Sensor arrangement optimization

2.1 Optimization procedure

The optimization was performed on capturing the back posture to determine the workload on the waist. Small (S), medium (M), and large (L) sensor suits were created. It was assumed that the suit fitted the body. The target motion in this study was bending the waist without twisting the torso. Body motion refers to the time-series joint angle, 𝜃𝜃𝑗𝑗, that was input into the DHM. The method to determine the optimal sensor position consisted of the following procedures.

1. Inputting primitive motions to the evaluation DHMs and getting joint angle 𝜃𝜃_𝑗𝑗 ( 𝑗𝑗 = 𝑝𝑝,𝑙𝑙,𝐷𝐷 ) of the motion.

2. Obtaining inclination angle 𝜓𝜓𝑛𝑛 of the sensor at candidate point P𝑛𝑛. 3. Producing a formula converting 𝜓𝜓𝑛𝑛 to 𝜃𝜃𝑗𝑗 for each suit size.

4. Substituting the converted angle into the evaluation function.

2.2 DHM “Dhaiba”

A DHM called “Dhaiba” (ENDO et al., 2014) was used in this research. Dhaiba model was developed by the Digital Human Research Group in the National Institute of Advanced Industrial Science and Technology, Japan. The Dhaiba model (Figure 2.1), consists of a linkage model armature composed of bones and a skin mesh model that forms the body surface shape. Feature points can be arranged anywhere on the body surface. The Dhaiba model deforms and can reproduce the body surface shape according to the change in the posture of the bones. The Dhaiba model can also model arbitrary physiques. In this paper, the model was individualized by using a small number of dimensions according to NOHARA et al. (2016).

2.3 Definition of the DHM posture and sensor inclination angles The trunk of the Dhaiba model, which was the measurement target of this study, was modeled by three links: pelvis (PELVIS), lumbar vertebrae (SPINE), and thoracic vertebrae (STERNUM). Each link had a local coordinate system based on its proximal link coordinate system (Figure 2.2). The root of all the bones was PELVIS.

The coordinate system of PELVIS, written as (𝑿𝑿_𝐿𝐿,𝒀𝒀_𝐿𝐿,𝒁𝒁_𝐿𝐿), was set in the same direction as the global coordinate system, (𝑿𝑿_𝑊𝑊,𝒀𝒀_𝑊𝑊,𝒁𝒁_𝑊𝑊), and all the bones’ X-axes were parallel to 𝑿𝑿_𝑊𝑊. The joint angle of PELVIS, SPINE, and STERNUM links was defined as that with respect to the direction of gravity (𝑿𝑿_𝑊𝑊axis), written as

𝜽𝜽_𝑗𝑗 = �𝜃𝜃_𝑗𝑗^𝑥𝑥

𝜃𝜃_𝑗𝑗^𝑦𝑦� ( 𝑗𝑗 = 𝑝𝑝,𝑙𝑙,𝐷𝐷) (2.1) where 𝜃𝜃_𝑗𝑗^𝑥𝑥 is the angle on the sagittal (𝒀𝒀𝑊𝑊-𝒁𝒁𝑊𝑊) plane and 𝜃𝜃_𝑗𝑗^𝑦𝑦 is the angle on the coronal (𝑿𝑿_𝑊𝑊-𝒁𝒁_𝑊𝑊) plane.

Fig. 2.1 Dhaiba model

The sensor attachment position was set on the spine at the center of the back. The candidate area was defined by dividing the curve of the spine from the seventh cervical vertebrae (C7) to the sacral bone into 10 equal sections. Each position was separated by feature points, which were arranged on a skin mesh. The center point of each divided curve was set as candidate point P𝑛𝑛 and the points were numbered in ascending order from the C7 side following the format P1, P2, P3, …, P10 (Figure 2.3).

