*2.1. Participants*

Seven healthy young adults participated in this study (6 females, 1 male, mean (SD) age = 22.6 (1.5) years, height = 1.67 (0.08) m, body mass = 65.4 (11.6) kg). Participants were included in the study if they were between 20 and 25 years old and free of any injury at the time of participation. The study protocol was approved by the ethics committee of our university (agreement number: B403201523492) and each patient provided written informed consent to the use of their anonymized data.

#### *2.2. Experimental Setup and Recordings*

To assess the lower limb joint kinematics, seven wearable IMUs; (x-IMU, x-io Techologies, Bristol, UK) were fixed in matched 3D-printed ABS (acrylonitrile butadiene styrene) enclosures and attached by means of a semi-elastic belt to seven lower body segments, as shown in Figure 1: the waistline at the level of the fifth lumbar vertebra (L5), the middle of the thighs, the middle of the shanks, and at the dorsal side of the feet. The IMUs were firmly strapped on the skin or clothes. Although this could lead to undesirable artifacts, it is more representative of records in an unconstrained context, such as outdoor conditions. Each IMU included a tri-axial accelerometer (full scale ±6 g), a gyroscope

(±2000◦/s), and a magnetometer (±8.1 G) that were sampled at a frequency of 128 Hz. The IMUs were connected to a computer by means of a Bluetooth connection using a custom application based on open source software [17] (C# program, github.com/xioTechnologies). Each movement was recorded independently. The synchronization between the IMUs was ensured by a custom-built magnetic coil that sent a magnetic impulse at the beginning of each recording.

**Figure 1.** Sensor locations: (**a**) x-IMU from xi-o Technologies, (**b**) 3D-printed **a**crylonitrile **b**utadiene **s**tyrene (ABS) enclosures (4 markers of 14 mm diameter) with the inertial measurement unit (IMU) reference frame, and (**c**) segmen<sup>t</sup> reference frame of the 7 IMUs on the subject.

Four reflective markers were fixed at each corner of the ABS enclosures to define clusters for each segmen<sup>t</sup> (Figure 1). Motion capture data were collected at a rate of 200 Hz using an eight-camera motion analysis system (Vicon V5 Motion Systems, Oxford Metrics Ltd., Oxford, UK)) and processed using Nexus 2.5 software. The position of each marker on the cluster allowed for the orientation of each segmen<sup>t</sup> to be computed in the lab reference frame.

#### *2.3. Functional Calibration and Test Movements*

The experimental protocol is illustrated in Figure 2. Four functional calibration movements were performed to assess their reproducibility and accuracy regarding lower limb joint angle measurement with the IMUs. These movements were designed to include a rotation in the sagittal plane of each lower body segment, including the pelvis, while being easy to explain and reproduce. Each functional calibration movement included (1) an upright static posture with the arms alongside the body and the feet parallel beside each other that was used to define the segmen<sup>t</sup> vertical axis and (2) a functional movement spanning a range of orientations for each segmen<sup>t</sup> in the sagittal plane that was used to define a second segmen<sup>t</sup> axis. In the static posture, the segmen<sup>t</sup> was supposed to have a zero angle in all three planes such that the segmen<sup>t</sup> reference frames were aligned with the lab reference frame. The X axis was defined as the medio-lateral axis, pointing to the left of the subject; the Y axis as the anterio-posterior axis, pointing in front of the subject; and the Z axis as the vertical axis, pointing downward (Figure 1c).

The instructions were as follows:


**Figure 2.** (**a**) Experimental protocol. (**b**) Functional calibration movements: for movements 1, 2, and 3, where the second axis was defined as the principal rotational axis as determined by a principal component analysis (PCA) on gyroscope signals; for movements 4a, 4b, and 4c, the second axis was defined as the principal acceleration axis through a PCA on accelerometer signals. (**c**) Two options to determine the segmen<sup>t</sup> reference frames, as shown in segmen<sup>t</sup> frontal views. (**d**) The accuracy was assessed using the root mean square error (RMSE), the absolute difference in the range of motion (ΔROM) between both systems, and the absolute drift accumulated during the movement (DRIFT).

The functional calibration movements were demonstrated by the operator and each participant received practice trials to ge<sup>t</sup> used to each movement. Each functional calibration movement was recorded three times before and three times after the execution of the test movements. The walking movement at self-selected speed was only performed two times, before and after the test movements.

Four test movements were performed in the same order:


The mean recorded times for test movements were 11 s for walking, 11 s for stepping over an obstacle, 14 s for the step ascent, 16 s for the step descent.

