Unmanned Aerial Vehicle routing and trajectory optimisation problems

Abstract

In recent years, employing Unmanned Aerial Vehicles (UAV) to collect data and making measurements has gained popularity. Often, the use of UAVs allows for a reduction in costs and improvements of other performance criteria. The academic routing community has acknowledged the interest of companies and organisations in adopting UAVs in their operations. However, constraints due to the flight dynamics of UAVs have often been neglected. Finding feasible trajectories for UAVs in a routing problem is a complex task, but it is necessary to ensure the feasibility of the routes. In this thesis we introduce the Unmanned Aerial Vehicle Routing and Trajectory Optimisation Problem (UAVRTOP), the problem of optimising the routes and trajectories of a fleet of UAVs subject to flight dynamics constraints. Motivated by a disaster assessment application, we propose a variant of the UAVRTOP, in which a fleet of autonomous aerial gliders is required to photograph a set of points of interest in the aftermath of a disaster. This problem is referred to as the Glider Routing and Trajectory Optimisation Problem (GRTOP). In this work, we propose a single-phase Mixed-Integer Non-linear Programming (MINLP) formulation for the GRTOP. Our formulation simultaneously optimises routes and the flight trajectories along these routes while the flight dynamics of the gliders are modelled as ordinary differential equations. We avoid dealing with non-convex dynamical constraints by linearising the gliders’ Equations of Motion (EOMs), reducing the proposed MINLP into a Mixed-Integer Second-Order Cone Programming (MISOCP) problem. Another contribution of this work consists of proposing a multi-phase MINLP formulation for a modified version of the GRTOP. We do not attempt to solve this formulation directly, instead we propose a hybrid heuristic method that is composed of two main building blocks: (i) a Sequential Trajectory Optimisation (STO) heuristic, designed to cope with the challenging task of finding feasible (flyable) trajectories for a given route; and (ii) a routing matheuristic, capable of generating routes that can be evaluated by STO. We perform computational experiments with real-life instances based on flood risk maps of cities in the UK as well as in a large number of randomly generated instances.

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ORCID for Joerg Fliege: orcid.org/0000-0002-4459-5419

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