A Geometric Nonlinear Stochastic Filter for Simultaneous Localization and Mapping

TL;DR

This paper introduces a geometric nonlinear stochastic filter for SLAM that accurately models 3D robot pose and landmark estimation, accounting for measurement noise and biases, with proven effectiveness through simulations and experiments.

Contribution

It presents a novel stochastic estimator on Lie groups for SLAM that incorporates velocity biases and noise, improving accuracy over existing methods.

Findings

Successfully estimates 6 DoF robot pose and landmarks.

Performs well with noisy measurements and biases.

Validated through simulations and real-world experiments.

Abstract

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.