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

Abstract

In this work, we propose a route planning strategy 1 for heterogeneous mobile robots in Precision Agriculture (PA) 2 settings. Given a set of agricultural tasks to be performed 3 at specific locations, we formulate a multi-Steiner Traveling 4 Salesman Problem (TSP) to define the optimal assignment of 5 these tasks to the robots as well as the respective optimal paths 6 to be followed. The optimality criterion aims to minimize the total 7 time required to execute all the tasks, as well as the cumulative 8 execution times of the robots. Costs for travelling from one 9 location to another, for maneuvering and for executing the task 10 as well as limited energy capacity of the robots are considered. 11 In addition, we propose a sub-optimal formulation to mitigate the 12 computational complexity by leveraging the fact that generally 13 in PA settings only a few locations require agricultural tasks in a 14 certain period of interest compared to all possible locations in the 15 field. A formal analysis of the optimality gap between the optimal 16 and the sub-optimal formulations is provided. The effectiveness 17 of the approach is validated in a simulated orchard where three 18 heterogeneous aerial vehicles perform inspection tasks. 19 Note to Practitioners-This paper aims at providing an efficient 20 solution to PA needs by deploying a team of robots able 21 to perform agricultural tasks at given locations in large-scale 22 orchards. In particular, a novel general optimization problem is 23 proposed that, given a set of mobile and possibly heterogeneous 24 robots and a set of agricultural tasks to carry out, defines the 25 assignment of these tasks to the robots as well as the routes to 26 follow, while minimizing the total and the cumulative execution 27 times of the robots. Existing approaches for route optimization 28 in PA generally involves complete coverage of the field by one 29 or multiple robots and do not account for maneuvering costs 30 with general layouts of the field. We consider costs for travelling 31 from one location to another, for executing the task and for 32 maneuvering without any restriction on the layout of the plants 33 as well as we take into account the limited energy capacity of the 34 robots. We also provide a sub-optimal formulation which reduces 35 the computational burden by relaxing the optimization of the 36 maneuvering costs at the locations where agricultural tasks are 37 Manuscript

IoT, UAV, BCI Empowered Deep Learning models in Precision Agriculture

“…This may mean proposing very simple trajectories: straight lines as in (Mesas-Carrascosa et al, 2018) or a grid pattern as in . Usually, the UAV dynamics are ignored when assessing battery consumption (Furchì et al, 2022). Still, the drone behavior and type of trajectories employed can have a disproportionate effect on battery life.…”

Orchard monitoring based on unmanned aerial vehicles and image processing by artificial neural networks: a systematic review

“…This may mean proposing very simple trajectories: straight lines as in ( Mesas-Carrascosa et al., 2018 ) or a grid pattern as in ( Mu et al., 2018 ). Usually, the UAV dynamics are ignored when assessing battery consumption ( Furchì et al., 2022 ). Still, the drone behavior and type of trajectories employed can have a disproportionate effect on battery life.…”

“…Most if not all graph-based methods are based on variations of the Traveling Salesman Problem (TSP). ( Furchì et al., 2022 ) uses a Steiner TSP implementation where only a subset of the nodes must be visited. The paper is also noteworthy for considering battery usage and integrating it as a weight for the graph edges.…”

“…In general, formulating decision problems (graph-based or otherwise) for efficient orchard travel leads to a difficult optimization problem. Authors ( Furchì et al., 2022 ) provided a mixed-integer formulation that makes use of binary variables to characterize decisions in the problem (which node is next, which path is followed from a given list, etc.). Such methods are prone to numerical issues and quickly become impractical for real-time implementations.…”

An autonomous spraying robot architecture for sucker management in large‐scale hazelnut orchards

“…This is motivated by the fact that these two problems are de-facto decoupled and for this reason we leave the autonomous selection of the best location for future work. In this regard, a possible approach would be to follow the framework we proposed in (Furchì et al, 2022), where a Multi-Platform Steiner Traveling Salesman Problem (MP-STSP) is designed for selecting the best routes for a team of robots that need to perform agronomical activities in an orchard.…”