1. Introduction
The use of compliant actuators is often associated with safe human–machine interaction, the reduction of peak torque, peak power, and energy consumption [
1,
2,
3]. Actuators with additional elasticity activatable via a clutch, as an extension of the actuators with constant, permanently-engaged springs, are moving into focus [
4]. Various approaches for using parallel elastic actuators (PEAs) have been introduced. Minimizing power consumption for the performance of periodic tasks is of great interest. A possible option for this is the addition of Parallel Elasticities (PEs). This applies generally to robots and particularly to all automated applications where a proper torque-angle profile is to be achieved. It was shown in an experiment with a Clutched PEA (CPEA) for use on a robot that the efficiency of the drive can be increased by 55%, whereby the comparison system recuperates the energy electrically [
5]. The application of PEAs in prosthetics has already proven successful with prototypes. The interaction between human and machine can be improved by optimizing the stiffness and foot alignment to the walking situation [
6]. Grimmer et al. showed in a simulation study that the energy consumption and the peak power are reduced by a PEA for the ankle joint over a range between 0.5 m/s and 2.6 m/s [
7].
Furthermore, there are prototypes including a PE that support the knee [
8]. Liu et al. developed a switching PEA, where the PE is activated in the stance phase to recycle energy and support the body weight, especially for the stance phase of robot legs during running. The actuator is designed for the knee, and it is not a motion support system for humans [
9]. A PEA for the hip was also presented for force enhancement and support in industrial applications [
10]. The PEAs are particularly interesting for active orthoses and exoskeletons of the lower limb, since the most important task, the upright gait, is a periodic process. It has been demonstrated simulatively that the Root Mean Squared (RMS) power consumption can be reduced by up to 61% by the insertion of PEs. At the same time, the drive torque provided by the active part of the actuator decreases by up to 66% [
11]. This can result in smaller actuators and batteries. There are further independent experimental results confirming the reduction of energy consumption by PEs during gait [
12,
13].
A disadvantage of the PEA is that it can have a negative effect on the energy requirement in the case of a non-cyclical positioning task. This can be bypassed by the switchable deactivation of the elasticity or by a dynamic adjustment of the equilibrium point [
14].
It is important for the design of an actuator to know which torques and speeds are to be assumed. Maximum torques for the knee, normalized with the subject’s weight, are set to 0.86 Nm/kg at a gait speed of 1.6 m/s [
15]. The maximum normalized knee torque at gait speeds of around 1.2 m/s is 0.38 Nm/kg–0.56 Nm/kg depending on the posture. Under the same conditions, the normalized hip torque varies from 0.82–0.94 Nm/kg [
16]. Actuators for hip support have been developed elsewhere [
17,
18,
19,
20,
21,
22,
23].
Table 1 summarizes the existing design for hip actuators, including PEA, RA (Rigid Actuator), SEA (Serial Elastic Actuator), cRSEA (clutched Rigid Series Elastic Actuator), and MAACEPA. In the summary, the torque at 100% support is between 18 Nm and 68.6 Nm, and the nominal velocity is between 25 rpm and 84.7 rpm. So far, no actuator prototype has been published that is designed as a CPEA for full support in hip rehabilitation.
An actuator is presented in this paper that has been designed for the hip joint of an exoskeleton or active orthosis. The hypothesis of this paper is that energy demand and peak load values can be reduced by using a PEA at the hip. The second section of this paper presents the CPEA with its functional structure, a model, and the prototype developed. In the third section, the actuator control including cascaded and iterative learning control are explained. In the fourth section, the procedure for the experimental validation for a step response and gait trajectories of the hip is presented. Subsequently, the experimental results are discussed. The paper closes with a conclusion.
4. Experiments
The step response of the cascaded system was recorded to examine the actuator with cascaded control. Two minutes of gait at 1.1 m/s on the treadmill were recorded in the motion laboratory. The data regarding the optimal spring from the paper by Wang et al. [
11] were confirmed by evaluating the gait data in Visual3D (C-Motion Inc., Germantown, MD, USA). As a later input of the system, the positional progression of the hip joint was determined by a Fourier synthesis. This allows a periodic and reproducible reference sequence to be generated. We recall that any periodic function can be represented by a sum of weighted and shifted cosine signals in the form:
where
is the magnitude,
the frequency and
the phase shift. The determined parameters of the Fourier synthesis are listed in
Table 4.
An averaged angle and torque trajectory from Visual3D measurement data was used to determine the spring and the preload angle optimally. The method of calculation was based on the procedure described by Wang et al. [
11]. The torque and joint angle profile is shown in
Figure 8. The joint torque of the hip in the sagittal plane is plotted over the angular position of the hip joint. To calculate the optimum spring for a complete gait cycle, the stiffness was obtained by linear regression [
31]. The spring characteristic curve is defined by:
The solution to Equation (
13) was determined using the Curve Fitting Tool in MATLAB. For the gait data selected, the preload angle
was about 20
, and the spring rate was about K
Nm/rad. The spring determined is inserted into the profile in
Figure 8.
