A unilateral robotic knee exoskeleton to assess the role of natural gait assistance in hemiparetic patients

Robotic exoskeleton design

The REFLEX prototype is a knee–ankle–foot orthosis (KAFO) composed of two joints aligned to the knee and ankle of the user (Fig. 1). The segments lengths and the braces positions can be tailored to the anthropometry of different users. The material of the major part of the prototype is aluminum 7075, so the result is a robust and lightweight device.

Fig. 1figure 1

REFLEX prototype for the assistance of the knee joint of the paretic leg. This joint is actuated by a DC motor coupled to a Harmonic Drive while the ankle remains unactuated. The sensors of the prototype are a potentiometer to measure the exoskeleton flexion in the sagittal plane, strain gauges to measure the interaction torque, inertial sensors (IMUs) to acquire the lower-limbs kinematics, and insole pressure sensors to detect floor contact events

The knee joint is actuated by a DC EC-60 flat 408,057 brushless motor (Maxon ag, Switzerland) coupled with a CSD-20-160-2AGR harmonic drive (Harmonic Drive LLC, EE.UU.). The transmission ratio of 1:60 of this system enables the application of a mean torque of 35 Nm, which is required to perform the limb movement [41]. The ankle joint of the prototype remains nonactuated and unconstrained, enabling its free movement in the sagittal plane. The total weight of the KAFO is approximately 4 kg. The prototype is equipped with four sets of sensors that provide information on system variables that are used for the control in real-time:

(1)

A potentiometer, coupled with the joint axis, is used to measure the flexion/extension angle of the active joint. This information enables the robot to follow trajectories using a closed-loop position control algorithm.

(2)

An interaction torque sensor is placed between the robot and the user. It consists of two pairs of strain gauges in a full Wheatstone bridge. This interaction torque is used to implement an impedance controller that adjusts the torque provided by the robotic system to the user’s leg. This controller is fully described in the subsection "Variable impedance low-level controller".

(3)

Three insole pressure sensors based on FSRs (Force Sensing Resistors) are used to assess the contact of each user’s foot with the floor. These measurements distinguish between swing and stance phases and adapt the controllers accordingly.

(4)

Four Inertial Measurement Units (IMUs) (TechMCS, Technaid, Spain) are used to compute the kinematics of both legs. They are attached to the shanks and thighs of both legs ensuring a proper alignment between the anatomical and sensors axes, and are used to measure the flexion/extension angles of the hips and knees [42].

 

The control system is based on the LaunchXL-F38377S board (Texas Instrument, USA), which runs the control algorithm and acquires sensor data at 1 kHz (except for IMUs, whose sample frequency is 50 Hz). The system can be used in a tethered version or a as portable setup where the exoskeleton’s control electronics and a Li-Po battery are embedded in a backpack that the user carries. The total weight of the power and electronic system is approximately 3 kg.

Gait assistive control strategies for the REFLEX prototype

The main aim of the REFLEX prototype is to deliver assistance to the paretic leg of hemiparetic subjects according to the movement of the nonparetic leg. As an example, Panel A of Fig. 2 shows the gait pattern of both lower limbs for a healthy subject and a hemiparetic patient. Although there are few differences in the functional gait pattern of both limbs in the healthy subject (as reported by Sadeghi et al. [43]), these differences are more significant in the hemiparetic patient. In Panel A of Fig. 2, we also represent the continuous gait phase, which is a function that increases monotonically from 0 to 100% between consecutive heel strikes. As reported in previous works, the phase of the movement of both limbs is shifted approximately 180º in healthy subjects [44, 45].

Fig. 2figure 2

Control paradigm. A Examples of healthy and hemiparetic gait patterns. B An overview of the control algorithm. The assistance provided by the robotic exoskeleton is synchronized with the movement of the unassisted leg. The unassisted hip angle feeds an adaptive frequency oscillator to estimate the unassisted leg’s gait phase in realtime. This phase is shifted 180° to obtain the gait phase for the assisted leg. The gait phase of both legs and the unassisted knee movement are used to generate the pattern to be followed by the exoskeleton through the low-level controller to assist the movement of the assisted limb

Our control approach uses the information of the nonparetic leg measured by the corresponding IMUs to assist the paretic leg synchronically (Fig. 2, Panel B). This approach is implemented in three phases. First, the synchronization is based on the real-time gait phase estimated by an adaptive frequency oscillator (AO) [46], a mathematical tool that is synchronized with the nonparetic hip angle by learning its features as variable states. Second, we estimate the desired gait phase of the assisted leg by shifting 180° the real-time gait phase calculated by the AO and the assistive gait pattern based on the kinematics of the nonparetic leg. Third, the low-level controller generates a force-tunnel around this desired kinematics pattern to assist the limb.

