How can I efficiently control agent formations using Gromov-Wasserstein distance?
Formation Shape Control using the Gromov-Wasserstein Metric
This paper proposes a novel method for controlling the formation of multiple agents (e.g., robots, drones) using the Gromov-Wasserstein (GW) distance. Instead of specifying precise target positions, it focuses on achieving a desired shape by minimizing the GW distance between the agents' final configuration and a target shape. This approach uses optimal control to steer agents towards the desired formation in an energy-efficient manner. The computationally challenging GW distance calculation is addressed using a semi-definite programming relaxation.
Key points for LLM-based multi-agent systems: The GW distance's focus on shape, rather than absolute position, offers flexibility, especially in dynamic environments or where precise positioning isn't critical. This aligns with the potential for LLMs to specify high-level goals ("form a circle") rather than micromanaging individual agent actions. The SDP relaxation provides a tractable way to approximate the GW distance, potentially enabling real-time formation control in web applications. This opens up possibilities for using LLMs to reason about and dynamically adjust formation shapes based on evolving task requirements.