Modeling and Stiffness-based Continuous Torque Control of Lightweight Quasi-Direct-Drive Knee Exoskeletons for Versatile Walking Assistance

A. Biomechanics of the Human Knee during Walking

The knee is essential for efficient locomotion, supporting body weight, absorbing shock, and providing foot clearance. Angle, moment, and power of the joint describe the action and function of the knee. The piecewise linear moment-angle relationship (also called quasi-stiffness) of the knee is a measure that characterizes knee stiffness and essentially models the knee joint as a torsional spring in distinct phases of stride [42]. Fukuchi et al. [43] collected biomechanics data from 23 subjects walking on a level treadmill at 1.24 ± 0.05 m/s and found an average peak torque of 31 Nm (0.46 Nm/kg) and the quasi-stiffness ranging from 0 to 176 Nm/rad.

Each stride can be split into 4 phases: 1) initial double First, looking at the torque assistive control from a state-space support, 2) single support, 3) second double support, and 4) swing phase, as illustrated in Fig. 2.

1. Initial double support: The body weight is transferred from the trailing limb (left) to the leading limb. The knee joint moment-angle relationship is very linear in this phase, and the quasi-stiffness is high.

2. Single support: The right leg supports the entire body weight in this phase. The moment-angle relationship is linear in this phase, with a similar quasi-stiffness to initial double support.

3. Second double support: The body weight is shifted from the right leg to the left leg in this phase. The knee moment-angle relationship is somewhat linear in this phase, although the quasi-stiffness is substantially lower than in the previous phases.

4. Swing phase: The knee flexes to assist with foot clearance, then extends in preparation for ground contact. Overall, the moment magnitude in the swing phase is lower than in the stance phase. Although the relationship is non-linear (especially around the transition from flexion to extension), most of the phase can be represented as linear with relatively small error due to the low moment magnitude.

The benefits of powered assistance to the knee joint are not well understood. One reason is that state-of-the-art powered knee exoskeletons are heavy, and the mass penalty affects natural movements [41]. There is no prior work to systematically investigate the effect of a powered portable knee exoskeleton in three conditions (powered, unpowered, and baseline without exoskeleton). Although the knee contributes less positive power than the ankle and hip joints in level walking [16, 44], the knee is vital for effectual walking. And it is beneficial for the knee to have external assistance. First, some of the muscles that actuate the knee joint are multi-articular, meaning the muscle crosses and actuates multiple joints simultaneously [45–47]. Augmenting the knee joint will affect the muscle biomechanics of the bi- and tri-articular muscles, which could improve muscle efficiency or network efficiency done at the joint. Second, studies have found that altering dynamics at one lower limb joint can modify the dynamics of the non-assisted joints, such that a knee exoskeleton may be able to improve walking or muscle efficiency not only at the knee joint but also at the ankle and hip joints [15, 48, 49]. Third, modern inverse dynamics techniques (using six degrees of freedom) found that traditional inverse dynamics (with three degrees of freedom) underestimated the positive work done at the knee. Thus, more positive work was done at the knee than reported in the biomechanical study [50]. The powered knee exoskeleton could potentially benefit the wearer by increasing the amount of positive work done at the knee. In addition to these energetic considerations, a knee exoskeleton that reduces load through the knee has the potential to prevent injury, reduce chronic pain, or improve the walking ability of people with musculoskeletal impairments [51–55].

B. Requirements for Design and Control

Portable exoskeletons should be lightweight to reduce the energetic penalty of wearing the exoskeleton and diminish impacts on the inertial properties of legs [56]. For our design, we set desired parameters such that it exceeds the performance defined by knee biomechanics at 1.25 m/s walking speed to ensure the versatility of the exoskeleton, e.g., providing assistance across different walking speeds and not impeding natural movements (e.g., squatting and stair climbing). The requirements are summarized in Table II. Exoskeleton joint stiffness is required to span the range of biological stiffness (0~176 Nm/rad). It is unnecessary to provide assistive torque equivalent to 100% biological torque because well-timed assistive torques (e.g., 30%) can impart substantial biomechanical benefits to able-bodied individuals [30, 57]. Prior art on knee exoskeletons has predominantly focused on assisting only during the stance phase [15, 18, 20], as most mechanical work of a knee occurs in this phase. Swing phase knee assistance is primarily used for rehabilitation or assistance to users with limited mobility [52, 53]. Lockheed Martin’s Onyx is one of the few knee exoskeletons for able-bodied augmentation that provides assistance in both the stance and swing phases for level ground walking [14]. Augmenting the knee during the swing phase would help compensate for the added mass on the leg, which needs to be carried through the swing phase. Furthermore, assisting the knee during the swing phase may also improve dynamics at the ankle or hip joint. Therefore, we chose to assist the entire stride.