The torque showed a hysteresis behavior in relation to the position
. Some reasons for this phenomenon can be identified. For the hip, two arcs of motion can be observed. On the one hand, for the extension in the stance phase, the maximum extension was reached right before the swing phase. On the other hand, this is the swing phase in which the hip flexes [
24]. As a result, the flexion and extension of the hip required an individual dynamic model. In stance and swing phase, maximum speed was approximately 1.2 rad/s and 2.3 rad/s respectively for a velocity of 1.1 km/h. Besides, the inertial torque was dependent on the acceleration and the current mass moment of inertia, which changed significantly during a gait cycle. This justifies why the torque characteristic showed the hysteresis behavior. Even if the tendency of the spring effect was nearly evident over the entire torque and joint angle profile, it could be argued why the coefficient of determination of the approximation was only 60.6%.
Experimental Setup
The test bench was set up according to the topology shown in
Figure 9 to perform the experiments. The spring was deactivated or activated by the switching agent in the experiments; a self-made relay board was built for its control. Current and speed controllers were integrated into the motor controller. The MLB was selected to implement the superimposed position control and the ILC. The values measured were recorded via the connection between the computer and the MLB.
The mechanical structure of the test bench during the experiments is shown in
Figure 10. The actuator CPEA (motor (1) and the PE with clutch (2)) were attached to an aluminum profile frame. Actuator output (3) and shaft (5) were connected by an Oldham coupling (4). The CPEA cross-roller bearing was supplemented by a floating bearing (6) (bearing block PBT25, Misumi, Koto, Tokyo, Japan) close to the load. During the tests, the actuator was equipped with a load pendulum (7) with a lever arm of 0.4 m and a mass of 5 kg, and the mass moment of inertia was J
m
kg, an approximation of the leg in the swing phase, when the thigh and the lower leg were considered as point masses [
25].
Figure 10 shows the test bench with mounted CPEA and load.
Figure 11 shows the load at different positions (0
, 10
, 20
, and 30
) during the experiment. One of the two coil springs was visible at this angle, and the greatest elongation in this experiment was only about half of the maximum allowed elongation of the spring. By reducing the diameter of the cable drum of the actuator, the range of rotation would increase, so that the spring constants would decrease.
5. Results and Discussion
The results of the step response and the controlled operation with a hip trajectory for 1.1 m/s follow. The ILC was only applied to the gait trajectories. For the step response, the cascaded control was applied as it was not a cyclic task. First, the step response is shown in
Figure 12.
The set point was reached after about 0.6 s with an input step of 20 to the cascaded controlled actuator without parallel springs. The motor allowed a 13-fold current overload at start-up, and the collusion torque of the gearbox was 98 Nm. For the safety of the gearbox, the over-current in the motor controller was limited accordingly to 8 A (twice the nominal value). The maximum torque of the motor limited the minimum response time. In the next paragraph, the experiments with reference trajectories of the hip are presented.
The angular course of the ILC-controlled actuator with PE and without elasticity was shown in this experiment, while they can hardly be separated in
Figure 13. The ILC did not work in the first cycle; therefore, the control deviation was larger. Since the load is a pendulum, and thus a non-linear load (see Equation (
8)), the controller was optimized for a particular operating point. Without ILC, this can lead to larger control deviations if the operating point is changed. By readjusting the controllers, a better working cascaded controller could be found especially for this task. Adaptive adaptation of the controllers would improve the disturbance transfer function in a test environment with stochastic disturbances. The ILC achieved a highly similar system response for both configurations for this input function. As can be seen from the second cycle onwards in
Figure 13, the error was reduced significantly. The root mean square error (RMSE) was calculated to evaluate the improvement of the control error:
where
n = 13,247 is the number of measurement samples during one gait cycle. The iterative improvement of the RMSE during experiments is listed in
Table 5.
It should be noted that the angle discretization during the experiment was 0.11°. By comparing the RMS errors of both configurations, it can be shown that the angle profile can be compared with and without PE, since the motion task was executed with identical accuracy. Thus, different characteristic values for the actuator with and without PE can be compared directly.
The motor current and the motor torque are important selection parameters for an electric motor. Therefore the current is the first metric of our analysis. The peak current at the reference trajectory for the hip has been reduced from 7.0 A to 5.2 A in the experiment, as shown in
Figure 13.
The motor power during the tests is shown in
Figure 14. When dimensioning the motor, the maximum power consumption was another selection criterion. The maximum power consumption was reduced from 94.7 to 71.1 W (24%) for the hip reference trajectory. The average RMS power and the energy consumption per step were important for the dimensioning of the entire system with battery or power supply. The RMS power was reduced from 26.9 to 19.1 W (29%) by using PE. The quantity of energy per step was reduced from 18.4 to 14.9 Ws (19%). The PE in the motion tests with the hip trajectory on the test bench reduced all characteristic specification values significantly. To summarize, the relative improvements of the characteristic specification values are shown in
Figure 15.
A reduction of the characteristic values was important in dimensioning the actuator, so that a smaller motor could be selected through this reduction and the gearbox could be designed smaller through the resulting reduced torques. In the long run, a portable power supply (battery) can be made smaller, potentially saving much weight in the overall design. A disadvantage that should be mentioned is that the mechanical spring with its mechanism was an extra weight compared to a rigid actuator. In our design, the additional weight due to the PE was between 380 and 690 g, depending on the spring rate desired. In order to give an impression of the component weight, the engine selected is available in a smaller configuration with about half the torque, which weighs 320 g less. This variation would at the same time reduce the axial length by 12 mm.