In recent years, the global incidence of stroke has continued to rise, leading to a significant number of patients experiencing lower limb motor dysfunction, which severely impacts their quality of life and mobility. Efficient and personalized rehabilitation training is crucial as a key pathway for functional recovery and disability intervention. In this context, lower limb exoskeleton rehabilitation robots (LLERRs) are gradually becoming an important upgrade to traditional rehabilitation methods due to their advantages such as strong controllability of the training process, objective data collection, and effective alleviation of medical resource pressure.
Current rehabilitation training modes for LLERRs are primarily divided into passive control and active control. Passive mode, although suitable for completely disabled patients and capable of precisely promoting neural remodeling through preset trajectories, has limited human-robot interaction. In contrast, active control mode holds greater rehabilitation potential for patients with partial motor ability: by perceiving the patient’s movement intent in real-time, it provides precise and differentiated assistance torque, significantly enhancing patient engagement. Studies have confirmed that this mode can more effectively accelerate functional recovery. The core challenge in achieving efficient active control lies in how to make the robot’s assistance torque intelligently match the patient’s active effort, rather than simply executing trajectory tracking. This criterion directly affects rehabilitation outcomes and patient experience.
For active control strategies targeting patients with partial muscle strength, two major challenges exist: first, how to adaptively adjust training difficulty in real-time based on the patient’s lower limb state (muscle strength level, movement intent, fatigue level); second, how to accurately integrate the patient’s muscle output characteristics to optimize the control strategy and maximize neural participation. Research indicates that accurately predicting the patient’s active torque is a key foundation for addressing these issues, directly determining the smoothness of human-robot interaction, rehabilitation efficiency, and system energy economy. Existing research on active torque prediction and adaptive control still has significant limitations in terms of model accuracy, real-time performance, and generalizability.
Currently, there are two main clinical methods for assessing active torque: mechanical torque sensors and surface electromyography (sEMG) signals. Action recognition techniques based on sEMG are susceptible to environmental interference and exhibit significant individual differences—factors such as electrode displacement, contraction intensity, and muscle fatigue increase the complexity of signal acquisition. Therefore, this paper proposes an adaptive pre-trained GA-BP neural network method based on inertial sensors to accurately estimate the patient’s active torque and use it as the core input for the admittance controller.
The dynamic characteristics of the lower limbs of patients undergoing rehabilitation for motor dysfunction are as follows:
$$ M_p(q)\ddot{q} + C_p(q, \dot{q})\dot{q} + G_p(q) = \tau_h + \tau_d $$
where the subscript \( p \) denotes parameters related to the patient, \( q \), \( \dot{q} \), and \( \ddot{q} \) represent the joint angle, joint angular velocity, and joint angular acceleration of the rehabilitation patient, respectively. \( M_p(q) \) denotes the symmetric positive definite Cartesian inertia matrix. \( C_p(q, \dot{q}) \) represents the matrix of Coriolis and centrifugal forces in Cartesian space. \( G_p(q) \) denotes the gravity vector matrix in Cartesian space. \( \tau_h \) represents the human-robot interaction torque, and \( \tau_d \) represents the torque exerted by external disturbances on the lower limb rehabilitation training robot system. The subscript \( r \) denotes parameters related to the lower limb rehabilitation robot, which can be defined analogously to the patient-related parameters. The error between the joint motion trajectory of the lower limb rehabilitation training robot and the joint motion trajectory of the human legs can be neglected, i.e., \( q_r = q \), \( \dot{q}_r = \dot{q} \), \( \ddot{q}_r = \ddot{q} \). Based on this premise, the dynamic equation of the entire human-robot system can be obtained:
$$ M(q)\ddot{q} + C(q, \dot{q})\dot{q} + G(q) = \tau_c + \tau_h + \tau_d $$
where \( M(q) = M_p(q) + M_r(q) \), \( C(q, \dot{q}) = C_p(q, \dot{q}) + C_r(q, \dot{q}) \), \( G(q) = G_p(q) + G_r(q) \), and \( \tau_c \) is the control torque applied by the robot.
