Aerospace 2015, 2, 155-170; doi:10.3390/aerospace2020155
OPEN ACCESS
aerospace
ISSN 2226-4310
www.mdpi.com/journal/aerospace
Article
Path Planning Using Concatenated Analytically-Defined
Trajectories for Quadrotor UAVs
†
Jonathan Jamieson * and James Biggs
Mechanical and Aerospace Engineering, University of Strathclyde, 75 Montrose Street,
Glasgow G1 lXJ, UK; E-Mail: james.biggs@strath.ac.uk
†
This paper is an extended version of our paper published in ECC 15, Linz, Austria.
* Author to whom correspondence should be addressed; E-Mail: jonathan.jamieson@strath.ac.uk;
Tel.: +44-141-574-5036.
Academic Editor: Konstantinos Kontis
Received: 23 February 2015 / Accepted: 16 April 2015 / Published: 21 April 2015
Abstract: This paper presents a semi-analytical trajectory planning method for quadrotor
UAVs. These trajectories are analytically defined, are constant in speed and sub-optimal
with respect to a weighted quadratic cost function of the translational and angular velocities.
A technique for concatenating the trajectories into multi-segment paths is demonstrated.
These paths are smooth to the first derivative of the translational position and pass through
defined waypoints. A method for detecting potential collisions by discretizing the path
into a coarse mesh before using a numerical optimiser to determine the point of the path
closest to the obstacle is presented. This hybrid method reduces the computation time
when compared to discretizing the trajectory into a fine mesh and calculating the minimum
distance. A tracking controller is defined and used to show that the paths are dynamically
feasible and the typical magnitudes of the controller inputs required to fly them.
Keywords:
UAV; trajectory planning; quadrotor; obstacle avoidance; sub-Riemannian curves
1. Introduction
Unmanned aerial system (UAS) applications often require the vehicle to fly in areas with many
obstacles. With this desire to fly in restricted space, such as urban environments, there is increasing
need for better path and trajectory planning. Typical UAS civilian applications, such as data collection,
