Wearable robotic systems have the potential to improve the quality of life for many by preventing injury, restoring function, and extending human physical capacities. Injury to the lower back is particularly common and costly (Goetzel et al., 2003). Exoskeletons are being developed (Naruse et al., 2005; Abdoli-E et al., 2006; Luo and Yu, 2013; Ulrey and Fathallah, 2013; Bosch et al., 2016) to reduce the risk of low-back injury by providing support in awkward work postures and during lifts. Designing an exoskeleton that seamlessly assists its wearer is challenging because the motions and forces of the human need to be anticipated during the design phase.

Using powerful optimization methods, human motion can be predicted in silico given a sufficiently accurate model of the body’s dynamics and a representative cost function. This approach has been exploited to accurately predict the movements and forces of walking (Anderson and Pandy, 2001; Ackermann and van den Bogert, 2010; Dorn et al., 2015), sprinting (Schultz and Mombaur, 2010), vaulting in gymnastics (Hiley et al., 2015), the backhand in tennis (Kentel et al., 2011), and platform diving (Koschorreck and Mombaur, 2011). Arriving at a sufficiently accurate model for the task is challenging. If the model is not accurate enough, the forces and motions of the solution will be of little value. In contrast, if the model is very detailed, 1000’s of CPU-hours (Anderson and Pandy, 2001; Dorn et al., 2015) may be required to arrive at a solution.

Although the methods to model large dynamic systems (Featherstone, 1983, 2008; Jain, 1991) and predict their movements (Bock and Pitt, 1984; von Stryk, 1993) are relatively well established, there are few applications of these methods to aid in the design of wearable robotic systems (see, e.g., Koch and Mombaur, 2015; Schemschat et al., 2016; Manns et al., 2017). In preliminary work, we showed that assisted lifting motions for human–exoskeleton models can be simulated with an optimal control framework (Manns et al., 2017). In the current work, we study a stoop motion while lifting a 15 kg box with handles off of the floor and expand on the initial proof-of-concept (Manns et al., 2017). First, we simulate the exoskeleton as an external rigid-body model connected to the human at contact points. This improvement allows us to more accurately model the exoskeleton and to compute human–exoskeleton contact forces. Second, we extend the formulation of our optimal control problem (OCP) to a three-phase bend–grip–lift motion. This enables a more realistic simulation of the experimental conditions. Third, we compare our simulation results to experimental data and evaluate how well our predictions compare to the motions and forces of real lifting.

Solving optimal control problems can be computationally intensive. It is important to balance computational efficiency and accuracy so that the resulting problem is tractable but still produces meaningful results. Though we simulate the entire body, we are particularly interested in assessing the risk of low-back injury.

The most commonly assumed mechanism for low-back injury is tissue damage at the vertebral joints caused by high muscular forces (McGill, 1997). For our human model, we have developed muscle torque generators (MTGs) that represent the moments that are generated by a group muscles (flexors and extensors) that act together about a joint. Since van Dieën and Kingma (2005) have shown that the forces acting between the vertebral joints are highly correlated with net lumbar moments, we can use the MTGs to assess the risk of low-back injury: a lower net lumbar-extension moment means that the forces acting on the lumbar joints are smaller, and thus, the risk of injury is reduced. By simulating groups of muscles, rather than hundreds of line-type muscles, the MTGs are easier to fit specific subjects and result in faster simulations and numerical results that are easier to interpret.

We choose to study a stoop motion because this is a technique that is commonly used when lifting objects from the ground (van Dieën et al., 1999). Though it may seem surprising, a stoop does not place greater demands on the lumbar back than a squat except when the load can be straddled (van Dieën et al., 1999). In addition, since the risk of low-back injury increases with the weight of the payload, we have included a 15 kg box in our problem (Coenen et al., 2013). The following sections outline the development of the dynamic model, the formulation of the optimal control problem, the experimental measurements, and finally the procedure to assess the results of this work.

The kinematics and dynamics of the model fit the recorded stoop motion well, with the largest kinematic errors occurring at the shoulder. The error of the inverse kinematics solution between the virtual markers on the model and measured markers is 14 ± 6.6 mm with a maximum error of 67.8 mm at the shoulders. The residual forces and moments of the inverse-dynamics analysis are 5.4 ± 3.4 N and 3.6 ± 2.5 Nm, with peaks of 19.3 N and 11.6 Nm, when the box is being picked up. The subject used in the experiments performs a stoop lift with substantially less lumbar flexion (14° vs. 39° ± 14°, Figure 4A) than was observed by Kingma et al. (2004). The net L5/S1 extension moments generated by the experimental subject are very close to those of Kingma et al.’s subjects (200 vs. 199 ± 12 Nm, Figure 4B) even though the box used in this experiment is 4.5 kg heavier. The maximum kinematic differences between the left and right legs are between 2.1° and 4.4°, while the differences between the left and right arms range between 2.8° and 15.9°.

