An integer linear programming model for efficient scheduling of UGV tasks in precision agriculture under human supervision

In precision agriculture more and more robots are being used to perform tasks that may include some farming activities, such as pruning, inspection or spraying, assigned to the robot as a result of a previous analysis activity or autonomously identified by the machine itself. In this sensitive scenario, reporting difficult situations to a decision maker, e.g., a human operator or some sophisticated software tools that cannot be integrated with the robot, could be useful to perform the correct action that the machine has to execute. Unfortunately, this key aspect is still neglected in current literature that focuses, instead, on fully automated operations by robots. Moreover, it is necessary to consider that in rural areas it often happens that successful data communication can only be achieved in certain locations in the field. In this context, we aim to address all the previous shortcomings by formulating a more comprehensive optimization problem, which also models the necessity to report to a central location and get instructions on the task to be done before proceeding to perform each action. After presenting two alternative analytical formulations of the problem, i.e. an integer linear programming model (ILP) and a mixed integer linear programming model, we propose a branch and bound algorithm that is guaranteed to find the global minimum cost solution in terms of navigation time. Simulation results show that our proposed algorithm performs about 20 to 30 times faster with respect to commercial linear programming solvers using any of the two analytical models proposed. Moreover, we also propose further improvements to reduce computational time while maintaining solution optimality. Finally, some insight into the development of future heuristics is given by analyzing the speed of convergence towards the optimal solution.