Geometric Backstepping Control of Omnidirectional Tiltrotors Incorporating Servo-Rotor Dynamics for Robustness against Sudden Disturbances

TL;DR

The paper addresses robustness of omnidirectional tiltrotors by incorporating rotor and tilt-servo actuator dynamics into the controller design. It proposes a geometric backstepping strategy leveraging a cascaded rigid-body and actuator-dynamics model and provides Lyapunov-based stability proofs showing exponential stability for known actuator parameters and boundedness under uncertainty. Key contributions include an actuator-aware control design with full-system stability guarantees, robustness to time-constant variations, and hardware validation across fast translational and rotational tasks and disturbance recovery, demonstrating clear advantages over a baseline. The work enhances the reliability and performance of agile omnidirectional flight under practical actuator delays and nonlinearities.

Abstract

This work presents a geometric backstepping controller for a variable-tilt omnidirectional multirotor that explicitly accounts for both servo and rotor dynamics. Considering actuator dynamics is essential for more effective and reliable operation, particularly during aggressive flight maneuvers or recovery from sudden disturbances. While prior studies have investigated actuator-aware control for conventional and fixed-tilt multirotors, these approaches rely on linear relationships between actuator input and wrench, which cannot capture the nonlinearities induced by variable tilt angles. In this work, we exploit the cascade structure between the rigid-body dynamics of the multirotor and its nonlinear actuator dynamics to design the proposed backstepping controller and establish exponential stability of the overall system. Furthermore, we reveal parametric uncertainty in the actuator model through experiments, and we demonstrate that the proposed controller remains robust against such uncertainty. The controller was compared against a baseline that does not account for actuator dynamics across three experimental scenarios: fast translational tracking, rapid rotational tracking, and recovery from sudden disturbance. The proposed method consistently achieved better tracking performance, and notably, while the baseline diverged and crashed during the fastest translational trajectory tracking and the recovery experiment, the proposed controller maintained stability and successfully completed the tasks, thereby demonstrating its effectiveness.

Figures (5)

• Figure 1: Time-lapse composite images from the experiments, where blue arrows indicate the commanded setpoint direction. Panels ①--③ show the time sequence under a sudden rotational disturbance from a falling object connected to the multirotor with a red cable. The proposed controller allows the omnidirectional multirotor to follow the setpoint in order ①$\rightarrow$②$\rightarrow$③ and remain stable, while the baseline diverges and crashes.
• Figure 2: Step responses of the rotor and servomotor to step commands of varying amplitude. The actuator time constant varies with step size, highlighting the need for robustness to uncertainty in this parameter.
• Figure 3: Experiment 1 results. Three trials were conducted along a lemniscate (figure-eight) trajectory at different average speeds. The mean and variance are shown, excluding the failed baseline case at the highest speed where only the proposed method succeeded. Overall, the proposed method tracks the desired trajectory more accurately.
• Figure 4: Experiment 2 results. With position held fixed, the roll angle was rapidly varied. The proposed controller (red) achieved more accurate position regulation and orientation tracking than the baseline (blue).
• Figure 5: Experiment 3 results. The initial disturbance, indicated by the yellow arrow, was caused when a 0.21 kg mass suspended by a string and initially resting on a table was pulled, applying a rotational disturbance to the multirotor. While the baseline diverged, the proposed controller stabilized the system and demonstrated superior performance.

Theorems & Definitions (8)

• Lemma 1
• proof
• Theorem 1
• proof
• Lemma 2
• proof
• Theorem 2
• proof