Optimal control simulations tracking wearable sensor signals provide comparable running gait kinematics to marker-based motion capture.

Objective: Inertial measurement units (IMUs) offer a method for assessing gait beyond the confines of a laboratory. Signal noise and calibration errors pose significant obstacles to accurately estimating joint angles, particularly during dynamic activities such as running. Advancements in dynamic optimisation tools could enable a more comprehensive analysis with fewer sensors and/or low-quality data. The objective of this study was to compare two IMU-based modelling approaches (inverse kinematics and optimal control simulations) with optical marker-based motion capture in reconstructing running gait kinematics.

Methods: Six participants performed treadmill running at three speeds whilst marker trajectories and IMU signals were collected concurrently. The subject-specific biomechanical model consisted of a 3D representation of the lower body and torso, with contact spheres added to simulate ground contact in the optimal control simulations. The objective of the optimal control simulations was to track the accelerations, angular velocities, and orientations of eight sensors with simulated signals from the model sensors. Additional constraints were enforced, reflecting physiological and biomechanical principles and targeting dynamic consistency. The objective of the IMU-based inverse kinematics was to minimize the difference between the input and simulated sensor orientations. The joint kinematics derived from both methods were compared against optical marker-based motion capture across a range of running speeds, evaluating the absolute and normalized root mean square errors.

Results: Compared with motion-capture joint angles, optimal control simulations resulted in lower absolute errors (RMSE 8° ± 1) that were consistent across all speeds. IMU-based inverse kinematics exhibited greater differences with motion capture (RMSE 12° ± 1), which was more significant at faster speeds. The largest absolute inaccuracies were observed in the sagittal angles when not normalizing for the joint range of motion. The computational times for the optimal control were 46 ± 60 min, whereas they were 19.3 ± 3.7 s for the IMU-based inverse kinematics.

Conclusions: Compared with traditional IMU-based inverse kinematics, the optimal control approach provides a more comparative representation of joint kinematics from optical motion capture. This method can mitigate errors associated with closely tracking IMU noise and drift, and it offers a dynamic analysis that considers the underlying forces and torques producing movement. However, these advantages come at the expense of challenges in parameter selection and computational cost.

Significance: These findings highlight the potential of using IMUs with optimal control methods to provide a comprehensive understanding of gait dynamics across diverse applications. IMU-based inverse kinematics remains a viable option for faster computation and when model fidelity is less of a concern.