Standard Practice for Multivariate Fit and Accommodation for Exoskeleton Manufacturers and Designers

Importancia y uso:

5.1 The U.S. exoskeleton marketplace currently lacks a consistent sizing structure and clear criteria for selecting sizes. This inconsistency likely stems from the absence of comprehensive national anthropometric data tailored to exoskeleton design applications. The significant variations in sizing structures among different exoskeleton manufacturers, coupled with considerable disparities in torso dimensions across users, create challenges in selecting and fitting exoskeletons appropriately. Additionally, the absence of a national standard or guideline for exoskeleton sizing and the adjustment range of components further complicates the issue. Exoskeleton sizing is a multifaceted matter, involving a combination of various body dimensions, and thus requires a multivariate approach.

5.1.1 In many equipment design applications, multiple parameters are used because various body measurements are relevant to the function of the products (1).4 The greater the number of dimensions involved, the more complex the product design process becomes. For upper-extremity exoskeleton development, key dimensions may include shoulder-elbow length, upper arm circumference, back breadth, chest girth, front lateral length, waist breadth, and other relevant measurements, all of which require a comprehensive assessment. The population to consider may be the general public or workers from a specific sector for which the exoskeletons are designed. The percentage of the population to be accommodated might be 95 % or 90 % of the target group. This practice focuses on demonstrating the process of selecting the essential dimensions and applying multivariate anthropometric procedures for exoskeleton fit and accommodation.

5.2 Not every element of this practice may be applicable to all exoskeletons, nor are the recommendations in this practice intended to be prescriptive (that is, manufacturers may already provide a variable level of adjustability inherent in the exoskeleton design, which may be described in their guidance). Additionally, this practice does not address musculoskeletal sex differences in human anatomy. The tools and methodology leveraged in this practice to perform a multivariate fit necessitates that the practitioner has a foundation in anthropometry and statistical analysis.

5.3 Comfort and Discomfort: 

5.3.1 Test Method F3585 – 24 provides a method to measure an exoskeleton’s cognitive fit, perceived safety, and acceptance. From a comfort and discomfort viewpoint, the criteria delineated within Test Method F3585 affords a subjective way to test that the exoskeleton and user are in accord from an individual perspective. Leveraging the ordinal data from the Likert Scale questionnaire in Test Method F3585 – 24 , in conjunction with this practice, will provide a more meaningful way to address comfort and discomfort beyond the individual with an eye on the population writ large.

5.4 Exoskeleton Multivariate Procedures—Two common techniques in multivariate analysis are principal components analysis (PCA) and cluster analysis (CA). PCA is a dimensionality reduction tool that takes large datasets and reduces them into smaller datasets while preserving variance. CA on the other hand, groups similar observations into clusters based on observed values from several variables of each individual. CA is not the same as classification analysis where the number of groups is known and the need is to reassign observations into a distinct group. The distinction about CA is that the number of groups and observations are unknown before starting the grouping process. Furthermore, the groups are determined by the similarity of each observation, clustering those with similar features together. PCA and CA are complementary to each other and both are widely used in medicine, artificial intelligence/machine learning, and engineering. PCA is often applied before CA to reduce noise and enhance effectiveness, while CA can then group observations within the reduced space for clearer separation. PCA and CA will be described in general terms in 5.5 and 5.6. For detailed instructions on how to conduct these analyses, refer to Refs. (2, 3).

5.4.1 Identifying Relevant Body Parameter Dimensions—Exoskeleton manufacturers and designers often select body parameters relevant to back and shoulder exoskeleton design, based on the adjustable components of the exoskeleton, such as “upper body length to adjust the length of the fasteners on back exoskeleton models” or “upper arm circumference for the attachment of shoulder exoskeletons” (4). Other parameters, such as shoulder breadth and hip breadth, may also be considered in the design process or product configuration. For example, a study by the Federal Institute of Occupational Safety and Health in Germany used seven parameters for shoulder exoskeletons (shoulder breadth, chest breadth, upper arm circumference, shoulder-elbow length, hip breadth, upper body length, and chest depth) and six parameters for back exoskeletons (shoulder breadth, high waist circumference, hip breadth, thigh length, thigh circumference, and shoulder height) (4). In more complex equipment or workspace design applications, such as farm tractor cab control compartments, multiple parameters (sometimes more than ten dimensions) are often considered (5). To minimize potential redundancy (such as multiple variables contributing to an aggregate variable), bivariate correlations between measurements can be analyzed to refine the list of parameters. For example, a high correlation (r = 0.9 or above) may suggest eliminating one of the two correlated parameters, particularly the one more prone to measurement errors (5). The principle is applicable to exoskeleton design applications where a significant number of body dimensions are relevant to the exoskeleton configuration or adjustment. Moreover, in protective equipment design, including exoskeletons, comfort and fit are crucial factors influencing usability and user acceptance. Correlating body measurements with fit and comfort ratings via surveys can help objectively identify the key parameters for effective multivariate analyses (6).

