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Simultaneous Calibration of Noise Covariance and Kinematics for State Estimation of Legged Robots Via Bi-Level Optimization

Denglin Cheng, Jiarong Kang, Xiaobin Xiong

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A bi-level optimization framework automatically calibrates noise covariances and kinematic parameters, significantly improving state estimation accuracy and consistency for legged robots without manual tuning.
Bi-level optimization State estimation Noise covariance calibration Kinematics calibration Legged robots Differentiable programming

Problem

Accurate state estimation in legged robots requires precise noise covariance matrices and kinematic models, which are typically unknown, expensive to identify, or manually tuned, leading to sub-optimal or inconsistent estimates.

Approach

The method uses a bi-level optimization structure where an upper-level optimizer adjusts covariance and kinematic parameters to minimize trajectory errors, while a lower-level full-information estimator computes the state estimates, with gradients propagated through the estimator for direct parameter updates.

Key results

  • Joint calibration of process and measurement noise covariances with kinematic offsets
  • Elimination of manual tuning via differentiable estimator-in-the-loop optimization
  • Significantly reduced estimation error and improved uncertainty consistency on quadrupedal and humanoid platforms
  • Physically plausible parameter values validated across diverse legged robotic systems

Why it matters

Automates a critical calibration bottleneck, enabling reliable, high-fidelity state estimation for complex legged robots and advancing data-driven robotics calibration.

Abstract

Accurate state estimation is critical for legged and aerial robots operating in dynamic, uncertain environments. A key challenge lies in specifying process and measurement noise covariances, which are typically unknown or manually tuned. In this work, we introduce a bi-level optimization framework that jointly calibrates covariance matrices and kinematic parameters in an estimator-in-the-loop manner. The upper level treats noise covariances and model parameters as optimization variables, while the lower level executes a full-information estimator. Dif- ferentiating through the estimator allows direct optimization of trajectory-level objectives, resulting in accurate and consistent state estimates. We validate our approach on quadrupedal and humanoid robots, demonstrating significantly improved estimation accuracy and uncertainty calibration compared to hand-tuned baselines. Our method unifies state estimation, sensor, and kinematics calibration into a principled, data-driven framework applicable across diverse robotic platforms. Video available at: https://youtu.be/1zFORUMdLbg.

Index terms

Sensor Fusion Legged Robots

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