For stiffness control of knee exoskeletons, state-of-the-art robots typically use discrete quasi-stiffness models [21], usually facilitated by finite state machines [39]. Aguirre-Ollinger et al. [21] recently developed a SEA actuation that operated between two discrete stiffness levels. However, discrete stiffness controllers tend to have large torque jerks between different stiffness modes, resulting in disruptive discontinuities in the assistance profile. One novelty of our work is a continuous stiffness controller based on the quasi-stiffness model of the knee joint, which provided a smoother and more natural assistance profile than switching among discrete stiffness values.

A. Quasi-Direct Drive (QDD) Actuation

To meet the design and control requirements, our actuator is designed to be lightweight, compliant, and with high bandwidth. Leveraging our high torque density motor [23, 24] and gear-embedded actuator design method [28], we customize a compact QDD actuator with fully integrated control electronics components (Fig. 3). The actuator is lightweight (485 g), compact (Φ100 mm × 37 mm height), and can generate 20 Nm peak torque. The actuator includes a custom high torque density brushless direct current (BLDC) motor with 3.3 Nm peak torque output capability, an embedded 6:1 ratio planetary gear, 14-bit magnetic encoder (AS5048A, AMS, USA), and a microcontroller (STM32F407, STMicroelectronics, France). Unlike SEA actuators that use a high gear ratio mechanism (e.g., harmonic driver) and spring mechanism, QDD actuators are based on low ratio gear without spring components. Thus, QDD actuators are generally simpler and more affordable in terms of mechatronics design.

We implement a low-level control loop in the motor microcontroller to realize position, velocity, and current control. Real-time communication with a high-level control device is executed through the Controller Area Network (CAN) bus protocol. Powered by a nominal voltage of 42 V, the actuator reaches a nominal speed of 250 RPM (26.17 rad/s). Moreover, thanks to the low gear ratio transmission of the QDD design, the actuator has low output inertia (32.2 kg·cm², see Table I for benchmark comparison with other exoskeletons), which is crucial to achieving low impedance that minimizes the resistance to human natural movements.

B. Mechatronic Design of Knee Exoskeleton

The design principle of this knee exoskeleton is to ensure a natural range of motion for multiple locomotion activities, e.g., walking, squatting, and stair ascent (lightweight and compliant features), and to minimize interference with external environments (compact feature). Thus the design avoids complicated mechanisms (e.g., our early work [58] that used a double rolling mechanism for knee exoskeleton). The main components of the exoskeleton include a waist belt, actuation system, thigh and shank support frames, and an adjustable elastic strap (Fig. 1). The knee joint actuation system includes a QDD actuator and a custom torque sensor (± 40 Nm full scale and ± 0.1 Nm resolution). The QDD actuator is connected to the thigh support frame, and the load cell is connected to the shank support frame. The design of the cuffs and straps ensure the assistive force on the wearer’s thigh and shank to be perpendicular to the surface of the respective segment, which reduces shear forces and discomfort.

We design the knee exoskeleton with the potential to assist multiple movements and for people with different body shapes. The wearable structures of the anterior lower thigh and shank do not interfere at maximum flexion (e.g., deep squatting). The range of motion of the knee exoskeleton is 0–160° (flexion), which is compatible with activities that require a wide range of motion, like stair ascent, sit-to-stand, and squatting. Additionally, different sizes of wearable structures are available. When combined with the adjustable linkage and single hinge structure, the design ensures the knee exoskeleton could fit a wide range of body sizes. The unilateral knee exoskeleton (without waist belt and battery) weighed 1.4 kg. The total weight of the bilateral knee exoskeleton (including all components) is 3.5 kg.

