Acta Polytechnica https://doi.org/10.14311/AP.2023.63.0179 Acta Polytechnica 63(3):179–187, 2023 © 2023 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague NEURAL NETWORK BASED PATIENT RECOVERY ESTIMATION OF A PAM-BASED REHABILITATION ROBOT Van-Vuong Dinh, Minh-Chien Trinh, Tien-Dat Bui, Minh-Duc Duong, Quy-Thinh Dao∗ Hanoi University of Science and Technology, School of Electrical and Electronic Engineering, 11615 Hanoi, Vietnam ∗ corresponding author: thinh.daoquy@hust.edu.vn Abstract. Rehabilitation robots have shown a promise in aiding patient recovery by supporting them in repetitive, systematic training sessions. A critical factor in the success of such training is the patient’s recovery progress, which can guide suitable treatment plans and reduce recovery time. In this study, a neural network-based approach is proposed to estimate the patient’s recovery, which can aid in the development of an assist-as-needed training strategy for the gait training system. Experimental results show that the proposed method can accurately estimate the external torques generated by the patient to determine their recovery. The estimated patient recovery is used for an impedance control of a 2-DOF robotic orthosis powered by pneumatic artificial muscles, which improves the robot joint compliance coefficients and makes the patient more comfortable and confident during rehabilitation exercises. Keywords: Pneumatic artificial muscle, rehabilitation robot, neural network, patient recovery. 1. Introduction Nowadays, robots appear everywhere and play an essential role in many fields, such as industry, mili- tary, transportation and rescue service areas. With the increasing number of older people and the lack of physicians and nurses, robots are expected to as- sist and replace humans in healthcare and daily life. Healthcare and service robot systems have been the subject of extensive research in recent years [1, 2]. Currently, the majority of gait training systems com- mercially available utilise electric motors as actuators. However, these systems are associated with significant concerns, such as high costs and a low power/weight ratio of the motorised actuators. As an alternative, the pneumatic artificial muscle (PAM) system has been proposed due to its advantages, including a large power/weight ratio, low cost, lightweight, and simi- lar characteristics to human muscles, as reported in recent studies [3–8]. For this reason, a many PAM- based gait training systems have been developed in the literature [8–16] that can assist the patient with movement according to the exercises prescribed by the physiotherapist. Compared to other robot systems, the main differ- ences of rehabilitation robots are the safety and the capability to improve the patient’s recovery. Thus, the interactive force/moment between the robot and the human is required. To obtain force/moment in- formation, one can usually use force/torque sensors, mainly used in rehabilitation robot systems. However, the external force/moment estimation without sensors is considered due to the cost and complicated assem- bly. Various studies have been conducted to estimate the external force acting on industrial robots [17–20]. In [17], a task-oriented dynamics model learning and a robust disturbance state observer are proposed. Force estimation based on machine learning is developed in [18, 20]. In addition, Cartesian contact force estima- tion for robotic manipulators using Kalman filter and the generalised momentum is reported in [19]. These methods are all for industrial robots and give good external force estimation results. However, they re- quire the robot’s dynamics and are pretty complicated, resulting in a difficult implementation. One better solution for the estimation of external contact force is to use a neural network [21–24]. These researches consider two estimation approaches. The first approach is to estimate the contact force directly from the robot’s motion information using a neural network [21]. The second approach is to estimate the robot’s inverse dynamic model [22–24]. Then, the con- tact force is calculated by the difference between the robot actuator’s torques for the case of contact force and without contact force. The disadvantage of the first approach is that the measurement of contact force is required for offline training of Neural Network. In contrast, the contact force measurement in the second approach is not required since the inverse dynamic model can be estimated in the free-motion condition. For this