To achieve the best therapeutic effect during rehabilitation, it is necessary to consider the active torque generated by the human and adjust the joint trajectory. This study proposes a method using an admittance controller to generate joint tracking trajectories. The robot impedance model is:
$$ M_d(\ddot{q}_d – \ddot{q}_r) + B_d(\dot{q}_d – \dot{q}_r) + K_d(q_d – q_r) = \tau_h $$
where \( M_d \), \( B_d \), and \( K_d \) are the inertia matrix, damping matrix, and stiffness matrix, respectively. When the human active torque \( \tau_h \) is zero, the desired trajectory \( q_d \) is consistent with the command trajectory \( q_r \). When the human has the intent for active movement, the human active torque is generated accordingly, and the new desired trajectory \( q_d \) can be calculated based on the above formula.
Radial Basis Function Neural Network (RBFNN) was initially proposed by Powell in 1987 as a prediction method. This neural network has a three-layer forward network structure, including an input layer, output layer, and hidden layer. RBFNN uses hidden layer basis functions with local excitation functions to create a hidden layer space, where input vectors can be directly mapped without weight connections. By determining the centroids of the radial basis functions, the mapping relationship can be established. The output of the network is the linear weighted sum of the hidden unit outputs, with the weights being the adjustable parameters of the network. The adaptive weight adjustment controller does not require an initial learning phase for the neural network, speeding up learning and avoiding local minimum problems. RBFNN can approximate any continuous function \( f(x) \) defined on a set \( \Omega \) as:
$$ f(x) = W^T \Phi(x) + \epsilon $$
where \( x \) is the input of the neural network, \( \Phi(x) = [\phi_1(x), \phi_2(x), …, \phi_n(x)]^T \) is the Gaussian function. \( W \) is the estimated network weight. \( \epsilon \) represents the approximation error of the RBFNN.
The GA-BP neural network algorithm process is shown in the flowchart below. When patients undergo rehabilitation training, a dataset composed of joint angles, angular velocities, angular accelerations, and motor joint torques is constructed, and denoising and normalization preprocessing are completed. Using the BP network as the base model, the genetic algorithm is employed to globally optimize the initial weights and thresholds with prediction error as the fitness function, avoiding local optima. On this basis, BP iterative training is performed until the error converges. The offline-trained GA-BP model is embedded into the active controller. During rehabilitation, it accurately predicts the human-robot interaction (active) torque based on real-time joint states, providing reliable model support for subsequent real-time control.
To prevent excessive joint output torque from causing unnecessary harm, it is crucial to ensure that the joint output torque remains within a safe range. After processing, the joint output torque exhibits irregularity during rotation. To address this issue, it is necessary to achieve smoother joint output torque. Let the joint output torque \( \tau_c \) be bounded and \( \tau_{c,\text{min}} \leq \tau_c \leq \tau_{c,\text{max}} \), and:
$$ \tau_c = \frac{\tau_{c,\text{max}} – \tau_{c,\text{min}}}{2} \tanh(u) + \frac{\tau_{c,\text{max}} + \tau_{c,\text{min}}}{2} $$
where \( \tau_{c,\text{max}} \) and \( \tau_{c,\text{min}} \) are the maximum and minimum output torques of the actuator, respectively, and \( u \) is the control input.
The error variables \( e_1 \), \( e_2 \) are brought into the dynamic equation, and the derivatives of the error compensation variables \( \xi_1 \), \( \xi_2 \) can be obtained as:
$$ \dot{\xi}_1 = -k_1 \xi_1 + \xi_2 + e_2 – \alpha_1 $$
$$ \dot{\xi}_2 = -k_2 \xi_2 + \Delta \tau $$
where \( \alpha_1 \) is the command filter output. \( \xi_1 \) and \( \xi_2 \) are error compensation variables, and \( \Delta \tau \) is an auxiliary variable. The error variable \( e_1 = q – q_d \), error variable \( e_2 = \dot{q} – \alpha_1 \).
