# A Geometric Approach to Rotor Failure Tolerant Trajectory Tracking Control Design for a Quadrotor

## TL;DR

This paper introduces a geometric control method enabling a quadrotor UAV to perform trajectory tracking despite the complete failure of one rotor, using only three rotors and advanced Lie-group based control laws.

## Contribution

It presents a novel two-stage geometric control design on Lie groups that ensures exponential trajectory tracking after rotor failure, extending control capabilities to aggressive maneuvers.

## Key findings

- Control law achieves exponential tracking for all initial conditions in an open-dense set.
- Numerical simulations demonstrate effectiveness on different quadrotor models.
- The approach maintains control despite complete rotor failure, enabling aggressive maneuvers.

## Abstract

This paper addresses the problem of designing a trajectory tracking control law for a quadrotor UAV, subsequent to complete failure of a single rotor. The control design problem considers the reduced state space which excludes the angular velocity and orientation about the vertical body axis. The proposed controller enables the quadrotor to track the orientation of this axis, and consequently any prescribed position trajectory using only three rotors. The control design is carried out in two stages. First, in order to track the reduced attitude dynamics, a geometric controller with two input torques is designed on the Lie-Group $SO(3)$. This is then extended to $SE(3)$ by designing a saturation based feedback law, in order to track the center of mass position with bounded thrust. The control law for the complete dynamics achieves exponential tracking for all initial conditions lying in an open-dense subset. The novelty of the geometric control design is in its ability to effectively execute aggressive, global maneuvers despite complete loss of a rotor. Numerical simulations on models of a variable pitch and a conventional quadrotor have been presented to demonstrate the practical applicability of the control design.