## *2.4. Signal Processing*

An open source attitude and heading reference system (AHRS) algorithm was used for sensor fusion between the accelerometer and gyroscope sensor data of the IMU (Mahony's AHRS algorithm) [18]; the magnetometer signals were omitted. The four calibration movements were used to compute the orientation of each segmen<sup>t</sup> relative to the lab reference frame in di fferent ways. The gravity vector during the static upright posture was used to define the vertical axis for each segment. A second segmen<sup>t</sup> axis was defined in one of two ways depending on the method of functional calibration. For functional calibration movements 1, 2, and 3, it was defined as the principal rotational axis as determined by a principal component analysis (PCA) on gyroscope signals. Two options were used to determine the segmen<sup>t</sup> reference frame (see frontal views of the segmen<sup>t</sup> reference frame in Figure 2c): either the gravity vector (g) was defined as the vertical axis and the lateral axis was forced to be the orthogonal axis closest to the rotation axis of the functional calibration movement (r), or the lateral axis was defined as the functional calibration movement rotation axis and the vertical axis was the orthogonal axis closest to the gravity vector (and thus the transversal plane was not perfectly horizontal in the static upright posture). For functional calibration movements 4a, 4b, and 4c, the second axis was defined as the principal acceleration axis through a PCA on accelerometer signals transformed in a lab-fixed reference frame. The 3D orientation of the pelvis and joint angles for the hips, knees, and ankles were calculated from the segmen<sup>t</sup> orientations based on the recommendations of the International Society of Biomechanics [6] for the di fferent functional calibration movements. Flexion-extension were rotations around the X axis, abduction-adduction was around the Y axis, and internal-external rotations were around the Z axis.

The lower body 3D kinematics derived from the optical system were computed in two di fferent ways. They were either computed in the lab frame or computed through the same functional calibration procedures described above, using the principal axis of rotation or acceleration determined from optical records.

For each participant, a static period (about 5 s) in a standing position was captured at the beginning of each test to define the segment's initial orientation for the IMU AHRS algorithm.

#### *2.5. Data Analysis*

Joint angles of the walking test movement were calculated for all functional calibration procedures. The accuracy of the IMU kinematics was computed for each calibration procedure as the di fference in joint angle between the IMU and optical measurements. The accuracy was assessed using the root mean square error (RMSE) during the movement period, the absolute di fference in the range of motion (ROM) between both systems ( ΔROM), and the absolute drift accumulated during the movement due to the error in the angular rate integration (DRIFT). The RMSE, ΔROM, and DRIFT parameters were computed using Matlab 2018 (Mathworks Inc, Natick, MA, USA) and are expressed in degrees.

A generalized linear model was used to assess the effect of (1) the functional calibration movement, (2) the option used to determine the segment's reference frame to compute the IMU orientation, and (3) the functional calibration method for the optical system on the amplitude of the RMSE, ΔROM, and DRIFT parameters for each joint angle and plane of motion. This analysis was performed with SPSS (version 25, IMB Corporation, Amonk, NY, USA) and the significance level was set to α = 0.05.

The reproducibility of each functional calibration movement was assessed as the difference in joint angle computed from each repetition of the functional calibration movement. The reproducibility of the ROM parameter in all movement planes and joints was determined based on the intra-class correlation coefficient (ICC) [19] and standard error of measurement (SEM) [19]. Values of ICC ≥ 0.90 were considered as excellent, 0.70–0.89 as good, 0.40–0.69 as acceptable, and <0.40 as low [20]. The SEM estimates the non-systematic variance and reflects the within-subject variability among repeated calibrations. A proportional SEM (SEM%) was calculated by expressing the SEM relative to the mean ROM (SEM% = (SEM/mean) × 100%)) [21]. An SEM% above 10% was considered as high.

Once the most accurate and reproducible functional calibration method was selected for a walking test, the accuracy was determined for the other test movements, namely the step ascent, descent, and stepping over an obstacle, using the RMSE and ΔROM parameters. The parameters were calculated for the front leg (i.e., the first leg to touch the step in the step ascent, the first leg to touch the floor leg in the step descent, and the first leg to touch the ground in obstacle stepping) and for the back leg in the different test movements. Differences in the RMSE and ΔROM parameters between test movements were assessed with a one-way ANOVA. Tukey's post hoc test was used to reveal which groups differed in the case of significant *p*-values. The significance level was set to α = 0.05.