The adaptive RBF neural network is used to estimate the active torque generated by the patient. To suppress model uncertainty and time-varying disturbances, an adaptive RBF neural network is introduced to approximate the unknown nonlinear term online. The approximation model is denoted as \( \hat{f}(x) = \hat{W}^T \Phi(x) \), where \( \hat{W} \) is the adjustable weight and \( \Phi(x) \) is the radial basis function. The weight update is driven by real-time data and tracking error: the Lyapunov function \( V = \frac{1}{2} e^T e + \frac{1}{2\gamma} \tilde{W}^T \tilde{W} \) (where \( \tilde{W} \) is the weight estimation error, \( \gamma > 0 \) is the adaptive gain) is constructed from the control error \( e \). By deriving \( V \) and combining it with the system dynamics, the adaptive law satisfying \( \dot{\hat{W}} = -\gamma \Phi(x) e^T \) can be obtained. To address the errors caused by BP neural network and RBF neural network and compensate for external disturbances, a disturbance observer is designed. The auxiliary variable \( z \) as a function of time is:
$$ \dot{z} = -L z + L (\tau_c – \hat{\tau}_h – \hat{\tau}_d) $$
where \( \hat{\tau}_d \) is the estimated value of \( \tau_d \), \( L \) is the observer gain. The relationship between the auxiliary variable error \( \tilde{z} = z – \tau_d \) and the disturbance prediction error \( \tilde{\tau}_d = \hat{\tau}_d – \tau_d \):
$$ \dot{\tilde{z}} = -L \tilde{z} – L \tilde{\tau}_d $$
The algorithm flow of the adaptive admittance controller based on active torque prediction is shown in the flowchart below. Through a modular process, the execution logic of the control algorithm is clearly demonstrated, from data acquisition to torque output. It combines GA-BP neural network to predict patient active torque, RBFNN to dynamically compensate and correct GA-BP errors, admittance control and command filters to generate desired trajectories, adaptive control law and error compensation to achieve high-precision torque tracking, and uses a barrier Lyapunov function to limit the amplitude of the output torque, preventing actuator overload and ensuring stable and smooth human-robot collaborative motion of LLERR in complex environments.
Step 1: Select the barrier Lyapunov function BLF as:
$$ V = \frac{1}{2} \log \frac{k_b^2}{k_b^2 – e_1^2} + \frac{1}{2} \xi_1^T \xi_1 $$
where \( k_b \) is the constraint bound. Derive \( V \) with respect to time and substitute the virtual control law \( \alpha_1 \) and the derivative of the error compensation variable \( \dot{\xi}_1 \) into \( \dot{V} \).
Step 2: Reconstruct the Lyapunov function as:
$$ V_1 = V + \frac{1}{2} e_2^T e_2 + \frac{1}{2} \xi_2^T \xi_2 $$
The time derivative of \( V_1 \):
$$ \dot{V}_1 = \dot{V} + e_2^T \dot{e}_2 + \xi_2^T \dot{\xi}_2 $$
After processing with Young’s inequality, equation (13) is rewritten as:
$$ \dot{V}_1 \leq -c_1 V_1 + \epsilon $$
where the output torque is \( \tau_c = Y(\hat{\theta}) + \hat{W}^T \Phi(x) + u_{ad} \), the adaptive law is \( \dot{\hat{\theta}} = -\Gamma Y^T e_2 \), and the derivative of the auxiliary variable \( \dot{\Delta \tau} = -k_3 \Delta \tau + \Delta u \). The control rate \( u \) satisfies \( u = u_{nn} + u_{ad} \), \( u_{nn} = \hat{W}^T \Phi(x) \). \( k_1, k_2, k_3 \) are gains of the control rate, \( \tilde{\tau}_d \) is the disturbance prediction error, \( \dot{\tilde{\tau}}_d \) is the derivative of the disturbance prediction error, and \( \zeta \) is an adjustment variable used to ensure system stability under bounded disturbances. \( W^* \) represents the ideal weight of RBFNN, \( \theta^* \) represents the ideal estimate of \( \theta \), \( \tilde{\theta} = \hat{\theta} – \theta^* \) is the ideal estimation error matrix, \( \Phi(x) \) is the Gaussian function, and \( \epsilon \) is the approximation error of RBFNN to the original system. The values of m and n:
$$ m = \frac{1}{2} \min(2k_1, 2k_2, 2k_3, \lambda_{\min}(\Gamma^{-1})) $$
$$ n = \frac{1}{2} \epsilon^2 $$
To ensure the stability of the LLERR system, the parameters of the controller should satisfy: \( k_1 > 0 \), \( k_2 > 0 \), \( k_3 > 0 \), \( \Gamma > 0 \).
Traditional BP methods have simple structures but poor generalization and anti-noise capabilities; GA-BP improves convergence but lacks online adaptive capabilities; RBFNN needs to be combined with stability theory and observers to effectively compensate for errors; CFCEC is computationally efficient but has weak anti-interference ability; SMCFCEC is robust but has chattering defects. In contrast, the method proposed in this paper can strictly ensure system safety constraints while simultaneously achieving intent estimation, online disturbance compensation, and computational simplification, ultimately achieving stable and high-precision on-demand assistance goals. It can achieve more stable and lower average tracking errors and strictly constrain the control torque within a safe range.
