The FES-assisted control for a lower limb rehabilitation robot: simulation and experiment
© Chen et al.; licensee Springer. 2014
Received: 4 May 2014
Accepted: 28 May 2014
Published: 2 October 2014
To design a control strategy for iLeg, an exoskeleton robot developed for lower limb rehabilitation aiming at investigating the feasibility of integrating functional electrical stimulation (FES) with robot-based rehabilitation training, an FES-assisted training strategy combined with impedance control, has been proposed in this paper. Through impedance control, an active compliance of the robot is established, and the patient’s voluntary effort to accomplish the training task is inspired. During the training process, the patient’s related muscles are applied with FES which provides an extra assistance to the patient. The intensity of the FES is properly chosen in order to induce a desired active torque which is proportional to the voluntary effort extracted from the electromyography signals of the related muscles using back propagation neural networks. This kind of enhancement serves as a positive feedback which reminds the patient of the correct attempt to fulfill the desired motion. FES control is conducted by a combination of neural network-based feedforward controller and a PD feedback controller. Simulation conducted using Matlab and the experiment with a spinal cord injury subject and a healthy subject have shown satisfactory results which verify the feasibility of this control strategy.
KeywordsRehabilitation robot FES Impedance control
2Background and literature review
Spinal cord injury (SCI) and stroke are the two main types of central nervous system injury which usually results in motor disorder such as paralysis and hemiparesis, cognitive dysfunction, as well as psychological problems. SCI is mainly caused by various kinds of accidents, while stroke is caused by an interruption of blood flow to the brain or an obstruction within a blood vessel in supplying blood to the brain ,. Rehabilitation is one of the prime treatments for SCI and stroke patients, aiming to provoke the motor plasticity and to actuate these patients to relearn the use of their limbs. According to the rehabilitation theory, the resulting sensory feedback of the patient is associated with the cortical changes that can bring recovery of functional movement during the rehabilitation process so that the functional deficits and the risk of consequential injuries can be minimized -.
Traditional rehabilitation is labor-intensive and requires several therapists to manually help the patient to perform training, especially for lower limb rehabilitation. Therefore, it imposes an enormous economic burden to any country’s health care system . Meanwhile, there are a number of factors which have been found to contribute to faster motor recovery, all of which have not been taken full advantage of due to the lack of rehabilitation services . Modern robotics technology has offered us a more convenient and efficient opportunity to carry out rehabilitation training, known as rehabilitation robot. Rehabilitation robot is a mechatronics system which could be used to replace the physical training effort of the therapists, allowing more intensive and repetitive motions . Since research has identified the treatment intensity as a critical element for successful therapeutic outcomes, the robotic-assisted rehabilitation is likely to increase the training effect ,. What is more, various kinds of sensors installed on the robot feed back the signals of interest, such as the force signal, electromyography (EMG) signal, and heart rate. Thereby, the states of the patient during training can be monitored. By measuring the force or EMG signal, it is possible for the robot to perceive the voluntary effort of the patient and to adjust the training pattern accordingly in order to actuate the participation of the patient ,.
Several training strategies for rehabilitation robot have been presented in recent years. These control strategies can be categorized into two types. The first one is the position-based passive training which is widely used for its simplicity. However, robot based on this training strategy only moves the patient along predefined, fixed trajectories, and the guidance provided by the robot is so strong that it suppresses the voluntary motor control of the patient . Therefore, this strategy is less likely to motivate the patient. The second one is the impedance-based active training. The rehabilitation robot designed for this type executes a task by amplifying human force or supplying the human operator with an assisting force ,. Under this type of control strategy, an active compliance environment between the patient and the robot is established, while the assistant level can be adjusted by the impedance parameters. When the movement of the patient deviates from the predefined trajectory, a restoring force is generated using an appropriately designed impedance and then applied to the patient . Unlike position-based training, impedance-based training is position error-tolerated, because research has emphasized that the kinematic errors generated during movement are a fundamental neural signal that drives motor adaptation .
On of the most commonly used technology for rehabilitation is the functional electrical stimulation (FES), which uses short electrical pulses to generate FES-induced contraction of the paralyzed muscles, and the level of the contraction can be controlled by modulating the intensity of FES , and the therapeutic effect of FES in rehabilitation is known to be increased when associated with a person’s voluntary effort . For this reason, some researchers has integrated FES into robotic-based rehabilitation to improve the training efficiency ,,, in which an extra actuator besides the motor of the robot is available (considering the muscle under FES as a ‘soft motor’). Therefore, the robot-generated assistance can be partially compensated by the FES-induced contraction of the muscle resulting in an increase of the muscle activity. If the level of FES assistance is regulated by the voluntary effort of the patient, a higher degree of functional recovery can be expected ,.