The human-only OCP has similar peak lumbar-flexion angles (49° vs. 39° ± 14°) and extension moments (192 vs. 199 ± 12 Nm) as the data from Kingma et al. (2004) (Figure 4). Correspondingly, the lumbar-flexion angle of the human-only OCP differs from the experimental subject (49° vs. 14°), though the angles match well at the hip. The largest differences between the human-only OCP and the experimental subject show up at the knee: the model flexes its knee more (60° vs. 49°, Figure 5B) and has different peak knee torques (55 vs. −56 Nm, Figure 5E).

With the ability to provide up to 67 Nm of torque (one-third of the peak lumbar extension from the ID analysis), the exoskeleton’s motors are able to reduce the lumbar flexion of the model so that the with-exo OCP solution matches the mean peak lumbar-flexion angle of Kingma et al. (2004) (43° vs. 39° ± 14°) better than the human-only OCP solution. The assistance provided by the exoskeleton reduces the peak lumbar-extension moment by 28 Nm from 192 to 164 Nm (Figure 4B). The peak flexion angles at the hip, knee, and ankle of the with-exo OCP deviate from the human-only OCP by between 4° and 7° (Figures 5A–C). The peak hip, knee, and ankle torques differ between the human-only OCP and with-exo OCP solutions by up to 47 Nm with the most pronounced differences at the hip (Figure 5D) and ankle (Figure 5F). Additional kinematic differences between the two OCP solutions and the experimental subject can be seen clearly by examining trajectories of the hands during the lift and the posture of the body when the box is picked up (Figure 6). When approaching the box (phase 1), the human-only OCP and the with-exo OCP swing the arms (slightly reducing the cost), while the experimental subject’s hands follow a more direct path. During the pickup phase (phase 3), the two OCP solutions are similar to the experimental subject.

The with-exo OCP solution shows that the hip actuator has to be driven with more complex signals than the lumbar actuator during the box pick up. Although both motors output the maximum torque at some point (Figure 8C), the hip motor has to undergo larger rotations (96° vs. 40°, Figure 7A) and has to sustain high velocities (145°/s, Figure 7B) for a large part of the movement. The interaction forces between the human and the exoskeleton show that the pelvis interface has to comfortably transmit large normal forces (338 N), shear forces (112 N), and torsional moments (51 Nm) to the human wearer (Figure 8A). Although the normal forces at the thigh (Figure 8B) and trunk (Figure 8C) interfaces are substantial (−184 and −216 N), the shear forces (31 and −41 N) and reaction moments (0.28 and −4.0 Nm) are small in comparison to the pelvis interface.

This work is motivated by the need to reduce the risk of back injury. Injury to the back is common and costly (Goetzel et al., 2003), and wearable robotic systems can decrease the risk by reducing the extension torques of the lumbar spine. The design of such systems is challenging with several aspects influencing this process: the exoskeleton can change the way the wearer moves, perhaps rendering the design ineffective; the interaction between the human and the exoskeleton may be too uncomfortable for long-term use; and/or the anticipated amount of support might differ from what the human wearer actually needs. To address some of these difficulties, the present study uses optimal control to predict the motions and forces of a dynamic model of a human lifting a 15 kg box from the floor with the aid of an exoskeleton.

We have presented an OCP of human lifting both without and with the aid of an exoskeleton. The solutions of the OCPs are physiologically realistic and dynamically consistent. The results of these simulations provide information that is useful to predict how exoskeleton might be used by the human, the requirements placed on the actuators, and finally the interaction forces between the human and the exoskeleton. The peak lumbar-flexion angles and L5/S1 extension moments predicted by the solution to the human-only OCP compare well with the 10.5 kg box stoop lift reported by Kingma et al. (2004). It is interesting to note that the L5/S1 extension moments match closely given that the box used in this work is 15 kg rather than 10.5 kg. This match likely arises because the subject used in this work is 13 cm shorter than the average subject in Kingma et al.’s study. While the predicted kinematics and loads of the lumbar spine compare favorably to the data of Kingma et al. (2004), it is clear that the cost function we have used does not do a good job of predicting the trajectory of the hands as the model moves to pick up the box (Figure 6). The solution likely converged to a motion with a large arm swing because this movement slightly reduces the muscle activity of the hip and lumbar extensors as the model approaches the box. Fortunately, the differences in arm trajectory appear to have little influence on the quantities that most affect the design of the exoskeleton: the kinematics and loads of the back and lower body.

The results indicate that indeed an exoskeleton can reduce the L5/S1 moment (Figure 4B) though this reduction might be lower than expected. Even though both the hip and lumbar motors could output a maximum torque of 67 Nm, the L5/S1 moment was only reduced by 28 Nm. Since the duration of the OCP lifts is shorter than the experimental subject, it is likely that the solver reduced the cost of the motion by lifting the box faster. Though it unclear if this will happen in real life, it is plausible: the support provided by the exoskeleton can be used to reduce the L5/S1 moment or to increase the maximum L5/S1 moment that the wearer can generate. With slight modifications to our problem formulation, we can simulate a lift in which the exoskeleton supports the wearer and also a lift in which the wearer uses exoskeleton to enhance their strength. Understanding this behavioral component in greater detail is important to the success of exoskeleton in reducing the risk of injury.

