Scaling Safe Multi-Agent Control for Signal Temporal Logic Specifications

TL;DR

This work combines a multi-agent collision avoidance controller with a Graph Neural Network (GNN) based planner, models the system in a decentralized fashion, and trains on STL-based objectives to generate safe and efficient plans for multiple agents, thereby optimizing the satisfaction of complex temporal specifications while also facilitating multi-agent collision avoidance.

Abstract

Existing methods for safe multi-agent control using logic specifications like Signal Temporal Logic (STL) often face scalability issues. This is because they rely either on single-agent perspectives or on Mixed Integer Linear Programming (MILP)-based planners, which are complex to optimize. These methods have proven to be computationally expensive and inefficient when dealing with a large number of agents. To address these limitations, we present a new scalable approach to multi-agent control in this setting. Our method treats the relationships between agents using a graph structure rather than in terms of a single-agent perspective. Moreover, it combines a multi-agent collision avoidance controller with a Graph Neural Network (GNN) based planner, models the system in a decentralized fashion, and trains on STL-based objectives to generate safe and efficient plans for multiple agents, thereby optimizing the satisfaction of complex temporal specifications while also facilitating multi-agent collision avoidance. Our experiments show that our approach significantly outperforms existing methods that use a state-of-the-art MILP-based planner in terms of scalability and performance. The project website is https://jeappen.com/mastl-gcbf-website/ and the code is at https://github.com/jeappen/mastl-gcbf .

Figures (3)

• Figure 1: (Left) GNN-ODE Planner Architecture for Multi-Agent Systems with STL Specifications. The planner $\pi^{\phi\ifstrempty{i}{}{_{i}}}_g\ifstrempty{}{}{()}$ generates a sequence of goals for agent $i$ given the initial state of the system $G\ifstrempty{0}{}{(0)}{}$. The safety controller $\pi_{i}\ifstrempty{}{}{()}$ ensures that the agents do not collide while following the generated goals. A GNN encodes the graph representing the collective initial state of the system to yield an initial goal $g_{i}\ifstrempty{0}{}{(0)}$ (red) for each agent $i$. This goal $g_{i}\ifstrempty{0}{}{(0)}$ is fed into a Multi-Layer Perceptron (MLP) network to generate a new goal $g_{i}\ifstrempty{1}{}{(1)}$ (blue) which is fed back into the MLP network in a feedback loop. This is repeated for $T-1$ steps to generate a sequence of goals for the agent. The losses $\mathcal{L}_{\text{STL}}$ and $\mathcal{L}_{\text{ach}}$ are detailed in Sec. \ref{['sec:app-diff-stl-planning']} and are used to update our planner. (Middle) Real world experiments on $N=5$ drones. (Right) An example trajectory for $N=8$ agents for a seq spec requiring agents to visit A then B and finally C in order.
• Figure 2: We provide bar plots with error bars notating the standard deviations of the metrics considered. These are complementary to Table \ref{['tab:rebuttal-perf']} and Table \ref{['tab:rebuttal-finish-safe']}.
• Figure 3: We provide bar plots with error bars notating the standard deviations of the metrics considered. These are complementary to Table \ref{['tab:rebuttal-perf']} and Table \ref{['tab:rebuttal-finish-safe']}.

Theorems & Definitions (2)

• Definition 1: Motion Planning in MA-STL
• Definition 2: GCBF