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Pro-Routing: Proactive Routing of Autonomous Multi-Capacity Robots for Pickup-and-Delivery Tasks

Daniel Garces, Stephanie Gil

TL;DR

This work addresses routing for a fleet of multi-capacity autonomous robots handling scheduled and real-time pickup-delivery requests under fixed maximum wait times. It introduces a proactive rollout framework based on one-request-at-a-time decisions, a stable greedy base policy, a time-series transformer–based generative model for future demand, and a promising-routes generator to produce feasible candidate routes. Theoretical results show that the greedy base policy is stable when the fleet is sufficiently large, and a Restart-and-Optimize fleet-sizing algorithm guarantees this condition asymptotically with online adaptivity. Empirical validation on Harvard's Evening Van data demonstrates that the approach achieves higher service rates, lower median waits, and faster planning compared to strong baselines, with ablations highlighting the benefit of the predictive model and the routing-swapping strategy.

Abstract

We consider a multi-robot setting, where we have a fleet of multi-capacity autonomous robots that must service spatially distributed pickup-and-delivery requests with fixed maximum wait times. Requests can be either scheduled ahead of time or they can enter the system in real-time. In this setting, stability for a routing policy is defined as the cost of the policy being uniformly bounded over time. Most previous work either solve the problem offline to theoretically maintain stability or they consider dynamically arriving requests at the expense of the theoretical guarantees on stability. In this paper, we aim to bridge this gap by proposing a novel proactive rollout-based routing framework that adapts to real-time demand while still provably maintaining the stability of the learned routing policy. We derive provable stability guarantees for our method by proposing a fleet sizing algorithm that obtains a sufficiently large fleet that ensures stability by construction. To validate our theoretical results, we consider a case study on real ride requests for Harvard's evening Van System. We also evaluate the performance of our framework using the currently deployed smaller fleet size. In this smaller setup, we compare against the currently deployed routing algorithm, greedy heuristics, and Monte-Carlo-Tree-Search-based algorithms. Our empirical results show that our framework maintains stability when we use the sufficiently large fleet size found in our theoretical results. For the smaller currently deployed fleet size, our method services 6% more requests than the closest baseline while reducing median passenger wait times by 33%.

Pro-Routing: Proactive Routing of Autonomous Multi-Capacity Robots for Pickup-and-Delivery Tasks

TL;DR

This work addresses routing for a fleet of multi-capacity autonomous robots handling scheduled and real-time pickup-delivery requests under fixed maximum wait times. It introduces a proactive rollout framework based on one-request-at-a-time decisions, a stable greedy base policy, a time-series transformer–based generative model for future demand, and a promising-routes generator to produce feasible candidate routes. Theoretical results show that the greedy base policy is stable when the fleet is sufficiently large, and a Restart-and-Optimize fleet-sizing algorithm guarantees this condition asymptotically with online adaptivity. Empirical validation on Harvard's Evening Van data demonstrates that the approach achieves higher service rates, lower median waits, and faster planning compared to strong baselines, with ablations highlighting the benefit of the predictive model and the routing-swapping strategy.

Abstract

We consider a multi-robot setting, where we have a fleet of multi-capacity autonomous robots that must service spatially distributed pickup-and-delivery requests with fixed maximum wait times. Requests can be either scheduled ahead of time or they can enter the system in real-time. In this setting, stability for a routing policy is defined as the cost of the policy being uniformly bounded over time. Most previous work either solve the problem offline to theoretically maintain stability or they consider dynamically arriving requests at the expense of the theoretical guarantees on stability. In this paper, we aim to bridge this gap by proposing a novel proactive rollout-based routing framework that adapts to real-time demand while still provably maintaining the stability of the learned routing policy. We derive provable stability guarantees for our method by proposing a fleet sizing algorithm that obtains a sufficiently large fleet that ensures stability by construction. To validate our theoretical results, we consider a case study on real ride requests for Harvard's evening Van System. We also evaluate the performance of our framework using the currently deployed smaller fleet size. In this smaller setup, we compare against the currently deployed routing algorithm, greedy heuristics, and Monte-Carlo-Tree-Search-based algorithms. Our empirical results show that our framework maintains stability when we use the sufficiently large fleet size found in our theoretical results. For the smaller currently deployed fleet size, our method services 6% more requests than the closest baseline while reducing median passenger wait times by 33%.

Paper Structure

This paper contains 51 sections, 3 theorems, 20 equations, 8 figures, 1 table, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Multi-capacity Robot Routing
  4. Fleet Sizing Algorithms
  5. Demand Prediction Methods
  6. Problem Formulation
  7. Environment
  8. Request Structure
  9. Robot Routes
  10. State Representation and Control Space
  11. Constraints and Cost Structure
  12. Stability of a Robot Routing Policy
  13. Challenges of the Proactive Multi-Capacity Robot Routing Problem
  14. Our Approach
  15. One-request-at-a-time Rollout
  16. ...and 36 more sections

Key Result

Theorem 1

Given Assumptions assumption:depots, assumption:buffer_time, assumption:bounded_requests, assumption:request_distribution, and a fixed fleet size $|\mathcal{L}|$, our proposed greedy policy $\pi^{\text{greedy}}$ is stable as defined in Def. def:stability if and only if the fleet size $|\mathcal{L}|$

Figures (8)

  • Figure 1: General overview of our proposed method with inputs and outputs. Our method is composed of three main modules: 1) Generative model for future request prediction; 2) Promising-routes generator; 3) Rollout-based dynamic allocation and redistribution of requests.
  • Figure 2: Example of executing the insertion procedure detailed in algo. \ref{['algo:insertion_procedure']}, when there is only one stop in the bus route besides the depot.
  • Figure 3: Simple routing example used as a counter-example that shows that the fleet size found using the single-pass algorithm is not sufficient for the stability of our proposed greedy policy $\pi^{\text{greedy}}$.
  • Figure 4: Street network of the operational area for Harvard's Evening Van system.
  • Figure 5: Box plots for the average wait time per request, average trip length per request, and the percentage of rejected requests for all baselines presented in Sec. \ref{['subsec:benchmarks']} and our approach.
  • ...and 3 more figures

Theorems & Definitions (10)

  • Definition 1
  • Definition 2
  • Theorem 1
  • proof
  • Proposition 1
  • proof
  • Remark 1
  • Theorem 2
  • proof
  • Remark 2