iLeg is a horizontal exoskeleton robot designed for lower limb rehabilitation. To develop a control strategy for iLeg, an FES-assisted training strategy combined with impedance control is introduced in this paper, aiming to achieve two goals. The first one is to create a compliance environment to inspire the voluntary effort of the patient, and the second one is to provide assistance through FES rather than purely through robot. Active compliance is guaranteed by impedance control in order to establish a soft interaction between the patient and the robot. The velocity of the movement depends on the measured voluntary effort. Basically, if no voluntary effort is measured, the rehabilitation robot only provides minimal assistance which is just sufficient to counterbalance the weight of the limb. The FES assistance, which is proportional to the patient’s voluntary effort, is applied to the patient. This kind of enhancement serves as a positive feedback which reminds the patient of the correct attempt to fulfill the desired motion. To ensure that the active torque induced by FES follows the desired torque calculated from the voluntary effort, a combination of an inverse model-based feedforward and a PD feedback controller is implemented to compose the FES controller.
The rest of the paper is organized as follows. In the ‘Methods’ section, the rehabilitation robot is described in detail; the dynamic model of the leg-robot hybrid system is introduced and analyzed, while the model of the FES-stimulated muscle is also given. Then the control strategy of both impedance control and FES control are proposed, and the methods used for estimating muscle torques by system identification process and the method used for extracting voluntary effort by EMG signals are also described. The simulation conducted using Matlab and experimental results are depicted in the ‘Results’ section. Finally, conclusions are drawn in the last section.
3Research design and methods
4.1 Model description
4.1.1 iLeg lower limb rehabilitation robot
4.1.2 Kinematic and dynamic of human leg and iLeg
where , and Mh(q), and Gh(q) are the inertia matrix, the Coriolis/centripetal matrix, and the gravity vector of the hybrid system, respectively. According to Equation 9, there are two types of inputs which contribute to the input torque of the system: the one from DC motor and the one from the muscle contraction.
4.1.3 FES-stimulated skeletal muscle
where fit is the fitness of the muscle, while fit min is the minimum fitness. Time constants for fatigue and recovery are given as Tfat and Trec. Final activation aact is the product of fitness fit and non-fatigue activation a with a constant time delay Tdel. After the maximum torque of the stimulated muscle at certain joint angle and angular velocity are being scaled by the activation aact, the active torque of the stimulated muscle can be obtained.
4.2 Control strategy
4.2.1 Impedance control
where, KP and KI are the proportional and integral gains of the speed controller. is the reference of the angular velocity given by , where J represents the Jacobian matrix.
where dis represents the distance between the actual and desired position at a specific time point; a, b define the shape of the sigmoid function. The task is error-tolerated, but if the endpoint deviates too far from the desired position, the patient will feel harder to maintain the incorrect effort, so he has to make a proper adjustment in order to accomplish the task. From the perspective of the patient, this impedance control provides a virtual channel with the predefined trajectory in its center, in which the motion is partially constrained in the desired direction.
4.2.2 FES control
where J is the Jacobian matrix, and θ represents the angle of Fvol to the predefined trajectory.
As shown in Figure 5, the FES torque control is achieved with the combination of a feedforward controller and a feedback controller. An inverse model of the stimulated muscle and a PD controller are employed and serve as the feedforward controller and the feedback controller, respectively. The advantage of using the combination of these two controllers compared with only using one of them is significant. The delay and highly nonlinear characters of muscle response to FES are easy to cause oscillation when the FES is regulated merely by the feedback controller. On the other hand, the feedforward controller is incapable of dealing with disturbance and eliminating error ,.
where d is the pulse width of the FES, and KP, KD are proportional and derivative gains of the feedback controller, respectively. e represents the error between desired torque calculated in (12) and the actual torque induced by FES.
4.3 FES-induced torque estimation
4.3.1 Hybrid-activated torque
where I i is the inertia moment of the i th link; ksfi and kdfi are the Coulomb and viscous friction of the i th joint.
k s f 1
k s f 2
k d f 1
k d f 2
The RMS error of the estimation torque (Nm)
4.3.2 Voluntary torque
The second step to obtain the FES-induced torque is to calculate the voluntary-controlled muscle torque τvol. EMG signal is a weak electrical potential generated by the muscle cells when these cells are activated , so it has the potential to reflect the level of voluntary intention and can be used to estimate the joint angle or torque -. In this study, EMG signal is also introduced to achieve joint torque estimation. As depicted in the ‘FES-stimulated skeletal muscle’ subsection, the active torque is the product of the contraction dynamics and the activation of the muscle. If the activation is induced by FES, the activation can be calculated using Equations 13, 14, and 15; if the activation is voluntary-controlled, the EMG signal can be utilized as the index of the level of activation. The nonlinear relationship of the contraction dynamics of the muscle is approximated by BP neural networks. For the hip joint and the knee joint, there are six muscle groups involved. They are gluteus maximus (GM), iliopsoas (LP), biceps femoris short head (BFs), rectus femoris (RF), rectus lateralis (RL), and vastus medialis (VM).
where RMS (t) is the RMS EMG signal at time t; y(i) is the i th sample of the raw EMG signal; N is the length of sliding window which contains samples of 200 ms before time t.
