Human motor coordination refers to the ability of the neurobiological motor system to generate complex movements involving multiple limbs or joints. Various types of coordinated movements can be executed by the lower limb, including sitting/standing, squatting/jumping. The most common coordinated movement is walking, which is a fundamental athletic skill for other activities.

In this paper, a variety of lower limb coordinated movement tasks using the knee joint are designed. The subjects walked on treadmills at different speeds and slopes. The speeds included 0.5 km/h, 1.5 km/h, and 3.0 km/h, and the slopes included 0°, 4°, and 8°. The slope 0° represent that the human walks on flat ground. The subjects initiated a gait cycle with the right heel touching the ground and end the gait cycle with the next right heel touching the ground. The gait trajectory is the knee joint position trajectory during walking in this paper (Tanghe et al., 2020; Challa et al., 2022; Song et al., 2023).

The coordinated movement data of the subjects are collected and recorded by the Delsys sEMG signal acquisition system. The position of the sEMG and angle sensors is displayed in Figure 3. The sEMG sensors are attached with special double-sided adhesive tape to the three muscles closely associated with the movement of knee joint, namely, rectus femoris, vastus lateralis, and biceps femoris. Two angle sensors are attached to the knee joints with ordinary double-sided tape.

Four healthy subjects were invited to participate in the data collection. This trial has been approved by Human Participants Ethics Committee from Wuhan University of Technology, and written informed consent was obtained from each participant. Participants walked while imitating patients with left lower limb injuries, with a reduction in force produced by the left lower limb muscles and an increase in force mainly produced by the right lower limb muscles. The data collected in the experiment were the sEMG of the three muscles and knee angle signal of the healthy lower limb, as well as knee angle signal of the affected lower limb.

Synergy mechanism is adopted in statistical regression to extract couplings between limbs in healthy synergetic motion. The synergetic gait prediction model can generate the individualized gait trajectory of the affected lower limb based on the sEMG signal and the knee joint angle of the healthy lower limb. Convolutional neural network (CNN) and long short-term memory (LSTM) neural network are widely applied in gait prediction. Standard CNN model is well suited for handling spatially autocorrelated data, which is unsuitable for dealing with complex and long-term dependencies. In contrast, LSTM model is more suitable in handling temporal autocorrelated data. Therefore, the hybrid CNN-LSTM model can effectively improve forecasting performance. Furthermore, the attention model can assign weights to important features, thus enhancing the prediction accuracy (Thakur and Biswas, 2022; Xu et al., 2022). Individualized gait prediction typically involves the collection and analysis of the data specific to an individual, such as motion capture data, the ground reaction forces, and sEMG data. Machine learning algorithms are adopted to analyze the data and develop personalized models that can accurately predict the individual’s gait characteristics.

The structure of attention-based CNN-LSTM model mainly includes four modules, namely, CNN module, spatial attention module, temporal attention module, LSTM module, as shown in Figure 4. The spatial attention module is as shown in Figure 5A, which refers to the Convolutional Block Attention Module (CBAM) (Woo et al., 2018). The input features are respectively subjected to maximum pooling and average pooling to obtain pooled features F a v g s ∈ R 1 × H and F m a x s ∈ R 1 × H . H represent the number of features. Then, the features pass through a 1D convolutional layer with a filter size of 7, and performs a sigmoid function operation to generate a spatial attention weight vector. The attention weight is multiplied element-by-element with the original feature to output the feature vector M _s ∈ R ^1×H , as shown in Eq. 1. M s F = σ f 7 A v g P o o l F ; M a x P o o l F = σ f 7 F a v g s ; F m a x s (1) where f ⁷ indicating that the filter size of the convolutional layer is 7, F a v g s , F m a x s represent pooled features after maximum pooling and average pooling operation, respectively. k = ψ C = log 2 C γ + b γ odd (2) where the size of the kernel k describes the size of the temporal neighborhood, and γ, b are constants.

The temporal attention module is as shown in Figure 5B, which refers to Squeeze-and-Excitation Network (SENet) (Wang et al., 2020). Firstly, global average pooling is performed on the input features F ∈ R ^C×H , and the dimensions of the input features are mapped from C × H to C × 1. C represents the number of time steps. Then, 1D convolution is performed on the features, and the sigmoid function operation is performed to generate a temporal attention weight vector. The attention weight is multiplied element-wise with the original feature to output the feature vector M _t ∈ R ^C×1. k is adaptive to the number of time steps C, determined by Eq. 2, where γ = 2, b = 1. Longer time steps mean longer distance interactions through mapping ψ(C).

