#### Landmark and IMU Data Fusion: Systematic Convergence Geometric Nonlinear Observer for SLAM and Velocity Bias

##### Hashim A. Hashim, Abdelrahman E. E. Eltoukhy

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.

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