The actual inertial sensor could not be put on the DHM’s body surface. The Fig. 2.2 Schematic of elements

inclination of the sensor placed on the candidate position was defined with the vector connecting feature points above and below the position. The coordinates of upper and lower marker of P_𝑛𝑛 were written as (^𝑢𝑢𝑥𝑥_𝑛𝑛 ,^𝑢𝑢𝑦𝑦_𝑛𝑛 ,^𝑢𝑢𝑧𝑧_𝑛𝑛) and (^𝑑𝑑𝑥𝑥_𝑛𝑛 ,^𝑑𝑑𝑦𝑦_𝑛𝑛 ,^𝑑𝑑𝑧𝑧_𝑛𝑛), respectively. The angle 𝝍𝝍_𝑛𝑛 = [𝜓𝜓_𝑛𝑛^𝑥𝑥 𝜓𝜓_𝑛𝑛^𝑦𝑦]^𝐿𝐿 was expressed by equations (2.2) and (2.3).

𝜓𝜓_𝑛𝑛^𝑥𝑥 = tan^{−1 � 𝑧𝑧}_{� 𝑦𝑦}^{𝑢𝑢 𝑛𝑛− 𝑧𝑧𝑑𝑑 𝑛𝑛�}

𝑢𝑢 𝑛𝑛− 𝑦𝑦𝑑𝑑 𝑛𝑛� (2.2)

𝜓𝜓_𝑛𝑛^𝑦𝑦 = tan^{−1 � 𝑧𝑧}_{� 𝑥𝑥}^{𝑢𝑢 𝑛𝑛− 𝑧𝑧𝑑𝑑 𝑛𝑛�}

𝑢𝑢 𝑛𝑛− 𝑥𝑥^𝑑𝑑 _𝑛𝑛� (2.3)

The joint angle 𝜃𝜃_𝑗𝑗^𝑟𝑟 around the 𝑟𝑟 axis (𝑟𝑟= 𝑥𝑥,𝑦𝑦) was obtained by the sensor inclination angle 𝜓𝜓_𝑛𝑛^𝑟𝑟(𝑟𝑟= 𝑥𝑥,𝑦𝑦). Although the spine is a structure made of multiple links, each candidate area can be considered as a rigid body due to its division into 10 parts.

Therefore, the relationship between 𝜓𝜓_𝑛𝑛^𝑟𝑟 and 𝜃𝜃_𝑗𝑗^𝑟𝑟 was assumed to be linear. A linear conversion was used to convert angle 𝜓𝜓𝑛𝑛𝑖𝑖 (equation (2.4)).

𝜽𝜽�_𝑗𝑗 = ^𝑑𝑑_𝑛𝑛ℎ_𝑗𝑗(𝝍𝝍_𝑛𝑛) = _𝑛𝑛^𝑑𝑑𝒂𝒂_𝑗𝑗𝝍𝝍_𝑛𝑛 +_𝑛𝑛^𝑑𝑑𝒃𝒃_𝑗𝑗 =�_𝑛𝑛^𝑑𝑑𝑎𝑎_𝑗𝑗^𝑥𝑥 0 0 𝑛𝑛𝑑𝑑𝑎𝑎_𝑗𝑗^𝑦𝑦� �𝜓𝜓𝑛𝑛𝑥𝑥

𝜓𝜓_𝑛𝑛^𝑦𝑦�+�_𝑛𝑛^𝑑𝑑𝑏𝑏_𝑗𝑗^𝑥𝑥 𝑏𝑏_𝑗𝑗^𝑦𝑦

𝑛𝑛𝑑𝑑 � (2.4) Coefficients _𝑛𝑛^𝑑𝑑𝒂𝒂_𝑗𝑗 and _𝑛𝑛^𝑑𝑑𝒃𝒃_𝑗𝑗 were composed of real-valued constants and calculated by linear regression analysis for each size 𝑑𝑑 (𝑑𝑑 = S, M, L) using 𝝍𝝍𝑛𝑛 and 𝜽𝜽𝑗𝑗 of motions used in the optimization.

