A2I-Calib: An Anti-noise Active Multi-IMU Spatial-temporal Calibration Framework for Legged Robots

TL;DR

A2I-Calib tackles the problem of spatial-temporal misalignment in multi-IMU legged-robot odometry by introducing an anti-noise active calibration framework. It combines a basis-function-based trajectory generator that minimizes the conditioning number $\kappa(\Sigma_{FF})$ with a reinforcement-learning–driven controller to robustly execute calibration motions, followed by canonical correlation analysis to estimate the foot-IMU rotation $\mathbf{R}_I^F$ and time offset $t_d$. The approach is validated in both simulation and real-world quadrupeds, showing reduced noise sensitivity and improved multi-IMU odometry accuracy, including up to substantial reductions in APE under varying IMU noise levels. The results support the framework’s potential to enable autonomous, high-fidelity calibration across arbitrary foot-mounted IMUs, enhancing legged-robot proprioceptive estimation in practical deployments.

Abstract

Recently, multi-node inertial measurement unit (IMU)-based odometry for legged robots has gained attention due to its cost-effectiveness, power efficiency, and high accuracy. However, the spatial and temporal misalignment between foot-end motion derived from forward kinematics and foot IMU measurements can introduce inconsistent constraints, resulting in odometry drift. Therefore, accurate spatial-temporal calibration is crucial for the multi-IMU systems. Although existing multi-IMU calibration methods have addressed passive single-rigid-body sensor calibration, they are inadequate for legged systems. This is due to the insufficient excitation from traditional gaits for calibration, and enlarged sensitivity to IMU noise during kinematic chain transformations. To address these challenges, we propose A$^2$I-Calib, an anti-noise active multi-IMU calibration framework enabling autonomous spatial-temporal calibration for arbitrary foot-mounted IMUs. Our A$^2$I-Calib includes: 1) an anti-noise trajectory generator leveraging a proposed basis function selection theorem to minimize the condition number in correlation analysis, thus reducing noise sensitivity, and 2) a reinforcement learning (RL)-based controller that ensures robust execution of calibration motions. Furthermore, A$^2$I-Calib is validated on simulation and real-world quadruped robot platforms with various multi-IMU settings, which demonstrates a significant reduction in noise sensitivity and calibration errors, thereby improving the overall multi-IMU odometry performance.

Figures (5)

• Figure 1: A$^2$I-Calib is a novel spatial-temporal calibration framework for arbitrary foot-mounted IMUs. In this framework, a basis function selection theorem is proposed to minimize the condition number in calibration correlation analysis, thereby reducing noise sensitivity. Moreover, a RL-based motion controller is designed to implement the optimal calibration trajectory. Finally, more precise calibration results from A$^2$I-Calib improve the overall multi-IMU odometry performance.
• Figure 2: System overview of A$^2$I-Calib. Firstly, the anti-noise trajectory generation module generates and optimizes leg trajectories that minimizes the condition number in the legged robot, based on the proposed basis functions. Secondly, In order to perform the ideally generated calibration actions on the ground for the legged robot, the RL-based calibration action controller is introduced. This module achieves robust execution of anti-noise calibration actions. The rewards for lifting a single leg and combining it with the flexibility of the calibration actions are adopted in the RL training. Thirdly, the generated calibration commands are implemented into a quadruped robot and canonical correlation analysis (CCA) is conducted to calibrate the foot IMU. Finally, The calibration results, including the external rotation matrix and time offset, are then input into the multi-IMU odometry.
• Figure 3: Simulation and real-world experiment results of joints positions, IMU's angular velocities and condition numbers.
• Figure 4: The estimated trajectories of MIPO with different calibration results in Gazebo.
• Figure 5: Experiments on the real-world quadruped robot platform, Unitree Go2. (a): The real-world multi-IMU system based on the Unitree Go2, equipped with Livox LiDAR for odometry ground truth collection and a NOITOM portable wireless multi-IMU suite. (b): The estimated trajectories of MIPO with different calibration results in real-world scenarios. The RMS of APE for MIPO-A$^2$I-Calib is 0.23 m, while for MIPO-WALK-Calib, it is 0.27 m, indicating a 15% improvement in accuracy for MIPO-A$^2$I-Calib.

Theorems & Definitions (2)

• Theorem 1
• proof