The coordinated gait trajectory of the affected lower limb can be generated based on the information of patient’s healthy lower limb, and the data is collected and inputted into the pre-trained synergetic gait prediction model in actual rehabilitation training. However, it is also necessary to consider the safety problems caused by excessive human-robot interaction force on the affected lower limb. The impedance control can modify the expected trajectory of the exoskeleton through the deviation between expected and actual human-robot interaction force, which can realize that the exoskeleton can move under the guidance of the coordinated gait trajectory as much as possible, while maintaining compliance and reducing the risk of injury.

As shown in Figure 6, the optimal coordinated gait trajectory is defined as the individualized gait of the affected lower limb generated through synergetic gait prediction model in the specific task or scene. Coordination space is defined as the space that extends outwards with the optimal coordinated gait trajectory as the center, and the movements in the coordination space are all in accordance with normal gait pattern. The robot shows the strong compliance near the optimal coordinated trajectory, and the patient’s motion intention can correct the expected trajectory. When deviating from the optimal coordinated trajectory, the compliance of the robot gradually decreases, but it still follows the optimal coordinated trajectory and ensures that it always cannot exceed the boundary of the coordination space. Meanwhile, the stiffness coefficient needs to be increased. The trajectory is closer to the boundary of coordination space, the faster the impedance parameter increases, and the inertia coefficient and damping coefficient also need to be increased synchronously to ensure the stability of system.

The APF method is widely adopted in obstacle avoidance in path planning, which can make the robot bypass the obstacle and gradually approach the target by controlling the gravitational field and the repulsive field. Similarly, the optimal coordinated gait trajectory is defined as the target, which is generated by synergetic gait prediction model, and the upper and lower boundaries of coordinated space are defined as the obstacles. The gravitational force near the target increases, and the repulsive force near the obstacle increases. The resultant force at the current position serves as the impedance control parameter, enabling small position corrections near the optimal coordinated gait trajectory and extensive position corrections near the boundary of coordination space.

Define the potential function U(p) of an object at the point p, which is the sum of the gravitational potential function U ₁(p) and the repulsive potential function U ₂(p), as shown in Eq. 3. U p = U 1 p + U 2 p (3) U 1 p = 1 2 ς ρ 2 p , p t arg e t (4) where ς is the gravitational gain factor, and ρ(p, p _obstacle ) represents the Euclidean distance between the object and the target. U 2 p = 1 2 η 1 ρ p , p obstacle − 1 ρ 0 2 (5) where η is the repulsion gain factor. ρ(p, p _obstacle ) represents the Euclidean distance between the object and the obstacle. ρ ₀ represents the maximum distance of the repulsion field generated by the obstacle, and 0 ≤ ρ(p, p _obstacle ) ≤ ρ ₀. When ρ(p, p _obstacle ) > ρ ₀, U ₂(p) = 0, and the repulsion field does not work.

When the object is close to the target, the potential function is small and changes slowly, otherwise the potential function is large and changes quickly. When approaching the boundary, the repulsive potential function approaches infinity, which prevents the object from crossing the boundary of coordination space. The potential safety concerns can be raised by infinite impedance. The compliant control gradually increases the impedance as the knee joint approaches the boundary and stops increasing the impedance once the safety threshold has been reached. Therefore, the adaptive impedance control based on the APF is designed as Eq. 6. M d = M d 0 + ω 1 U t B d = B d 0 + ω 2 U t K d = K d 0 + ω 3 U t (6) where M _d0, B _d0, and K _d0 represent the initial values set by inertia coefficient M _d , damping coefficient B _d , and stiffness coefficient K _d , respectively. U(t) represents the potential function at the time t. ω ₁, ω ₂ and ω ₃ represent the positive weights on the potential function.

The paper employs a single-input single-output model-free adaptive controller (SISO-MFAC) as the position controller to achieve trajectory tracking. SISO-MFAC only adopts the input and output of the controlled system to automatically modify the control signal, which can overcome uncertainty interference and obtain strong robustness against disturbances and unknown model dynamics, as shown in Eq. 7. u k = u k − 1 + ρ ϕ C k θ d k + 1 − θ k λ + ϕ C 2 k ϕ ⌢ C k = ϕ ⌢ C k − 1 + η Δ θ k − ϕ ⌢ C T k − 1 Δ u k − 1 Δ u k − 1 μ + Δ u k − 1 2 ϕ ⌢ C k = ϕ ⌢ C 1 , i f ϕ ⌢ C k < b o r Δ u k − 1 < b  o r s i g n ϕ ⌢ C k ≠ s i g n ϕ ⌢ C 1 (7) where u k and θ k represent the input and output of the system at time k, respectively. ϕ C k ∈ R m is the pseudo-gradient of the system. ϕ C ⌢ k is an estimate of ϕ C k λ and μ are weighting factors. ρ and η are step factors. ϕ C ⌢ 1 is the initial value of ϕ C ⌢ k . 0 < 1 − η Δ u 2 k − 1 μ + Δ u k − 1 2 ≤ d 1 < 1 0 < 1 − ρ ϕ C k ϕ ⌢ C k λ + ϕ ⌢ C 2 k ≤ d 2 < 1 (8) where d ₁ and d ₂ are constants.

