TWIN is a 25-kg lower-limb exoskeleton used in this study. Shown in Figure 1, it has four active DOFs in the hips and knees, and is made for people with paraplegia (Vassallo et al., 2020). The device is controlled by a tablet connected via Bluetooth, and the tablet is operated by another person. TWIN has two walking modes: each step is either manually triggered by pressing a button in Manual Walk Mode, or each step is initiated by the wearer based on the exoskeleton trunk's forward incline in Automatic Walk Mode. TWIN can also sit and stand, such that the kinematics of the sitting trajectory is an opposite of the standing trajectory. To walk, sit, and stand with TWIN, one must use crutches for safety and stability. Particularly for sit and stand, the person must properly push up (for standing) or support (for sitting) from behind, otherwise they can fall backwards.

Two motion capture scenarios, which are part of a larger dataset, are collected in this study:

The first scenario aids in understanding the dynamics of the exoskeleton's default STS trajectory, which can only be activated at a specific seat height due to predefined initial joint angles. The second scenario does not demonstrate the intended use of the device; it simply shows that it is possible to stably do crutch-less STS with TWIN for feasibility reasons. A higher seat height is chosen for the second scenario because we assume it is easier to perform the motion at a higher seat height.

One 25-year-old female participant experienced in moving with TWIN was recruited for a pilot study. This is because the second scenario is just for showing the feasibility of crutch-less STS and not a lot of people can do it. Kinematics are recorded with a 12-camera Vicon Vantage motion capture system. A modified version of the Istituto Ortopedico Rizzoli (IOR) marker set is used (Leardini et al., 2007). To obtain more accurate translation and position values, the Vicon skeleton model (VSK) is modified on Procalc. Forces exerted at the crutches/feet are captured with Bertec force plates. The human data collected from this study has received ethics clearance from the ethics board of the University of Waterloo.

Besides performing motion capture experiments, STS is also investigated using numerical optimization techniques. The three simulation scenarios are described as follows and summarized in Figure 2.

In the motion synthesis scenario with TWIN, the resulting torques are assumed to be an ideal combination of torques exerted by the elderly woman and device. Therefore, the purpose of including the motion synthesis scenario without TWIN is for determining whether the elderly woman's torque contribution is feasible.

The first scenario involving the default exoskeleton trajectory lasts 11.36 s, which includes 2 s to bend the trunk to prepare for STS, 2 s to pause between trunk bend and standing up, and 4 s to stand up from sitting. The total mass of the human, exoskeleton, and crutches is 83.1 kg and the peak combined ground reaction force in the crutches is measured to be 330.3 N (see Figure 6). Using Equation 4 and estimating the CoM acceleration with the floating base origin acceleration, the force at feet is estimated to be 484.9N. The hip and knee angles describe the default motor trajectories, whereas the xiphisternal and ankle joints represent the user's behavior. The shoulder angle plots depict that the crutches are first placed behind the body to push off during lifting phase, and later placed forward for balance once standing. The position plots can be found in Figure 7.

Force plate results reveal that a peak maximum ground reaction force of 330 N is required in the crutches. The participant also made a remark on shoulder discomfort, yet the ready position is required for a proper push-off for the lifting phase. The kinematics results show an initial shoulder extension of 1.4 rad and the entire STS duration lasts 11.36 s.

The second scenario lasts 4.3 s. The total mass of the human and exoskeleton is 82 kg and the feet forces reach a peak value of 898.0 N. This indicates that the user must accelerate upwards to stand up from sitting. The kinematics data show that the person first swings their arms and bends their trunk forward before standing up. The shoulder range of motion (ROM) is less than the first scenario because the user does not have to bring the crutches from the back to the front of the body. The force plots can be found in Figure 6, and the joint position plots can be found in Figure 7. The position plots and the calculated underlying joint torques from the crutch-less scenario will be analyzed in more detail later.

Figure 7 illustrates the angular positions in the lower and upper body joints in all motion capture and OCP scenarios.

In OCP analysis, the optimizer is able to closely track upper body joints and there are minor tracking differences in the lower limb joints. A maximum offset of 0.27, 0.19, and 0.10 rad are observed in the hip, knee, and ankle joints respectively.

Comparing the hip joint angles from OCP synthesis results, the scenarios OCP analysis (0.57 rad) and motion capture passive TWIN without crutches (0.46 rad) exert the highest upper body forward bend. OCP synthesis with TWIN shares a similar forward bend angle of 0.45 rad, and OCP synthesis without TWIN exerts 0.39 rad of forward bend.

The final position for the hip, knee, and ankle joints are 0 rad for the OCP synthesis solutions, which means the model is standing straight. Meanwhile, the values in OCP analysis are 0.379, –0.602, and 0.363 rad respectively.

When standing up, the OCP synthesis results share a similar pattern of flexing the upper trunk forward, but the OCP analysis slightly arches the upper trunk back before flexing forward. The motion capture result with passive TWIN without crutches flexes up to 1rad, whereas the OCP analysis flexes up to 1.06 rad. The OCP synthesis with TWIN flexes up to 0.60 rad, though the OCP synthesis without TWIN has a larger flexion of 0.85 rad.

