Iterated Invariant EKF for Quadruped Robot Odometry

A research team from Istituto Italiano di Tecnologia and MINES Paris has developed a significant advancement in robot navigation with their Iterated Invariant Extended Kalman Filter (IterIEKF). This open-source algorithm tackles the core challenge of state estimation for mobile robots, specifically quadruped platforms. Traditional Kalman filters rely on linear assumptions that break down in real-world, nonlinear environments. The IterIEKF extends these concepts to nonlinear spaces using Lie group theory, creating a more robust foundation for calculating a robot's position and orientation.

The key innovation lies in the filter's update step, which uses only proprioceptive measurements—data from the robot's own sensors. It exploits kinematic constraints, such as foot velocity during ground contact and base-frame velocity. This approach makes the system inherently resilient to poor lighting, slippery surfaces, or other challenging environmental conditions that often confuse vision-based systems. The team validated their work through extensive simulations and real-world dataset evaluations.

Results demonstrate that the IterIEKF consistently outperforms previous state-of-the-art filters, including the vanilla Invariant EKF and the SO(3)-based Kalman Filter and its iterated variant. The improvements are measured in both accuracy (how close the estimated position is to the true position) and consistency (how well the filter's uncertainty estimate matches its actual error). By providing a more reliable and computationally efficient odometry solution, this work removes a major bottleneck for autonomous legged robots operating in unstructured environments.