The Friedkin-Johnsen (FJ) model describes how agents adjust their opinions through repeated interactions while accounting for the influence of agents who are partially stubborn. In this work, we demonstrate that the FJ model is stepwise equivalent to solving the average consensus problem via distributed gradient descent. This perspective provides a unifying framework that bridges opinion dynamics and optimization, enabling the application of well-established results from the optimization literature. To illustrate this, we examine the recently proposed FJ model with diminishing stubbornness and extend prior results that were concerned with fixed communication graphs to time-varying and jointly connected communication graphs. We derive convergence guarantees and analyze convergence rates under these relaxed assumptions. Finally, we present numerical experiments on random graphs to showcase the impact of diminishing stubbornness dynamics on convergence in both static and time-varying settings.

This letter studies the Friedkin-Johnsen (FJ) model with diminishing competition, or stubbornness. The original FJ model assumes that each agent assigns a constant competition weight to its initial opinion. In contrast, we investigate the effect of diminishing competition on the convergence point and speed of the FJ dynamics. We prove that, if the competition is uniform across agents and vanishes asymptotically, the convergence point coincides with the nominal consensus reached with no competition. However, the diminishing competition slows down convergence according to its own rate of decay. We study this phenomenon analytically and provide upper and lower bounds on the convergence rate. Further, if competition is not uniform across agents, we show that the convergence point may not coincide with the nominal consensus point. Finally, we evaluate our analytical insights numerically.

In this paper we propose a novel algorithm, Wi-Closure, to improve the computational efficiency and robustness of loop closure detection in multi-robot SLAM. Our approach decreases the computational overhead of classical approaches by pruning the search space of potential loop closures, prior to evaluation by a typical multi-robot SLAM pipeline. Wi-Closure achieves this by identifying candidates that are spatially close to each other measured via sensing over the wireless communication signal between robots, even when they are operating in non-line-of-sight or in remote areas of the environment from one another. We demonstrate the validity of our approach in simulation and in hardware experiments. Our results show that using Wi-closure greatly reduces computation time, by 54.1% in simulation and 76.8% in hardware experiments, compared with a multi-robot SLAM baseline. Importantly, this is achieved without sacrificing accuracy. Using Wi-closure reduces absolute trajectory estimation error by 98.0% in simulation and 89.2% in hardware experiments. This improvement is partly due to Wi-Closure's ability to avoid catastrophic optimization failure that typically occurs with classical approaches in challenging repetitive environments.