Both OCP synthesis solutions encourage the elderly woman model to swing her arms forward in the sitting phase, and swing the arms back while abducting the shoulders during lift-off. Towards the end of the lifting phase, OCP synthesis with TWIN recommends the elderly woman to abduct the shoulders when bringing the arms to the front, though OCP synthesis without TWIN does not show shoulder abduction or adduction at this stage.

The duration of each phase in the OCP analysis scenario must be aligned with the user-driven trajectory motion capture data because of the problem formulation. The OCP synthesis scenarios left time as a free variable ranging between 0.5 and 2 s per phase, and the formulation does not directly minimize time. The sitting and standing duration are expressed in Table 1.

In the passive TWIN crutch-less motion capture data, OCP analysis, and OCP synthesis with and without TWIN, the xiphisternal joint consistently reaches maximum flexion before the hips. At the moment of maximum hip flexion in the passive TWIN crutch-less motion capture data, there is a second peak in shoulder flexion and the knee is already extending (see purple dots in Figure 7). In the OCP synthesis results with and without TWIN, maximum shoulder flexion occurs at the same instance of maximum hip flexion and immediately before knee extension (see yellow and orange dots in Figure 7).

The CoM trajectory is computed for all OCP scenarios using biorbd. Since 2D dynamic models with 3D shoulder joints are used, the overall CoM trajectories for the medial-lateral direction are zero and hence omitted. In motion analysis, the CoM trajectory begins at a more posterior position and ends at a more anterior position than the synthesis cases. During lifting phase, a slight decrease in the Y-axis of the CoM trajectory is observed in both motion synthesis cases, which corresponds to the CoM paths curving out slightly anteriorly (see Figure 8).

Figure 9 shows the joint torques from OCP analysis, OCP synthesis with TWIN, and OCP synthesis without TWIN. Recall that left and right lower limbs are lumped due to STS' symmetrical nature, so the torque values for these joints are the sum of both sides. The torques calculated from the motion capture data are based on motions performed with a passive exoskeleton, meaning the motors are disengaged, and the bioMod files do not include any information about motor friction. Therefore, the torques reported in this paper are technically net torques. In the OCP analysis, the values are the torques exerted by the human participant, whereas the values in OCP synthesis with TWIN are the total ideal torque combination of human and exoskeleton.

The xiphisternal joint exerts the highest torque in the OCP synthesis scenario with TWIN (43.12 Nm) and the least in the OCP synthesis scenario without TWIN (38.77 Nm). The OCP analysis scenario exerts less hip joint torque than OCP synthesis with TWIN, but applies the most knee and ankle torques.

The highest peak frontal shoulder joint torque is observed in OCP analysis because the arms are consistently abducted to avoid collision with the exoskeleton structure (see angle in Figure 7). The torque trajectories from the two OCP synthesis solutions seem jerky in the upper limbs, but note that the maximum range of the torque values are within ± 9 Nm.

Combining left and right, 120.03 Nm in the hips and 137.26 Nm in the knees are required to perform STS in OCP synthesis with TWIN. In reality, the device's existing hip and knee motors can exert a total of 112 and 88 Nm respectively (Vassallo et al., 2020), meaning it can only provide partial STS assistance. According to the results from OCP synthesis without TWIN, the elderly woman would be able to exert a maximum absolute torque of 95.79 and 111.79 Nm in the hips and knees respectively. Assuming an ideal combination from the human and exoskeleton, the user would need to contribute a total of 8.03 Nm in the hips and 49.26 Nm in the knees. These values are summarized in Table 2.

In OCP analysis, the tracking offset observed in the hip, knee, and ankle joints could stem from different reasons. The offset could be influenced by the very small regularization term ϕ(·) in the objective function, which prevents the joint positions from tracking the reference data perfectly. Another reason could be the slight difference in model definition between the VSK and bioMod. The segments declared in the VSK heavily depend on the motion capture marker layout. Given the presence of TWIN, some markers in the original IOR marker set must be relocated to accommodate the device and avoid marker occlusion. Although one can redefine the variables on Procalc to reduce model discrepancy between the VSK and bioMod, there will always be some error, thus introducing an offset in the tracking results. A third reason could be related to the motion capture data. When recording the user-driven STS scenario involving a passive TWIN without crutches, it is possible that the person did not begin the motion at exactly zero velocity and zero torque. Figure 4 emphasizes that STS is to be modeled with zero velocity at the start, so the offset could be a result of this constraint contradicting the measurements.

Regarding the upper body forward bend in the lifting phase, OCP analysis' minor tracking error in the hip joint has led to a 0.11 rad increase compared to the motion capture data of passive TWIN without crutches. That said, it is reasonable to see a larger bend angle when an exoskeleton is worn, since more effort is required to move with the additional mass.

The hip, knee, and ankle final positions from OCP analysis in Figure 7 do not reflect that the person in the motion capture experiment is not fully standing up. This is caused by a fitting error between the younger adult and TWIN, such that the exoskeleton's lower limbs are longer than the human's. Although the exoskeleton is customized to the wearer's size, fine adjustments in the modules cannot be made to allow for a perfect fit. Therefore, even when the person's legs are vertical, the exoskeleton segments remain bent. With the motion capture markers placed on the exoskeleton segments, the fitting error is propagated into the position and torque profiles of these joints.

