02 / Robotics · State Estimation
Estimating quadruped velocity by combining inertial measurements and foot contacts. Six filter variants explore how contact representation and IMU bias modeling change estimation performance.
Approach
The project compares right-invariant EKF configurations on a Unitree Go2 in Isaac Lab. Contact parameterization and online IMU bias estimation define the six variants.
Track one front-left foot anchor as a minimal baseline.
Add contact states at touchdown and marginalize them at liftoff.
Keep all four anchors in the state, retaining a constant covariance size.
Each contact representation is tested with and without online gyroscope and accelerometer bias estimation.
Isaac Lab 0.54.2 with Isaac Sim 5.1.0. The repository reports verification on DGX Spark (Linux aarch64) and Windows x86_64.
Simulation results
All variants use the same command sequence and a 10-second metric window. The fixed four-foot configuration with bias estimation has the lowest reported 3D RMSE.
| Contact representation | Bias estimation | vₓ | vᵧ | vz | 3D RMSE |
|---|---|---|---|---|---|
| Single-foot | No | 0.4686 | 0.4465 | 0.1582 | 0.6663 |
| Single-foot | Yes | 0.4564 | 0.4418 | 0.1318 | 0.6488 |
| Dynamic contacts | No | 0.2156 | 0.2182 | 0.1346 | 0.3350 |
| Dynamic contacts | Yes | 0.1921 | 0.2310 | 0.1300 | 0.3274 |
| Fixed four-foot | No | 0.2159 | 0.2008 | 0.1451 | 0.3286 |
| Fixed four-foot | Yes | 0.2074 | 0.1949 | 0.1287 | 0.3123 |
What the results suggest
The multi-foot variants roughly halve 3D RMSE relative to the single-foot baseline in this experiment. More feet provide observations through contact switching during trot gait.
Bias estimation brings a modest improvement in these simulations, where the simulated IMU has no true bias. These results do not establish real-hardware performance; the balance may change with sensor bias and noise.
Touchdown impacts remain a source of vertical velocity error across the tested variants.
Project team
Team members are listed in the order shown on the project poster. View the poster ↗
Code & research
The repository contains the formulation, evaluation scripts, trained policy checkpoint, comparison plots and project deliverables.
R. Hartley et al., “Contact-Aided Invariant Extended Kalman Filtering for Robot State Estimation,” International Journal of Robotics Research, 39(4), 2020.