Application of Log-Linear Dynamic Inversion Control to a Multi-rotor

TL;DR

This paper introduces a novel control approach for multi-rotors using log-linearization and dynamic inversion within Lie group theory, improving robustness and providing safety guarantees under disturbances.

Contribution

The paper develops a log-linear dynamic inversion controller based on Lie group theory, offering exact linear error dynamics and disturbance bounds for multi-rotor systems.

Findings

Enhanced robustness of multi-rotor control under disturbances

Validated safety guarantees through invariant set analysis

Effective tracking error bounds demonstrated in simulations

Abstract

This paper presents an approach that employs log-linearization in Lie group theory and the Newton-Euler equations to derive exact linear error dynamics for a multi-rotor model, and applies this model with a novel log-linear dynamic inversion controller to simplify the nonlinear distortion and enhance the robustness of the log-linearized system. In addition, we utilize Linear Matrix Inequalities (LMIs) to bound the tracking error for the log-linearization in the presence of bounded disturbance input and use the exponential map to compute the invariant set of the nonlinear system in the Lie group. We demonstrate the effectiveness of our method via an illustrative example of a multi-rotor system with a reference trajectory, and the result validates the safety guarantees of the tracking error in the presence of bounded disturbance.