The electronic architecture of the knee exoskeleton facilitated high-level torque control, motor control, sensor signal conditioning, data communication, and power management, as shown in Fig. 3. The low-level controller embedded in the smart actuator measures the motor motion to realize motor current, velocity, and position control. The high-level microcontroller runs on Teensy 3.6 and implements continuous torque control (Section V). The microcontroller acquires knee joint angles from two wireless IMU sensors of each limb and conditioned torque signals from the custom loadcells in real-time. A Bluetooth microcontroller (nRF52840 Express, Adafruit, USA) connected to the main controller acts like a transceiver to communicate with a remote desktop computer for real-time data logging and monitoring.

A. Torque Control Modeling of Human-Exoskeleton Interaction

As discussed in Section II, a variable stiffness model can capture the dynamics of the human knee joint during walking. Here, we propose stiffness control to generate the torque for knee assistance with the QDD actuation paradigm. As shown in Fig. 5, the inner loop is the torque control, in which the input is the torque reference τ_r and the output is the actual torque applied to the human shank. In the model, the transmission damping coefficient b_c is small and sets to zero; k_p and k_i are the proportional and integral gain, respectively. In this work, we derive the stiffness model and investigate stiffness dynamics by analysis (section IV.B) and experiments (section VI. A).

B. Stiffness Model of Torque-Controlled Exoskeletons and Benchmark of Three Actuation Paradigms

To establish the stiffness model, the input torque reference is given by

where the torque reference τ_r is generated proportionally to the knee angle θ_h via the reference stiffness k_r. The transfer function for joint stiffness is modeled by

If we consider the motor inductance L approximate zero, then (2) is reduced to

To investigate the bandwidth of the stiffness control, the first and second corner frequencies (the corner frequency is defined as the boundary where frequency response begins to be attenuated or amplified) of the closed-loop stiffness control are found in Equation (4). Because the transmission stiffness k_c and torque constant k_t of the QDD system are larger and the gear ratio n is smaller than SEA system (see Table IX), the corner frequency of the stiffness control will be larger with the QDD system than in SEA and conventional high gear ratio actuation (CON).

To investigate the stiffness tracking performance in the frequency domain, the transfer function is given by

Considering that human motion is characterized by low frequency (ω → 0), the system stiffness is represented as

Additionally, when k_p is large enough, such that k_p → ∞, the system stiffness can be approximated by k_r, i.e.,

which indicates that the stiffness controller can accurately track the reference stiffness k_r for low-frequency human motion.

Conversely, when the motion frequency is high (ω → ∞), the transfer function approximates the transmission stiffness k_c, i.e.,

Therefore, the stiffness controller cannot track the reference stiffness k_r in high-frequency motion. Our QDD exoskeleton can provide sufficient bandwidth for dynamic stiffness tracking.

To illustrate the performance of stiffness control, the transfer function in Equation (2) is depicted in the Bode diagram in Fig. 6. We use the derived stiffness control model Equation (8) to benchmark the three actuation methods 1) a conventional (CON) high gear ratio knee exoskeleton [59]; 2) a SEA-based knee exoskeleton [60]; 3) our QDD knee exoskeleton. The SEA and CON have a higher ratio gear than the QDD actuation, and the SEA has a low stiffness constant due to the mechanical spring. For simplicity of the benchmark comparison, we set a large transmission stiffness of 500 Nm/rad for the CON and QDD actuators and set a small transmission stiffness of 200 Nm/rad for the SEA. The parameters from these three representative knee exoskeletons are listed in Appendix Table IX.