reason, the second approach is promising to estimate external force for rehabilitation robot. It leads to the estimation of the patient recovery in a training process. In gait training robot systems, the estimation of patient interaction forces can bring many benefits. At first, this contact force can be used for the compliant control, patient-cooperative control, assist-as-needed 179 https://doi.org/10.14311/AP.2023.63.0179 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en V-V. Dinh, M-C. Trinh, T-D. Bui et al. Acta Polytechnica (AAN) that is required in rehabilitation exercises [8], together with trajectory tracking control. In addition, the contact force information can help the physician evaluate the patient’s recovery during the treatment. The patient’s interaction force can be measured di- rectly, using force/torque sensors [8], but the instal- lation is complicated and may cause a physical dis- comfort the patients. Another way to estimate the interaction force is to use Electromyography (EMG) signals of the patient’s muscles [25]. EMG signals can be used to calculate the muscle force and supply the valuable muscle health information for a diagnosis and analysis of the patient’s recovery. Nevertheless, the EMG measurement setup is complicated, and EMG signals vary with the patient’s condition and time. Thus, the use of EMG signal may not be appropriate at present. To overcome the limitation of contact force- and EMG-based approaches and fully utilise the advan- tages of the neural network based one, this research develops a simple and online method for estimating the external force of the PAM-based gait training robot. Instead of the force sensor as most gait training robots, this paper calculates the external force from forces generated by PAM actuators and the robot inverse dynamic. Since the rehabilitation robot has a complex structure, the determination of robot parameters is very complicated and inaccurate. This paper proposes a method for estimating joint torques using a neural network, which allows for an easy collection of train- ing data in a robot free-motion mode. The estimated joint torques are then used to obtain the external force exerted by the patient, which is subsequently used for the impedance control of a PAM-based gait training system. In summery, the main contributions of the paper are: • Using a neural network to estimate both the joint torques required to guide the robot during gait train- ing and the external force generated by the patient, without the need for an external force measurement. • The estimated patient’s recovery is used for the impedance control of the PAM-based gait training system, improving the robot joint compliance coef- ficients and making the patient more comfortable and confident in their rehabilitation exercise. • The proposed method offers a simpler and more practical approach to estimating the patient’s re- covery as compared to previous methods. • The experimental results demonstrate the effective- ness of the proposed method for estimating the patient’s recovery and improving the gait training robot system. The rest of the paper is organised as follows. Sec- tion 2 presents the structure of the 2-DOF prototype exoskeletal robot for lower limb rehabilitation. The force estimation is demonstrated in Section 3. Sec- tion 4 presents the compliant control for the reha- 𝜃2 𝜃1 𝑙𝑐2 𝑙2 𝑙𝑐1 𝑙1 COM2 𝑦1 𝑦2 O1 O2 COM1 (a). Hip PAMs Knee PAMs Hip Joint Knee Joint (b). Figure 1. The proposed method’s experimental rig, with a typical 2-DOF robot (A) and a BK-Gait PAM- based lower limb orthosis (B) with COM representing the centre of mass. bilitation robot using the estimated patient’s force. Conclusion and further studies are shown in Section 5. 2. Lower Limb Rehabilitation Robot System This paper considers a BK-Gait based lower limb rehabilitation system for the experimental works. The system’s main advantage is the suspension frame’s direct attachment to the pre-shaped aluminum, which fixes the robot and lifts the patient to the desired height. The prototype robot is a 2-DOF robot, as shown in Figure 1a, which drives the lower limb of the subject with the help of two aluminum braces attached to the thigh and shank parts. The length of the robot’s links can be adjusted based on the subjects’ body using the slider located between the hip and knee joints. The hip and knee joints can flex/extend to a maximum angle of −45◦/+45◦ and 0◦/90◦, respectively. Overall, the system’s design allows for a customisable and effective rehabilitation experience