Inter-Robots Position Estimation Using UWB Positioning Devices for Distributed Cooperative Control of Multiple Robots

Ultra-wide band (UWB)-based positioning methods for static environments have been continuously improved; how-ever, many existing approaches rely on fixed reference nodes, and methods for directly computing relative positions among mobile units have not been sufficiently investigated. This paper presents a relative positioning approach for multi-robot systems using UWB wireless communication within a distributed cooperative control framework. In the proposed approach, multiple UWB positioning devices are arranged in regular polyhedral configurations to improve the uniformity of ranging accuracy. Robot coordinates are estimated using a nonlinear least-squares optimization method formulated from a system of simultaneous distance equations, enabling mutual relative position estimation among robots. Simulation experiments were conducted to evaluate estimation accuracy and error characteristics under different geometric configurations. Four configurations: square, tetrahedron, regular tetrahedron, and regular octahedron were considered, and their error magnitudes and axis-wise distributions were compared. The simulation results indicate that the proposed configuration achieve lower estimation errors than the other configurations evaluated. Based on these findings, experimental verification was performed, and the observed trends were consistent with the simulation results. This work provides a systematic investigation of a mutual positioning system that enables robots to estimate their positions with respect to one another without relying on fixed landmarks. Unlike existing method, our approach enables the determination of relative positions between robots based on distances measured by each robot. The proposed approach is expected to be applicable to autonomous decentralized control in multi-robot systems operating in static environments.