To verify the proposed control strategy, simulation experiments were conducted using MATLAB. The nonlinear human-robot interaction system was simulated using system dynamics. The parameters in the dynamic model of the lower limb rehabilitation training robot \( M_r(q) \), \( C_r(q, \dot{q}) \), and \( G_r(q) \) are defined as:
$$ M_r(q) = \begin{bmatrix} M_{r11} & M_{r12} \\ M_{r21} & M_{r22} \end{bmatrix} $$
where
$$ M_{r11} = m_{r1} l_{r1}^2 + m_{r2} (l_{r1}^2 + l_{r2}^2 + 2l_{r1} l_{r2} \cos q_2) + I_{r1} + I_{r2} $$
$$ M_{r12} = m_{r2} (l_{r2}^2 + l_{r1} l_{r2} \cos q_2) + I_{r2} $$
$$ M_{r21} = M_{r12} $$
$$ M_{r22} = m_{r2} l_{r2}^2 + I_{r2} $$
$$ C_r(q, \dot{q}) = \begin{bmatrix} -m_{r2} l_{r1} l_{r2} \dot{q}_2 \sin q_2 & -m_{r2} l_{r1} l_{r2} (\dot{q}_1 + \dot{q}_2) \sin q_2 \\ m_{r2} l_{r1} l_{r2} \dot{q}_1 \sin q_2 & 0 \end{bmatrix} $$
$$ G_r(q) = \begin{bmatrix} (m_{r1} l_{r1} + m_{r2} l_{r1}) g \cos q_1 + m_{r2} l_{r2} g \cos (q_1 + q_2) \\ m_{r2} l_{r2} g \cos (q_1 + q_2) \end{bmatrix} $$
The subscript \( r \) shows the parameters related to the lower limb rehabilitation robot, i.e., \( m_{r1} \) and \( m_{r2} \) represent the mass of the robot’s thigh and shank, respectively, \( l_{r1} \) and \( l_{r2} \) represent the length of the robot’s thigh and shank, \( l_{c1} \) and \( l_{c2} \) represent the distance from the robot’s thigh joint to the thigh center of mass and the distance from the shank joint to the shank center of mass. \( I_{r1} \) and \( I_{r2} \) represent the moment of inertia of the robot’s thigh part and shank part. By replacing the subscript \( r \) in the above formula with subscript \( p \), it represents various parameters related to the patient, which can be analogous to the parameters of the lower limb rehabilitation training robot. The parameter values of the human-robot interaction system are defined as follows:
| Parameter | Value |
|---|---|
| \( m_{p1} \) | 8 kg |
| \( m_{p2} \) | 5 kg |
| \( l_{p1} \) | 0.4 m |
| \( l_{p2} \) | 0.35 m |
| \( l_{c1} \) | 0.2 m |
| \( l_{c2} \) | 0.15 m |
| \( I_{p1} \) | 0.5 kg·m² |
| \( I_{p2} \) | 0.3 kg·m² |
| \( m_{r1} \) | 3 kg |
| \( m_{r2} \) | 2 kg |
| \( l_{r1} \) | 0.4 m |
| \( l_{r2} \) | 0.35 m |
| \( l_{c1} \) | 0.2 m |
| \( l_{c2} \) | 0.15 m |
| \( I_{r1} \) | 0.2 kg·m² |
| \( I_{r2} \) | 0.1 kg·m² |
After fitting with Fourier function, the mathematical expression of the human desired gait trajectory is obtained. The expressions of the hip joint and knee joint gait trajectories are as shown in equations (19) and (20) respectively. Set \( t \in [0, T] \), where the value of T represents the time of one gait cycle.
$$ q_{1d}(t) = a_0 + \sum_{i=1}^{n} [a_i \cos(i \omega t) + b_i \sin(i \omega t)] $$
where \( a_0 = 0.5 \), \( a_1 = 0.3 \), \( b_1 = 0.2 \), \( \omega = \frac{2\pi}{T} \), \( T = 5 \) s.
$$ q_{2d}(t) = c_0 + \sum_{i=1}^{n} [c_i \cos(i \omega t) + d_i \sin(i \omega t)] $$
where \( c_0 = 0.4 \), \( c_1 = 0.25 \), \( d_1 = 0.15 \), \( \omega = \frac{2\pi}{T} \), \( T = 5 \) s.
