Development of a Series Elastic Tendon Actuator (SETA) Based on Gait Analysis for a Knee Assistive Exosuit

Abstract

An exosuit is a wearable robot that assists the muscular strength of a human that wears it by using multiple wires with similar functions to human muscles. This study focuses on the development of a series elastic tendon actuator (SETA) for the actuation of an exosuit. A gait analysis was performed for walking on stairs to deduce the design requirements of SETA, and the necessary performances were then determined based on these requirements. The SETA is designed to assign compliance to rigid wires using linear springs. The deformation in linear springs generated during tension was measured through an encoder to calculate the human robot interaction (HRI) force. By utilizing the HRI force as feedback of an admittance controller, the SETA was capable of providing wire tensions required by an exosuit. The performance of the SETA was verified through series elastic component (SEC) deformation and force control experiments. The SEC deformation increased from 0 to 3.86 mm when the wire tension increased from 0 to 100 N. This force controller demonstrated a slight vibration owing to the mechanical properties of the springs constituting the SEC during the step input; however, the value gradually converged to 100 N. The developed SETA was applied to an exosuit system for supporting knee strength of the elderly when walking on stairs.

1. Introduction

Wearable robots are systems that have been developed for the purpose of assisting humans’ muscular strength in various situations [1]. They can be categorized into exoskeletons and exosuits depending on the mechanism type. An exoskeleton is effective for transporting heavy objects exceeding physical capability or supporting the weight of the wearer, as it includes various types of robotic mechanisms integrated with the human body [2,3,4,5]. However, an exoskeleton has a lower degree of freedom (DOF) than the body of the wearer, while the mass and inertia of the mechanism may affect one’s balance when walking [6,7]. Thus, wearable robots in the form of an exosuit have recently been widely investigated in order to overcome such problems [8,9,10,11,12,13,14]. An exosuit uses multiple actuators with similar functions to human muscles to directly supply torque to human joints, thus assisting the power of the user [13]. Although these systems entail structural limitations for supporting the weight of the wearer or supplying great power, they can be beneficial for workers exposed to prolonged physical loads at industrial sites or the elderly and people with disabilities requiring assistance in everyday life [8].

The main role of a wearable robot is accurate delivery (in terms of magnitude and timing) of the actuator modules’ torques applied to the wearer’s joint [15,16,17]. Wearable robots require force control for providing natural power assistance to the wearer [18]; therefore, an actuator module must be designed to enable interactions with humans [19]. For example, Zhang developed a series elastic actuator (SEA) for a hip exoskeleton including a clutch that heightens mechanical stability [16,20]. SEAs have been widely adopted in human orthotics/exoskeletons [21,22,23,24,25]. An elastic element of SEAs provides several unique characteristics including high force control accuracy, low mechanical impedance, large frequency bandwidth, resistance to impact loads, and passive, mechanical energy storage [26]. However, because exosuits do not use mechanisms involving rigid bodies, unlike exoskeletons, it is difficult for them to apply the mechanism of existing SEAs. Moreover, exosuits provide tensile force to the wearer’s body through well-defined load paths by textile architecture [27]. Therefore, research must be conducted on actuator modules capable of delivering force while having flexibility when developing exosuits. The bowden cable transmission is the most widely employed solution in exosuit applications owing to its advantage in terms of durability, weight, safety, and flexibility [28]. Exosuits incorporate soft components, therefore, they have extremely low inertia and eliminate the challenges associated with joint misalignments [29]. However, this feature also makes actuator modules and sensors more difficult to be mounted [27]. Various studies have been conducted on actuator modules for exosuits to overcome such limitations.