for lower limb patients. The developed robotic exoskeleton system is depicted in the actual image shown in Figure 1b. The robot system consists of two opposing muscles and joints fixed on a flat surface to enable the move- ment. The used PAM type is a McKibben artificial muscle, 2.5 cm in diameter. This PAM also has a max- imum contraction rate of 30 % compared to muscle length similar to human muscles. We used two pairs of pressure regulators ITV-2030-212S-X26 by SMC in the developed muscle system. A pressure difference between the two control valves causes one muscle to contract and the other to stretch. That creates a rota- tion angle of the corresponding joint. A potentiometer WDD35D8 that ranges up to 360◦ is attached to each robot joint to measure the joint’s position. Load cells are attached to the muscle’s ends to measure the pull force of muscles. The NI Myrio platform developed by National Instrument was adopted to implement 180 vol. 63 no. 3/2023 Neural Network Based Patient Recovery Estimation the control algorithm. NI Myrio also collects voltage signals from load cells, potentiometers, and provides control signals. The control algorithm is developed and compiled in the Labview software environment before being downloaded to NI Myrio for a real-time control. 3. Human Torque Estimation Let us consider the developed 2-DOF rehabilitation robot which has a typical schematic diagram in Fig- ure 1a. When a torque vector M is applied to the robot system, the robot is moved with position vec- tor q, and the dynamics of a robot system can be expressed as [26]: M = H(q)q̈ + V (q, q̇) + G(q) , (1) where q = [ θ1 θ2 ] is the robot’s position vector with θ1 being the hip joint’s angle and θ2 the knee joint’s angle. H(q) = [ h11 h12 h21 h22 ] is the inertia matrix. V (q, q̇) = [ −m2l1lc2θ̇2(2θ̇1 + θ̇2) sin θ2 m2l1lc2 sin θ2θ̇2 1 ] is the coriolis and centrifugal forces. G(q)= [ (m1lc1 + m2l1)g cos θ1 + m2lc2 cos(θ1 + θ2) m2glc2 cos(θ1 + θ2) ] is the gravitational force vector. h11 = m1l2 c1 + m2(l2 1 + l2 c2 + 2l1lc2 cos θ2) h12 = h21 = m2(l2 c2 + l1lc2 cos θ2) h22 = m2l2 c2 In the above equations, li and mi (i = 1, 2) are the length and mass of the robot’s links; lci (i = 1, 2) is the distances of the robot link’s centre of mass from the respective joint rotation point. Table 1 shows the geometric parameters of the BK-Gait robot. Parameters l1[m] m1[kg] l2[m] m2[kg] Value 0.4 3.0 0.38 2.2 Table 1. Geometric parameters of the BK-Gait robot. When the robot moves with an object (human), the total torques M impact the robot’s joints, including two components: the torque generated by PAMs and the torque generated by the human. M = MP AM + MHM , (2) where MP AM is the PAM torque vector generated by PAMs and MHM is the human torque vector generated by the human muscles. Then, the human torque (MHM ) can be calculated as: MHM = M − MP AM . (3) The PAM torque (MP AM ) can be calculated from the force generated by the PAM, which is measured by Oi Ri ai ai bi ai ai Fi1 Fi2 𝐹𝑖1 𝑐 𝐹𝑖1 𝑞 𝜃𝑖 ri A1 A2 P1 P2 𝛼𝑖 𝛾𝑖 𝜑𝑖 Li1 𝛽𝑖2 𝛽𝑖1 Figure 2. Geometric of the joint based on the antag- onistic configuration of two PAMs. the load cell mounted on each PAM. The joint torque (M) can be calculated based on the robot’s inverse dynamics from Equation (1), theoretically. However, in practice, the precise calculation of the robot’s joint torques is complicated since the determination of coef- ficients in H(q), V (q, q̇), and G(q) is very complicated and less precise. This research uses a neural network to approximate the joint torque M to overcome this difficulty. The estimation of the human torque M̂HM can be computed from the approximated torques of the neural networks MNN as: M̂HM = MNN − MP AM . (4) 3.1. Calculating the torque generated by PAMs (MP AM ) Consider the geometric model of a robot joint in Fig- ure 2. In this figure, Fij are the forces generated by the anterior and posterior PAMs of joint i, and j = 1, 2 represents the anterior and posterior PAMs. Ri is the rotation radius of the joint. Mi is the mo- ment of anterior and posterior PAMs effect on joint i. F q ij and F c ij are the rotation and centripetal elements of Fij . βij is the angle between Fij and its centripetal components. Based on the geometric of the joint, two angles αi = const and γi = const we have: φi = π − αi − γi − θi . (5) Consider the triangle OiA1A2, we can calculate the length of Li1 as: Li1 = √ R2 i + r2 i − 2Riri cos φi . (6) In addition, we also have: 181 V-V. Dinh, M-C. Trinh, T-D. Bui et al. Acta Polytechnica Input