Landmark and IMU Data Fusion: Systematic Convergence Geometric Nonlinear Observer for SLAM and Velocity Bias (2011.10635v3)

Abstract: Navigation solutions suitable for cases when both autonomous robot's pose (\textit{i.e}., attitude and position) and its environment are unknown are in great demand. Simultaneous Localization and Mapping (SLAM) fulfills this need by concurrently mapping the environment and observing robot's pose with respect to the map. This work proposes a nonlinear observer for SLAM posed on the manifold of the Lie group of $\mathbb{SLAM}_{n}\left(3\right)$, characterized by systematic convergence, and designed to mimic the nonlinear motion dynamics of the true SLAM problem. The system error is constrained to start within a known large set and decay systematically to settle within a known small set. The proposed estimator is guaranteed to achieve predefined transient and steady-state performance and eliminate the unknown bias inevitably present in velocity measurements by directly using measurements of angular and translational velocity, landmarks, and information collected by an inertial measurement unit (IMU). Experimental results obtained by testing the proposed solution on a real-world dataset collected by a quadrotor demonstrate the observer's ability to estimate the six-degrees-of-freedom (6 DoF) robot pose and to position unknown landmarks in three-dimensional (3D) space. Keywords: Simultaneous Localization and Mapping, Nonlinear filter for SLAM, Nonlinear filter for SLAM on Matrix Lie group, pose, asymptotic stability, prescribed performance, adaptive estimate, feature, inertial measurement unit, inertial vision unit, IMU, SE(3), SO(3), noise.

• The paper introduces a nonlinear observer on SLAMn(3) that fuses landmark, IMU, and velocity data for precise pose and map estimation.
• It employs a prescribed performance function to ensure systematic convergence of errors from large initial bounds to desired limits.
• The observer effectively compensates for velocity bias and demonstrates robust performance in real-world quadrotor experiments.

An Overview of "Landmark and IMU Data Fusion: Systematic Convergence Geometric Nonlinear Observer for SLAM and Velocity Bias"

In the field of autonomous navigation, the task of Simultaneous Localization and Mapping (SLAM) has become pivotal, especially in environments where GPS is unavailable or unreliable. Hashim and Eltoukhy's paper presents a significant advancement in SLAM methodologies by designing a nonlinear observer operating on the Lie group SLAMn(3). This addresses the inherent nonlinearities of the SLAM problem more effectively than traditional Gaussian filters.

Technical Contributions

The paper introduces a nonlinear observer developed on the manifold Lie group of SLAMn(3) to concurrently estimate a robot's pose and map its environment. This approach is notable for its systematic convergence properties, leveraging a prescribed performance function (PPF) to ensure transient and steady-state performance constraints are met. The primary innovations are as follows:

1. Nonlinear Observer Design: The observer is crafted directly on SLAMn(3), ensuring it closely follows the true nonlinear dynamics of SLAM by integrating angular and translational velocity measurements, landmark positions, and data from an Inertial Measurement Unit (IMU).
2. Systematic Convergence: Through the use of PPF, the observer guarantees the error starts within a large predefined set and decreases systematically to a smaller preset region. This aspect is critical as it enables the precise control of observer performance over time.
3. Bias Compensation: A novel aspect of the observer is its ability to compensate for unknown biases in velocity measurements, anchoring the estimates within realistic bounds.

Experimental Validation

The experimental validation of the proposed observer was conducted using real-world datasets collected by a quadrotor. A remarkable finding is the observer's robustness against measurement noise and bias, indicating its practical viability in dynamic and uncertain environments. The results demonstrate the observer's efficacy in maintaining six-degrees-of-freedom (6 DoF) robot pose estimates and accurately positioning landmarks within a 3D space.

Implications and Future Work

The introduction of a nonlinear observer with systematic convergence on the Lie group SLAMn(3) expands the theoretical framework for SLAM. It opens pathways for further research into advanced observer designs that can handle other dynamic elements like time-varying biases or more complex environments. Additionally, this work may bolster applications across robotics and autonomous systems, enhancing navigation capabilities in GPS-denied settings.

Future developments could explore integrating this observer with other sensory data, such as depth sensors or laser scans, to improve robustness in diverse conditions. Moreover, extending this framework to collaborative multi-agent systems could further enhance the reach of this research, enabling coordinated efforts in complex tasks such as search-and-rescue missions or environmental monitoring.

In conclusion, Hashim and Eltoukhy have provided a substantial contribution to the field of SLAM by presenting a nonlinear observer capable of handling the problem's inherent nonlinearities with precision and reliability. This research not only pushes the boundaries of theoretical modeling but also lays the groundwork for innovative practical implementations in the field of autonomous navigation.