Dynamical Vehicle Orienteering Problem for Multi-Rotor Unmanned Aerial Vehicles

2026-07-15

AI Summary

This study addresses the problem of maximizing the reward collected by a multirotor unmanned aerial vehicle (UAV) when visiting high-value spatial targets within a finite time horizon, under the coupled effects of gravity and propulsion dynamics. The authors extend the classical Orienteering Problem to a Dynamic Vehicle Orienteering Problem (DVOP) by introducing, for the first time, a full dynamic optimization framework incorporating a 3D point-mass model with explicit constraints on maximum velocity and acceleration. They propose a trajectory-primitive-based mixed-integer linear programming (MILP) formulation to construct upper bounds, complemented by a thrust-decomposition acceleration strategy. An integrated solution approach combining branch-and-bound, nonlinear programming, and large neighborhood search metaheuristics is developed for efficient computation. Experimental results demonstrate a 37% improvement in collected reward over benchmark methods, and real-world flight tests confirm the feasibility and superiority of the generated trajectories.

Abstract

This paper introduces the Dynamical Vehicle Orienteering Problem (DVOP), a generalization of the Orienteering Problem (OP). The OP maximizes the reward collected from spatial targets under a limited travel budget; the DVOP extends it by accounting for both external and vehicle-actuated forces. We study the DVOP in the context of multi-rotor Unmanned Aerial Vehicle (UAV) flight planning, using a three-dimensional Point-Mass Model (PMM) constrained by maximum velocity and acceleration magnitudes and subject to gravitational acceleration, with the travel budget expressed as a maximum flight time. Because the DVOP couples reward maximization with time-optimal trajectory planning, it cannot be formulated as a simple graph problem and solved exactly without relaxing or under-actuating the vehicle dynamics. We therefore propose two solution approaches: a Branch-and-Bound (BnB) procedure that combines Non-Linear Programming (NLP) and Mixed-Integer Linear Programming (MILP) to provide high-quality solutions, and a Large Neighborhood Search (LNS) metaheuristic that supplies an initial reward bound and scales to instances intractable for the BnB. The BnB relies on a novel MILP formulation of travel costs based on minimum-time trajectory primitives through target triplets, yielding a tight reward upper bound, while the LNS uses limited thrust decomposition to compute fast, high-quality PMM trajectories. Experiments on benchmark instances show improvements of up to 37 % over state-of-the-art solutions for the Kinematic Orienteering Problem, and a real-world deployment on a multi-rotor UAV verifies the proposed PMM solution trajectories.

Problem

• Dynamical Vehicle Orienteering Problem
• Unmanned Aerial Vehicle
• trajectory planning
• reward maximization
• flight time constraint

Innovation

• Dynamical Vehicle Orienteering Problem
• Multi-rotor UAV
• Point-Mass Model
• Branch-and-Bound
• Large Neighborhood Search