Ding et al. developed the bowden cable actuator box for exosuits [30]. The inner cable is attached to a ball-screw actuator carriage that can drive the inner cable back and forth. At the distal ends of the bowden cable, there is a load cell for measuring the actual force applied to the exosuit and wearer. However, because this type of actuator module is extremely rigid, it cannot have compliance resembling human muscles, and, thus, requires improvements for user safety. Cappello et al. developed the bowden cable transmission having a clutch function to improve safety, and further arranged series elastic elements outside the bowden cable transmission to assign compliance between the human and exosuit [31]. This system, however, has spatial limitations when designing an exosuit because series elastic elements are placed outside the actuator module. Accordingly, we developed a series elastic tendon actuator (SETA) for exosuits in a previous study [27]. This actuator module was designed with series elastic components placed inside the module to be easily applicable to exosuits. Torsion springs connect the motor shaft and two pulleys. Thus, the SETA can assign compliance to rigid wires, and the force between human and exosuit can be calculated by measuring the deformation of torsion springs using an encoder. However, the spring constant is difficult to manage when fabricating torsion springs, and the assembly is challenging because the mechanism for assigning a preload is complicated.

This study proposes a new type of SETA that uses a linear spring instead of a torsion spring. The SETA employs a mechanism where wire tension generated by the human robot interaction (HRI) induces linear deformation in a linear spring. This deformation is then measured using an encoder and used as feedback for a controller supporting the strength of the user. The developed SETA was applied to an exosuit system for supporting knee strength of the elderly when walking on stairs (Figure 1) [8]. The remainder of this paper is organized as follows. The design requirements for the new type of SETA are presented in Section 2. In Section 3, we describe the development of SETA including mechanism and control. Section 4 presents the experimental evaluation and its results. A discussion and conclusion are presented in Section 5.

2. Design of SETA

2.1. Experimental Environment for Gait Analysis

A human gait analysis was performed for deducing the design specifications of the SETA. The description of anatomical human motion used in medicine explains the movement between the bones of each joint in the anatomical planes. The anatomical planes that define the perpendicular axes around which rotation occurs are frontal, transverse, and sagittal planes [32]. Most of the gait occurs along the sagittal plane, therefore, the movements in frontal and transverse planes are distinguished by sagittal plane functions. It is reasonable that the considerations based solely on kinematics and kinetics in the sagittal plane should capture dominant characteristics of knee joint function during the gait [33]. Therefore, the design of the SETA focused on the analysis of data of the sagittal plane.

Figure 2 illustrates the experimental environment for the gait analysis. For this experiment, we employed a motion capture camera system (VICON MX–T160, Vicon Motion Systems Ltd., Oxford, UK) and a ground reaction force measurement system (AMTI–OR6–7–2000, Advanced Mechanical Technology Inc., Watertown, MA, USA). In gait analysis, angle data are typically collected via human video motion capture. Torque and power data are calculated by estimating limb mass and inertia and applying dynamic equations to motion data. In this experiment, subjects ascended and descended a three-step staircase, and kinematic data were collected for one stride between the first and third steps.

2.2. Gait Analysis Results

The experiments were conducted with 12 subjects. All the subjects were men in their twenties, their average height was 174.4 cm (standard deviation: 4.97 cm), and their average weight was 71 kg (standard deviation: 5.03 kg). Figure 3 shows the mean and standard deviation (SD) of the angle, moment, and power of the knee joint measured when walking on stairs. The moment and power of the knee joint were normalized by body weight (BW) and presented for 100% of the gait cycle. Consequently, the knee flexion ranged from 3.1° to 92.7° during the stair ascent and descent. At this time, the maximum moment was required to be 0.73 Nm/kg. The knee joint required positive power (peak value of 2.04 W/kg) in the stair ascent and negative power (peak value of −2.34 W/kg) in the stair decent.

2.3. Design Criteria

The SETA is an actuator module for an exosuit that can assist the muscular strength of elderly people when walking on stairs. To determine the design requirements of the SETA, we made the following assumptions regarding the exosuit conditions: (1) The user’s weight is 70 kg, and the exosuit does not support the weight; (2) the exosuit assists 10% of the user’s joint moment when walking on stairs; and (3) the knee joint has one axis of rotation, and its radius is 60 mm.

The exosuit developed in this study does not support the weight of the wearer and robot. To design the SETA, peak values of the angle, moment and power were analyzed and are shown in

Table 1. Peak values of knee joint parameters during stair ascent and descent.

Parameters	Max. (Mean/SD)	Min. (Mean/SD)	Unit
Angle	92.7/11.7	3.1/0.7	°
Moment	0.73/0.203	−0.29/0.137	Nm/kg
Power	2.04/0.708	−2.34/0.945	W/kg

. Here, moment and power were reflected the user’s weight (70 kg) assumed previously.