5.5 Principal Component Analysis (PCA) for Developing Anthropometric Body Models for Exoskeleton Accommodation Testing—The ultimate goal of principal component analysis (PCA) is to use a small number of principal components to explain the anthropometric variations within a product user population. The measurements relevant to exoskeleton accommodation can first be stratified into male and female categories, then standardized with respect to their weighted mean and standard deviation. PCA can then be applied separately to these standardized values using statistical software such as Statistical Analysis System (SAS),5 R, or Statistica.6 This process can reduce the overall dimensions to two or three principal components (PCs) that define body models.

5.5.1 The number of principal components to retain can be determined using a scree plot, where eigenvalues for the PCs are greater than one (Ref. (7)). These PCs would be orthogonal to each other and can be described as approximating a circle for two PCs or a spheroid for three PCs, with enclosed data points that account for a desired percentage (such as 95 % or 90 %) of the anthropometric variance of exoskeleton users.

5.5.2 For example, with three principal components, the transformed data in eigen-coordinates can be described as approximating a spheroid. Each of the three principal components is a method to score the most relevant variable based on measurements of the original dataset in a single plot. The Bonferroni method can be applied with a radius value (r) as the 95 % data enclosure criterion, achieving a 95 % confidence level for each group’s sex (8). There are 14 points on the spheroidal surface representing the most diverse body size and shape combinations based on the three principal components (Fig. 1)—six intercept points on the spheroidal surface along the three axes (points U, V, W, X, Y, and Z), and eight octant midpoints located at the surface center of each of the eight sections (octants) divided by the three axes of the spheroid (points A, B, C, D, E, F, G, and H) (Fig. 2).

Note 1: There were 14 points on the spheroid surface representing the diverse body size and shape combinations within each group’s sex: models X, Y, Z, W, U, and V locate at axis intercept points and models A, B, C, D, E, F, G, and H are models that locate at surface-center octant points. In addition, the center of the spheroid or “average” model center is at the point O with the eigen-coordinate {0, 0, 0}, defined by the mean for each dimension. Adopted from Ref. (9).

5.5.3 These 14 points, along with the centroid of the spheroid (point O), serve as the basis for selecting the theoretical anthropometric models. The 14 points represent the diverse body size and shape combinations within each group’s sex, while the centroid (point O) represents the mean for each dimension.

5.5.4 In addition, the center of the spheroid or “average” model center is at the point O with the eigen-coordinate {0, 0, 0}, defined by the mean for each dimension. The hypothetical models on the axes intercept points are at the eigen-coordinates: U{1, 0, 0}, V{0, 1, 0}, W{-1, 0, 0}, X{0, -1, 0}, Y{0, 0, 1}, and Z{0, 0, -1}. The hypothetical models on the octant’s center points are at the eigen-coordinates: A{1/2, 1/2, √1/2}, B{-1/2, 1/2, √1/2}, C{1/2, -1/2, √1/2}, D{-1/2, -1/2, √1/2}, E{1/2, 1/2, -√1/2}, F{-1/2, 1/2, -√1/2}, G{1/2, -1/2, -√1/2}, H{-1/2, -1/2, -√1/2}. Adopted from Ref. (9).

5.5.5 From a design perspective, the theoretically derived PCA case models mentioned above serve as valuable design targets. To facilitate practical exoskeleton design evaluation, either real subjects or virtual subjects (digital avatars) are necessary for exoskeleton accommodation tests. These individuals are the closest representation of “real persons” to the theoretical user models. Theoretically derived case models are idealizations of human anthropometry; thus, real subjects or virtual subjects will provide a much closer measure of human anthropometry or the “real person.” The closest “real person” models also provide additional dimensions that may not be included in the original PCA analysis. For example, chest girth is an important dimension to consider when evaluating the human-exoskeleton interface. Due to its correlation with other length measurements or its lower sensitivity in the PCA process, it may not be part of the original PCA dimensions. As a result, the PCA case models would lack chest girth data, and the closest “real person” models can fill this gap.

5.5.6 To identify the closest “real person” models that match the theoretical PCA models, the corresponding anthropometric values of these 15 models for each sex must be calculated through reverse processes using the eigenvalues and eigenvectors. The Euclidean distance from each participant to each model point is then assessed, and the closest-neighbor participant for each model is selected. Their corresponding closest-neighbor human participants and their dimensions can then be summarized. Depending on the sample size and variation of body dimensions, the Euclidean distance from each participant to each model point would likely range from a small to a medium number. For instance, a range was found in a body model study from 0.07 to 0.25 for models derived from roughly 750 participants, and from 0.07 to 0.42 for models derived from 200 participants (9). The closest-neighbor principal is stronger with smaller Euclidean distances.

5.5.7 The PCA-based “real person” models would serve as effective templates for exoskeleton accommodation testing. In other words, if an exoskeleton or a series of exoskeletons (with multiple sizes) can fit the 15 body models for a given sex, their designs (including adjustment ranges) are expected to accommodate 95 % or 90 % of the exoskeleton users. The range of each body measurement for the 15 “real person” models can also define the adjustment range for any body measurement corresponding to an adjustable component of an exoskeleton or series of exoskeletons.