The torque waveforms computed for the hip and lumbar motors on the exoskeleton indicate that the demands on the hip and lumbar motors are quite different (Figure 7C). While the torque that the lumbar motor must provide is similar to the net torque at the L5/S1 joint of the wearer (Figure 4B), the torque that the hip motor must provide is different from the hip torque developed by the human (Figure 5D). The torque of the hip motor drops below 0 just as the box is touched because the hip MTG is deeply flexed. This deep hip flexion stretches the passive element in the MTG enough to generate the 125 Nm required to hold the position. This places an additional demand on the exoskeleton design. Not only should it be adjustable to physically fit the subject, but also it should be adjustable to fit the flexibility of the subject.

The interaction forces between the exoskeleton and the human subject indicate that extra attention must be given to the design of the interface between the exoskeleton and the pelvis. It must comfortably transmit large normal forces, shear forces, and moments to the human wearer. In our present approach, these forces are computed but do not influence the motion. For future extensions of this work, we are evaluating how the reduction of these forces could be made as a part of the OCP. As well, it would be of interest to replace our current kinematic constraints at the contact points with force-based constraints, allowing a relative movement of the exoskeleton.

We have necessarily made simplifications in modeling the human body and its interaction with the exoskeleton and the box. At the kinematic level, we have simplified the movement of the lumbar spine by approximating it as two coupled revolute joints. In addition, the shoulder joint is approximated as a revolute joint and does not include a scapulothoracic joint. Both of these approximations likely contributed to the kinematic error between the real and virtual shoulder markers. At the dynamic level, we have ignored activation dynamics of the muscles. The lack of activation dynamics has likely contributed to the relative roughness of the joint torques that appear in our results.

The solutions of the OCPs provide information that is useful during the mechanical design of the exoskeleton: the torque and power requirements of the actuators; the forces and moments that the parts of the exoskeleton must withstand; and the forces acting between the exoskeleton and the wearer. The detailed model and accurate OCP solutions that we have presented cannot be computed in real time and thus cannot be used to control the exoskeleton. However, the results of the OCPs are nonetheless useful for identifying two control strategies that the exoskeleton might employ.

One control strategy is to use the exoskeleton to compensate for the extension moment created by the weight of the upper body. To employ this strategy, the exoskeleton needs to know the mass and CoM location of the upper body and its inclination angle with respect to the vertical. The mass and CoM location of the upper body can be calculated using a few measurements of the subject’s body (Zatsiorsky, 2002) and then manually entered into the control system of the exoskeleton as part of a one-time customization of the device to the subject. The inclination angle of the wearer’s upper body with respect to the vertical can be measured using an inertial measurement unit (IMU) placed on the torso module. This strategy could reduce the L5/S1 extension moment of the subject in this study by up to 112 Nm—a 56% reduction of the L5/S1 moment required to perform the 15 kg box lift. For many applications, an exoskeleton that compensates for the weight of the torso will provide a meaningful reduction in the L5/S1 moment and thus lower the risk of low-back injury.

A second control strategy is to compensate for the weight of the upper body and the load being lifted. This strategy is more difficult to realize because the exoskeleton needs to have measurements of the kinematics of the lower body and the external forces acting on the lower body. This approach can be realized if the human subject is wearing (in addition to the exoskeleton) force-sensing insoles, goniometers at the knees, and goniometers at the ankles. Alternatively, the kinematics of the upper body could be measured along with the forces acting between the hands and the load being moved. Measuring or calculating the forces acting between the hands and the load would require the use of specialized gloves, or instrumented objects—options that are impractical for many applications. In principle, this approach could reduce the L5/S1 extension moment of the subject in this study by 199.4 Nm—100% of the L5/S1 moment required to perform the task.

While humans can adapt to working in novel environments quickly (Franklin et al., 2008), adaptation does not happen instantaneously. Thus, it is likely that an additional layer of control, beyond the two strategies discussed, will be needed so that the human has time to get used to lifting with the extra assistance. How best to adapt the online control of the exoskeleton to the human wearer remains an open area of research.

The recordings were conducted according to the guidelines of the Declaration of Helsinki 2013 and approved by the ethics committee of Faculteit der Gedrags- en Bewegingswetenschappen (Faculty of Behavioural and Movement Sciences) at Vrije Universiteit.

MM undertook most of the research and the manuscript preparation. MS assisted in the research and the manuscript preparation. KM conceived of the research idea, obtained funding for the project, assisted in the work, and in the preparation of the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.