A Tightly Coupled IMU-Based Motion Capture Approach for Estimating Multibody Kinematics and Kinetics

TL;DR

This work targets robust IMU-based multibody motion capture by tightly integrating IMU measurements with a full 3D dynamic model using an Iterated Extended Kalman Filter (IEKF). The state $x=[q,\dot{q},\tau]^T$, with $q,\dot{q},\tau\in\mathbb{R}^{N_D}$, is estimated by coupling accelerometer/gyroscope data (and optional optical/MoCap inputs) to OpenSim-derived dynamics, enabling simultaneous estimation of kinematics and kinetics. Validation on a 3DoF pendulum and a 6DoF Kuka robot demonstrates RMSD in joint angles up to $3.75^\circ$ (pendulum) and $3.24^\circ$ (Kuka), and joint torque RMSD up to $2\ \mathrm{Nm}$ (pendulum) and $3.73\ \mathrm{Nm}$ (Kuka), with marker-assisted IEKF providing further improvements. The approach is robust to magnetic disturbances and supports incorporating diverse sensor data, offering portable, accurate MoCap for rehabilitation, robotics, and beyond.

Abstract

Inertial Measurement Units (IMUs) enable portable, multibody motion capture (MoCap) in diverse environments beyond the laboratory, making them a practical choice for diagnosing mobility disorders and supporting rehabilitation in clinical or home settings. However, challenges associated with IMU measurements, including magnetic distortions and drift errors, complicate their broader use for MoCap. In this work, we propose a tightly coupled motion capture approach that directly integrates IMU measurements with multibody dynamic models via an Iterated Extended Kalman Filter (IEKF) to simultaneously estimate the system's kinematics and kinetics. By enforcing kinematic and kinetic properties and utilizing only accelerometer and gyroscope data, our method improves IMU-based state estimation accuracy. Our approach is designed to allow for incorporating additional sensor data, such as optical MoCap measurements and joint torque readings, to further enhance estimation accuracy. We validated our approach using highly accurate ground truth data from a 3 Degree of Freedom (DoF) pendulum and a 6 DoF Kuka robot. We demonstrate a maximum Root Mean Square Difference (RMSD) in the pendulum's computed joint angles of 3.75 degrees compared to optical MoCap Inverse Kinematics (IK), which serves as the gold standard in the absence of internal encoders. For the Kuka robot, we observe a maximum joint angle RMSD of 3.24 degrees compared to the Kuka's internal encoders, while the maximum joint angle RMSD of the optical MoCap IK compared to the encoders was 1.16 degrees. Additionally, we report a maximum joint torque RMSD of 2 Nm in the pendulum compared to optical MoCap Inverse Dynamics (ID), and 3.73 Nm in the Kuka robot relative to its internal torque sensors.

Figures (9)

• Figure 1: Overview of the tightly coupled sensor and model dynamics approach. Given the initial states, IEKF couples sensor measurements and the multibody system model to estimate generalized joint angles, velocities, and torques.
• Figure 2: Displays the definitions of the navigation frame $n$, the optical MoCap frame $c$, the body frame $b_k$, the IMU frame $s_k$, and the marker frame $m_\gamma$. It also includes the translation vectors $\boldsymbol{r}^{b_k}_{b_k s_k}$ and $\boldsymbol{r}^n_{m_{\gamma} b_k}$
• Figure 3: IEKF process: (1) Predict the states using the prior states and the OpenSim model, (2) Refine the state predictions by iteratively linearizing the measurement model either from the IMUs only or the combination of IMUs and other sensors to account for non-linearities then compute the Kalman gain $\boldsymbol{K}$, (3) Update the state estimation and covariance.
• Figure 4: An experimental setup with 3DOF is shown on the left, where optical markers and an IMU are attached to each body segment. On the right is an OpenSim model with corresponding IMU and marker placements. Sensor locations on the model were registered using Optical MoCap measurements.
• Figure 5: On the left the actual KUKA LBR iiwa R800 that was used where a set of 4 markers and an IMU were placed on each body segment. On the right an OpenSim model that describes the system is shown.