M^3RS: Multi-robot, Multi-objective, and Multi-mode Routing and Scheduling

TL;DR

This work defines $M^3RS$, a multi-robot routing and scheduling framework that treats task-level disinfection quality as a decision variable through multiple execution modes. It formulates a MILP with multi-objective optimization and mode selection, enabling explicit QoS–throughput trade-offs under time and energy constraints. To tackle scalability, it introduces clustering-based column generation (CCG), achieving competitive quality with up to 60% reductions in compute time. Across synthetic, simulated, and hardware experiments in disinfection settings, $M^3RS$ demonstrates consistent improvements over fixed-mode baselines and highlights the practical value of QoS-aware planning for healthcare hygiene tasks and similar multi-robot missions.

Abstract

Task execution quality significantly impacts multi-robot missions, yet existing task allocation frameworks rarely consider quality of service as a decision variable, despite its importance in applications like robotic disinfection and cleaning. We introduce the multi-robot, multi-objective, and multi-mode routing and scheduling (M3RS) problem, designed for time-constrained missions. In M3RS, each task offers multiple execution modes with varying resource needs, durations, and quality levels, allowing trade-offs across mission objectives. M3RS is modeled as a mixed-integer linear programming (MIP) problem and optimizes task sequencing and execution modes for each agent. We apply M3RS to multi-robot disinfection in healthcare and public spaces, optimizing disinfection quality and task completion rates. Through synthetic case studies, M3RS demonstrates 3-46$\%$ performance improvements over the standard task allocation method across various metrics. Further, to improve compute time, we propose a clustering-based column generation algorithm that achieves solutions comparable to or better than the baseline MIP solver while reducing computation time by 60$\%$. We also conduct case studies with simulated and real robots. Experimental videos are available on the project page: \href{https://sites.google.com/view/g-robot/m3rs/}{https://sites.google.com/view/g-robot/m3rs/}.

Figures (8)

• Figure 1: Traditional Multi-Robot Task Allocation models overlook Quality of Service (QoS) as a decision variable, assuming agents provide a uniform service level, which can lead to inefficiencies in routing and scheduling under time and resource constraints. The visualization compares three cases: (a) Agents operate at the highest service level (Mode 1), ensuring maximum quality but consuming more time and energy, resulting in missed tasks (e.g., Tasks 2 and 3). (b) Agents operate at the lowest service level (Mode 3), completing all tasks but at reduced quality. (c) M$^3$RS incorporates QoS as a decision variable, allowing agents to balance quality and quantity dynamically--choosing from Mode 1, Mode 2 (moderate quality), and Mode 3--ensuring all tasks are addressed at appropriate service levels. Unlike conventional methods, M$^3$RS enables flexible task allocation by integrating QoS into decision-making, making it well-suited for multi-robot applications such as disinfection and cleaning, where balancing quality and quantity is crucial.
• Figure 2: (a) Column Generation (CG) decomposes an optimization problem into a master problem and a subproblem. The master problem selects the best combination of solutions from a solution pool ($\Omega$), while the subproblem uses dual values from the master to generate promising new candidates. Since $\Omega$ can be very large the CG operates on a smaller subset of solutions, $\textit{i.e.}$$\Omega \subset \Omega'$. This process iterates until no improving solutions are found or a termination condition is met. (b) We propose Clustering-based Column Generation (CCG), which incorporates a clustering heuristic to efficiently solve the subproblem. To reduce computational cost, tasks in the orignal task set $\mathcal{T}$, are first grouped into clusters using $k$-means based on time windows. For each agent, a MIP with a time limit is solved on a reduced subset of tasks $\mathcal{T'}$, obtained by uniformly sampling from these clusters. The resulting solutions are added to the subset solution pool ($\Omega'$) for use in the master problem.
• Figure 2: A list of parameters used to simulate disinfection missions to assess the impact of quality. A mission consists of disinfection tasks spread across a space, see Fig. \ref{['fig:layout']}.
• Figure 3: A sample physical layout of locations of different disinfection tasks. Here, the color coding is used to present different categories of tasks.
• Figure 4: Comparison of M$^3$RS and RS-F (Min/Max) solutions to assess the impact of quality of service (QoS) decision variables. Unlike RS-F, which considers only quantity, M$^3$RS explicitly incorporates QoS decision variables. Different $\lambda$ values in M$^3$RS prioritize quantity over quality. Both formulations are solved using MIP-solver laborie2018ibm with a 10-minute time limit on synthetic instances (30–60 tasks, four robots). The figures depict box-plot generated using solutions of 15 random instances, with higher values of metrics indicating better performance. M$^3$RS achieves 1.5$\%$–45$\%$ gains across quality and quantity metrics.