The bandwidths of the stiffness control for the QDD, SEA, and CON actuation with 25 Nm/rad reference stiffness are approximately 12 Hz, 0.18 Hz, and 1.8 Hz, respectively. The bandwidth of the stiffness control with 100Nm/rad reference stiffness for the QDD, SEA, and CON are approximately 80 Hz, 0.6 Hz, and 7.5 Hz, respectively. These results show that the QDD has the highest stiffness bandwidth in both 25 Nm/rad and 100 Nm/rad. At high frequencies, the actuator stiffness is dominated by the transmission spring stiffness k_c. Therefore, the actual stiffness of the SEA, CON, and QDD at high frequency (see the stiffness in Fig. 6 as the frequency approaches 10⁴ Hz) is approximated as k_c.

A. Architecture of High-Level and Low-Level Controller

The main objective of the control law is to estimate the biological knee moment continuously during walking and assist the subject with a torque profile proportional to the estimated biological moment. Traditional finite state machine control methods, such as [42, 56, 61], are composed of two steps: 1) the gait cycle or phase-detection algorithm, and 2) assistive torque generation in terms of the gait phase of the gait cycle. Therefore, for different gait phases [40], the generated torque profiles are discontinuous, and the accuracy of assistive torque is dependent on the accuracy of gait phase detection. To overcome the problem of inaccurate gait phase estimation and discontinuous stiffness-based torque assistance (e.g., piecewise quasi-stiffness torque profiles), we develop a continuous stiffness model to estimate the knee joint moment. Our real-time control method combines gait phase detection and knee joint moment estimation into a unique estimation model, which identifies both the instantaneous gait phase and the required stiffness through an optimization process.

In Section II, we note that the knee joint quasi-stiffness transitioned between a high stiffness in the stance phase and low stiffness in the swing phase. The proposed control scheme is shown in Fig. 7. The variable stiffness control generated by the continuous phase stiffness model is employed as the high-level controller, which is given by

where, τ_r is the reference torque of the variable stiffness control, ${\widehat{\tau }}_{k,r}$ is the normalized estimated knee moment (described in Section IV. B), k_w is the user’s body weight (in kg), and k_a is the assistive proportional gain. The inputs of the variable stiffness control are the right knee angle θ_k,r, and left knee angle θ_k,l. The output is the torque reference τ_r. The control law for knee assistance can be calculated from Equation (9). Assistive control is achieved with a k_a in the range [0,1]. We use IMUs on each shank and thigh (2 IMUs of each leg) to calculate the right and left knee angles (θ_k,r, and θ_k,l, respectively). The inner-loop controller implements torque control, and the feedback signal is the measured assistive torque τ_a (measured from the torque sensor of the knee exoskeleton).

B. Stiffness-based Continuous Torque Controller with Biological Torque Estimation

We propose a simple and analytical model that uses a smooth function (e.g., sigmoid function) to generate a continuous output between 0 and 1, which is given by

The parameters a could regulate the width of the transition area of the sigmoid function. The function S(θ_k,r,θ_k,l) is the likelihood to apply the swing phase stiffness model. The function [1 − S(θ_k,r,θ_k,l)] is the likelihood to apply the stance phase stiffness model. The continuous nature of the gait phase detection output ensures that the estimation of the knee moment is also a continuous signal. An additional benefit of continuous gait phase detection is that transitions between gait phases can be easily and automatically processed instead of rule-based methods like a finite state machine. The proposed estimation function is given by

where S(θ_k,r,θ_k,l) is the sigmoid function given by Equation (10), ${\widehat{\tau }}_{k,r}$ is the estimation of right knee moment, k_st is the joint stiffness of stance phase, k_sw is the joint stiffness of the swing phase, θ_k,r is the right limb knee angle, θ_k,l is the left limb knee angle, θ_k,r,0 is the equilibrium angle for stiffness model of stance phase, θ_k,st,0 is the equilibrium angle for stiffness model of stance phase, and θ_k,sw,0 is the equilibrium angle for the stiffness model of the swing phase. Here, we propose to use two stiffness modes (high stiffness and low stiffness) to estimate the knee moments τ_k,r, and τ_k,l. In addition, the proposed method is not limited to stiffness control. It can be extended to a higher-order model of generic impedance controller with mass, spring, and damper terms, which needs angular velocity and angular acceleration (the derivatives of the knee angle and angular velocity, respectively). When implemented, the differential operation for the angular acceleration and angular velocity generates a non-causal system and introduces noise. Therefore, we choose to use stiffness control (without angular velocity and angular acceleration) that requires only joint angle feedback to approximate the knee moments τ_k,r, and τ_k,l.

