Multi-Robot Routing Problem with Min–Max Objective

Jennifer David,Thorsteinn Rögnvaldsson

doi:10.3390/robotics10040122

Abstract

In this paper, we study the “Multi-Robot Routing problem” with min–max objective (MRR-MM) in detail. It involves the assignment of sequentially ordered tasks to robots such that the maximum cost of the slowest robot is minimized. The problem description, the different types of formulations, and the methods used across various research communities are discussed in this paper. We propose a new problem formulation by treating this problem as a permutation matrix. A comparative study is done between three methods: Stochastic simulated annealing, deterministic mean-field annealing, and a heuristic-based graph search method. Each method is investigated in detail with several data sets (simulation and real-world), and the results are analysed and compared with respect to scalability, computational complexity, optimality, and its application to real-world scenarios. The paper shows that the heuristic method produces results very quickly with good scalability. However, the solution quality is sub-optimal. On the other hand, when optimal or near-optimal results are required with considerable computational resources, the simulated annealing method proves to be more efficient. However, the results show that the optimal choice of algorithm depends on the dataset size and the available computational budget. The contribution of the paper is three-fold: We study the MRR-MM problem in detail across various research communities. This study also shows the lack of inter-research terminology that has led to different names for the same problem. Secondly, formulating the task allocation problem as a permutation matrix formulation has opened up new approaches to solve this problem. Thirdly, we applied our problem formulation to three different methods and conducted a detailed comparative study using real-world and simulation data.

Highlights

In Multi-Robot Systems (MRSs), a group of robots aim to perform one or more tasks together or individually
Some examples of task/problem constraints are—a specific task cannot be done until another task is completed [7], tasks should be done on a specific schedule [8], some tasks require multiple robots [9], the robots should come back to their initial position after completing all the tasks [10], tasks should be done within a given time frame [11], the number of robots required to do all the tasks should be minimized [12], and robots should adapt to human intervention [13], etc
Related Work we review the “Multi Robot Routing Problems (MRR)-MM problem”, as dealt with by different research communities and the approaches by robotics community

Summary

Introduction

In Multi-Robot Systems (MRSs), a group of robots aim to perform one or more tasks together or individually. These systems are widely used in real world applications like warehouse automation [1], search and rescue [2], exploration [3], mapping and surveying [4], etc. The problem comes in different variants depending on the assumptions, constraints, and objective function. The difference depends on the assumptions of the problem, the objective function of the problem, and the constraints. Some examples of task/problem constraints are—a specific task cannot be done until another task is completed (precedence constraints) [7], tasks should be done on a specific schedule (scheduling problem) [8], some tasks require multiple robots (multi-robot tasks) [9], the robots should come back to their initial position after completing all the tasks (depot problem) [10], tasks should be done within a given time frame (timed tasks) [11], the number of robots required to do all the tasks should be minimized (minimum robot utilisation) [12], and robots should adapt to human intervention (human-robot collaboration) [13], etc

Methods

Results

Discussion

Conclusion