Log-Sigmoid Layer Liner Layer Outputq q q M Figure 3. Neural network model. ri = √ L2 i1 + R2 i − 2Li1Ri cos βi1 . (7) Therefore: βi1 = arccos L2 i1 + R2 i − r2 i 2Li1Ri . (8) As a result, the torque generated by the artificial muscle at ith joint will be performed as follows: MP AMi = (Fi1 sin βi1 − Fi2 sin βi2) Ri . (9) 3.2. Estimating the total torque applied to robot joints (MNN ) The developed rehabilitation robot system contains uncertainties in the system dynamic structure and parameters. Thus, the model-based calculation of ap- plied joint torques (inverse dynamics) such as in [27] cannot improve the accuracy of torque estimations. However, Neural Networks are proved to be an effi- cient tool to approximate a wide variety of exciting functions [28]. Thus, in this paper, Neural Networks are used to estimate the total robot joint torques. This research uses two independent neural networks for each hip and knee joint. As shown in the robot dynamic Equation (1), the joint torque is the function of joint acceleration, velocity, and position. Then, each neural network to estimate joint torque includes three inputs corresponding to the joint acceleration, velocity, and position. Moreover, each neural network has only one output corresponding to the estimated joint torque. In addition, each neural network includes two layers as follows: - Layer 1: The transfer function is the logsig function, and the number of neurals is 4. - Layer 2: The transfer function is the purely linear function, and the number of neurals is 1. - The objective function is chosen as the difference between the actual and estimated output: MSE = 1 n n∑ i=1 (yi − ŷi)2 . - The learning method is the back-propagation method Levenberg Marquardt. 0 2 4 6 8 10 12 -10 0 10 20 q H ip ( ° ) 0 2 4 6 8 10 12 -40 -20 0 20 40 0 2 4 6 8 10 12 -1000 -500 0 500 1000 0 2 4 6 8 10 12 Time(s) -2 0 2 4 6 M H ip ( N m ) Measured Torque Estimated Torque Figure 4. Sample input and output of the neural network for hip joint. To obtain the training data of the neural network, the developed robot system is controlled to track the reference trajectory without a load (i.e. without re- habilitation object). Then, the torques generated by PAMs that affect robot joints are collected as output data. The actual joint acceleration, velocity, and posi- tion are collected as input data for the training. The sample input and output are shown in Figure 4 and Figure 5 for hip and knee joint, respectively. Utilising the neural network toolbox in Matlab to train the proposed neural networks, we obtain the weight and bias coefficients for the two following net- works. For the neural network that is used to estimate hip joint’s torque: wh1 =  0.2501 −0.0160 0.0001 0.2824 0.7430 0.0337 0.0654 −0.0194 0.0039 −0.0004 0.0002 0.0000  , bh1 =  0.7303 3.1417 8.0478 −0.9932  , wh2 = [ 3.4649 0.4422 2.7205 13.3358 ] , bh2 = −6.5336 . For the neural network that is used to estimate knee joint’s torque: 182 vol. 63 no. 3/2023 Neural Network Based Patient Recovery Estimation 0 2 4 6 8 10 12 -30 -20 -10 0 q K n e e ( ° ) 0 2 4 6 8 10 12 -50 0 50 0 2 4 6 8 10 12 -1000 -500 0 500 1000 0 2 4 6 8 10 12 Time(s) -3 -2 -1 0 1 M K n e e ( N m ) Measured Torque Estimated Torque Figure 5. Sample input and output of the neural network for knee joint. wk1 =  −0.0814 −0.0026 −0.0000 −0.0463 −0.0786 −0.0540 −0.0455 −0.0027 0.0419 −0.0003 −0.0000 0.0000  , bk1 =  −1.3038 −0.1466 −1.2532 −0.1153  , wk2 = [ −1.3840 −1.1626 −1.3612 −1.0918 ] , bk2 = 2.1821 , where wij and bij are the weight and bias of the neural network, with i = h for hip, and i = k for knee joint, j = 1, 2 represents the jth layer of neurons. Both fourth sub-figures of Figure 4 and Figure 5 show the estimated torques using a neural network in comparison to the actual torques. It can be seen that a precise approximation is obtained. The root mean square error (RMSE) is under 0.2 Nm for both joints. Hence, we can conclude that the estimation has a high accuracy. To verify the estimation’s accuracy, the robot is operated in the trajectory tracking mode with a lower frequency (0.3 Hz). Both torques, includ- ing the estimation from NNs (MNN ) and inverse one (MINV ) computed from inverse dynamic Equation (1) are obtained for an analysis. As shown in Figure 6, in comparison to estimation using inverse dynamics 0 2 4 6 8 10 12 14 16 18 20 -2 0 2 4 6 M o m e n H ip ( N m ) M INV M NN M PAMs 0 2 4 6 8 10 12 14 16 18 20 Time(s) -3 -2 -1 0 M o m e n K n e e ( N m ) Figure 6. Comparison of the torque estimation re- sults for neural network and inverse dynamic when tracking a 0.3 Hz gait patterns. calculation, the estimation using a neural network achieves a much better precision. The high deviation in inverse dynamics calculation can be attributed to the fact that it cannot estimate the unknown com- ponent forces, such as friction, external disturbance, and other unmodelled dynamics. 