How many sensors are enough? Trajectory optimization using sparse inertial sensor sets

Nitschke M, Mayer M, Dorschky E, Koelewijn A (2022)

Publication Status: Accepted

Publication Type: Conference contribution, Abstract of lecture

Future Publication Type: Conference contribution

Publication year: 2022

Event location: Taipei TW



Inertial sensors are a promising alternative to optical motion capturing since they can enable cheap measurements outside the laboratory. However, most methods for inertial motion capturing are based on error-prone computation of sensor orientations[1,2]. Previously, we proposed trajectory optimization of a planar musculoskeletal model to estimate dynamically consistent gait kinematics and kinetics directly from the acceleration and gyroscope data of seven inertial sensors at the lower extremities[3].

A sparse sensor placement without sensors at each body segment of interest would simplify measurements and increase mobility. Therefore, we investigate whether gait kinematics and kinetics of the lower body can be estimated from sparse sensor sets using musculoskeletal simulations.

We created gait simulations of planar a musculoskeletal model with a trajectory optimization minimizing the difference between measured and simulated accelerations and angular velocities[3]. We evaluated walking and running at three speeds respectively for ten participants[3] and seven symmetric sensor sets at the lower body with up to seven sensors:
1. Feet
2. Feet & trunk
3. Feet & shanks
4. Feet & thighs
5. Feet & shanks & trunk
6. Feet & thighs & trunk
7. Feet & shanks & thighs & trunk (full)

Joint angles, joint moments, and ground reaction forces were compared to optical motion capturing using relative root mean squared deviation (rRMSD) and Pearson correlation.

The figure shows estimated biomechanical variables for running of one participant. No sensor setup performed best or worst for all biomechanical variables. Nevertheless, the foot sensor set 1 generally resulted in higher rRMSDs (9.5% to 62.0%) and lower Pearson correlations (0.51 to 0.99), compared to for example the full sensor set 7 (rRMSD: 10.5% to 51.2%; Pearson correlation: 0.69 to 0.99). When using only the foot sensor set 1, knee angles and moments were overestimated during stance. Simulations without trunk sensor resulted in an increased forward lean.

We found that gait can be reconstructed from sparse inertial sensor measurements with musculoskeletal simulations to estimate lowerbody kinematics and kinetics. Even when tracking only two sensors at the feet, the Pearson correlations were strong to excellent (≥0.81) except for the knee moment for walking (0.51). Adding the trunk sensor or other proximal sensors improved the results considerably.

Future research should investigate the weighting of the sensor signals and objective terms in the trajectory optimization. We weighted all sensor signals equally. However, errors in inverse kinematics were smaller when weighting distal sensor orientations less[2]. Furthermore, we determined the weights of the objective terms using the full sensor set. The weights might therefore be suboptimal for the sparse sets.

It can be concluded that all sensor sets are suitable to reconstruct lower-body kinematics and kinetics. The sensor set should be selected based on the required accuracy and conditions of an application.

This work was (partly) funded by the DFG – SFB 1483 – Project-ID 442419336.

1.Karatsidis A et al. (2019). Med Eng Phys, 65: 68-77.
2.Al Borno M et al. (2021). bioRxiv.
3.Dorschky E et al. (2019). J Biomech, 95: 109278.

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How to cite


Nitschke, M., Mayer, M., Dorschky, E., & Koelewijn, A. (2022). How many sensors are enough? Trajectory optimization using sparse inertial sensor sets. Paper presentation at 9th World Congress of Biomechanics 2022 Taipei, Taipei, TW.


Nitschke, Marlies, et al. "How many sensors are enough? Trajectory optimization using sparse inertial sensor sets." Presented at 9th World Congress of Biomechanics 2022 Taipei, Taipei 2022.

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