# Computing minimum-time trajectories for quadrotors via transverse coordinates

## TL;DR

This paper introduces a new method using transverse coordinates to efficiently compute minimum-time trajectories for quadrotors in constrained environments, accounting for physical limitations.

## Contribution

It presents a novel re-formulation of the trajectory optimization problem using transverse coordinates, enabling fixed horizon planning and easier constraint handling.

## Key findings

- Successful numerical simulations in complex scenarios
- Efficient handling of position constraints
- Fixed horizon problem formulation

## Abstract

In this paper we present a novel strategy to compute minimum-time trajectories for quadrotors. In particular, we consider the motion in constrained environments, taking into account the physical limitations of the vehicle. Instead of approaching the optimization problem in its standard time-parameterized formulation, the proposed strategy is based on an appealing re-formulation. Transverse coordinates, expressing the distance from a "reference" path, are used to parameterize the vehicle position and a spatial parameter is used as independent variable. This re-formulation allows us to (i) obtain a fixed horizon problem and (ii) easily formulate (even complex) position constraints. The effectiveness of the proposed strategy is proven by numerical computations on two different illustrative scenarios.