# Contact-Aided Invariant Extended Kalman Filtering for Robot State Estimation

arXiv: https://arxiv.org/abs/1904.09251 · HTML: https://mlsanity.com/paper/1904.09251/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2019.

## Built on by (most cited first, 18 of 18)

- [Concurrent Training of a Control Policy and a State Estimator for Dynamic and Robust Legged Locomotion](https://mlsanity.com/paper/2202.05481/) (2022)
- [Coupling Vision and Proprioception for Navigation of Legged Robots](https://mlsanity.com/paper/2112.02094/) (2021)
- [Robust and Versatile Bipedal Jumping Control through Reinforcement Learning](https://mlsanity.com/paper/2302.09450/) (2023)
- [VILENS: Visual, Inertial, Lidar, and Leg Odometry for All-Terrain Legged Robots](https://mlsanity.com/paper/2107.07243/) (2021)
- [Design and Control of a Bipedal Robotic Character](https://mlsanity.com/paper/2501.05204/) (2025)
- [EqNIO: Subequivariant Neural Inertial Odometry](https://mlsanity.com/paper/2408.06321/) (2024)
- [Olaf: Bringing an Animated Character to Life in the Physical World](https://mlsanity.com/paper/2512.16705/) (2025)
- [Perception for Humanoid Robots](https://mlsanity.com/paper/2309.15616/) (2023)
- [Fast Ergodic Search with Kernel Functions](https://mlsanity.com/paper/2403.01536/) (2024)
- [Legged Robot State Estimation With Invariant Extended Kalman Filter Using Neural Measurement Network](https://mlsanity.com/paper/2402.00366/) (2024)
- [MARG: MAstering Risky Gap Terrains for Legged Robots with Elevation Mapping](https://mlsanity.com/paper/2509.20036/) (2025)
- [Equivariant Neural Networks for General Linear Symmetries on Lie Algebras](https://mlsanity.com/paper/2510.22984/) (2025)
- [Learning Linear Policies for Robust Bipedal Locomotion on Terrains with Varying Slopes](https://mlsanity.com/paper/2104.01662/) (2021)
- [Attention-Based Neural-Augmented Kalman Filter for Legged Robot State Estimation](https://mlsanity.com/paper/2601.18569/) (2026)
- [CoCo-InEKF: State Estimation with Learned Contact Covariances in Dynamic, Contact-Rich Scenarios](https://mlsanity.com/paper/2605.15122/) (2026)
- [SRL: Combining SLIP Model and Reinforcement Learning for Agile Robotic Jumping](https://mlsanity.com/paper/2606.18625/) (2026)
- [TRACE: Learned Proprioceptive Odometry for Legged Robots under Unreliable Contact Conditions](https://mlsanity.com/paper/2608.05975/) (2026)
- [GINIO: A Geometric SO(3)-Equivariant Interface for Neural Inertial Odometry](https://mlsanity.com/paper/2609.25338/) (2026)

## Abstract (arXiv)

Legged robots require knowledge of pose and velocity in order to maintain stability and execute walking paths. Current solutions either rely on vision data, which is susceptible to environmental and lighting conditions, or fusion of kinematic and contact data with measurements from an inertial measurement unit (IMU). In this work, we develop a contact-aided invariant extended Kalman filter (InEKF) using the theory of Lie groups and invariant observer design. This filter combines contact-inertial dynamics with forward kinematic corrections to estimate pose and velocity along with all current contact points. We show that the error dynamics follows a log-linear autonomous differential equation with several important consequences: (a) the observable state variables can be rendered convergent with a domain of attraction that is independent of the system's trajectory; (b) unlike the standard EKF, neither the linearized error dynamics nor the linearized observation model depend on the current state estimate, which (c) leads to improved convergence properties and (d) a local observability matrix that is consistent with the underlying nonlinear system. Furthermore, we demonstrate how to include IMU biases, add/remove contacts, and formulate both world-centric and robo-centric versions. We compare the convergence of the proposed InEKF with the commonly used quaternion-based EKF though both simulations and experiments on a Cassie-series bipedal robot. Filter accuracy is analyzed using motion capture, while a LiDAR mapping experiment provides a practical use case. Overall, the developed contact-aided InEKF provides better performance in comparison with the quaternion-based EKF as a result of exploiting symmetries present in system.