Sequential Covariance-weighted Quasiconvex solution to Mapping in Visual SLAM

Abstract

This paper presents a new sequential real time algorithm that solves the mapping problemin Visual SLAM. The considered problem is a particular example from the triangulation problem, thathas direct applications to robotic vision domain. In other words, the problem is handled as 3D estimateproblem. The estimation process is formulated as a minimization problem of quasiconvex objectivefunction. The minimization process is realized using the well-known bisection algorithm. The bisectionalgorithm runs sequentially solving one convex feasibility problem in each iteration, trying to reducethe bound on the 3D estimate. New image measurements arrive after every new iteration, new convexvisibility problem is solved, and the bounds on the 3D estimates are updated. These steps are repeated tillconvergence. We conducted a set of experiments to show the applicability to the general reconstruction(triangulation) problem as well as the application to mapping Visual SLAM.