2.4 Physique of evaluation DHMs

DHMs used in the optimization had physiques corresponding to the S, M, and L suits.

The physique was defined by the height and chest measurements in the Japanese Industrial Standards (JIS) L4004. Five evaluation DHMs were generated for each size and were used as the evaluation DHM. The height and chest measurements of the evaluation DHM, k𝑖𝑖, for size k (k = S, M, L) are shown in Figure 2.4. However, circumferences, such as chest circumference, cannot be used to designate the physique of the Dhaiba model. Thus, the length of the bust breadth and bust depth were used to generate DHMs instead of chest circumference. These dimensions were calculated for the chest using the linear regression equation created by the body database collected by the Research Institute of Human Engineering for Quality Life in size-JPN project (2004-2006).

Fig. 2.3 Candidate points Fig. 2.4 Height and chest girth of each model

2.5 Primitive motions used in the optimization

The measurement target was the posture of the waist during motion without twisting the torso. Two primitive motions of bending the trunk forward and laterally at the waist were used. The motions were obtained by measuring 1 actual human’s motions with an optical motion capture system (VICON; 10 MX-13 cameras and five T-160 cameras). Input motions for evaluating DHMs were expressed by time-series full-body joint angles, which were acquired by fitting motion capture data to the DHM, which realized the subjects’ individual physique (ENDO et al., 2012).

2.6 Evaluation index for sensor position

It was assumed that sensors placed in the optimal position would measure the joint angle that was the least affected by the individual differences and the least affected by the deviation of the sensor position. Thus, these two requirements were considered in choosing the sensor position.

Individual differences

The effect of individual differences was assessed by angle conversion error using same converting formula, 𝑛𝑛𝑑𝑑ℎ𝑗𝑗(𝝍𝝍_𝑛𝑛), for all models 𝑑𝑑1, 𝑑𝑑2, …, 𝑑𝑑5 generated for the same size 𝑑𝑑 (𝑑𝑑 = S, M, L). The error value was expressed by the root-mean-square error (RMSE) of all elements for each size. The number of frames of motion used in the optimization was 𝐹𝐹, and ^{𝑑𝑑𝑖𝑖}𝝍𝝍_𝑛𝑛(𝑓𝑓) defined the angle of the sensor at P_𝑛𝑛 of evaluation DHM 𝑑𝑑_𝑖𝑖 at frame 𝑓𝑓 (0≤ 𝑓𝑓 ≤ 𝐹𝐹). The joint angle, ^𝑑𝑑_𝑛𝑛^𝑖𝑖𝜽𝜽�_𝑗𝑗(𝑓𝑓), expressed the angle conversion, ^{𝑑𝑑𝑖𝑖}𝝍𝝍𝑛𝑛(𝑓𝑓), by formula 𝑛𝑛𝑑𝑑ℎ𝑗𝑗. RMSE value ^𝑑𝑑𝐸𝐸𝑗𝑗(𝑛𝑛), which was the conversion error of 𝑑𝑑𝑛𝑛_𝑖𝑖𝜽𝜽�𝑗𝑗(𝑓𝑓) of 𝑀𝑀 models for size 𝑑𝑑, was calculated by equation (2.5).

𝐸𝐸_𝑗𝑗(𝑛𝑛)

𝑑𝑑 = ∑ �^{𝑥𝑥,𝑦𝑦}_{𝑟𝑟 𝐹𝐹𝐹𝐹}¹ ∑^𝐹𝐹_𝑖𝑖=1∑^𝐹𝐹_𝑓𝑓=0� 𝜃𝜃�^𝑑𝑑_𝑛𝑛^𝑖𝑖 _𝑗𝑗^𝑟𝑟(𝑓𝑓)− 𝜃𝜃_𝑗𝑗^𝑟𝑟(𝑓𝑓)�² (2.5)