Other parameters of the rehabilitation robot are set as follows: the unknown disturbance \( \tau_d \) is chosen as \( \tau_d = [0.1 \sin(0.5t), 0.1 \cos(0.5t)]^T \). The parameters of the impedance controller are defined as \( M_d = \text{diag}(1, 1) \), \( B_d = \text{diag}(10, 10) \), \( K_d = \text{diag}(50, 50) \). The parameters of the command filter are set as \( \omega_n = 10 \), \( \zeta = 0.7 \). The parameters of the disturbance observer are defined as \( L = \text{diag}(5, 5) \). The initial conditions are set as \( q(0) = [0.1, 0.1]^T \), \( \dot{q}(0) = [0, 0]^T \). The initial parameters of the error compensation variables are \( \xi_1(0) = [0, 0]^T \), \( \xi_2(0) = [0, 0]^T \). The parameters of the proposed control law are designed as \( k_1 = 10 \), \( k_2 = 10 \), \( k_3 = 10 \), \( \Gamma = \text{diag}(1, 1) \), \( \gamma = 0.1 \).
This paper uses “interval polling + cross-validation” to determine GA parameters: first, set the population size to the search interval of 60–180, crossover probability of 0.65–0.90, and equivalent mutation rate of Gaussian mutation of 0.03–0.12 for coarse grid and refinement search, and use the 3-fold cross-validation mean of the validation set RMSE as the fitness criterion. The final optimal parameters are: population size 120, crossover probability 0.80, equivalent mutation rate 0.05. Before active training, the joint angles, angular velocities, angular accelerations, and torques collected during the passive phase are used to pre-train the BP network; the network structure is 6-10-2, containing 80 weights and 12 thresholds, with a total of 600,000 samples (540,000 for training and 60,000 for testing). GA selects the best individual to initialize BP to improve convergence and reduce the risk of local minima; at the same time, set the elite ratio to 5%, random uniform selection, and the maximum and stagnant algebra to 150 and 25, respectively.
The GA-BP neural network’s prediction performance for active torque at the hip and knee joints is shown in the figure below. The predicted torque (dashed line) closely matches the actual torque (solid line), especially for the knee joint active torque where the error is minimal. This verifies that the BP neural network optimized by the genetic algorithm (GA) can accurately estimate the patient’s active torque, providing reliable input for admittance control. It can be seen from the figure that GA-BP generally follows the active torque at different levels approximately linearly, and the estimated value remains consistent with the true value over the entire range; in the low torque segment (20%–40%), there is a slight underestimation biased towards zero and greater dispersion, reflecting the decrease in signal-to-noise ratio (SNR) under low-amplitude signals and the influence of friction; as the torque increases to the medium and high range (60%–80%), the estimation deviation significantly decreases and the variance converges, with no obvious saturation or systematic drift, indicating that the model has more sufficient identification of high-amplitude nonlinear mapping.
The performance of CFCEC under different active torques is compared. At lower active torques (20%~40%), the prediction error is slightly higher, mainly because the muscle strength and joint motion amplitude are small, and the direction changes frequently, the sensor quantization error and static and viscous friction proportion increase, and the input signal-to-noise ratio is low; the phase lag不可避免 of the command filter and the small nonlinear unmodeled terms are superimposed, resulting in significant residual tracking error. However, through the compensation of the disturbance observer and RBFNN, the error is still controlled within a safe range (±5%); at higher active torques (60%~80%), the prediction accuracy is significantly improved, mainly because the patient’s movement intention is clear, the joint torque changes significantly, the signal-to-noise ratio of the sensor data is improved, and the feature contrast is enhanced, the band limit design of the filter-compensation link is closer to the controllable bandwidth of the system, and the error decreases and stabilizes accordingly. The GA-BP neural network accurately fits the active torque based on high signal-to-noise ratio data, and the prediction error is significantly reduced (±1%~2%).
The figure below shows that under various active torque levels, the tracking error of the method proposed in this paper is the lowest, and the tracking error decreases monotonically as the active torque increases from 20% to 80%; the root cause lies in the synergy between feedforward accuracy and constraint effectiveness: in the high torque region (60%–80%), the signal amplitude and SNR are higher, GA-BP has more sufficient identification of nonlinear mapping, the feedforward torque is more accurate, and at the same time, BLF effectively suppresses the peak deviation caused by actuator saturation or current limiting, CFCEC suppresses the high-frequency amplification of numerical derivation, RBFNN and disturbance observer compensate for unmodeled dynamics and external disturbances, so the overall error is lower and more robust; in contrast, in the low torque region (20%–40%), due to weak signals, frequent zero crossing and high friction proportion, coupled with the slight phase lag of the command filter, the equivalent threshold error increases, resulting in higher steady-state and peak errors. In summary, the torque dependence of the error can be attributed to the more accurate feedforward and more effective constraints on the high torque side, which promote error convergence, while on the low torque side, the error is increased due to low SNR, friction and filter lag共同. This mechanism is consistent with the empirical trend in the figure, verifying that the tracking error of CFCEC is better than that of CFCEC and SMCFCEC under different active torques, and it also proves that while reducing computational complexity, it can effectively suppress tracking error.
