EqVIO: An Equivariant Filter for Visual Inertial Odometry (2205.01980v2)

Abstract: Visual Inertial Odometry (VIO) is the problem of estimating a robot's trajectory by combining information from an inertial measurement unit (IMU) and a camera, and is of great interest to the robotics community. This paper develops a novel Lie group symmetry for the VIO problem and applies the recently proposed equivariant filter. The symmetry is shown to be compatible with the invariance of the VIO reference frame, lead to exact linearisation of bias-free IMU dynamics, and provide equivariance of the visual measurement function. As a result, the equivariant filter (EqF) based on this Lie group is a consistent estimator for VIO with lower linearisation error in the propagation of state dynamics and a higher order equivariant output approximation than standard formulations. Experimental results on the popular EuRoC and UZH FPV datasets demonstrate that the proposed system outperforms other state-of-the-art VIO algorithms in terms of both speed and accuracy.

• The paper introduces a novel Lie group symmetry model that enables exact linearization of bias-free IMU dynamics in visual inertial odometry.
• The proposed Equivariant Filter (EqF) significantly reduces linearization errors by maintaining higher-order equivariant approximations.
• Performance evaluations on EuRoC and UZH FPV datasets demonstrate substantial improvements in computational speed and accuracy over traditional VIO algorithms.

The paper "EqVIO: An Equivariant Filter for Visual Inertial Odometry" presents an advanced approach to solving the Visual Inertial Odometry (VIO) problem, which is a key challenge in robotics for estimating a robot's trajectory using data from an inertial measurement unit (IMU) and a camera. The novel contribution of this work lies in the implementation of a Lie group symmetry specifically tailored for the VIO problem and the utilization of an equivariant filter (EqF).

Key Contributions:

1. Lie Group Symmetry: The authors introduce a symmetry model that aligns with the invariance properties of the VIO reference frame. This symmetry allows for an exact linearization of the IMU's bias-free dynamics. Such an alignment ensures that the solution respects the inherent geometric structure of the problem, leading to more consistent state estimation.
2. Equivariant Filter (EqF): By integrating this Lie group symmetry, the EqF achieves reduced linearization errors when propagating state dynamics compared to traditional methods. The approach maintains a higher-order equivariant output approximation, which contributes to enhanced estimator performance.
3. Performance Evaluation: Through experiments using the widely regarded EuRoC and UZH FPV datasets, the proposed EqVIO system demonstrates superior performance both in terms of computational speed and accuracy over existing state-of-the-art VIO algorithms. This indicates the potential of the proposed method to improve real-time robotics applications significantly.

By leveraging the mathematical structure provided by Lie groups, the paper provides a robust framework for improving the accuracy and efficiency of VIO systems, offering valuable insights for researchers and practitioners in robotics seeking to enhance navigation and control mechanisms.