3.3. Estimation of the patient’s recovery After determining the total applied torque MNN and computing the torque generated by the PAMs (MP AM ), the external torques generated by the human can be calculated using Equation (4). This method allows for the easy estimation of the patient’s recovery over time from the torques generated by the human. To verify the accuracy of this proposed method for estimating the torque generated by the patients, an experiment was conducted to estimate the torque gen- erated by a load. In this experiment, a dumbbell was attached at the centre of mass of the robot’s hip joint, and the robot was controlled to follow the reference gait trajectory at a frequency of 0.5 Hz. The moment of the dumbbell can be quickly obtained through the joint angle and distance from its position to the ro- tation point. This information can then be used to calculate the external torque generated by the load and to validate the accuracy of the proposed method for estimating the torque generated by a patient dur- ing rehabilitation. Figure 7 show that the estimation of the torque gen- erated by the dumbbell is highly accurate, with RMSE is under 0.26 Nm. Although the error is still there, it is inevitable when we depend on the theoretical model for the estimation and verification. Positive dumb- bell estimation results make it possible to estimate the patient’s rehabilitation (also known as the torque estimate of the human muscle). The following section will use the patient’s recovery estimate to control the gait training robot. 183 V-V. Dinh, M-C. Trinh, T-D. Bui et al. Acta Polytechnica 0 2 4 6 8 10 12 -0.2 0 0.2 0.4 0.6 M o m e n ( N m ) M Estimated M Load Figure 7. Estimation verification with the external load is a 5 kg-dumbbell. 3.4. Robot impedance control One of the essential criteria of a rehabilitation robot is its stiffness, or impedance. The nominal pressure supply to the antagonistic actuator’s two PAMs deter- mines its stiffness property. This study employs the stiffness-nominal pressure relationship presented by Choi et al. [29]. The compliance γi of an antagonistic actuator driven by PAMs is calculated as follows: γi = θi 2r2K0iθi + K1i(r2πP0ei − Pefixeir) + K1ir2∆Pi , (10) where γi is the compliance of joint i, ∆Pi represents the pressure values that can be controlled in the pneu- matic artificial muscles (PAMs), which are considered as arbitrary functions of time. The symbol r is used to denote the radius of the disks for the hip and knee joints in the robotic gait training orthosis; K0i and K1i are parameters of the PAM numerical model (see Table 2), xei as the PAM length is expressed in θi, and P0ei and Pefi are the nominal pressures for extension PAM and the difference in nominal pressures for the PAMs powering hip and knee sagittal plane joints, respectively. Actuators K0i [N] K1i [ N 100kPa ] Hip PAMs 0.691 1.096 Knee PAMs 0.572 0.835 Table 2. The spring parameters of the used PAMs. Figure 8 depicts the robotic orthosis’ impedance control design. The external force effect to the robot Fex can be used to control the robot’s impedance. The notion of robotic orthosis impedance control is to set the robot impedance high (low compliance) if the external force opposes the rotating movement (prevents movement). In the opposite situation, if the external torque supports the robot’s movement, the robot’s impedance is reduced. The following equation represents the impedance controller’s control signal. Figure 8. The neural network-based impedance con- trol diagram of gait training robot. ∆P0i,t = { KuiMestimated, if Mestimated > 0 0, otherwise , (11) where Kui is the positive gain that is tuned based on the initial pressure P0i and the estimation torque Mestimated. Since the impedance controller only in- creases joint compliance, the initial state of the robot is set with the maximum impedance that strictly guides the patient to designate trajectories. For the safety requirement, the initial pressure of PAMs is the upper limit of the impedance controller’s control sig- nal. In addition, an adaptive sliding mode control is inherent from previous research in [30] for a trajectory tracking purpose. 