Spectral Trade-Off for Measurement Sparsification of Pose-Graph SLAM

Abstract

In this letter, we propose a trade-off optimization algorithm to compute an appropriate number of edges for measurement (edge) sparsification in pose-graph simultaneous localization and mapping (SLAM). The greater the amount of measurement data, the larger is the computational burden. To reduce computational burden, one can remove a portion of measurements. However, reliable data, such as odometric measurements, can be lost if measurements are removed without any principle. To remove measurements which is redundant, we propose a trade-off optimization algorithm between maximization of the Fiedler value and minimization of the largest eigenvalue of adjacency matrix for measurement graph. This problem formulation gives virtues twofold. First, it is scalable. For any dataset, when a weight for trade-off is given, this algorithm determines the appropriate number of edges since this is a trade-off optimization problem. Second, the edges of the measurement graph can be distributed evenly. The algorithm considers the minimization of the largest eigenvalue of the adjacency matrix, so it suppresses the upper bound of the maximum degree of the measurement graph. It removes the redundant information concentrated on a few nodes, and improves the estimation accuracy of the sparsified graph. To validate the performance of the proposed trade-off optimization algorithm, we apply our approach to CSAIL, Intel, and Manhattan datasets.