A Geometric Nonlinear Stochastic Filter for Simultaneous Localization and Mapping
This addresses the SLAM problem for robotics, offering a novel method that accounts for biases and noise in velocity measurements, though it appears incremental as it builds on existing geometric approaches.
The paper tackles the Simultaneous Localization and Mapping (SLAM) problem in robotics by proposing a geometric nonlinear stochastic filter that estimates a robot's pose and landmark positions in 3D space, with simulation and experimental results showing successful estimation of the six-degrees-of-freedom pose.
Simultaneous Localization and Mapping (SLAM) is one of the key robotics tasks as it tackles simultaneous mapping of the unknown environment defined by multiple landmark positions and localization of the unknown pose (i.e., attitude and position) of the robot in three-dimensional (3D) space. The true SLAM problem is modeled on the Lie group of $\mathbb{SLAM}_{n}\left(3\right)$, and its true dynamics rely on angular and translational velocities. This paper proposes a novel geometric nonlinear stochastic estimator algorithm for SLAM on $\mathbb{SLAM}_{n}\left(3\right)$ that precisely mimics the nonlinear motion dynamics of the true SLAM problem. Unlike existing solutions, the proposed stochastic filter takes into account unknown constant bias and noise attached to the velocity measurements. The proposed nonlinear stochastic estimator on manifold is guaranteed to produce good results provided with the measurements of angular velocities, translational velocities, landmarks, and inertial measurement unit (IMU). Simulation and experimental results reflect the ability of the proposed filter to successfully estimate the six-degrees-of-freedom (6 DoF) robot's pose and landmark positions. Keywords: Simultaneous Localization and Mapping, nonlinear stochastic observer for SLAM, stochastic differential equations, pose estimator, position, attitude, Brownian motion process, inertial measurement unit, landmarks, features, SDE, SO(3), SE(3), SLAM.