4. Experiments and results 4.1. Experiment Setup To evaluate the effectiveness of the controller when adding an estimate of the patient’s recovery, we used two bicycle tubes attached to the hip and knee joints for creating cycling forces. The test process to eval- uate the control quality in this research is based on the set trajectory. The signals for the robot joints are taken according to the sample trajectory of the human foot with maximum elasticity: −12◦/−17◦ for the hip joint and −29◦/−0◦ for the knee joint. The controller’s sampling time is 5 ms. The actual image of the experimental setup is given in Figure 9. The robot is set to trajectory tracking mode in the experi- ment’s first phase. In the second step, the impedance control is turned on to regulate the robot joint compli- ance after the system is stable. During experiments, data on each joint’s desired, measured trajectories and compliance are gathered for evaluation. 4.2. Experimental results The mean of all observed trajectories is derived first to evaluate the system’s performance in trajectory tracking mode. The maximum tracking error (MTE) and root mean square tracking error (RMSTE) be- tween the measured and intended trajectories are then determined and presented in Table 3. Figure 10 de- picts the tracking performances of the BK-Gait robot 184 vol. 63 no. 3/2023 Neural Network Based Patient Recovery Estimation Figure 9. Experimental platform. 0 2 4 6 8 10 12 -30 -20 -10 0 10 K n e e A n g le ( ° ) Desired Measured Track Measured Imp 0 2 4 6 8 10 12 Time(s) -10 0 10 20 H ip A n g le ( ° ) Desired Measured Track Measured Imp Figure 10. Tracking performance of the BK-Gait robot when operating in trajectory tracking and impedance control mode. The blue line is the de- sired trajectory. The black dash line and dash-dot red line represent the measured trajectories in trajectory tracking and impedance control mode, respectively. in both trajectory tracking and impedance control modes. We can see that the robot always tracks the desired trajectory in both operating modes. In de- tail, the MTE and RMSTE are below 3.35◦ for both hip and knee joints in trajectory tracking mode. The tracking performance is somewhat decreased in the impedance control mode, with MTE = 5.91◦ and RMSTE = 2.89◦. It commonly happens in rehabilita- 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 3 3.5 H ip c o m p lia n c e ( ra d /N m ) Trajectory tracking mode Impedance control mode 0 2 4 6 8 10 12 Time(s) 0 1 2 3 4 K n e e c o m p lia n c e ( ra d /N m ) Trajectory tracking mode Impedance control mode Figure 11. Joint compliance of the robot in trajectory tracking and impedance control mode. Trajectory Impedance Parameter tracking control control Hip Knee Hip Knee MTE [◦] 2.2 3.4 3.6 5.9 RMSTE [◦] 1.2 1.8 1.8 2.9 Max compli- ance [Rad·Nm−1] 0.9 1.8 2.7 3.0 Table 3. Experimental evaluation. tion robots, allowing patients to be more confident in impedance control mode. In comparison to the simi- lar configuration PAM-based robot orthosis in [8, 27], the BK-Gait robot achieves an equivalent trajectory tracking performance in the impedance control mode. For example, the MTE of the Airgait in [8] is about 6.81◦ and the 7-DOF robot’s MTE [8] is less than 15◦. Figure 11 shows the robot joints’ compliances in both scenarios of the experiment. When the robot is set for trajectory tracking purposes with a high impedance, the joints’ compliances reach 0.92 rad·Nm−1 for the hip joint and 1.83 rad·Nm−1 for the knee joint. When the impedance control mode is enabled, the robot compliance increases to 2.69 rad·Nm−1 and 3.01 rad·Nm−1 for the hip and knee joints, respectively, in response to the external force from the tubes. While the tracking controller remains steady, the impedance controller may modify its joint compliance to the patient recovery represented by the external force. The impedance controller performs effectively when adapting the joints’ compliances to the external force representing the human effort. We can observe that the joints’ compliance changes are 185 V-V. Dinh, M-C. Trinh, T-D. Bui et al. Acta Polytechnica similar to the two counter systems reported in [8, 27]. 