The diagram of the proposed compliant controller is shown in Figure 7. The compliant controller of knee exoskeleton consists of synergetic gait prediction model, adaptive impedance controller, position controller, and knee exoskeleton. The synergetic gait prediction model is used to generate individualized gait trajectories, and the coordinated gait trajectory of the affected lower limb is generated according to the knee joint angle and sEMG signals of the healthy lower limb. The adaptive impedance controller corrects the expected trajectory in the coordination space according to the deviation between the expected and actual human-robot interaction force. The SISO-MFAC controller can realize the actual trajectory of the exoskeleton to accurately track the expected trajectory. The knee exoskeleton driven by SEA is used as the control object to assist the patient to perform rehabilitation training. Furthermore, the human-robot interaction force between the patient and the exoskeleton is measured by the spring compression at the end of SEA, and the displacement sensor with the range of 50 mm is installed on the spring, which avoids inaccurate measurement due to the relative displacement between the sensor and the human body or the robot. When the actual human-robot interaction force is not equal to the expected human-robot interaction force, the compliant controller generates the correction of expected trajectory, and the position controller controls the exoskeleton to move according to the corrected trajectory. The APF method can ensure that the gait trajectory does not exceed the boundary of coordination space, and the actual trajectory can be guaranteed to be located in the coordination space.

The sampling frequency of the signal acquisition system is 200 Hz, and the time step is 5 ms, and each sample is 50 s. The knee joint data of the affected lower limb at the current moment is influenced by the healthy lower limb at the previous moment, and there is the delay in actual application from gait prediction to data transmission. After comprehensive considerations, the time step is set to 10, and the knee joint angle of the affected lower limb is predicted based on the information of the healthy lower limb in the previous 100 ms. The dimension of dataset under each task is 8980 × 4. The dataset is split into training (60%), validation (20%) and test (20%) subsets. The input dimension of each dataset is 20 × 4 and the output dimension is 1 × 1. The model is trained based on intra-subjects, and the data is obtained from the trained subject with varying speeds and inclines.

Figure 8 shows gait prediction performance of the subject S1 when walking at different speeds on different slopes, in which the red curve represents actual trajectory, and the blue curve represents predicted trajectory. The prediction error is lowest when the speed is 3 km/h, and the prediction performance is worst at the speed of 0.5 km/h. The prediction error at the speed of 0.5 km/h is 42.79% higher than that at the speed of 3 km/h and 12.67% higher than that at the speed of 1.5 km/h. The muscle activity of the subjects is low when walking at low speed, and the periodicity and amplitude of EMG signals is weaker, so the performance of gait prediction at the speed of 0.5 km/h is worst. Similarly, the prediction performance is best when the slope is 8°, and the prediction error is highest on the slope of 0°. Moreover, although the prediction performance is worst at low speed and flat slope, the trend of angle can still be reflected.

To test the applicability of the synergetic gait prediction model, the performance of gait prediction of four subjects at different speeds is analyzed, as shown in Figure 9. The prediction error of S3 is 123.65% higher than that of S1, 64.89% higher than that of S2, and 109.27% higher than that of S4. We have selected five metrics in the time and frequency domains to analyze the sEMG signal, including root mean square (RMS), mean absolute value (MAV), median frequency (MF), mean power frequency (MPF), and signal-to-noise ratio (SNR), and the RMS, MAV, MF, MPF, and SNR metrics show positive correlation with the prediction performance. However, the above metrics are not a dependable basis of prediction performance and can only be adopted as the preliminary reference.

