Geometric Tracking Control of Omnidirectional Multirotors for Aggressive Maneuvers

TL;DR

This work tackles tracking for omnidirectional multirotors during aggressive maneuvers by integrating a first-order rotor thrust dynamics model into the full vehicle dynamics and designing a geometric PD controller that compensates rotor dynamics without requiring rotor-state measurements. The translational and rotational loops are decoupled, with commanded wrench terms $\mathbf{F}_{cmd}=\mathbf{F}_{d}+\alpha \dot{\mathbf{F}}_{d}$ and $\mathbf{M}_{cmd}=\mathbf{M}_{d}+\alpha \dot{\mathbf{M}}_{d}$, and stability is established via Lyapunov analysis: global exponential stability for translation, almost global exponential stability for rotation, and exponential stability for the full system under prescribed gain conditions. The approach is validated experimentally on an eight-rotor platform, showing substantial improvements in translational and rotational tracking over a baseline controller that neglects rotor dynamics, demonstrating the practical impact of accounting for rotor dynamics in fully actuated multirotors. These results advance the capability of omnidirectional multirotors to perform precise, aggressive maneuvers in dynamic environments without extra rotor-state sensing hardware.

Abstract

An omnidirectional multirotor has the maneuverability of decoupled translational and rotational motions, superseding the traditional multirotors' motion capability. Such maneuverability is achieved due to the ability of the omnidirectional multirotor to frequently alter the thrust amplitude and direction. In doing so, the rotors' settling time, which is induced by inherent rotor dynamics, significantly affects the omnidirectional multirotor's tracking performance, especially in aggressive flights. To resolve this issue, we propose a novel tracking controller that takes the rotor dynamics into account and does not require additional rotor state measurement. This is achieved by integrating a linear rotor dynamics model into the vehicle's equations of motion and designing a PD controller to compensate for the effects introduced by rotor dynamics. We prove that the proposed controller yields almost global exponential stability. The proposed controller is validated in experiments, where we demonstrate significantly improved tracking performance in multiple aggressive maneuvers compared with a baseline geometric PD controller.

Figures (14)

• Figure 1: Coordinate frames of a general omnidirectional multirotor, where $n$ denotes the number of rotors and $\boldsymbol{l}_i \in \mathbb{R}^{3}$ is the position of rotor $i$ from $O_B$. Note that $n\geq 6$ should hold for bidirectional rotors and $n\geq 7$ for unidirectional ones.
• Figure 2: Step response of a rotor with a propeller. The thrust from the rotor is scaled by the maximum thrust generated from the rotor. A 2000KV brushless rotor attached with Gemfan 513D 3-blade 3D propeller has been used for the measurement. Note that $\alpha$ represents the rotor time constant, and the subscripts $f$ and $m$ indicate the time constants of the TD and DCMD models, respectively. The desired and the no-model thrusts are the same, as the latter does not consider rotor dynamics. The time constants are determined experimentally.
• Figure 3: The control diagram of the proposed controller.
• Figure 4: (L-R): Comparison of the omnidirectional multirotor’s position and attitude error between the proposed and baseline controllers over the purely translation trajectory shown on top. Position error of the proposed method reveals significantly lower transient and steady-state tracking errors in the $x$ and $y$ directions, highlighting the enhanced translational tracking performance. Attitude errors are shown via Euler angles for clear interpretation.
• Figure 5: (L-R): The comparison of position and attitude tracking errors of the omnidirectional multirotor with the proposed and baseline controllers over the single-axis rotational trajectory shown on top. The proposed controller demonstrates superior attitude tracking performance, particularly around the z-axis where high angular jerk is applied while maintaining comparable positional stability with regards to the baseline controller.

Theorems & Definitions (3)

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