Relative Position Estimation for Multi-Robots Based on Vertex Distance Between Regular Tetrahedral Units

Optimal decentralized cooperative control in multi-robot systems requires simultaneous local sensing and inter-agent communication. Ultra-wide band (UWB) wireless communication has been investigated as a self-contained positioning system capable of supporting both functions within a single device. Conventional UWB-based positioning methods estimate absolute positions using distance measurements relative to fixed anchors in the environment; moreover, while relative position estimation methods based on antenna configurations have been studied, mutual relative position estimation with respect to the reference coordinate frames of the agents themselves has not yet been investigated. To address this gap, this paper proposes a three-dimensional relative position estimation method for distributed cooperative control based on inter-vertex distances sharing. In the proposed system, inter-vertex distances between units are measured, where each unit is equipped with four UWB devices arranged in a regular tetrahedral geometric structure. An optimization-based estimation process is applied and enhanced with a k-means clustering method to mitigate convergence to local minima. The estimation accuracy was evaluated through both simulations and real-world experiments. The results demonstrate that the proposed method can accurately estimate relative positions between units and is effective for multi-robot systems operating on planar surfaces.