Global Asymptotic Convergent Observer for SLAM

Abstract

This paper examines the global convergence problem of SLAM algorithms, an issue that faces topological obstructions. This is because the state-space for attitude kinematics is defined on a noncontractible manifold: the special orthogonal group of order three SO(3). Therefore, this paper presents a novel, gradient-based hybrid observer to overcome these topological obstacles. Moreover, the integral action is applied into the proposed observer to estimate unknown constant bias, which results in an increase in bias estimation. Accordingly, a new projection scheme is defined to cope with the integral action. The Lyapunov stability theorem is used to prove the globally asymptotic convergence of the proposed algorithm. Experimental and simulation results are provided to evaluate the performance and to demonstrate the effectiveness and robustness of the proposed scheme.

Task Space Control of Robot Manipulators based on Visual SLAM

“…In this section, a numerical simulation study is performed to assess the performance of the proposed VSLAM-based control structure given by (21). This study uses a 6-DOF manipulator with a long arm, illustrated in Figure (2).…”

“…Likewise, Kalman-type methods and optimization-based strategies suffer from performance dependency on the initialization and also cannot ensure stability. Consequently, this paper makes use of the VSLAM algorithm introduced by the authors in [21], where it was proven that the provided VSLAM method can guarantee global asymptotic stability and overcome problems associated with existing VSLAM algorithms.…”

“…The following equation describes the dynamics of the VS-LAM algorithm introduced by the authors in [21]:…”

“…Theorem 2: Consider the robot dynamic equation (11) in a closed loop with the proposed hybrid feedback law (21) and observer (18). Then, the compact set…”