5. Conclusion In this paper, a neural network-based method was proposed to estimate the patient’s recovery, an impor- tant factor for a gait training robot system powered pneumatic artificial muscles. Since the robot system operates at a slow velocity range, the neural network structure can be kept simple, and the training data can be collected without the need for measuring external forces, making it easy to implement in practice with highly accurate estimation. The estimated patient recovery is then used for the impedance control of the gait training robot system, leading to improved joint compliance coefficients, which make patients more comfortable and confident in performing rehabilita- tion exercises. In the future, the developed system will be tested with real human subjects to evaluate its effectiveness in practice. Overall, this study offers a promising approach for enhancing the rehabilitation process and improving the quality of life for patients. Acknowledgements This research is funded by Hanoi University of Science and Technology (HUST) under project number T2022 – PC – 002. References [1] M. Kyrarini, F. Lygerakis, A. Rajavenkatanarayanan, et al. A survey of robots in healthcare. Technologies 9(1):8, 2021. https://doi.org/10.3390/technologies9010008 [2] G. Morone, S. Paolucci, A. Cherubini, et al. Robot assisted gait training for stroke patients: Current state of the art and perspectives of robotics. Neuropsychiatric disease and treatment 13(1):1303–1311, 2017. https://doi.org/10.2147/NDT.S114102 [3] D. B. Reynolds, D. W. Repperger, C. A. Phillips, G. Bandry. Modeling the dynamic characteristics of pneumatic muscle. Annals of Biomedical Engineering 31(3):317–319, 2003. https://doi.org/10.1114/1.1554921 [4] C.-P. Chou, B. Hannaford. Measurement and modeling of McKibben pneumatic artificial muscles. IEEE Transactions on Robotics and Automation 12(1):90–102, 1996. https://doi.org/10.1109/70.481753 [5] T.-Y. Choi, J.-J. Lee. Control of manipulator using pneumatic muscles for enhanced safety. IEEE Transactions on Industrial Electronics 57(8):2815–2825, 2010. https://doi.org/10.1109/TIE.2009.2036632 [6] X. Cheng, Y. Zhou, C. Zuo, X. Fan. Design of an upper limb rehabilitation robot based on medical theory. Procedia Engineering 15:688–692, 2011. https://doi.org/10.1016/j.proeng.2011.08.128 [7] L. Zhao, H. Cheng, Y. Xia, B. Liu. Angle tracking adaptive backstepping control for a mechanism of pneumatic muscle actuators via an AESO. IEEE Transactions on Industrial Electronics 66(6):4566–4576, 2019. https://doi.org/10.1109/TIE.2018.2860527 [8] Q.-T. Dao, S.-i. Yamamoto. Assist-as-needed control of a robotic orthosis actuated by pneumatic artificial muscle for gait rehabilitation. Applied Sciences 8(4):499, 2018. https://doi.org/10.3390/app8040499 [9] M.-C. Trinh, T.-H. Do, Q.-T. Dao. Development of a rehabilitation robot: Modeling and trajectory tracking control. ASEAN Engineering Journal 12(4):121–129, 2022. https://doi.org/10.11113/aej.v12.17196 [10] P. Beyl, M. Van Damme, R. Van Ham, et al. Pleated pneumatic artificial muscle-based actuator system as a torque source for compliant lower limb exoskeletons. IEEE/ASME Transactions on Mechatronics 19(3):1046–1056, 2014. https://doi.org/10.1109/TMECH.2013.2268942 [11] C.-T. Chen, W.-Y. Lien, C.-T. Chen, et al. Dynamic modeling and motion control of a cable-driven robotic exoskeleton with pneumatic artificial muscle actuators. IEEE Access 8:149796–149807, 2020. https://doi.org/10.1109/ACCESS.2020.3016726 [12] Z. Q. Tang, H. L. Heung, X. Q. Shi, et al. Probabilistic model-based learning control of a soft pneumatic glove for hand rehabilitation. IEEE Transactions on Biomedical Engineering 69(2):1016–1028, 2022. https://doi.org/10.1109/TBME.2021.3111891 [13] C. M. Thalman, M. Debeurre, H. Lee. Entrainment during human locomotion using a soft wearable ankle robot. IEEE Robotics and Automation Letters 6(3):4265–4272, 2021. https://doi.org/10.1109/LRA.2021.3066961 [14] Q.-T. Dao, V.-V. Dinh, M.-C. Trinh, et al. Nonlinear extended observer-based ADRC for a lower-limb PAM-based exoskeleton. Actuators 11(12):369, 2022. https://doi.org/10.3390/act11120369 [15] Y. Wang, Q. Xu. Design and testing of a soft parallel robot based on pneumatic artificial muscles for wrist rehabilitation. Scientific Reports 11:1273, 2021. https://doi.org/10.1038/s41598-020-80411-0 [16] P. Ohta, L. Valle, J. King, et al. Design of a lightweight soft robotic arm using pneumatic artificial muscles and inflatable sleeves. Soft Robotics 5(2):204– 215, 2018. https://doi.org/10.1089/soro.2017.0044 [17] A. Colomé, D. Pardo, G. Alenyà, C. Torras. External force estimation during compliant robot manipulation. In 2013 IEEE International Conference on Robotics and Automation, pp. 3535–3540. 2013. https://doi.org/10.1109/ICRA.2013.6631072 [18] E. Berger, S. Grehl, D. Vogt, et al. Experience-based torque estimation for an industrial robot. In 2016 IEEE International Conference on Robotics and Automation (ICRA), pp. 144–149. 