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A lifting method for analyzing distributed synchronization on the unit sphere Thunberg, Johan ; Markdahl, Johan ; et al in Automatica (2018) This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted ... [more ▼] This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted to the (d+1)-dimensional Euclidean space. The consensus protocol on the unit sphere is the classical one, where agents move toward weighted averages of their neighbors in their respective tangent planes. Only local and relative state information is used. The directed interaction graph topologies are allowed to switch as a function of time. The dynamics of the lifted variables are governed by a nonlinear consensus protocol for which the weights contain ratios of the norms of state variables. We generalize previous convergence results for hemispheres. For a large class of consensus protocols defined for switching uniformly quasi-strongly connected time-varying graphs, we show that the consensus manifold is uniformly asymptotically stable relative to closed balls contained in a hemisphere. Compared to earlier projection based approaches used in this context such as the gnomonic projection, which is defined for hemispheres only, the lifting method applies globally. With that, the hope is that this method can be useful for future investigations on global convergence. [less ▲] Detailed reference viewed: 106 (1 UL)Distributed synchronization of euclidean transformations with guaranteed convergence Thunberg, Johan ; Goncalves, Jorge ; in 56th IEEE Conference on Decision and Control (2017, December) This paper addresses synchronization of Euclidean transformations over graphs. Synchronization in this context, unlike rendezvous or consensus, means that composite transformations over loops in the graph ... [more ▼] This paper addresses synchronization of Euclidean transformations over graphs. Synchronization in this context, unlike rendezvous or consensus, means that composite transformations over loops in the graph are equal to the identity. Given a set of non-synchronized transformations, the problem at hand is to find a set of synchronized transformations approximating well the non-synchronized transformations. This is formulated as a nonlinear least-squares optimization problem. We present a distributed synchronization algorithm that converges to the optimal solution to an approximation of the optimization problem. This approximation stems from a spectral relaxation of the rotational part on the one hand and from a separation between the rotations and the translations on the other. The method can be used to distributively improve the measurements obtained in sensor networks such as networks of cameras where pairwise relative transformations are measured. The convergence of the method is verified in numerical simulations. [less ▲] Detailed reference viewed: 104 (1 UL) |
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