A Geometric Nonlinear Stochastic Filter for Simultaneous Localization and Mapping

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.

References in corpus (8)

• Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age
• Nonlinear Stochastic Attitude Filters on the Special Orthogonal Group 3: Ito and Stratonovich
• Systematic Convergence of Nonlinear Stochastic Estimators on the Special Orthogonal Group SO(3)
• Landmark and IMU Data Fusion: Systematic Convergence Geometric Nonlinear Observer for SLAM and Velocity Bias
• Nonlinear Stochastic Estimators on the Special Euclidean Group SE(3) using Uncertain IMU and Vision Measurements
• Nonlinear Pose Filters on the Special Euclidean Group SE(3) with Guaranteed Transient and Steady-state Performance
• Guaranteed Performance Nonlinear Observer for Simultaneous Localization and Mapping
• Attitude Determination and Estimation using Vector Observations: Review, Challenges and Comparative Results

Cited by in corpus (5)

• Advances in UAV Avionics Systems Architecture, Classification and Integration: A Comprehensive Review and Future Perspectives
• Geometric Stochastic Filter with Guaranteed Performance for Autonomous Navigation based on IMU and Feature Sensor Fusion
• Quaternion-based Unscented Kalman Filter for 6-DoF Vision-based Inertial Navigation in GPS-denied Regions
• Quaternion-based Unscented Kalman Filter for Robust Wrench Estimation of Human-UAV Physical Interaction
• Asymptotically Stable Observer-based Controller for Attitude Tracking with Systematic Convergence