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Destination-to-Chutes Task Mapping Optimization for Multi-Robot Coordination in Robotic Sorting Systems

Yulun Zhang, Alexandre O. G. Barbosa, Federico Pecora, Jiaoyang Li

TL;DR

This work defines Task Mapping Optimization (TMO) for Robotic Sorting Systems (RSS), formalizing the mapping from destinations to chutes and addressing interdependent subproblems like robot coordination and target assignment. It introduces an RSS simulator that models movement, chute status changes, and recirculation, and proposes an Evolutionary Algorithm (EA) with MILP-based repair to optimize static task mappings, complemented by Quality Diversity (QD) analysis using MAP-Elites. Empirical results show that optimized task mappings can significantly improve throughput and reduce recirculation compared to greedy baselines, with insights into how spatial clustering of chutes and diversity of mappings influence performance. The paper also provides implementation details (Pyribs, CPLEX) and resources, enabling reproducibility and further study of TMO in RSS. Overall, the work advances understanding of how destination-to-chute mappings affect RSS throughput and offers a practical optimization framework for real-world sorting systems.

Abstract

We study optimizing a destination-to-chutes task mapping to improve throughput in Robotic Sorting Systems (RSS), where a team of robots sort packages on a sortation floor by transporting them from induct workstations to eject chutes based on their shipping destinations (e.g. Los Angeles or Pittsburgh). The destination-to-chutes task mapping is used to determine which chutes a robot can drop its package. Finding a high-quality task mapping is challenging because of the complexity of a real-world RSS. First, optimizing task mapping is interdependent with robot target assignment and path planning. Second, chutes will be CLOSED for a period of time once they receive sufficient packages to allow for downstream processing. Third, task mapping quality directly impacts the downstream processing, as scattered chutes for the same destination increase package handling time. In this paper, we first formally define task mappings and the problem of Task Mapping Optimization (TMO). We then present a simulator of RSS to evaluate task mappings. We then present a simple TMO method based on the Evolutionary Algorithm and Mixed Integer Linear Programming, demonstrating the advantage of our optimized task mappings over the greedily generated ones in various RSS setups with different map sizes, numbers of chutes, and destinations. Finally, we use Quality Diversity algorithms to analyze the throughput of a diverse set of task mappings. Our code is available online at https://github.com/lunjohnzhang/tmo_public.

Destination-to-Chutes Task Mapping Optimization for Multi-Robot Coordination in Robotic Sorting Systems

TL;DR

This work defines Task Mapping Optimization (TMO) for Robotic Sorting Systems (RSS), formalizing the mapping from destinations to chutes and addressing interdependent subproblems like robot coordination and target assignment. It introduces an RSS simulator that models movement, chute status changes, and recirculation, and proposes an Evolutionary Algorithm (EA) with MILP-based repair to optimize static task mappings, complemented by Quality Diversity (QD) analysis using MAP-Elites. Empirical results show that optimized task mappings can significantly improve throughput and reduce recirculation compared to greedy baselines, with insights into how spatial clustering of chutes and diversity of mappings influence performance. The paper also provides implementation details (Pyribs, CPLEX) and resources, enabling reproducibility and further study of TMO in RSS. Overall, the work advances understanding of how destination-to-chute mappings affect RSS throughput and offers a practical optimization framework for real-world sorting systems.

Abstract

We study optimizing a destination-to-chutes task mapping to improve throughput in Robotic Sorting Systems (RSS), where a team of robots sort packages on a sortation floor by transporting them from induct workstations to eject chutes based on their shipping destinations (e.g. Los Angeles or Pittsburgh). The destination-to-chutes task mapping is used to determine which chutes a robot can drop its package. Finding a high-quality task mapping is challenging because of the complexity of a real-world RSS. First, optimizing task mapping is interdependent with robot target assignment and path planning. Second, chutes will be CLOSED for a period of time once they receive sufficient packages to allow for downstream processing. Third, task mapping quality directly impacts the downstream processing, as scattered chutes for the same destination increase package handling time. In this paper, we first formally define task mappings and the problem of Task Mapping Optimization (TMO). We then present a simulator of RSS to evaluate task mappings. We then present a simple TMO method based on the Evolutionary Algorithm and Mixed Integer Linear Programming, demonstrating the advantage of our optimized task mappings over the greedily generated ones in various RSS setups with different map sizes, numbers of chutes, and destinations. Finally, we use Quality Diversity algorithms to analyze the throughput of a diverse set of task mappings. Our code is available online at https://github.com/lunjohnzhang/tmo_public.

Paper Structure

This paper contains 19 sections, 2 equations, 3 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Existing Research in RSS
  3. Problem Definition
  4. Robotic Sorting System
  5. Task Mapping Optimization
  6. Initialization
  7. Mutation
  8. MILP
  9. Experimental Evaluation
  10. Experiment Setup
  11. Results
  12. Empirical Analysis via QD Optimization
  13. Quality Diversity Algorithms
  14. Experiment Setup and Results
  15. Conclusion
  16. ...and 4 more sections

Figures (3)

  • Figure 1: Overview of our RSS simulator. (a) Map of the sortation floor of the RSS. (b) At the workstations, each robot picks up a package and decides the target endpoint with a task mapping and a TA policy. (c) Status change of the chutes. Packages can be dropped into OPEN chutes. (d) At the endpoints, each robot drops off the package and decides the next target workstation with a TA policy.
  • Figure 2: Throughput with different numbers of robots. The task mappings are optimized with $N_a$ robots shown in \ref{['tab:exp-setup']}. The solid line shows the average and the shaded area shows the 95% confidence interval.
  • Figure 3: The archives of MAP-Elites in all setups. The two axes show the diversity measures while the color indicates the throughput. Two representative task mappings are shown for each setup. Each square in the task mappings represents a chute and the color represents the destination the chute is assigned to. The color bars underneath the task mappings shows the indices of the destinations. Smaller indices indicate larger volumes. For simplicity, we only show the top 10 destinations.

Theorems & Definitions (1)

  • Definition 1: Task Mapping and TMO