High-Dimensional Optimal State-Feedback Mapping using Deep Neural Networks for Agile Quadrotor Flight

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For most robotics applications, optimal control remains a promising solution for solving complex control tasks. One example is the time-optimal flight of Micro Air Vehicles (MAVs), where strict computational requirements fail to resolve such algorithms onboard. Recent work on the use of deep neural networks for guidance and control (G&CNets) has shown that these biologically inspired models approximate well the optimal control solution while requiring a fraction of the computational cost. Although previous attempts resulted in successful flight tests, training occurred on large-scale datasets based on a 3-DoF model. Since model refinement leads to higher generation time, in this work, we show that G&CNets trained on small-sized datasets can mimic the optimal control solution of a full 6-DoF quadrotor model. The cost function used in the generation process penalizes the altitude error and mixes both time and power-optimal objectives weighted by a varying homotopy parameter. Trained networks output the vertical thrust command and body rates based on the vehicle's position, velocity, and attitude. The proposed controller transfers well onboard for different flight scenarios: (i) longitudinal, lateral and diagonal flight; (ii) hovering with and without the effect of disturbances and (iii) waypoint tracking experiment. Through a Monte-Carlo test campaign, it is demonstrated that G&CNets trained on small datasets provide similar results to those with 100 times more samples. To the best of our knowledge, this work is the first implementation of a high-dimensional G&CNet in the control loop of a real MAV.