Real-time gait phase estimation

We use an AO to estimate the real-time gait phase and thus synchronize the REFLEX prototype with the user’s healthy side movement [47, 48]. Compared with other published control paradigms that synchronize the robot’s action, such as Finite-State-Machines (FSM) [49,50,51,52] or EMG-based controllers [53,54,55,56], AOs present several advantages. Compared with FSM controllers, AOs generate continuous signals instead of discrete trigger events, enabling more versatile strategies and the use of these signals in low-level controllers. In addition, compared with EMG controllers, the required sensory system is simpler and more robust.

AOs are dynamic systems that can be synchronized to periodic signals by learning their features as state variables [46]. Considering the hip flexion angle of the unassisted leg, which is measured by the thigh IMU, \(\theta_\), as input, an AO can estimate the phase of the unassisted leg \(\varphi_ \left( t \right)\) according to the next dynamic system [47]:

$$\varepsilon \left( t \right) = \theta_ \left( t \right) - \hat_ \left( t \right)$$

(1)

$$\dot = - \nu_ \varepsilon \left( t \right)\sin \varphi_$$

(2)

$$\dot_ = \omega - \nu_ \varepsilon \left( t \right)\sin \varphi_$$

(3)

$$\dot_ = \eta \cos \left( } \right)\varepsilon \left( t \right)\quad \left( } \right)$$

(4)

$$\dot_ = \eta \sin \left( } \right)\varepsilon \left( t \right)\quad \left( } \right)$$

(5)

$$\hat_ = \sum\limits_^ }} \cos \left( } \right) + } \beta_ \sin \left( } \right)$$

(6)

where \(\varphi_\) and \(\omega\) are the phase and frequency of the oscillator synchronized with the unassisted leg; \(\alpha_\) and \(\beta_\) are the Fourier coefficients used for estimating \(\hat_\); and \(\varepsilon \left( t \right)\) is the error in this estimation. \(\nu_\) and \(\nu_\) are learning constants and \(\eta\) is a coupling factor that determine the dynamic response of the error \(\varepsilon \left( t \right)\). At every time step, a new input \(\theta_\) is considered, and it is used to update all the variables involved in the AO.

The gait phase \(\varphi_\) should be a variable that increases monotonically and is reset when the gait cycle is completed. However, the convergence of the AO may not fulfill the criteria of \(\varphi_ = 0\) at heel strike. A phase offset correction is introduced to ensure that \(\hat_ = 0\) at heel strike and give kinematic meaning to the gait phase estimation. According to [57], a phase correction was implemented, so an offset in the phase estimation \(\rho\) is updated every time the insole pressure sensors detect the heel-strike event. This offset is low-pass filtered with a first-order Butterworth filter with a cutoff frequency of 0.5 Hz to avoid abrupt changes in the phase estimation due to phase correction.

$$\rho = \varphi_ }}$$

(7)

$$\hat_ = \varphi_ - \rho$$

(8)

Once the AO estimates the corrected phase of the unassisted leg, we calculate the phase of the assisted leg \(\varphi_\) by shifting it \(\pi\) rad according to the following equation.

$$\varphi_ = \hat_ + \pi$$

(9)

For convenience to gait analysis, the following changes of variables are performed:

$$\phi_ \left( t \right) = \frac_ \left( t \right)}} \cdot 100$$

(10)

$$\phi_ \left( t \right) = \frac \left( t \right)}} \cdot 100$$

(11)

$$f\left( t \right) = \frac}$$

(12)

By doing so, the gait phases \(\phi_ \left( t \right)\) and \(\phi_ \left( t \right)\) are maintained within the range of 0–100%, and they indicate the real-time percentage within the step. Likewise, the gait frequency \(f\left( t \right)\) is the real-time frequency in steps per second.

Assistive pattern generators

Based on the estimation of the gait phase of both legs, the prototype generates an assistive pattern to render a given trajectory to the paretic leg that should contribute to improving gait symmetry. This reference trajectory also depends on the motion of the unassisted leg’s motion acquired in real-time by the corresponding IMUs.

We developed two different assistive strategies, namely, the Echo-control strategy, which aims to replicate the average movement of the unassisted leg, and the Adaptive healthy pattern strategy, which aims to synchronize the application of a healthy reference from the literature.

