Virtual Force-Based Routing of Modular Agents on a Graph

TL;DR

This paper addresses the problem of efficiently routing $n$ modular agents on a graph to visit a predetermined set of targets while minimizing total travel cost, allowing modules to join and split to share edge costs. It introduces a force-based heuristic that combines attractive forces toward targets and toward other agents, using a discretized inverse-square law computed over the first edges of $k$ shortest paths; target assignment relies on greedy nearest-neighbor search and path options are generated via Yen’s algorithm. The approach scales to multiple agents and dense graphs, achieving comparable performance to the existing two-agent method for small $n$ and showing substantial cost savings over non-modular routing in large-scale Champaign-Urbana experiments (e.g., 81/100 cases). The method also includes a waiting policy to avoid local equilibria and demonstrates faster computation than some modular-routing baselines. The results suggest practical potential for urban delivery and modular transit, with future work including learning-based target assignment and extension to real-world transportation planning.

Abstract

Modular vehicles have become an area of academic interest in the field of multi-agent systems. Modularity allows vehicles to connect and disconnect with each other mid-transit which provides a balance between efficiency and flexibility when solving complex and large scale tasks in urban or aerial transportation. This paper details a generalized scheme to route multiple modular agents on a graph to a predetermined set of target nodes. The objective is to visit all target nodes while incurring minimum resource expenditure. Agents that are joined together will incur the equivalent cost of a single agent, which is motivated by the logistical benefits of traffic reduction and increased fuel efficiency. To solve this problem, we introduce a heuristic algorithm that seeks to balance the optimality of the path that an agent takes and the cost benefit of joining agents. Our approach models the agents and targets as point charges, where the agents take the path of highest attractive force from its target node and neighboring agents. We validate our approach by simulating multiple modular agents along real-world transportation routes in the road network of Champaign-Urbana, Illinois, USA. For two vehicles, it performed equally compared to an existing modular-agent routing algorithm. Three agents were then routed using our method and the performance was benchmarked against non-modular agents using a simple shortest path policy where it performs better than the non-modular implementation 81 percent of the time. Moreover, we show that the proposed algorithm operates faster than existing routing methods for modular agents.

Figures (4)

• Figure 1: A map showing the CUMTD bus routes along the southern part of Champaign-Urbana mtd_schedule_2024. As they pass through UIUC campus there is significant overlap, sharing stops along the way. Outside of campus, they tend to take their own paths.
• Figure 2: A visualization of node-to-node force-based computation. The module starts at node zero denoted in green, and the target is node 4 denoted in red.
• Figure 3: A toy graph showing the benefits of delaying movement. There are three agents on this graph, whose paths are represented by red, blue, and green edges. Their targets are denoted by gray nodes.
• Figure 4: A graph of the campus and surrounding area of Champaign-Urbana. Three agents with paths red, blue, and green start at their respective colors and reach points of interest around the city denoted by black nodes.