On-Manifold Preintegration for Real-Time Visual-Inertial Odometry (1512.02363v3)

Abstract: Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. However, real-time optimization quickly becomes infeasible as the trajectory grows over time, this problem is further emphasized by the fact that inertial measurements come at high rate, hence leading to fast growth of the number of variables in the optimization. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes into single relative motion constraints. Our first contribution is a \emph{preintegration theory} that properly addresses the manifold structure of the rotation group. We formally discuss the generative measurement model as well as the nature of the rotation noise and derive the expression for the \emph{maximum a posteriori} state estimator. Our theoretical development enables the computation of all necessary Jacobians for the optimization and a-posteriori bias correction in analytic form. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated into a visual-inertial pipeline under the unifying framework of factor graphs. This enables the application of incremental-smoothing algorithms and the use of a \emph{structureless} model for visual measurements, which avoids optimizing over the 3D points, further accelerating the computation. We perform an extensive evaluation of our monocular \VIO pipeline on real and simulated datasets. The results confirm that our modelling effort leads to accurate state estimation in real-time, outperforming state-of-the-art approaches.

• The paper introduces an on-manifold preintegration theory that directly integrates high-rate IMU measurements on SO(3) to enhance VIO performance.
• It employs a factor graph representation and a structureless vision model to seamlessly combine inertial and visual data while reducing computational demands.
• Experimental results show real-time operation with improved drift reduction and robust bias estimation for enhanced autonomous navigation.

On-Manifold Preintegration for Real-Time Visual-Inertial Odometry

The paper "On-Manifold Preintegration for Real-Time Visual-Inertial Odometry" by Christian Forster, Luca Carlone, Frank Dellaert, and Davide Scaramuzza presents a novel preintegration theory that addresses the computational challenges associated with visual-inertial odometry (VIO) in real-time applications. The discussion centers on how to efficiently combine high-rate inertial measurements with visual data to maintain accurate state estimation over extended trajectories. This work is accepted for publication in the IEEE Transactions on Robotics.

Motivation and Challenges in VIO

The authors identify the main bottleneck in VIO systems as the rapid increase in the number of variables in the optimization problem, exacerbated by high-rate IMU measurements. Current approaches often balance between filtering, which can be fast but accumulates linearization errors, and full smoothing, which is accurate but computationally demanding. The challenge is to derive a system that combines high precision with computational efficiency.

Contributions

1. Preintegration on the Manifold:

The primary contribution is the development of preintegration theory on the rotational manifold SO(3). The proposed methodology significantly diverges from earlier approaches that either approximate integration using Euler angles or treat IMU integration in Euclidean space without due consideration to the non-Euclidean nature of rotations. The authors provide a formal derivation of the preintegrated measurements by accounting for the manifold structure of the rotation group. This involves the computation of the maximum a posteriori (MAP) state estimator using the exponential and logarithm maps to handle rotations directly on the manifold:

• They present an improved treatment for the rotation noise.
• The derivation includes analytic forms for Jacobian computations, crucial for optimization.

2. Factor Graph Representation:

The paper outlines how these preintegrated IMU measurements can be incorporated into a visual-inertial system using factor graphs. This framework facilitates the seamless integration of the IMU model with a visual odometry subsystem while supporting incremental smoothing algorithms. Specifically, the use of a structureless vision model enables the avoidance of explicit optimization over 3D feature points, leading to significant computational savings.

Experimental Validation

Real-Time Performance and Accuracy:

The authors report extensive evaluations on both simulated and real-world datasets. Utilizing the incremental smoothing algorithm iSAM2, the proposed system achieves real-time performance (with update rates around 10ms) while maintaining high accuracy. Notably, the system consistently outperforms state-of-the-art methods such as OKVIS and MSCKF. In particular, the paper shows substantial reductions in drift over long trajectories, both indoors and outdoors.

Bias Estimation and Consistency:

The simulation results demonstrate that the on-manifold preintegration model enables precise bias estimation for the IMU sensors. Moreover, the system is shown to be consistent, in terms of maintaining accurate confidence bounds on estimated states and avoiding overconfident estimates, which could otherwise be detrimental in a VIO framework.

Implications and Future Directions

Practical Applications:

The methodologies presented have significant ramifications for autonomous navigation in GPS-denied environments, robotic mapping, and augmented reality applications. The computational advantages allow for deployments on resource-constrained platforms such as drones and mobile devices, broadening the applicability of VIO.

Theoretical Contributions and Extensions:

The formalization of IMU preintegration on the manifold may inspire future research tailored toward extending these principles to even broader classes of sensor fusion problems. Potential future directions include the incorporation of more complex dynamic models, advanced retraction schemes for different manifolds, and real-time loop closure mechanisms to further enhance accuracy and robustness in larger-scale environments.

Conclusion

The rigorous treatment of IMU preintegration on SO(3) developed in this paper addresses the critical challenges facing real-time VIO systems. By leveraging the geometric properties of rotations and integrating these within a factor graph framework, the authors offer a solution that excels in both accuracy and computational efficiency. This work provides valuable insights and tools that can be built upon for continued advancements in the fields of robotics and autonomous systems. The source code and supplementary material made available also underline the practical commitment to advancing research and development in this domain.