We address the problem of sparse selection of visual features for localizing a team of robots navigating an unknown environment, where robots can exchange relative position measurements with neighbors. We select a set of the most informative features by anticipating their importance in robots localization by simulating trajectories of robots over a prediction horizon. Through theoretical proofs, we establish a crucial connection between graph Laplacian and the importance of features. We show that strong network connectivity translates to uniformity in feature importance, which enables uniform random sampling of features and reduces the overall computational complexity. We leverage a scalable randomized algorithm for sparse sums of positive semidefinite matrices to efficiently select the set of the most informative features and significantly improve the probabilistic performance bounds. Finally, we support our findings with extensive simulations.

翻译：针对未知环境下多机器人协同导航中需稀疏选择视觉特征的问题（机器人可与邻居交换相对位置测量值），本文通过预测时间窗口内模拟机器人轨迹，预判特征对定位的重要性，从而选取最具信息量的特征子集。通过理论证明，我们建立了图拉普拉斯矩阵与特征重要性之间的关键关联，表明强网络连通性会使特征重要性趋于均匀分布，这为均匀随机采样特征提供了理论依据，并有效降低了整体计算复杂度。我们利用一种可扩展的随机化算法来逼近正半定矩阵的稀疏和，以便高效选择最具信息量的特征子集，同时显著改进概率性能边界。最后，通过大量仿真实验验证了所提方法的有效性。