Since TWIN is passive and all the actuation originates from the human's joint in the crutch-less motion capture scenario, it is reasonable to observe the largest flexion in the xiphisternal joint since the person is generating as much forward angular momentum as possible to stand up without falling. On the contrary, OCP synthesis with TWIN has the least flexion in the xiphisternal joint, so further investigation is recommended.

The arm-swing results suggest that the sagittal and frontal arm movements could aid in generating angular momentum and maintaining stability to stand up without crutches. Note that the average shoulder frontal joint angles are larger in OCP analysis, since the person is preventing the arm from swinging into the exoskeleton's structure in real life, yet this is not reflected in the OCP synthesis simulations. It is recommended to further investigate the effects of these arm motions on a stable and successful crutch-less STS motion.

When standing up without crutches with or without the exoskeleton, the timing coordination of maximum xiphisternal flexion first then maximum hip and shoulder flexion may suggest that this sequence is important for generating angular momentum to stand up without falling backwards. Knee extension begins at maximum hip and shoulder flexion in both OCP synthesis cases, but the start of knee extension and maximum shoulder flexion have already occurred before maximum hip flexion is reached in OCP analysis. It could be that the subject in the motion capture experiment has to overcome motor friction when moving, yet the bioMod model with TWIN does not include such information, hence the earlier occurrence of knee extension and shoulder flexion. Although keeping the amount of motor friction consistent across scenarios could possibly confirm the proper coordination, this is not possible given the circumstances of this study. Nonetheless, a future recommendation is to investigate the multi-joint coordination presented in the OCP synthesis results with and without TWIN.

Without an exoskeleton, it is assumed that it would take less time to complete both phases due to less mass and inertia. OCP synthesis without TWIN lasts 0.33 s less than OCP synthesis with TWIN in the lifting phase, yet it takes 0.15 s longer than OCP synthesis with TWIN in the sitting phase. It is unknown why this occurs, so more investigation is needed to explore the influence of ankle torque bounds.

The cardiovascular system becomes more affected as a person ages, so any sudden change in blood flow can be more pronounced and cause dizziness in an older adult. To create a STS trajectory suitable for the geriatric population, suggestions include investigating more weight combinations between the objective function's torque and mechanical power terms, tuning the torque-derivative bounds to better reflect the joint capabilities of an older adult, and incorporating the change in blood flow of the geriatric cardiovascular system in the formulation.

The dynamic models used in the simulations are primarily 2D, so all OCP cases do not have any CoM deviation in the medial-lateral direction. It is observed that the CoM trajectory in motion analysis begins more posteriorly and ends more anteriorly than in motion synthesis cases. Recall that motion analysis tracks the joint angular positions from the motion capture data. One reason could be the weight of the TWIN exoskeleton trunk module causing the participant to lean more backward during the sitting phase, and she has to lean forward to prevent herself from falling backwards at the end of lifting phase. Meanwhile, the motion synthesis cases assume the lower-limb joint torques to be the total ideal torque combination of human and exoskeleton, hence the smaller anterior-posterior range. Another reason for different CoM behaviors could be the influence of the angle of shoulder extension and xiphisternal joint flexion, but a detailed analysis would be required to identify the amount of influence each joint movement has on the CoM based on the STS trajectories.

It is reasonable for OCP synthesis without TWIN to exert the least torque in the trunk and lower limbs, since the absence of an exoskeleton requires less effort from these joints to generate forward momentum to stand up from sitting. When comparing the OCP analysis and OCP synthesis with TWIN results, it seems that more hip torque leads to less knee and ankle torques required to stand up, but further verification is needed.

It is unsure how much torque frailer older adults could exert in the xiphisternal joint given the ROM of the optimal results and torque value. It is therefore recommended to further tune the physical parameters of this joint, so that the resulting motion can better represent this population.

The range of upper limb joint torques are within ± 9 Nm, but they seem jerkier than those in the xiphisternal and lower limb joints. Future recommendations for smoother plots include decreasing the torque-derivative bounds and tuning objective function term weights.

TWIN's current motors are unable to fully assist an elderly woman to do STS, since the hips and knees could only exert a total of 112 and 88 Nm respectively. For full assistance, the device would need stronger motors that can exert a minimum total torque of 121 Nm in the hips and 140 Nm in the knees. However, assuming the ideal scenario where the torques required to perform crutch-less STS are shared between the exoskeleton and human, partial assistance is possible because the remaining contribution needed from the user is feasible per the torques calculated in OCP synthesis without TWIN.

The joint torques reported in this paper are specific to the 25-kg TWIN, but these values can be applicable to other exoskeletons of similar mass distributions. The presented optimal control approaches, in fact, can be replicated on any exoskeleton to generate the required joint torques for performing STS, supposing the mass distributions of the exoskeleton of interest are available. After determining the target population, one would create an appropriate dynamic model that also incorporates the device's mass distributions, formulate the OCP as described in Section 2.2.3, then run the simulation.