2016. https://doi.org/10.1109/ICRA.2016.7487127 [19] A. Wahrburg, E. Morara, G. Cesari, et al. Cartesian contact force estimation for robotic manipulators using Kalman filters and the generalized momentum. In 2015 IEEE International Conference on Automation Science and Engineering (CASE), pp. 1230–1235. 2015. https://doi.org/10.1109/CoASE.2015.7294266 [20] Y. Lu, Y. Shen, C. Zhuang. External force estimation for industrial robots using configuration optimization. Automatika 64(2):365–388, 2023. https://doi.org/10.1080/00051144.2023.2166451 186 https://doi.org/10.3390/technologies9010008 https://doi.org/10.2147/NDT.S114102 https://doi.org/10.1114/1.1554921 https://doi.org/10.1109/70.481753 https://doi.org/10.1109/TIE.2009.2036632 https://doi.org/10.1016/j.proeng.2011.08.128 https://doi.org/10.1109/TIE.2018.2860527 https://doi.org/10.3390/app8040499 https://doi.org/10.11113/aej.v12.17196 https://doi.org/10.1109/TMECH.2013.2268942 https://doi.org/10.1109/ACCESS.2020.3016726 https://doi.org/10.1109/TBME.2021.3111891 https://doi.org/10.1109/LRA.2021.3066961 https://doi.org/10.3390/act11120369 https://doi.org/10.1038/s41598-020-80411-0 https://doi.org/10.1089/soro.2017.0044 https://doi.org/10.1109/ICRA.2013.6631072 https://doi.org/10.1109/ICRA.2016.7487127 https://doi.org/10.1109/CoASE.2015.7294266 https://doi.org/10.1080/00051144.2023.2166451 vol. 63 no. 3/2023 Neural Network Based Patient Recovery Estimation [21] A. C. Smith, F. Mobasser, K. Hashtrudi-Zaad. Neural-network-based contact force observers for haptic applications. IEEE Transactions on Robotics 22(6):1163–1175, 2006. https://doi.org/10.1109/TRO.2006.882923 [22] N. Yilmaz, J. Y. Wu, P. Kazanzides, U. Tumerdem. Neural network based inverse dynamics identification and external force estimation on the da Vinci research kit. In 2020 IEEE International Conference on Robotics and Automation (ICRA), pp. 1387–1393. 2020. https://doi.org/10.1109/ICRA40945.2020.9197445 [23] Z. Chua, A. M. Okamura. Characterization of real-time haptic feedback from multimodal neural network-based force estimates during teleoperation. In 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1471–1478. 2022. https://doi.org/10.1109/IROS47612.2022.9981662 [24] J. Y. Wu, N. Yilmaz, U. Tumerdem, P. Kazanzides. Robot force estimation with learned intraoperative correction. In 2021 International Symposium on Medical Robotics (ISMR), pp. 1–7. 2021. https://doi.org/10.1109/ISMR48346.2021.9661568 [25] M. Chiako, B. Mahdi, A. Vahid. Muscle force estimation from lower limb EMG signals using novel optimised machine learning techniques. Medical and Biological Engineering and Computing 60(3):683–699, 2022. https://doi.org/10.1007/s11517-021-02466-z [26] B. Siciliano, L. Sciavicco, L. Villani, G. Oriolo. Robotics: Modelling, Planning and Control. Springer London, London, 1st edn., 2009. [27] S. Hussain, S. Q. Xie, P. K. Jamwal. Adaptive impedance control of a robotic orthosis for gait rehabilitation. IEEE Transactions on Cybernetics 43(3):1025–1034, 2013. https://doi.org/10.1109/TSMCB.2012.2222374 [28] R. Uhrig. Introduction to artificial neural networks. In Proceedings of IECON ’95 – 21st Annual Conference on IEEE Industrial Electronics, vol. 1, pp. 33–37. 1995. https://doi.org/10.1109/IECON.1995.483329 [29] T.-Y. Choi, J.-J. Lee. Control of manipulator using pneumatic muscles for enhanced safety. IEEE Transactions on Industrial Electronics 57(8):2815–2825, 2010. https://doi.org/10.1109/TIE.2009.2036632 [30] Q.-T. Dao, V. V. Dinh, C. T. Vu, et al. An adaptive sliding mode controller for a PAM-based actuator. Engineering, Technology and Applied Science Research 13(1):10086–10092, 2023. https://doi.org/10.48084/etasr.5539 187 https://doi.org/10.1109/TRO.2006.882923 https://doi.org/10.1109/ICRA40945.2020.9197445 https://doi.org/10.1109/IROS47612.2022.9981662 https://doi.org/10.1109/ISMR48346.2021.9661568 https://doi.org/10.1007/s11517-021-02466-z https://doi.org/10.1109/TSMCB.2012.2222374 https://doi.org/10.1109/IECON.1995.483329 https://doi.org/10.1109/TIE.2009.2036632 https://doi.org/10.48084/etasr.5539 Acta Polytechnica 63(3):179–187, 2023 1 Introduction 2 Lower Limb Rehabilitation Robot System 3 Human Torque Estimation 3.1 Calculating the torque generated by PAMs (MPAM) 3.2 Estimating the total torque applied to robot joints (MNN) 3.3 Estimation of the patient’s recovery 3.4 Robot impedance control 4 Experiments and results 4.1 Experiment Setup 4.2 Experimental results 5 Conclusion Acknowledgements References