Analytical SLAM without linearization

Abstract

This thesis solves the classical problem of simultaneous localization and mapping (SLAM) in a fashion which avoids linearized approximations altogether. Based on creating virtual synthetic measurements, the algorithm uses a linear time-varying (LTV) Kalman observer, bypassing errors and approximations brought by the linearization process in traditional extended Kalman filtering (EKF) SLAM. Convergence rates of the algorithm are established using contraction analysis. Different combinations of sensor information can be exploited, such as bearing measurements, range measurements, optical flow, or time-to-contact. As illustrated in simulations, the proposed algorithm can solve SLAM problems in both 2D and 3D scenarios with guaranteed convergence rates in a full nonlinear context. A novel distributed algorithm SLAM-DUNK is proposed in the thesis. The algorithm uses virtual vehicles to achieve information exclusively from corresponding landmarks. Computation complexity is reduced to 0(n), with simulations on Victoria Park dataset to support the validity of the algorithm. In the final section of the thesis, we propose a general framework for cooperative navigation and mapping. The frameworks developed for three different use cases use the null space terms of SLAM problem to guarantee that robots starting with unknown initial conditions could converge to a shared consensus coordinate system with estimates reflecting the truth.