A. Echo-control assistive strategy

Figure 3 illustrates the concept of the Echo strategy, which aims at replicating the movement of the unassisted leg of the user [58]. In the first stage, we consider the movement of the unassisted leg, so the knee flexion/extension angle is mapped over the gait phase estimated by the AO. By using linear interpolators, the system reconstructs the step kinematics regularly separated by 2% of the step cycle. This information is stored in a buffer that retains the kinematics of the last five steps; thus, the average unassisted pattern is calculated as the mean of this buffer’s content.

Fig. 3figure 3

Pattern generation according to the Echo-control assistive strategy based on replicating the kinematics of the unassisted leg. The knee movement during a step is stored in a five-step buffer and used to calculate the mean pattern of the unassisted knee; afterward, this averaged movement is provided as the targeted reference for the robotic exoskeleton according to the gait phase estimated for the assisted limb

The average kinematic pattern is smoothed by using a fifth-order zero-lag Butterworth filter designed for a sampling frequency of 50 Hz (the sampling frequency of the signal if the step has a duration of 1 s) and a cutoff frequency of 10 Hz (the fifth part of the sampling frequency). Once the signal is smoothed, it is derived to yield the velocity and acceleration patterns for the flexion movement, according to the following equations:

$$\dot_ = \frac }} = \frac }} }}\cdot\frac }}$$

(13)

$$\ddot_ = \frac \theta_ }} }} = \frac \theta_ }}^ }} \cdot \left( }}} \right)^$$

(14)

The instantaneous values for \(\theta_\), \(\dot_\) and \(\ddot_\) are calculated by linearly interpolating the current desired gait phase for the assisted leg between the points that define the three kinematic patterns (angle, velocity, and acceleration).

B. Adaptive healthy pattern assistive strategy

The healthy pattern strategy uses the information of the unassisted leg to adapt a reference trajectory to the user’s movement; see Fig. 4. This pattern is generated based on the joint reference trajectory for robotic gait support published by Koopman et al. [59].

Fig. 4figure 4

Assistive pattern generation based on synchronizing a healthy gait pattern. The knee pattern is scaled and shifted according to the features extracted from the movement of the unassisted leg; afterward, it is provided as the set point for the robotic exoskeleton according to the gait phase estimated for the assisted limb

This strategy analyzes the kinematic pattern of the unassisted leg to extract the range of motion and the phase of maximum knee flexion during each step. These features are stored in a five-step buffer, so the average features of the last five steps are used to scale and shift the reference pattern. First-order low-pass Butterworth filters with a cutoff frequency of 0.5 Hz smooth these factors prior to their application to avoid abrupt changes.

Similar to the previous strategy, velocity and acceleration references are also generated. In this case, the first and second derivatives of the angular healthy pattern with respect to the gait phase are computed offline, and, afterward, they are scaled and shifted by the same factors as the angle reference. Applying Eqs. (13) and (14), these derivatives with respect to the gait phase are changed to the time domain to be used as velocity and acceleration references for the assisted leg. Once these reference patterns are fully defined, cubic splines are used to interpolate the values for \(\theta_\), \(\dot_\) and \(\ddot_\) according to the desired gait phase for the assisted movement.

Variable impedance low-level controller

The assistance provided by the exoskeleton is based on a variable impedance model that aims to control the interaction between the robot and wearer [60]. As in previous related works [39, 61, 62], the controller used in the prototype has a twofold objective depending on the current gait phase:

(1)

During the stance phase, the robot aims to reinforce the limb so that the system composed of the leg and the exoskeleton can load the user’s weight and not collapse. A high impedance model is responsible for this reinforcement since it avoids substantial deviations from the assistive kinematic pattern.

(2)

During the swing phase, the robot guides the limb’s movement according to the assisted-as-needed (AAN) paradigm. The computed error between the reference kinematics and the actual movement serves as the input for the impedance model that defines the torque applied by the device to assist the user gait. No torque is applied if the error is null, while higher errors correspond to greater assistive torques. The impedance model depends on the assistance level selected by the therapist or the user, so the force tunnel around the desired trajectory can be changed according to the user’s needs. This assistance can vary from 0 to 100%, where an assistance of 0% commands the robot to not interfere with the user’s movement while an assistance of 100% does not allow the user to deviate from the prescribed trajectory.

According to the force-tunnel paradigm, the impedance model calculates the interaction torque that the exoskeleton should provide due to the angular reference tracking error. The system uses a PID controller to follow this torque interaction reference and provide it to the user (Fig. 5).

