Trajectory Generation and Control for Quadrotors

A method for the control of quadrotors is presented. It is composed of a high-level reference smoothing step and a low-level reference tracking step. The high-level step leverages the Dubins airplane model for dimensionality reduction and reduced computational complexity, and exploits its structure for decoupling, spatial modeling and the formulation of a small linear program. The low-level step leverages a geometric tracking controller, which is based on the full quadrotor model. The method is designed for the tracking of references subject to lateral constraints along the path. An example is the tracking of references along obstacle contours. It is differentiated between two different setups. Either the high-level planning step is conducted once and offline, or, alternatively, the high-level planning step is conducted recedingly online in closed-loop over a limited spatial prediction horizon.

Quadrotor controller comparisons commonly report a single tracking error, although the resulting ranking also depends on tuning effort, reference information, actuator prediction, optimizer fallback, and command timing. We quantify these effects for cascade PID, hover LQR, boundary-layer sliding-mode control (BL-SMC), linear MPC with LQR fallback (LMPC-F), a preview-enabled LMPC-F, and a geometric $SO(3)$ controller on a common nonlinear plant with rotor gyroscopic coupling, motor lag, and saturation. A primary study (556 episodes at 50Hz) combines matched twelve-candidate tuning, 400 paired evaluation episodes, and a 48-cell MPC factorial; a confirmation study (1462 episodes) repeats the evaluation on 50 fresh realizations with tuning budgets of 12, 24, and 48 candidates. A matched twelve-candidate tuning protocol changed the mean-RMSE ordering obtained with the fixed baseline settings, moving BL-SMC from last to first; the new ordering recurred on the fresh realizations, and a 48-candidate budget left it unchanged. Reference preview substantially reduced MPC tracking error and, on the figure-eight task, removed fallback activity. On an abrupt step, the outcome depended on the interplay between fallback policy, predictor, and actuator authority. Command timing also changed the outcome: replaying measured command-call delays terminated three of four nominal MPC configurations on a desktop computer and all four on a Raspberry Pi5, whereas capping the solver at 100 iterations removed every deadline miss in the tested nominal timing profiles. Controller rankings therefore depend not only on tracking accuracy but also on the tuning protocol, reference information, fallback behavior, and implementation timing. We propose a reporting checklist covering tracking accuracy, tuning effort, completion and failure rates, fallback activity, applied-input variation, and command timing.

This paper derives an analytical differential flatness transform for a tailsitter Unmanned Aerial Vehicle (UAV) under coordinated flight conditions using a simplified aerodynamic model. The proposed framework is formulated exclusively using rotation matrices, avoiding the ambiguities inherent to Euler angle representations. The method extends the applicability of an existing state-of-the-art differential flatness-based controller to flight regimes involving a significant vertical velocity component, where the previous approach becomes inapplicable. The proposed framework is validated experimentally with trajectories that highlight its advantages in these regimes.