To further quantitatively evaluate the performance, this paper adopts the mean absolute error (MAE) and Pearson correlation coefficient (CC) as the metric. Net1 represents the CNN-LSTM network without attention mechanism, and Net2 refers to the CNN-LSTM network with attention mechanism used in paper (Zhu et al., 2021), and Net is the proposed networks in this paper. The attention mechanism in the Net2 model is the weighted average sum of the output vectors of the LSTM layer. Taking the scene with a slope of 4° as an example, the prediction performance using different model are shown in Table 1. To evaluate the performance of model adopting multi-sensors fusion, the results are shown in Table 2. The Net model adopts the information of the knee joint angle and EMG signal in healthy lower limb as the network input, while the Net3 model only employs the information of the knee joint angle in healthy lower limb.

As shown in Table 1, taking the subject S1 as an example, compared with Net1, the MAE of the model proposed in this paper decrease by 12.42%, 8.82% and 13.99% at 0.5 km/h, 1.5 km/h and 3 km/h, and the CC increase by −0.42% and 0.99%, and 0.72%. Compared with Net2, the MAE of the model proposed in this paper decrease by 3.01%, 5.71% and 9.21%, and the CC increase by 0.12%, −0.32% and 0.18%. The above trend is also reflected in the prediction results of subjects S2, S3 and S4. In summary, the prediction performance of proposed model in this paper is better than Net1 and Net2.

As shown in Table 2, taking the subject S1 as an example, compared with Net3, the MAE of the model adopting multi-sensors input decrease by 7.43%, 19.33%, and 25.26% at 0.5 km/h, 1.5 km/h, and 3 km/h, and CC increase by 0.5%, 2.92% and 1.72%. It is worth noting that although the CC of the model using single input is higher, and the MAE is lower when the subject S3 is at 3 km/h, the mean of CC and MAE at three speeds are still better than Net3. Furthermore, the results of the subjects S1, S2, and S4 are consistent, which shows that multi-sensor fusion can further improve the accuracy of gait prediction. Figure 10 visually shows the prediction results of different methods for different subjects at different speeds on slope 4°. The model using multi-sensors information has smaller MAE and higher CC compared with the model adopting single input. Meanwhile, the mean of MAE at three speeds is smaller than that of the other network, and the mean of CC is higher than that of the other network, which shows that the model proposed in this paper has smaller prediction error and better applicability to different individuals.

Experiments are carried out on a SEA-driven knee exoskeleton to assess the effectiveness of the proposed compliant control method. Considering the site conditions and safety factors, the experimental scenes are divided into two types, namely, walking on the slope 0° and 4° at the speed of 0.5 km/h, respectively. The boundary range of the coordination space is set to a constant value Δd = 5°, and the distance between the upper and lower boundaries of the coordination space is 10°. To guarantee participant safety, the knee exoskeleton’s motion angle has been limited to −5°–65° degrees via the software.

The results of compliant control of the subjects S1 and S2 in different scenes are shown in Figure 11, in which the red curve represents the optimal coordinated trajectory, and the blue curve represents the corrected trajectory, and the green curve represents the actual trajectory of the exoskeleton. The original trajectory is defined as the gait trajectory generated by the prediction model and filtered to comply with the normal human gait pattern. The corrected trajectory represents the trajectory modified by the compliant controller when the actual human-robot interaction force is not equal to the expected human-robot interaction force. The actual trajectory is defined as the angle signal collected by the angle sensor on the knee exoskeleton. Furthermore, the optimal coordinated gait trajectory, the corrected trajectory, and the actual trajectory are all in the coordination space, which proves that the compliant control method can adaptively and nonlinearly modify the impedance parameters according to the actual conditions, and ensure the safety and coordination of rehabilitation training.

The results of the human-robot interaction force is shown in Figure 12, in which the blue curve represents the expected human-robot interaction force, and the red curve represents the actual human-robot interaction force, and the green curve represents the deviation between the expected and actual human-robot interaction force. The expected force is defined as the human-robot interaction force of healthy subjects collected by the force sensor in advance. The actual force is defined as the human-robot interaction force of patients during rehabilitation training. Combining Figures 11, 12, it is evident that the trajectory correction is not proportional to the force deviation. The deviation of force is positive, which indicates that the motion intention of the subject is consistent with the direction of the robot.

The experiment with fixed impedance parameters on the subject S1 are conducted, and the experimental results are shown in Figure 13. When the actual human-robot interaction force deviates from the expected human-robot interaction force, the impedance controller with fixed parameters can also correct the trajectory. However, if the deviation of force is large, the corrected trajectory may exceed the boundary of the coordination space. Consequently, the impedance control system with fixed impedance parameters cannot completely guarantee the safety and coordination of rehabilitation training. The adaptive impedance control proposed in this paper can not only nonlinearly and adaptively modify the expected trajectory according to the human-robot interaction force, but also restrict the actual trajectory to always be in the coordination space.