# Minimum-time trajectory generation for quadrotors in constrained environments

## TL;DR

This paper introduces a new method for computing minimum-time trajectories for quadrotors in environments with obstacles, using a re-formulation that simplifies constraints and fixed horizon problems, validated through simulations and real-world experiments.

## Contribution

The paper proposes a novel trajectory generation strategy based on transverse coordinates and spatial parameterization, enabling efficient constrained minimum-time solutions.

## Key findings

- Effective trajectory planning in complex environments demonstrated through simulations.
- Successful real-world execution of planned trajectories with a nano-quadrotor.
- Re-formulation simplifies handling of constraints and fixed horizon optimization.

## Abstract

In this paper, we present a novel strategy to compute minimum-time trajectories for quadrotors in constrained environments. In particular, we consider the motion in a given flying region with obstacles and take 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 frame path, are used to parameterise 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 (fairly complex) position constraints. The effectiveness of the proposed strategy is proven by numerical computations on two different illustrative scenarios. Moreover, the optimal trajectory generated in the second scenario is experimentally executed with a real nano-quadrotor in order to show its feasibility.