The estimated optimal hyperplane is given by

Equation (12) separates the gait cycle into two gait phases by minimizing the torque estimation error. The parameters b could regulate the center of the transition area of the sigmoid function, respectively. The only input variables required to estimate the gait phase are right and left limb knee angles (θ_k,r, and θ_k,l, respectively). Hence, this control law is more stable compared to gait estimation methods that use angular velocity and/or acceleration. The output of the estimation function Equation (11) is the estimated right knee moment ${\widehat{\tau }}_{k,r}$.

To find the optimal parameters (k_st, k_sw, θ_k,st,0, θ_k,sw,0, a, b) of the continuous phase stiffness model (Fig. 7), we solve an offline optimization problem over a collection of training data from 23 subjects walking overground [43]. Each subject was asked to perform overground walking trials at three speeds (a self-selected comfortable speed, a fast speed which is 30% faster than the self-selected speed, and slow speed which is 30% slower than the self-selected speed and the dataset for each speed include the averaged knee joint angles and moments from multiple trials. The dataset for each speed includes the averaged knee joint angles and moments from multiple trials. The time series of the data is converted to the percentage of the gait cycle and the joint moment is normalized to body mass (Nm/kg). We use the data at all three walking speeds to optimize the stiffness model parameters. Specifically, nonlinear regression is used to minimize the sum of the squared error between estimated and actual knee moment, employing the cost function in Equation (13). Here, ${\widehat{\tau }}_{k,r,i}$ and τ_{k,r i} are the estimated and actual knee moment at data point i, respectively, while the parameter m is the total number of data points in the training data. In this way, a nonlinear regression method is able to optimize parameters, including the width of the transition area (parameter a), the stiffness (k_st & k_sw ), and the equilibrium angles (θ_k,st,0 & θ_k,sw,0 ) of the two-phase stiffness models. The optimal hyperplane $f\left({\theta }_{k,r},{\theta }_{k,l}\right)=0$ separates the gait cycle into two gait phases (corresponding to $f\left({\theta }_{k,r},{\theta }_{k,l}\right)=0$) to minimize the error between estimated biological moment and actual biological moment.

C. Optimization of Biological Torque Estimation for Continuous Stiffness Torque Control

Optimal parameters of the continuous phase stiffness model are shown in TABLE III. The hyperplane (in the space of the angle difference between the right and left knee joint) is close to zero degrees.

In our exoskeleton control law, the assistive torque is proportional to the estimated knee moment. We evaluate the accuracy of the estimated torque with respect to the actual knee moment using the correlation between the actual knee joint moment and moment estimated by the continuous stiffness model at the three different walking speeds (TABLE IV). The average correlation is 90%. The highest correlation (about 94.5%) is found in the comfortable walking condition, while the slow walking speed data has the lowest correlation (80.9%). These results indicate that the proposed joint moment estimation method is more suitable for self-selected and fast walking speeds than slow walking speeds.

The trained continuous phase stiffness model and the corresponding training dataset are visualized in Fig. 8. Notably, the transition between stance and swing phase stiffness models is smooth, as intended by the continuous stiffness design.

D. Evaluation of the Continuous Phase Stiffness Model

We tested the generalization of our model by training with data from 22 subjects and then testing it on a new subject (not from the training set) to evaluate the knee moment estimation. The estimated knee moment for this subject walking at three speeds is shown in Fig. 9. The root mean square errors (and percentage) of the torque tracking at slow speed, self-selected speed, and fast speed is 0.0583 Nm/kg (13.68%), 0.0585 Nm/kg (8.27%), and 0.0874 Nm/kg (8.40%), respectively. The results demonstrate that the estimated knee moments were close to the actual knee moments, and the generated moment profiles were continuous and smooth. The black dashed line in the right column of Fig. 9 depicts the value of the sigmoid function S(θ_k,r, θ_k,l) ∈ [0,1] in Equation (11) across the entire gait cycle. It shows that the stiffness model is more inclined to the stance phase model (S(θ_k,r, θ_k,l) = 0) during the first double support and single support phase, while the swing phase stiffness model has a higher weight during the second double support and swing phase (S (θ_k,r, θ_k,l) = 1).

