Kinematic Orienteering Problem With Time-Optimal Trajectories for Multirotor UAVs

TL;DR

This paper introduces the Kinematic Orienteering Problem (KOP), combining location prioritization with time-optimal UAV trajectories, and proposes an exact formulation and heuristic solution, validated through benchmarks and simulations.

Contribution

It formulates the Kinematic Orienteering Problem, integrating time-optimal trajectory generation with location selection, and provides an exact mixed-integer model and a heuristic approach.

Findings

The proposed approach outperforms existing methods on benchmark instances.

Simulations show trajectories can be tracked accurately by MPC controllers.

An improved analytical method for time-optimal trajectory generation is presented.

Abstract

In many unmanned aerial vehicle (UAV) applications for surveillance and data collection, it is not possible to reach all requested locations due to the given maximum flight time. Hence, the requested locations must be prioritized and the problem of selecting the most important locations is modeled as an Orienteering Problem (OP). To fully exploit the kinematic properties of the UAV in such scenarios, we combine the OP with the generation of time-optimal trajectories with bounds on velocity and acceleration. We define the resulting problem as the Kinematic Orienteering Problem (KOP) and propose an exact mixed-integer formulation together with a Large Neighborhood Search (LNS) as a heuristic solution method. We demonstrate the effectiveness of our approach based on Orienteering instances from the literature and benchmark against optimal solutions of the Dubins Orienteering Problem (DOP) as the state-of-the-art. Additionally, we show by simulation \color{black} that the resulting solutions can be tracked precisely by a modern MPC-based flight controller. Since we demonstrate that the state-of-the-art in generating time-optimal trajectories in multiple dimensions is not generally correct, we further present an improved analytical method for time-optimal trajectory generation.