A Discrete-time Dynamical Model for Optimal Dispatching and Rebalancing of Autonomous Mobility-on-Demand Systems

TL;DR

The paper tackles optimal dispatch and rebalancing for autonomous mobility-on-demand by formulating a discrete-time, linear AMoD model on a transformed complete graph and deploying a model predictive control (MPC) framework to compute optimal rebalancing and scheduling. It derives a complete-graph based dynamic model with Poisson-origin-demand inputs and a first-order delay approximation for link flows, and proves well-posedness and equilibria, including a method to compute a desired rebalancing reference via an optimization problem with linear or quadratic cost. The MPC is designed to regulate the system around the equilibrium, using either linear or quadratic tracking costs and enforcing feasibility through convex constraints, with a robust integer-control implementation. Simulation on the University of Minnesota campus network shows that LMPC with a linear reference (LMPC_LRef) tends to minimize average waiting time and queue length while keeping rebalancing distance reasonable, outperforming both QMPC variants and the IARR baseline in key service metrics. The work demonstrates a scalable control framework for real-time AMoD operations and points to future directions in scalability, model-free reinforcement learning, and integration with electric vehicles and public transit for first/last-mile improvement.

Abstract

Autonomous vehicles are rapidly evolving and will soon enable the application of large-scale mobility-on-demand (MoD) systems. Managing the fleets of available vehicles, commonly known as "rebalancing," is crucial to ensure that vehicles are distributed properly to meet customer demands. This paper presents an optimal control approach to optimize vehicle scheduling and rebalancing in an autonomous mobility-on-demand (AMoD) system. We use graph theory to model a city partitioned into virtual zones. Zones represent small areas of the city where vehicles can stop and pick up/drop off customers, whereas links denote corridors of the city along which autonomous vehicles can move. They are considered vertices and edges in the graph. Vehicles employed in the AMoD scheme are autonomous, and rebalancing can be executed by dispatching available empty vehicles to areas undersupplied. Rebalancing is performed on the graph's vertices, i.e., between city areas. We propose a linear, discrete-time model of an AMoD system using a transformed network. After acquiring the model, the desired number of rebalancing vehicles for the AMoD model is derived through an optimization problem. Moreover, the well-posedness of the model is illustrated. To leverage the proposed model, we implemented the model predictive control (MPC) framework to find the optimal rebalancing and scheduling policy. We show the MPC's effectiveness and how the MPC framework can be implemented in real-time for a real-world case study. The numerical results show that the MPC with a linear cost function and linear reference, which it tracks, is effective, outperforming other MPC-based and state-of-the-art algorithms across all evaluation criteria.

Figures (7)

• Figure 1: A network (graph) with four stations. (a) The original network; (b) The transformed (complete) network.
• Figure 2: The University of Minnesota-Twin Cities campus network map for testing the proposed model and control strategy. Zone 1 denotes the west bank of the Minneapolis campus, Zones 2, 3, 4, and 5 represent the east bank of the Minneapolis campus, and Zone 6 denotes the St. Paul campus. Zones have been extracted using Lloyd’s k-mean algorithm and travel data.
• Figure 3: The University of Minnesota zones.
• Figure 4: Histogram of the daily demand for the UMN's campuses.
• Figure 5: The average queue length and number of customer-carrying vehicles for Case Studies 1 and 2.

Theorems & Definitions (13)

• Remark 1
• Proposition 1
• proof
• Proposition 2: Equilibrium Points
• proof
• Corollary 1
• proof
• Corollary 2
• Theorem 1: Closed-Loop Stability
• proof