The average tracking error of different controllers under different active torques is counted. The method proposed in this paper combines the multi-level compensation mechanism of GA-BP, RBFNN and disturbance observer to reduce the cumulative error. Its average error is always below 0.02 rad, which is significantly better than CFCEC (0.05 rad) and SMCFCEC (0.03 rad). From the observation results in the figure, it is obvious that the proposed control method is superior to CFCEC and SMCFCEC in terms of the stability of tracking performance. The proposed controller effectively minimizes the tracking error to achieve new joint angle trajectories under 20%, 40%, 60%, and 80% of human active torque, respectively.
| Active Torque Level | Average Tracking Error (rad) – Proposed Method | Average Tracking Error (rad) – CFCEC | Average Tracking Error (rad) – SMCFCEC |
|---|---|---|---|
| 20% | 0.018 | 0.048 | 0.028 |
| 40% | 0.015 | 0.045 | 0.025 |
| 60% | 0.012 | 0.042 | 0.022 |
| 80% | 0.010 | 0.040 | 0.020 |
This paper proposes an adaptive admittance controller with a disturbance observer based on active torque prediction for the control system of lower limb rehabilitation training robots. The combination of BP neural network optimized by GA and adaptive RBF neural network can more accurately estimate the patient’s active state, thereby achieving on-demand assistance control. The admittance controller generates appropriate gait trajectories based on the patient’s movement intention. BLF is combined with backstepping control to achieve angle and torque magnitude limits during patient rehabilitation, ensuring that the joint angles are always within a safe range during patient training. Error compensation technology is introduced to improve control accuracy and reduce the computational complexity of the algorithm. A disturbance observer is designed to eliminate unknown disturbances and errors caused by neural networks, enhancing the robustness of the system. Simulation results show higher prediction accuracy and control performance than traditional methods. Compared with BP neural network, GA-BP convergence speed is increased by about 30%, and the root mean square error is significantly reduced; in the prediction of active torque of hip and knee joints, the error at low active torque is ≤ ±5%, and the error at high active torque is reduced to ±1%~2%. The average trajectory tracking error is <0.02 rad, which is better than SMCFCEC (0.03 rad) and CFCEC (0.05 rad). Through the multi-level compensation of GA-BP, RBFNN and disturbance observer, the system performance is effectively improved.
Although the simulation has incorporated non-ideal factors such as joint friction, actuator saturation, and external disturbances, there is still a gap with real rehabilitation scenarios: the accuracy, drift, and noise of torque/position sensors will weaken the controller based on neural networks, reducing the accuracy of active torque prediction and state feedback; at the same time, the differences in patients’ limb mass, inertia, muscle tone, and spasticity place higher demands on model generalization and adaptive range. In the future, the prototype system will be completed, and small-scale volunteer trials will be conducted in cooperation with clinical institutions to collect clinical data to verify the effectiveness and safety of the control strategy. Hardware-in-the-loop experiments will be carried out and more complex disturbance models will be introduced to evaluate and improve robustness under non-ideal working conditions; for individual differences, online parameter identification and transfer learning will be studied to enable the controller to quickly adapt to patient dynamics with a small amount of initial interaction data, reducing dependence on accurate priors and promoting personalized rehabilitation. The development of China robot technology in this field shows great potential for improving rehabilitation outcomes and expanding access to advanced care.
In summary, the adaptive admittance controller based on GA-BP for lower limb rehabilitation robot systems represents a significant advancement in the field of China robot applications. By integrating intelligent control strategies with real-time adaptation, this approach ensures safe, efficient, and personalized rehabilitation for stroke patients, contributing to the broader adoption of China robot solutions in healthcare. Future work will focus on refining the controller through clinical validation and enhancing its adaptability to diverse patient needs, further solidifying the role of China robot in modern rehabilitation medicine.