核心概念
The authors propose a planning framework that translates the problem of planning under Timed Partial Order (TPO) specifications into a Generalized Traveling Salesman Problem (GTSP) with timing and precedence constraints, which they solve using a Mixed Integer Linear Programming (MILP) formulation.
摘要
The paper addresses the challenge of planning a sequence of tasks to be performed by multiple robots while minimizing the overall completion time subject to timing and precedence constraints, specified using the Timed Partial Orders (TPO) model. The authors propose a general planning framework that translates the problem into a Generalized Traveling Salesman Problem (GTSP) variant with timing and precedence constraints, which they solve using a Mixed Integer Linear Programming (MILP) formulation.
The key contributions of the work include:
- A general planning framework for TPO specifications that can be applied to single or multiple robots.
- A MILP formulation that accommodates time windows (global time with respect to the start event) and precedence constraints (local time between sub-tasks), and an extension to the multi-robot setting.
- A method to quantify the robustness of the synthesized plans by capturing the lower and upper bounds on the delays that the plan can tolerate with respect to the given TPO.
- Illustrative case studies and benchmarks that demonstrate the effectiveness of the approach, including a physical experiment for an aircraft turnaround task with three Jackal robots.
The authors show that the TPO constraints actually narrow down the search space, speed up the computation time, and enable scaling up the algorithm to 160 nodes and 40 robots.
統計資料
The aircraft turnaround task with three robots had a makespan of 59 time units.
The single robot case studies had makespans of 152, 155, and 163 time units.
引述
"Our benchmark results show that our MILP method outperforms state-of-the-art open-source TSP solvers OR-Tools."
"Our evaluations of the algorithm on various case studies demonstrate the time-effectiveness of our plans for up to 40 robots with 160 nodes."