# RSSI−based Relative Localisation for Mobile Robots

*L. Oliveira‚ H. Li‚ L. Almeida and T. E. Abrudan*

### Abstract

In this work, we develop an anchor-less relative localisation algorithm aimed to be used in multi-robot teams. The localisation is performed based on the Received Signal Strength Indicator (RSSI) readings collected from the messages exchanged between nodes. We use the RSSI as a rough estimate of the inverse of distance between any pair of communicating nodes, and we claim that such estimates provide a coarse information of the nodes relative localisation that is still suitable to support several coordination tasks. In addition, we introduce a relative velocity estimation framework based on the RSSI measurements. This framework uses consecutive distance measurements and position estimates to provide the relative velocity vectors for all the nodes in the network. To accomplish this, we propose using a Kalman filter and the Floydâ€“Warshall algorithm to generate smooth RSSI pairwise signal distance for all nodes. Then we use Multidimensional Scaling to obtain relative positions from the pairwise distances. Finally, due to anchor unavailability, relative positions are adjusted to reflect the continuous mobility by using geometric transformations, thus obtaining smoother trajectories for mobile nodes. This allows us to estimate velocity and to establish a correspondence between orientation in the physical world and in the relative coordinates system. Additionally, we study the impact of several parameters in calculating the network topology, namely different approaches to provide a symmetric distances matrix, the period of the matrix dissemination, the use of synchronisation of the transmissions, and the filtering of the RSSI data. Experimental results, with a set of MicaZ motes, show that the period of matrix dissemination is the most relevant of the parameters, specifically with larger periods providing the best results, however, shorter periods are shown to be possible as long as the transmissions are synchronised.