Visual SLAM on lie groups

Abstract

This work focuses on leveraging the potential of Lie theory in state estimation to derive a nonlinear approach for solving the Simultaneous Localization And Mapping problem. As a matter of fact, the groups SE(3) and SO(3) have proven to be very convenient in representing body motions in 3D space. Therefore, it becomes possible to design nonlinear observers for solving the SLAM problem using Lyapunov stability analysis, which we demonstrate in our thesis by presenting the work of [1]. Our contribution consists of endowing the observer with two practical features: a System re-dimensioning feature, to give a vehicle the ability to dynamically change the dimension of the state matrix, and a Fault Detection and Isolation block that detects and corrects faulty measurements from the camera and the IMU used to implement the proposed observer