A. Benchtop Experiments

B. Human Subject Experiments

The objective of the human experiments is 1) to evaluate the movement synergy of our continuous torque controller with humans at different walking speeds 2) to evaluate the capability of the system to track the desired torque and show that our exoskeleton with the proposed controller does not cause a significant change of knee kinematics 3) to understand the effect on lower limb muscle activities.

A. Advantages of Stiffness Modeling and Stiffness-Based Continuous Torque Control

Leveraging the analytical stiffness model, theoretical and experimental benchmark results demonstrate that the QDD actuator outperforms SEA in terms of both torque control and stiffness control. We showed that our QDD actuator has large stiffness bandwidth that covers the frequency of normal human walking and running. It also achieved a small torque tracking error under a wide range of stiffnesses.

We also proposed a control framework to generate a stiffness-based continuous torque assistance profile while ensuring a smooth transition during speed changes. Previous studies [26, 33] involving stiffness models were not able to adapt to speed changes and would generate a discontinuous torque profile. Since they depend on gait phase estimations, the sudden jump will appear at these points.

B. Neuromuscular Response and Interpretations

We investigated the effect of a portable high-performance knee exoskeleton on able-bodied subjects during level-ground walking. Previous studies demonstrated that it is possible to reduce muscle activities with a portable knee exoskeleton or exosuit. However, such benefits have only been shown in more torque demanding conditions, e.g., incline/decline walking [20, 30], or in particular, pre-swing and swing gait phases for inflatable exosuits pressure control [26]. This work comprehensively evaluates the effect of a portable knee exoskeleton on able-bodied subjects for level-ground walking. The results suggest that a powered lightweight portable knee exoskeleton has the potential to reduce several lower-limb muscle activations for level-ground walking.

Compared with the unpowered condition, the RMS and maximum EMG of all 8 muscles decreased in the powered condition. This reduction is remarkable in terms of RMS EMG for all 3 knee extensors examined (VM, VL, RF) and 2 knee flexors (LG, BF), and for all 8 muscles in terms of maximum EMG (Fig. 18, Table VIII). This result illustrates that our controller can effectively assist level-ground walking when compared with the unpowered case. Further improvement may be possible by separately optimizing the assistance profile in the stance and swing phase.

Interestingly, although the torque assistance is applied to the knee joint, a reduction in peak ankle extensor (TA) muscle activation is also observed. This agrees with the finding reported in [15, 48, 49] that altering the dynamics of the assisted joint may affect the dynamics of other joints. Therefore, although the knee joint primarily dissipates energy during the gait cycle [63], benefits to the overall level-ground walking performance may still be possible thanks to a corresponding reduction in muscle activity at other joints.

The reduction in muscle activation between powered exoskeleton and baseline is lower than that between powered and unpowered, with two muscles (SEM and BF) showing significant differences in peak EMG across the entire gait cycle. The two main factors limiting the reduction in muscle activity between baseline and powered conditions were device weight and standardized assistance profiles. Although we optimized the design of our exoskeleton to be lightweight (3.5 kg bilateral weight) and compliant (0.22 Nm backdrive torque), the increase in muscle activity between baseline and unpowered demonstrates that mass and/or friction had an effect. The torque assistance essentially mitigates the impact of mass/friction, but the benefit does not yet substantially exceed the imposed mass penalty. Further improvement of hardware design might alleviate the impact of mass on muscle activity during walking. Second, the torque assistance profile is based on a pre-trained population-averaged dataset and is not tailored to each participant. Individualized torque assistance profiles could provide further reduction of muscle activity between powered and baseline conditions. We discuss this limitation in Section VII.C.

