Route Optimization in Precision Agriculture Settings: A Multi-Steiner TSP Formulation

Abstract

In this work, we propose a route planning strategy for heterogeneous mobile robots in Precision Agriculture (PA) settings. Given a set of agricultural tasks to be performed at specific locations, we formulate a multi-Steiner Traveling Salesman Problem (TSP) to define the optimal assignment of these tasks to the robots as well as the respective optimal paths to be followed. The optimality criterion aims to minimize the total time required to execute all the tasks, as well as the cumulative execution times of the robots. Costs for travelling from one location to another, for maneuvering and for executing the task as well as limited energy capacity of the robots are considered. In addition, we propose a sub-optimal formulation to mitigate the computational complexity by leveraging the fact that generally in PA settings only a few locations require agricultural tasks in a certain period of interest compared to all possible locations in the field. A formal analysis of the optimality gap between the optimal and the sub-optimal formulations is provided. The effectiveness of the approach is validated in a simulated orchard where three heterogeneous aerial vehicles perform inspection tasks. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper aims at providing an efficient solution to PA needs by deploying a team of robots able to perform agricultural tasks at given locations in large-scale orchards. In particular, a novel general optimization problem is proposed that, given a set of mobile and possibly heterogeneous robots and a set of agricultural tasks to carry out, defines the assignment of these tasks to the robots as well as the routes to follow, while minimizing the total and the cumulative execution times of the robots. Existing approaches for route optimization in PA generally involves complete coverage of the field by one or multiple robots and do not account for maneuvering costs with general layouts of the field. We consider costs for travelling from one location to another, for executing the task and for maneuvering without any restriction on the layout of the plants as well as we take into account the limited energy capacity of the robots. We also provide a sub-optimal formulation which reduces the computational burden by relaxing the optimization of the maneuvering costs at the locations where agricultural tasks are carried out and formally derive the optimality gap. The proposed approach is flexible and can be easily adapted to any PA setting involving multiple mobile robots that are required to accomplish given tasks in an area of interest. We validate its effectiveness in a realistic simulated setup composed of three heterogeneous aerial vehicles performing inspection tasks. In future research, we aim to design algorithms to solve the proposed optimization problems in an efficient manner as well as to validate the formulations on real-world robotic platforms.