Learning to Swarm with Knowledge-Based Neural Ordinary Differential Equations

TL;DR

This work considers the important task of learning decentralized single-robot controllers based solely on the state observations of a swarm's trajectory and presents a general framework by adopting knowledge-based neural ordinary differential equations (KNODE) ─ a hybrid machine learning method capable of combining artificial neural networks with known agent dynamics.

Abstract

Understanding decentralized dynamics from collective behaviors in swarms is crucial for informing robot controller designs in artificial swarms and multiagent robotic systems. However, the complexity in agent-to-agent interactions and the decentralized nature of most swarms pose a significant challenge to the extraction of single-robot control laws from global behavior. In this work, we consider the important task of learning decentralized single-robot controllers based solely on the state observations of a swarm's trajectory. We present a general framework by adopting knowledge-based neural ordinary differential equations (KNODE) -- a hybrid machine learning method capable of combining artificial neural networks with known agent dynamics. Our approach distinguishes itself from most prior works in that we do not require action data for learning. We apply our framework to two different flocking swarms in 2D and 3D respectively, and demonstrate efficient training by leveraging the graphical structure of the swarms' information network. We further show that the learnt single-robot controllers can not only reproduce flocking behavior in the original swarm but also scale to swarms with more robots.

Figures (11)

• Figure 1: Decentralized information network for robot $0$ with time delay $\tau$, and $3$ active neighbors. The image shows robot $0$'s egocentric view, where 8 neighbors are within its communication range $d_{cr}$. Only the closest three neighbors contribute to the information structure of robot $0$. Their states from $t-\tau$ are ordered based on their proximity to robot $0$ to form $\mathbf{Y}_0(t)$.
• Figure 2: Predicted trajectory of 10 robots using the learnt controller ($d_{cr} = 5, k = 6$) with the same initial states as the testing trajectory (ground truth). The subfigures (a)(b)(c)(d) show the snapshots of the swarm at $t=0, 100, 600$, and $1200$ respectively.
• Figure 3: The metrics for the learnt 2D controller ($d_{cr} = 5, k = 6$) show (a) average velocity difference, and (b) average minimum distance to a neighbor. The $95\%$ confidence intervals are based on 20 sets of testing trajectories.
• Figure 4: Predicted trajectory of 100 robots using the learnt controller ($d_{cr} = 5, k = 6$) with uniformly initialized positions. The subfigures (a)(b)(c)(d)(e)(f) show the snapshots of the swarm at $t=0, 200, 400, 800, 1000$ and $1200$ respectively.
• Figure 5: Box plot of (a) average velocity difference ($avd$), and (b) average minimum distance to a neighbor ($amd$) on scaling to different swarm sizes using a trained controller in 2D. For each swarm size, the box represents the statistics of 15 runs using different initial conditions.