A Study on Distance-Based Control of Mobile Agents for Formation Avoiding Entire and Partial Reflection

This paper proposes a feedback control law for navigating mobile agents to form a desired shape consisting of their positions. The objective is to achieve the formation without assuming the agents to start from a sufficiently small neighborhood of the desired shape. The global setting allows one to address reflections and partial reflections of agent positions. Target shapes are defined by excluding reflections and partial reflections which are often undesirable in practice. For agents represented by single-integrator models, this paper demonstrates how targets in a standard control based on their relative position measurements can be switched to generate feedback control input preventing reflected positions with reasonable routing. The effectiveness of the proposed mechanism is studied through numerical simulations.