Optimal Planning for Timed Partial Order Specifications

TL;DR

This paper presents a MILP-based planning framework for multi-robot task scheduling under timed partial order constraints, improving solution quality and robustness over existing methods.

Contribution

It introduces a novel MILP formulation for TPO-based planning, extending it to multi-robot scenarios and demonstrating superior performance on real-world case studies.

Findings

MILP approach outperforms existing TSP solvers

Framework effectively handles timing and precedence constraints

Demonstrated on aircraft turnaround with multiple robots

Abstract

This 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. Our approach uses the Timed Partial Orders (TPO) model to specify these constraints. We translate this problem into a Traveling Salesman Problem (TSP) variant with timing and precedent constraints, and we solve it as a Mixed Integer Linear Programming (MILP) problem. Our contributions include a general planning framework for TPO specifications, a MILP formulation accommodating time windows and precedent constraints, its extension to multi-robot scenarios, and a method to quantify plan robustness. We demonstrate our framework on several case studies, including an aircraft turnaround task involving three Jackal robots, highlighting the approach's potential applicability to important real-world problems. Our benchmark results show that our MILP method outperforms state-of-the-art open-source TSP solvers OR-Tools.