From Knowledge to Leverage: How to Use Musculoskeletal Simulation to Design Exoskeleton Concepts

Abstract

Background: An exoskeleton and its wearer form a mutually dependent biomechanical system, where design choices for the exoskeleton can affect the wearer in complex and often unforeseeable ways, and this makes exoskeleton design challenging. Advanced simulation methods provide an insight into the consequences of design choices, but such analysis is usually employed towards the end of the design process. This paper demonstrates an option for musculoskeletal simulation to be used already in the conceptual design phase. Methods: We present the workflow by means of an example of box lifting. We show that the mathematical algorithm underlying the solution of the redundant equilibrium equations in musculoskeletal modeling has a structure that can be exploited to gain information about ideal actuator forces for an exoskeleton supporting the selected work task. Results: Based on the identified forces, passive or active actuators can be selected, and control strategies can be devised. Conclusions: We conclude that this methodology can save design cycles and improve exoskeleton development.

1. Introduction

Passive exoskeletons are wearable devices characterized by the absence of energy input from motors and usually also absence of control systems. They support the human body by structures through which forces can flow around and offload anatomical joints, allowing energy to be stored temporarily in elastic elements for subsequent release to level peak muscle loads. For a comprehensive classification of industrial exoskeleton types, please refer to [1].

Technical simplicity and potentially inexpensive production have enabled passive exoskeletons to penetrate the market for assistance of manual labor tasks. Typical applications are in the construction and production industries, where some work tasks involve repetitive motion of limbs and tools against gravity, for instance, in painting or drywall mounting and in warehouse or delivery work involving handling of boxes and other goods, as shown in Figure 1, which serves throughout this paper to exemplify the presented and generally applicable methodology.

Due to passive exoskeletons’ lack of net energy input, they can only have supportive functions and/or level peak power exertion. The combination of added mass and zero energy input means that they cannot decrease the total mechanical energy consumption of a work task. However, levelling the maximal effort by releasing elastic energy stored in springs can potentially decrease the metabolic energy consumption because even negative mechanical muscle work requires positive metabolic energy input. Ideally, elastic energy is stored in the springs during sequences of negative mechanical work. To avoid an increase in muscle effort in these sequences, the power transfer to the springs should not exceed the negative mechanical power.

These physics-based limitations of passive exoskeletons narrow the window of opportunity for their use and require additional care in the combination of exoskeleton design and intended application field. The exoskeleton and human body form a combined mechanical system, where the human body with its control system and safety requirements is by far the more complicated part. The design task must consider the entire system and the mutual influence between the anatomical body and the exoskeleton, and so must simulation methods employed in the process. In this paper, we illustrate how musculoskeletal simulation methods can be exploited in the conceptual design of an exoskeleton for a typical industrial work task illustrated by the example of Figure 1.

The process presented in the present study can be summarized in these steps:

• Perform a motion capture experiment to record the motions of the work task;
• Import the data into a musculoskeletal simulation system to perform a baseline analysis;
• Identify highly loaded tissues, i.e., particular muscles and joints;
• Add idealized reaction forces or moments to the model to offload the identified tissues;
• Repeat the analysis, record the idealized forces and moments, and plot them against joint angles and/or point connections over which a prospective exoskeleton could work;
• Perform a linear regression to identify the linear elastic element that best approximates the idealized forces and moments;
• Replace the idealized forces and moments with the identified linear springs in the model and evaluate their offloading effect;
• Proceed with detailed design of the exoskeleton when suitable springs have been identified.

Living human bodies working in concert with environments, such as exoskeletons, can be simulated by software systems for musculoskeletal modeling. We used an inverse dynamics simulation paradigm implemented in the AnyBody Modeling System (AnyBody Technology, Aalborg, Denmark) [2]. For exoskeleton modeling, this system has the advantage of a Cartesian multibody formulation [3], which can cope with the closed kinematic loops typically formed in the connectivity between the exoskeleton and the human. The technology can simulate ground reaction forces with good accuracy for a broad class of movements [4], and it has been repeatedly and independently validated for prediction of knee forces [5,6,7,8] and for lumbar spine forces [9,10,11,12,13].

