# Trajectory Generation for Underactuated Multirotor Vehicles with Tilted Propellers via a Flatness-based Method

## TL;DR

This paper introduces a flatness-based trajectory generation method for underactuated multirotor vehicles with tilted propellers, enabling precise 3D path following through a numerical collocation approach.

## Contribution

It demonstrates that such vehicles' position and heading are flat outputs and provides a numerical strategy for trajectory planning and control input computation.

## Key findings

- Validated on tricopter, quadrotor, and hexacopter models
- Effective trajectory generation for vehicles with tilted propellers
- Numerical verification confirms method's practicality

## Abstract

This paper considers a class of rotary-wing aerial robots with unaligned propellers. By studying the dynamics of these vehicles, we show that the position and heading angle remain flat outputs of the system (similar to conventional quadrotors). The implication is that they can be commanded to follow desired trajectory setpoints in 3D space. We propose a numerical strategy based on the collocation method to facilitate the trajectory generation. This enables convenient computation of the nominal robot's attitude and control inputs. The proposed methods are numerically verified for three multirotor robots with different dynamics. These include a tricopter with a tilting propeller, and a quadrotor and a hexacopter with unparalleled propellers.