C. Limitations of the Study

Here, we note some limitations of our study. First, we chose an assistive torque that mimics biological torque. Although it is an intuitive control approach in wearable robotics, some literature reports that the optimal exoskeleton torque profile for human performance augmentation may not be proportional to the biological torque [56]. Determining the optimal exoskeleton torque profile is challenging as the human-exoskeleton interaction must be fully understood, including how assistive torque impacts the dynamics of human muscles. Nonetheless, a proportional biological torque profile was worth investigating since it is unlikely to have a negative impact on human performance and is viable and simple for assisting wearers.

A second limitation is the misalignment of the exoskeleton and the human knee joint. While this is a common issue for a rigid powered exoskeleton, the misalignment may induce undesired interaction force that affects the comfortable operation of the exoskeleton [64]. Our previous work [55] developed a novel mechanism that used a rolling knee joint and double-hinge structure to reduce 74% of the joint misalignment at maximum knee flexion. However, due to the complexity of the mechanical structure, our previous design increases the total weight of the exoskeleton. It thus induces an undesired mass penalty to the overall human performance. Another approach to solving this problem is to use a jointless actuator design that eliminates the need for joint alignment in the first place. An example is the soft inflatable pneumatic knee exosuit developed by Sridar et al. [26]. Although the exosuit does not have joint alignment issues thanks to its soft nature, its actuator is powered by an external pneumatic source. Thus the tethered pneumatic design limits its portability and bandwidth.

D. Conclusion And Future Work

In this work, a continuous-phase stiffness model and the corresponding stiffness-based continuous torque controller are proposed and evaluated on a portable knee exoskeleton with 8 able-bodied subjects during treadmill walking. This stiffness model can achieeve a large and sufficient stiffness bandwidth (16 Hz) to cover normal human walking frequency rang, and the controller achieves a small torque tracking error (0.23 Nm) under different stiffness. Our continuous torque controller requires no gait phase estimation but can adapt to varying speeds and generate a continuous torque profile. Reducing the muscle activity of able-bodied subjects for level-ground walking using a portable knee exoskeleton has traditionally been considered a difficult task [65]. However, by leveraging our lightweight portable knee exoskeleton and our proposed continuous stiffness based torque controller, our neuromuscular walking experiments demonstrate that both the RMS and maximum EMG of all 8 muscles decreased (remarkable for 3 extensors and 2 flexors) in the powered condition relative to the unpowered condition and 2 out of 8 lower extremity muscles have a significant reduction in muscle activation in the powered condition relative to the baseline (no-exoskeleton) condition. Compared with the result of the baseline condition in Table VIII, the results showed the powered exoskeleton could reduce the maximum EMG of knee extensors (VM, VL, RF), knee flexors (BF, SEM), and ankle muscle (TA) and reduce the RMS of knee extensor (RF), knee flexors (BF, SEM), and ankle muscle (TA). But the RMS and maximum EMG of the ankle plantar flexors (MG, LG) were increased by 3.55% and 2.18%, respectively. Therefore, it can be concluded that the knee exoskeleton can reduce the EMG signal of the knee flexor and extensor muscles. In contrast, the weight of the exoskeleton might cause a slight increase in the EMG signal of the ankle plantar flexors, and it cannot be mitigated by knee joint torque assistance.

A recent study [49] demonstrated that a portable knee exoskeleton could only improve mobility for stroke subjects with a moderate level of neurological impairments because the device was too heavy and stiff. Since our knee exoskeleton is more lightweight and compliant (3.5 Kg vs. 5.4 Kg Keeogo), we will study whether the robot and associated stiffness-based continuous torque controller can benefit broader populations with mild, moderate, and severe levels of neurological impairments.

It may be worthwhile in future work to use an assistive torque profile other than the proportional biological torque profile or optimize the torque profile using human-in-the-loop methods [56, 66]. In addition, the adaptability of the controller to different terrains such as incline/decline walking and stair climbing will be thoroughly studied and evaluated. We are investigating the quasi-stiffness profiles during level-ground walking, incline walking [14] and loaded walking [38]. In future work, we will investigate the hypothesis that the continuous stiffness model (two modes) from this work can be generalized to multiple stiffness modes to produce assistive torque for different terrain conditions.