In the broader context of computer-aided engineering (CAE), simulation is mainly useful in the later stages of the design process since a model cannot be created until there is a design to simulate. In this function, musculoskeletal simulation can, for instance, be used to adjust details or assistance settings [14], to derive torque controllers for active exoskeletons [15], to select among different design options [16], or to optimize exoskeleton design [17,18,19]. However, musculoskeletal simulation can also be applied early in the exoskeleton design process. Agarwal et al. [20] demonstrated an iterative approach in which virtual moments were applied to offload joints and used stepwise to infer the design of an exoskeleton for dumbbell lifting. This is remarkable because decisions in the early part of the design process tend to commit the larger part of the total product cost [21]. In this paper, we demonstrate that this process can be automated and applied to full body working tasks if a particular structure in its underlying mathematical formulation is exploited.

2. Methods

In the inverse dynamics paradigm, the dynamic equilibrium equations take the form of a mathematical program [22]:

Minimize

$${\sum }_{i=1}^{n_m}{\left({\displaystyle \frac{f_i^{\left(M\right)}}{N_i}}\right)}^p,$$

(1)

subject to

$$\mathbf{C}\left\{\begin{array}{c}{\mathbf{f}}^{\left(M\right)}\\ {\mathbf{f}}^{\left(R\right)}\end{array}\right\}=\mathbf{r}$$

(2)

$$f_i^{\left(M\right)}\ge 0, \mathrm{f}\mathrm{o}\mathrm{r} i=1...n_m$$

(3)

where vector f = {f^(M), f^(R)}^T contains the unknown forces in the system, separated into n_m muscle forces (M) and joint reactions (R). The right-hand side, r, contains externally applied forces and velocity-dependent forces that are known when the kinematic analysis is completed; p is the power of the convex combination that forms the objective function, and C is the coefficient matrix of the equilibrium equations. Normalization factors, i.e., N_i, express the strength of the ith muscle. Depending on the value of p, the mathematical programming problem can be solved efficiently by a variety of convex programming algorithms.

We notice that forces of the mathematical program (1)–(3) separate into three categories:

• The right-hand side forces, r: these forces can be specified as any time-varying function, including exoskeleton actuator forces, and they can be applied anywhere in the system without further complicating the problem;
• The reaction forces (and moments), f^(R): these are dependent variables determined by equilibrium, and they can take on any positive or negative value necessitated by the equilibrium;
• The muscle forces, f^(M): these are affiliated with perceived effort and restricted in sign as shown in (3) because muscles can only pull.

Forces from categories 1 and 2 do not appear in the objective function, so they are costless. However, they do influence the objective function indirectly because they influence the equilibrium for better or worse from the point-of-view of the muscles. Muscle forces (category 3), on the other hand, directly influence the cost of the objective function. In order of priority, the algorithm (i) honors the specified values of right-hand side forces in category 1 while (ii) minimizing muscle forces in category 3 at the expense of (iii) costless reaction forces from category 2. In other words, the algorithm returns the values of reaction forces that minimize the muscle effort. The optimization problem (1)–(3) can therefore be perceived as a minimum effort or laziness criterion [22,23]. Although the optimization problem is formulated in terms of muscles, the circumstances of most ergonomic situations are such that the moment arm of the external loads, for instance, the weight of the box in Figure 1, exceeds the moment arms of the muscles around the joints. This relationship attributes the majority of the joint reaction forces to muscle actions rather than direct load application from the external forces, so reduction in muscle effort will also in most cases reduce the joint reaction forces.

In the formulation of the biomechanical system, the user can place forces in the different categories, and this opportunity can be exploited to gain knowledge about favorable exoskeleton design decisions. Specifically, if exoskeleton actuator forces are placed in category 2, they will automatically attain the most favorable values in terms of reduction in muscle effort. These values can subsequently be studied and used to select an actual actuator and its control strategy. Once selected, its characteristics can be placed in category 1 for verification of the effect. This technique is illustrated in the subsequent sections by means of an example.

We herein consider a typical warehouse task of lifting a box, as illustrated in Figure 1. The box dimensions are 0.53 m wide by 0.40 m high by 0.36 m deep, and its mass is 10 kg. The box is held by hand slots cut out in its sides. Informed consent was obtained before the study, which did not require explicit ethical permission under the rules of the Ethical Review Board of the North Denmark Region.

The test subject was a healthy male, age 29, stature 1.89 m, and body weight 82 kg, and he lifted the box from the floor to a shelf at the height of 1.58 m after taking a step forward. The test subject was wearing an Xsens Awinda motion capture system (Xsens, Enschede, The Netherlands). The Awinda system is wireless and allows for the measurement to take place in situ at the workplace. The motion was recorded and saved as a BVH file for import into the AnyBody Modeling System, where the musculoskeletal analysis was subsequently performed, including simulation of the ground reaction forces [4]. The human body model was imported from the AnyScript Managed Model Repository [24]. The combination of software and models has been validated repeatedly for spine and lower extremity simulations [5,6,10,11,12,13,25,26,27,28].