Fig. 5figure 5

Low-level controller of REFLEX. A The block diagram of the variable impedance controller; this controller assists the knee movement following the kinematic reference and according to an Assisted-As-Needed paradigm. B The two assistance strategies followed during a single step: the exoskeleton reinforces the joint during the stance phase while it guides the movement during the swing phase; following the Assisted-As-Needed paradigm, the exoskeleton is able to provide different assistance levels by using different force tunnels as depicted in the image

Experimental validation

The validation of the REFLEX prototype was implemented in 3 phases. First, we implemented the technical validation of the controller’s performance, assessing the phase estimation provided by the AO and the pattern generated by the two assistive strategies. Then, in the second phase, we tested the device with healthy subjects to ensure its proper operation during human interaction. Finally, in the third phase, the prototype was evaluated with stroke patients.

In total, six volunteer subjects participated in the experiments. We recruited three healthy subjects (3 males, age: 24. 7 ± 3.8 years, height: 1.78 ± 0.02 m, weight: 77.7 ± 2.5 kg; mean ± standard deviation) and three chronic stroke patients (demographic data are summarized in Table 1). The patients had no cognitive impairment according to the Mini-Mental State Examination (MMSE). All of them required a trekking stick to shift medium and long distances and presented a modified independency according to the Functional Independence Measurement Scale (FIM).

Table 1 Stroke subjects’ demographic data

All subjects gave their informed consent for the experiment; the study was conducted in accordance with the Declaration of Helsinki, and it was approved by the local ethics committee. All subjects were also instructed to walk on a treadmill at a constant speed during trials of 5 min each, and they carried out four different kinds of trials: (1) NoExo: subjects only wore the inertial sensors and the insole pressure sensors to acquire their basal motion; (2) Free: subjects wore the exoskeleton although the actuator was mechanically decoupled, so it enabled the free movement of the knee; (3) Echo: the device provided gait assistance following the Echo-control strategy; and (4) Pattern: the device provided gait assistance following the Pattern strategy. During trials, subjects used the tethered version of REFLEX, so they only wore the robotic KAFO (carrying a total weight of 4 kg). Additionally, stroke patients wore a safety harness that did not support any weight. Prior to the execution of the trials, the gait velocity was self-selected to a comfortable level by the subjects.

Healthy subjects also performed a previous trial to assess the controller’s performance under variable gait speed (VariableSpeed). They walked over the treadmill as in the NoExo condition, although the gait speed randomly varied from 1 to 3 km/h in 0.2 km/h steps for at least 15 s.

Subjects rested between trials for at least 5 min to avoid adaptation and learning effects from trial to trial. In addition, in the NoExo, Free, Echo, and Pattern trials, only the last 2 min of the trials were processed to evaluate the gait once the steady state was reached. For the processing of the data, we considered the beginning of each step when the insole pressure sensors detected heel strikes. All experimental data were recorded at 50 Hz.

Data analysis

To compare joint motion between the two conditions, we used the phase portraits of these movements. This representation shows the angular position in the X-axis and the angular velocity in the Y-axis, so the resulting portrait’s shape is representative of the dynamics of the motion [63]. We defined the next metric to evaluate the similarity between two phase portraits:

$$Similarity\left( \% \right) = \frac} \cdot 100$$

(15)

where \(A\) and \(B\) are the areas of two phase portraits, so \(A \cap B\) is the common area between them and \(A \cup B\) is the union of both areas.

We also evaluated the symmetry of gait metrics by using the Symmetry Index (SI) introduced by Arazpour et al. [64]:

$$SI\left( \% \right) = \frac_ - \overline_ }}\left( _ + \overline_ } \right)}} \times 100$$

(16)

where \(\overline_\) and \(\overline_\) are the mean values for a metric in the assisted and unassisted leg, respectively. A SI of zero value indicates a complete symmetry, so a higher absolute value means a higher asymmetry in the metric. The sign of the SI is related to the leg that showed the highest value for the metric; if the assisted leg presents the highest average metric, the SI is positive, while SI is negative if the unassisted leg shows the highest value.

When data distributions were compared, they were composed of the metrics calculated in each step during an experimental condition. After checking the nonnormality of the data (Kolmogorov–Smirnov test; P < 0.005) and the heteroscedasticity (Levene test; P < 0.005), we looked for significant differences between experimental conditions (Kruskall–Wallis test; P < 0.005).

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