Misregistration of the sensing position

Owing to individual differences, a sensor on the suit can be located at different places on the wearer. The deviation from the assumed sensing position was assumed to fall within the adjacent sensing positions. It was also assumed that the more the sensor slipped, the more the angle conversion error increased. Measuring motion with the sensor slipped δ mm from the assumed position along the backbone, the angle converting error was written as ^𝑑𝑑𝐸𝐸_𝑗𝑗(𝑛𝑛,𝛿𝛿) by using equation (2.5). If the deviation affected motion measurement, the value of ^𝑑𝑑𝐸𝐸_𝑗𝑗(𝑛𝑛,𝛿𝛿) would change greatly owing to 𝛿𝛿. Hence, the variation of ^𝑑𝑑𝐸𝐸_𝑗𝑗(𝑛𝑛,𝛿𝛿) was used to assess the effect of the deviation. Considering a sensor at P_𝑛𝑛, RMSE value ^𝑑𝑑𝐸𝐸_𝑗𝑗(𝑛𝑛,𝛿𝛿) was calculated for measuring motion with a sensor that had slipped to an upper adjacent position P𝑛𝑛−1 �𝛿𝛿= 𝑧𝑧𝐿𝐿_𝑛𝑛−1− 𝑧𝑧𝐿𝐿_𝑛𝑛�, to a lower adjacent position P𝑛𝑛+1 �𝛿𝛿= 𝑧𝑧𝐿𝐿_𝑛𝑛+1− 𝑧𝑧𝐿𝐿_𝑛𝑛�, and without slipping (𝛿𝛿= 0). Next, a curve passing through the three points, �𝛿𝛿,^𝑑𝑑𝐸𝐸𝑗𝑗(𝑛𝑛,𝛿𝛿)�, was approximated by the least squares method to determine 𝑛𝑛𝑑𝑑𝑒𝑒_𝑗𝑗^𝑟𝑟(𝛿𝛿), which was a quadratic curve of 𝛿𝛿. Evaluation index ^𝑑𝑑𝐷𝐷_𝑗𝑗(𝑛𝑛) was defined as

𝐷𝐷_𝑗𝑗(𝑛𝑛)

𝑑𝑑 = ∑ ∫ �^{𝑥𝑥,𝑦𝑦}_{𝑟𝑟 𝛿𝛿}^𝛿𝛿_𝑑𝑑^{𝑢𝑢 𝜕𝜕 𝑒𝑒𝑛𝑛𝑑𝑑}_{𝜕𝜕𝛿𝛿}^{𝑗𝑗𝑟𝑟(𝛿𝛿)}�𝑑𝑑𝛿𝛿 (2.6) where 𝛿𝛿_𝑢𝑢 = 𝑧𝑧_{𝐿𝐿𝑛𝑛−1}− 𝑧𝑧_{𝐿𝐿𝑛𝑛} and 𝛿𝛿_𝑑𝑑 =𝑧𝑧_{𝐿𝐿𝑛𝑛+1}− 𝑧𝑧_{𝐿𝐿𝑛𝑛}. Accordingly, evaluation function ^𝑑𝑑𝑋𝑋_𝑗𝑗(𝑛𝑛) for sensor position was composed of ^𝑑𝑑𝐸𝐸𝑗𝑗(𝑛𝑛) and ^𝑑𝑑𝐷𝐷𝑗𝑗(𝑛𝑛) as

𝑋𝑋𝑗𝑗(𝑛𝑛)

𝑑𝑑 =α 𝐸𝐸^𝑑𝑑 𝑗𝑗(𝑛𝑛,𝛿𝛿 = 0)+𝛽𝛽 𝐷𝐷^𝑑𝑑 𝑗𝑗(𝑛𝑛) . (2.7) Point P_𝑛𝑛, which minimized ^𝑑𝑑𝑋𝑋_𝑗𝑗(𝑛𝑛), was chosen as the optimal sensor position.