratios. Finally, the arbitrary desired trajectory might not be dynamically feasible (i.e., impossible to stay on such a trajectory), which necessities long-horizon reasoning and optimization in real-time. For instance, to stay close to the five-star trajectory in Figure 1, which is infeasible due to the sharp changes of direction, the quadrotor must predict, plan, and react online before the sharp turns.

A major challenge in robotics is to design robust policies which enable complex and agile behaviors in the real world. On one end of the spectrum, we have model-free reinforcement learning (MFRL), which is incredibly flexible and general but often results in brittle policies. In contrast, model predictive control (MPC) continually re-plans at each time step to remain robust to perturbations and model inaccuracies. However, despite its real-world successes, MPC often under-performs the optimal strategy. This is due to model quality, myopic behavior from short planning horizons, and approximations due to computational constraints. And even with a perfect model and enough compute, MPC can get stuck in bad local optima, depending heavily on the quality of the optimization algorithm. To this end, we propose Deep Model Predictive Optimization (DMPO), which learns the inner-loop of an MPC optimization algorithm directly via experience, specifically tailored to the needs of the control problem. We evaluate DMPO on a real quadrotor agile trajectory tracking task, on which it improves performance over a baseline MPC algorithm for a given computational budget. It can outperform the best MPC algorithm by up to 27% with fewer samples and an end-to-end policy trained with MFRL by 19%. Moreover, because DMPO requires fewer samples, it can also achieve these benefits with 4.3X less memory. When we subject the quadrotor to turbulent wind fields with an attached drag plate, DMPO can adapt zero-shot while still outperforming all baselines. Additional results can be found at https://tinyurl.com/mr2ywmnw.