5.5.8 If an exoskeleton is designed for both men and women, a combined set of male and female models is needed for the design to be effective. To minimize the number of models in the combined set, the models from each sex need to be tested within the 95 % enclosure space of the other sex. Models found to be within the opposite sex’s enclosure space are considered redundant and can be discarded. For example, to determine if a female model is redundant, the derived body dimensions of that female model can be first converted into z-scores using the means and standard deviations of the corresponding variables in the male sample. Then, the three PCs can be derived by multiplying the set of z-scores with the matrix of component score coefficients. The Euclidean distance of this female model to the centroid of the male 95 % enclosure can be calculated using the three PCs. If the distance is smaller than the set r value for the male enclosure criterion (for example, r = 2.6), the female model was considered redundant and discarded. Otherwise, the model was retained for the combined male and female space. Male models can be evaluated for redundancy in the same way by placing each model into the female 95 % enclosure with the set r value for females (for example, r = 2.61) and following the same accept/reject procedure. The recombination process typically results in a joint male and female enclosure space of fewer than 30 models (that is, a combination of 15 models for men and 15 models for women).

5.6 Cluster Analysis (CA) for Developing a Sizing System of Exoskeletons: 

5.6.1 Exoskeleton sizing is a complex process, and cluster analysis offers a practical solution to this sorting challenge. This approach allows for grouping exoskeleton users based on their torso dimensions and shapes, ensuring that individuals within each group are more similar to each other than to those in other groups. However, determining the optimal number of clusters is not straightforward and requires practical exoskeleton design criteria to guide the selection of cluster numbers and optimal sizing options.

5.6.2 One consideration is the trade-off between cluster overlap and size prediction precision. Fewer clusters reduce overlap between groups on primary torso dimensions, improving the accuracy of size prediction. This minimizes the likelihood of a person’s body dimensions falling between two adjacent exoskeleton sizes. However, assigning a size to each cluster in this scenario could result in substantial differences in torso dimension means between adjacent sizes, making exoskeleton fitting and adjustment challenging.

5.6.3 On the other hand, selecting a higher number of clusters would lead to significant overlap in multiple torso dimensions between clusters, resulting in mis-assignment of sizes, as an end user’s torso dimensions are likely to fit into more than one size. This would be cost-ineffective for manufacturing and inefficient for exoskeleton sizing selection.

5.6.4 In garment and protective equipment sizing, the gradations between sizes are typically incremental and evenly spaced, although manufacturers may introduce larger differences for the smallest or largest sizes. Since there is limited information in the literature regarding the criteria for exoskeleton size grading, two alternatives can be explored. One option is to set the range between two grades (sizes) of exoskeletons and the boundary (adjustment span) for each primary component of the exoskeleton as criteria for exploring optimal sizing options. The other option is to pre-select a set number of sizes based on sales data, manufacturing costs, and customer feedback. Implementation of the adjustment span based on two sizes can come in the form of sliding buckle straps, elastic straps, spring mechanisms, or actuators, or combinations thereof.

5.6.5 For option one, the tolerance criteria-based approach, one criterion would be to set ranges for chest circumference (89 mm (3.5 in.)), waist circumference (102 mm (4 in.)), and waist front length (25 mm (1 in.)) for the exoskeleton’s configuration. These values are derived from a market survey of body armor sizing, combined with common garment grading practices (9, 10). Additionally, the second criterion would involve establishing a target dimension span (for example, 10th percentile to 90th percentile) within each exoskeleton user cluster. For example, spans of 102 mm (4 in.) for chest circumference and 127 mm (5 in.) for waist circumference could be used, based on military body armor sizing plans. This would define the accommodation range for a cluster of exoskeleton users and further refine sizing options. By comparing the range between two sizes (grades) and the boundary (adjustment span) of exoskeleton components, an optimal number of clusters can be determined. It should be noted that multivariate cluster analysis involves all relevant dimensions necessary for the clustering process, though only a few primary body dimensions are typically used when finalizing the optimal number of sizes for practical purposes.

5.6.6 For option two, manufacturers can pre-select the number of sizes they are comfortable with, based on their sales data and production costs. All dimensions relevant to exoskeleton design would be used in the multivariate cluster analysis with the pre-selected number of clusters. Manufacturers and designers can then evaluate the adjustment span (boundary) of primary exoskeleton components for each size, as well as the range (mean values) between two sizes of exoskeletons, to ensure the sizing structure meets their needs. An iterative process of increasing or decreasing the number of clusters would help finalize the optimal number of sizes.

Subcomité:

F48.02

Volúmen:

15.13

Palabras clave:

anthropometry; clustering; ergonomics; exoskeleton; exosuit; fit; Likert scale; multivariate; nonparametric; parametric; principal components analysis; spearman;