Coverage Trajectory Planning Problem on 3D Terrains with safety constraints for automated lawn mower: Exact and heuristic approaches

Recent technological advancements in automation have attracted increased interest in automated lawn mowers. Developing a safe and efficient trajectory to cover entire terrains is crucial for autonomous mowing. Unlike the simplified indoor environments with flat surfaces commonly assumed in existing literature, lawn maintenance typically occurs in complex outdoor settings characterized by irregular terrains, including obstacles and slopes. These irregularities pose significant safety risks, such as the potential for the mower to tip over. This paper introduces the Coverage Trajectory Planning Problem on 3D Terrains (CTPP-3DT), which involves determining both the path and speed profile for an automated lawn mower to effectively cover a general 3D terrain with varying slopes. The objective of the CTPP-3DT is to minimize the completion time, including the time for turning, which satisfies safety constraints on the robot’s speed and acceleration on various slopes. To address this challenge, we first propose a Mixed-Integer Linear Programming (MILP) model based on a graph expansion method, suitable for solving small-scale instances. For larger instances, we develop a decomposition-based heuristic algorithm using Simulated Annealing. Extensive experiments conducted on benchmark instances demonstrate the effectiveness of our proposed MILP model and heuristic algorithm for small-size and large-size instances. The comparison between the optimized strategy and the conservative strategy highlights the necessity of incorporating safety constraints in trajectory planning, resulting in an average reduction of more than 40% in completion time. Furthermore, sensitivity analyses reveal that technological advancements in mowers, such as increasing the maximum speed and acceleration and reducing turning speed, can significantly reduce the overall completion time. Our code and data are available at https://github.com/CATS-Lab/Mower-CTPP-3D.