MA-DV2F: A Multi-Agent Navigation Framework using Dynamic Velocity Vector Field

TL;DR

This work tackles scalable multi-agent navigation for dynamic fleets under collision constraints by introducing MA-DV2F, a decentralized framework that computes independent dynamic velocity vector fields (DV2Fs) for each vehicle. Each DV2F provides a reference orientation and speed that guide agents toward their targets while accounting for nearby obstacles and other vehicles, with dynamic updates to prevent imminent collisions. A key feature is the optional self-supervised training of a Graph Neural Network (GNN) that leverages DV2F-derived controls as supervision, enabling online learning without labeled data. Empirical results show MA-DV2F achieving high safety and reach rates with strong scalability and significantly lower runtimes compared to state-of-the-art learning and search-based methods, and the self-supervised GNN variant exhibits robust performance as the number of agents grows.

Abstract

In this paper we propose MA-DV2F: Multi-Agent Dynamic Velocity Vector Field. It is a framework for simultaneously controlling a group of vehicles in challenging environments. DV2F is generated for each vehicle independently and provides a map of reference orientation and speed that a vehicle must attain at any point on the navigation grid such that it safely reaches its target. The field is dynamically updated depending on the speed and proximity of the ego-vehicle to other agents. This dynamic adaptation of the velocity vector field allows prevention of imminent collisions. Experimental results show that MA-DV2F outperforms concurrent methods in terms of safety, computational efficiency and accuracy in reaching the target when scaling to a large number of vehicles. Project page for this work can be found here: https://yininghase.github.io/MA-DV2F/

Figures (8)

• Figure 1: Shows the pipeline for MA-DV$^2$F. The state of all vehicles at time $t$ is used to create the dynamic velocity vector field (DV$^2$F) from which the reference control commands are determined. These commands are in turn used to determine the next state at time $t+1$ using the kinematic motion model. Note that the reference control commands can optionally be used to train a GNN in a self-supervised manner (indicated by dotted arrows). Meanwhile, the DV$^2$F is shown for the black ego-vehicle with 2 other vehicles (blue & maroon) and 2 obstacles (green & brown) in the scene. The target state for the black ego-vehicle is shown by the dotted rectangle with a solid arrow at the top of the map. The dotted circle around the target state is the parking region. The black arrows indicate the ideal reference orientation as unit vectors which the ego-vehicle should attain at each different position on the map. The colored dotted circles around other vehicles and obstacles show the collision avoiding regions for the black ego-vehicle. Each black arrow in these regions is composed of an attractive target approaching component (gray arrow) and a repulsive collision avoidance component (colored arrow). Note that due to kinematic constraints, the reference orientation ($\mathbf{u}_\mathbf{ref}$) might not be attainable for the ego-vehicle at its existing location. The shaded wedge in front of the ego-vehicle shows the region of reachable orientation at the next time step. The real orientation ($\mathbf{u}_\mathbf{real}$) is therefore the physically attainable orientation by the ego-vehicle that is closest to the reference. An example of the dynamic velocity vector field is shown in the project page: https://yininghase.github.io/MA-DV2F/#VD. Note that DV$^2$F for the neighboring blue & maroon vehicles is likewise created separately (not shown in this figure).
• Figure 2: Shows the constituents of the reference orientation vector $\mathbf{u}_{ref}$ near an obstacle. It comprises of a target approaching ($\mathbf{u}_{tar}$) and the collision avoiding ($\mathbf{u}_{obs_{k}}$) components. $\mathbf{u}_{obs_{k}}$ includes $\mathbf{v}_{n}=\mathbf{f_{uni}}(\mathbf{X}^{(i)}_{obs_{k}}) \cdot \alpha^{(i)}_{obs_{k}}$ guiding the vehicle to drive away from the obstacle and $\mathbf{v}_{t}=\mathbf{R}^{(i)}_{obs_{k}} \cdot \beta^{(i)}_{obs_{k}}$ leading the vehicle to go around the obstacle. When the ego-vehicle is between the obstacle and target, it is not necessary for it to go around the obstacle and thus $\mathbf{v}_{t} = \mathbf{0}$. The formulation to calculate $\mathbf{u}_{obs_{k}}$ is described in Equation \ref{['equ:reference orientation obstacle avoiding']}.
• Figure 3: Shows two different scenarios when the black ego vehicle is in a collision avoiding region. In Fig. \ref{['fig:subfigure_a']}, the ego vehicle is facing the obstacle, i.e. $\mathbf{u}^{T} \cdot \mathbf{X}_{obs}>0$, in which case the vehicle should be forbidden to move forwards. In Fig. \ref{['fig:subfigure_b']}, the ego vehicle is oriented away from the obstacle, i.e. $\mathbf{u}^{T} \cdot \mathbf{X}_{obs}<0$, in which case the vehicle should be prevented from moving backward.
• Figure 4: Shows the Safe and Reach rate metrics (Higer is better) for the different models, i.e. our MA-DV$^{2}$F, our self-supervised GNN model, supervised GNN model multiagent2023, CSDO 10628993, CL-MAPF wen2022cl and GCBF+ zhang2024gcbf+.
• Figure 5: Shows the two different circumstances of the ego-vehicle overshooting its target and entering the marginal parking region (shaded blue region). In Fig. \ref{['fig:subfigure_5a']}, The reference orientation vector $\mathbf{u}_{ref} = \mathbf{f_{uni}}(\mathbf{X}^{(i)}_{tar})$ points towards the target, while the current vehicle orientation is opposite to the reference orientation. Thus, the vehicle needs to turn around again to match the reference orientation. In Fig. \ref{['fig:subfigure_5b']}, the reference orientation vector $\mathbf{u}_{ref} = - \mathbf{f_{uni}}(\mathbf{X}^{(i)}_{tar})$ is flipped based on the current vehicle orientation. In this case, the vehicle does not need to turn around but directly move backwards to the target.