As a baseline comparison, a model of body forces in normal gait was also created and analyzed based on the argument that walking for healthy humans is considered a safe and even beneficial motion that can be repeated thousands of times daily without negative side effects. The experimental protocol was previously described in detail [29].

3. Simulation-Based Design

As illustrated in Figure 1, the model has a significant level of detail, and it returns thousands of muscle forces and joint reactions, which could be compared systematically between the lifting model and the baseline gait model to identify anatomical structures that are prone to overloading. For the purpose of illustrating the workflow, we selected just two joint reaction forces, namely the compression force between the patella and the femur on each leg and the compression force between the fifth lumbar vertebra, L5, and the sacrum, S1 (Figure 2). These forces were selected because they peaked at, respectively, three and four times of the values for a normal gait cycle and could potentially cause injury if repeated many times over a work life. The L5–S1 joint reaction force has an additional peak towards the end of the motion, when the subject reaches forward to place the box and thereby increases the moment about the L5–S1 joint of the external load, as shown in the right frame of Figure 1. The patella–femoral force peaks at the extreme knee flexion in the beginning of the motion because the quadriceps tendon and the patella ligament simultaneously pull the patella into the trochlear groove.

3.1. Conceptual Knee Exoskeleton Design

Based on the selected joint reaction forces, the initial analysis indicated that an exoskeleton for this work task should offload knees and the spine, and since these are different body parts, an obvious initial approach was to design two exoskeleton components for the two knees and one for the spine.

We began with the knees and added to the model costless reaction moments, i.e., category 2, for knee extension. In the context of the dynamic equilibrium Equations (1)–(3), these become motors that perfectly offload the knee extensor musculatures. The motors’ moment contributions are shown in Figure 3 as functions of the knee angles. It is not surprising that such an idealized knee extension contribution almost eliminates the patella–femoral forces, as shown in Figure 4. The small remaining patella–femoral forces are due to activation of the biarticular rectus femoris muscle. Figure 3 shows the ideal motor compensations for the knee extension moments. They are complicated but can be approximated by a linear regression trend line. The trend line represents knee moments provided by a linear torsional spring with stiffness indicated by the slope, i.e., 1.38 Nm/degree. To avoid any action of the springs in the upright posture, we set the neutral position to zero degrees knee flexion. Replacement of the idealized motors in the model (category 2) with such springs (category 1) results in the patella–femoral forces depicted in Figure 5. As expected, this intervention has no influence on the spinal forces, but the patella–femoral forces in both legs are drastically reduced despite the crude approximation by simple, linear springs.

The initial placement of the exoskeleton’s knee extension moments among the dependent reaction forces of category 2 allowed us to arrive at optimal spring parameters in a single iteration. In the absence of musculoskeletal simulation, this progress would have required physical user tests and production of prototypes with multiple spring configurations.

3.2. Knee and Spine Exoskeleton

At this point of the design process, it would be obvious to repeat the methodology for the spine, i.e., equip the three-dimensional rotations between the pelvis and the thorax with idealized motors, examine the relationship between angles and required support moments, and design a passive, spring-loaded upper body exoskeleton based on these specifications. However, designing a three-degree-of-freedom exoskeleton for the spine is significantly more complicated than a single degree-of-freedom spring for the knee. Furthermore, we can see from Figure 2 that the patella–femoral forces and the spinal compression forces peak simultaneously in the beginning of the movement, where Figure 1 shows that the knees and the spine are simultaneously flexed. From this knowledge, we conceived the idea that a multiarticular exoskeleton spanning the knees and lumbar spine simultaneously may be a simpler solution for both body parts.

This can be obtained by bilateral rods spanning points on the shank and thorax, as depicted in Figure 6. The distal parts of the shanks have relatively little soft tissue and are well-suited for anchoring such rods, for instance, to special-made boots, while harness-like straps can affix the proximal ends of the rods on the thorax.

In the formalism of the multibody simulation system, these rods represent measurable degrees-of-freedom to which reaction forces, i.e., forces of category 2, can be assigned. This simultaneously offloads the spine and knees, as shown in Figure 7. We can see that the potential for knee offloading is significant, albeit smaller than with the designated knee exoskeleton. We can also see that the spinal compression is drastically reduced and now peaks in the last third of the movement.

