Robust L ∞ convex pose-graph optimisation for monocular localisation solution for unmanned aerial vehicles

Abstract

In this study, a robust L_∞ convex pose-graph optimisation solution for unmanned aerial vehicles (UAVs) monocular motion estimation with loop closing is presented. Most solutions proposed in literature formulate the pose-graph optimisation as a least-squares problem by minimising a cost function using iterative methods such as Gauss–Newton or Levenberg–Marquardt algorithms. However, with these algorithms, there is no guarantee to converge to a global minimum as they, with high probabilities, converge to a local minimum or even to an infeasible solution. The solution we propose in this work uses a new robust convex optimisation pose-graph technique, which efficiently corrects the UAV’s pose after loop-closure detections. Uncertainty estimation using derivative method and its propagation through multiview geometry algorithms are included in the developed solution. The detection of the visual loop closures, in appearance-based navigation, is achieved with our innovative, fast and efficient method based on Bayes decision theory with Gaussian mixture model in combination with the KD-tree data structure. Our navigation solution has been validated using real-world data in both indoor and outdoor environments acquired by a UAV equipped with a monocular system.