The torques of the hip joint and the knee joint as well as the EMG signals are acquired during the robot performing the predefined trajectory, and at the same time, the subject makes random efforts. Ten groups of samples are collected, and leave-one-out cross validation process is carried out: nine groups of the samples are used for training and the rest for validation, then the data set for training and validation are changed; this procedure is executed ten times, which means that every group will be served as validation group for one time. The overall estimation error is the average error of each times.
5.1 Simulation results
The above control strategy is verified using Simulink toolbox of Matlab. The link lengths and the masses are set to be l1=0.5 m, l2=0.45 m, kg, kg, kg, and kg. The parameters to construct the simulation models of gluteus maximus and quadriceps femoris are chosen according to ,. For the leg press exercise, the patient is requested to accomplish the motion following a predefined trajectory substantially, and the predefined trajectory is a linear path with the start point set as (0.5, 0.1), and target point set as (0.8, 0) in the Cartesian space coordinates. The patient is encouraged to accomplish the task within about 10 s.
where t represents time, and θ is the angle of the desired path to the horizontal.
The FES control is conducted first by determining the desired torque induced by FES. The idea is to amplify the voluntary effort towards the target point. Using Equation 21, the force component of the voluntary effort parallel to the predefined trajectory is calculated, amplified, and then translated to the desired active torque for FES control in joint space. The blue arrows in Figure 13b represent the desired active force expected being induced by FES. All of them point to the same direction, the direction of the target point. This indicates that the FES assistance is not only proportional to the voluntary effort but also provided in the correct direction. The blue dash line in Figure 13a shows the trajectory of the endpoint when the same voluntary effort is made, but this time, no FES assistance is applied. The comparison of these two trajectories verifies the contribution of FES-induced torque which assists the patient during the leg press task by enhance the ‘correct part’ of the voluntary effort.
5.2 Experiment results
The proposed control strategy is also verified by the experiment conducted on iLeg lower limb rehabilitation robot. The method described in ‘FES-induced torque estimation’ subsection is utilized to obtain voluntary torque τvol and FES-induced torque τfes. An SCI subject (male, age 65) and a healthy subject (male, age 28) are invited to participate in the experiment. The SCI patient has been injured in T11 for 16 months, and he remains with partial muscle force. The speed control of the robot is carried out by the PID controller of the motor drivers. The stiffness and damping parameters in Equation 18 are set as Kd=diag(2,500;2,500) and Bd=diag(2,000;2,000). is set as zero. Considering that the SCI subject’s motion ranges of his lower limb are limited, we decrease the length of the predefined trajectory, and set the start point to be (0.5, 0.1) and the target point to be (0.7, 0).
At the pre-training stage, the tolerance of the subject applied with FES is tested. For each stimulated muscle, the pulse width of FES is firstly fixed at 700 μ s, and the amplitude of FES is increased from 15 mA until obvious muscle contraction being observed. Then the amplitude of the FES is fixed during training, and the intensity of FES is regulated by adjusting the pulse width through FES controller. To construct the BP neural networks which serve as the FES feedfoward controller, the muscles are applied with FES of random intensity while the robot running in the predefined trajectory. The pulse width d of the FES uniformly distributed on the interval [ 150 500] µs.
In this paper, an FES-assisted training strategy combined with impedance control for the lower limb rehabilitation robot is presented and the controller used to accomplish this task is developed, aiming to achieve two goals. The first one is to create a compliance environment to inspire the voluntary effort of the patient, and the second one is to provide assistance through FES rather than purely through robot. Impedance control is ideal for establishing active compliance of the robot, and through the mechanism of impedance control, the patient has to make effort to accomplish the task rather than passively waiting the assistance from the robot so that it increases the participation of the patient’s voluntary effort. Two muscle groups are stimulated with FES to provide extra assistance to the patient during the training process. The intensity of the FES is properly chosen so as to induce the desired active torque which is proportional to the voluntary effort of the patient. The control of active torque of FES-stimulated muscle is achieved using the combination of a neural network-based feedforward controller and a PD feedback controller which have been proven to be competent for this task. The dynamic parameters of the leg-robot hybrid system are estimated using system identification method; the voluntary torques are also estimated according to the EMG signals acquired from the related muscle groups. These two methods are utilized to obtain the actual FES-induced torque so that the FES control can be accomplished. Both simulation conducted in Matlab and experiments conducted in iLeg reveal satisfactory results, from which the feasibility and effectiveness of the proposed control strategy are verified. In the future, more SCI and stroke subjects will be recruited to carry out a 3 to 6-month training session. During this follow up study, we will evaluate whether the proposed control strategy is capable of improving the rehabilitation effects.
biceps femoris long head
biceps femoris short head
degrees of freedom
functional electrical stimulation
root mean square
This work was supported in part by the National Natural Science Foundation of China (Grants 61225017, 61175076) and the International S&T Cooperation Project of China (Grant 2011DFG13390).
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