Figure 8 shows the relationship between idealized rod forces and rod length. We see that the relationship is close to linear, except for a sharp increase towards the end of the movement. However, the latter applies to the upright standing posture for which Figure 2 reveals little need for support, and we can consequently disregard this part and create a common trend line only for the descending parts of the two curves in Figure 8. This trend line has a slope of −604 N/m, which is the ideal spring constant, and it crosses the first axis at rod length 1.57 m, which is therefore the ideal slack length of the spring. Replacing the idealized motor (category 2) in the rods with springs (category 1) of these characteristics yielded the joint reaction forces of Figure 9, which in comparison with Figure 2 shows reduction in all the reaction forces of interest.

4. Discussion

The example demonstrates how a systematic approach to musculoskeletal simulation can spark ideas for exoskeleton design and allow the designer to arrive at optimal design parameters in a single or a few iterations performed in silico. The general nature of the approach indicates that it has potential to be used for design scenarios beyond the chosen example.

The presented methodology tends to minimize muscle exertion rather than joint loads because the objective function (1) is formulated in terms of forces. However, because more of the joint load in the human body is typically generated by muscle actions than by external forces, design choices that minimize muscle effort also tend to reduce joint reaction forces, as we can see in the example. It should be noted, though, that the offloading of some body parts by an exoskeleton may lead to increased loads on other body parts, so a practical design process should consider body loads more comprehensibly than what was demonstrated here, and a method to systematically evaluate all simulated tissue loads relative to their normative loads should be devised before applying this method to practical exoskeleton design.

Other examples may reveal situations where no approximately linear relationship between a degree of freedom and the required force can be identified, in which case the design task would include creation of nonlinear forces and/or active actuator strategies. This obviously leads to more complicated designs, but the insight would enable the designer to quickly move on from the search for linear spring solutions to more advanced options.

In Figure 3, the linear regression is not a very close representation of the data, so it is surprising that the result of using the approximated spring presented in Figure 5 is almost as good as the result of using the idealized joint motors in Figure 4. To understand this, we should bear in mind that the idealized moments shown in Figure 3 are costless for the algorithm and therefore prone to large fluctuations with small benefits. It is possible that a hybrid formulation with a small activation cost on the idealized joint motors could produce a clearer guideline for the designer. Investigation of this idea is left to future work.

The assumption of a passive exoskeleton can be made when the results of Figure 3 and Figure 8 are subjected to linear regression. Without linear regression, the results could indicate baseline actuation strategies for active exoskeletons, but this would require advanced dynamic control systems, the regulation of which cannot be inferred from these simulation results.

The reliance on inverse dynamics simulation causes the inherent assumption that the movement is independent of the presence of the exoskeleton; i.e., after donning the exoskeleton, the user will complete the work task exactly as it was measured in the first place. This is likely false to some extent and is a limitation of the method that is hard to mitigate until a physical prototype has been created much later in the process. Only practical experience with the method in real design processes can reveal whether this limitation is problematic.

Whether the exemplified exoskeleton concept will work in practice can only be investigated by further design iterations and physical tests. In a practical design case, simulation should be performed in a variety of movements, including normal walking, to investigate the influence of the exoskeleton beyond the single movement for which it was designed. In particular, it may turn out that the exoskeleton prevents certain important postures like deep knee squat, in which case it must be modified.

The methodology presented should address the benefit of a prospective exoskeleton for non-repetitive tasks without any changes if diverse motions in a workplace were captured over an extended period. In this case, data presented in Figure 3 and Figure 8 would contain more points. The correlation coefficient of the linear regression would then reveal to which extent the prospective exoskeleton would be beneficial for the extended motion, and outliers would indicate postures in which the exoskeleton would be a disadvantage.

One of the inherent drawbacks of multiarticular exoskeleton concepts is their space requirement and the possible interference with movements and work tasks for which they were not directly designed. Furthermore, bulky exoskeletons may collide with obstacles in the environment and scratch or dent products and production facilities. The proposed solution has the advantage of passing close to the sides of the body with slack springs in the upright posture, but it may become a nuisance in crouched postures other than the initial stages of box lifting. In gait, the rods will be subjected to the acceleration forces of the moving legs, so subsequent design iterations should endeavor to limit the mass of the rods as much as possible and prevent them from wobbling during walking.

5. Conclusions

Musculoskeletal simulation of work tasks such as the manual handling of materials holds potential to speed up exoskeleton design cycles, identify optimally offloading solutions, and potentially reduce the cost of the product incurred by early design decisions. Practical application of the method is necessary to further clarify its potential.