2.4. Required Performance

The design requirements of the SETA can be deduced by assuming the weight, pow-er–assist ratio, and knee-joint radius of the wearer, as shown in

Table 2. Required performance of series elastic tendon actuator (SETA).

Requirements	Value	Unit
Maximum wire tension	100	N
Maximum wire speed	0.6	m/s
Wire operating range	100	mm

. When a person weighing 70 kg walks on stairs, the knee joint requires a moment of at least 51.1 Nm; the SETA wire must be capable of generating tension corresponding to 10% of this moment. The wire tension is calculated to be approximately 85.2 N when the knee joint radius was assumed to be 60 mm. We set the maximum wire tension of the SETA to 100 N considering deviations among users. The angular velocity of human knee joint can be calculated based on the relationship between the power and moment of the gait analysis results where the maximum angular velocity is approximately 6.74 rad/s. The wire speed of the SETA requires at least 0.4 m/s when the radius of the knee joint is reflected. Therefore, we set the maximum wire speed of the SETA to 0.6 m/s considering deviation by the user. In the gait-analysis results, the knee flexion ranged from 3.1° to 92.7° during the stair ascent and descent. Therefore, the operating range of the human knee joint is 89.6°, and the SETA must be capable of moving the wire by at least 93.8 mm. Hence, we set the wire operating range of the SETA to 100 mm by adding a small margin to the calculated value.

3. Development of SETA

3.1. Design Concept

The SETA must be capable of providing a certain amount of moment through the front and rear wires during flexion and extension of the knee joint. Furthermore, the HRI force should be acquired by measuring the tension of each wire for controlling an exosuit. Therefore, this study proposes a SETA mechanism capable of measuring tension of each wire while generating the driving power for the front and rear wires according to the driving direction of a motor.

Figure 4 illustrates the design concept of the SETA. The wires of the SETA can have compliance through a linear spring. The wires made of rigid bodies can have a small margin when body joints are moved due to compliance; then, the HRI force can be measured by measuring the deformation of the linear spring. One motor can operate front and rear wires in which two series elastic components (SECs) exhibit straight motions along linear shafts when the motor rotates. The two SECs are configured in a closed loop by a drive wire and a guide wire, which makes pushing and pulling the SECs possible. SECs are structured such that four compression springs connect the input and output parts. These springs are assembled to receive a preload corresponding to 50% of maximum deformation. The input part receives the driving power from the motor through a drive wire, while the output part outputs the driving power through the front or rear wire. The HRI force generates tension in wires, and the deformation in springs due to such tension is measured using an encoder.

3.2. System Sizing

The performance of SETA depends on the combination of motor power, gear reduction, and pulley radius. We determined the combination of motor, gear, and pulley that satisfies the required performance deduced from the gait analysis. Gait analysis data were used to approximate the force and velocity required by the system [34]. We first selected the motor to be used, and then proceeded with system sizing by adjusting the gear reduction and pulley radius. The SETA system was configured using a 50 W motor. We selected the components so that the speed and tension of the SETA outweighs the required performances presented in Table 2.

Table 3. Details of series elastic tendon actuator SETA components.

Motor	$\mathrm{Supply}\mathrm{voltage}(U_m$)	36 V
	$\mathrm{Nominal}\mathrm{current}(I_N$)	1.71 A
	$\mathrm{Starting}\mathrm{current}(I_A$)	28.6 A
	$\mathrm{Torque}\mathrm{constant}(k_m$)	46.1 mNm/A
	$\mathrm{Speed}\mathrm{constant}(k_n$)	207 rpm/V
Gear	$\mathrm{Reduction}(i_G$)	30
	$\mathrm{Efficiency}({\eta }_G$)	81%
	$\mathrm{Maximum}\mathrm{continuous}\mathrm{moment}({\tau }_{G_{max}}$)	7.5 Nm
Pulley	$\mathrm{Radius}(r_P$)	50 mm

presents the detailed information of the selected components.

Figure 5 displays the results of the SETA system sizing in which the tension and speed of the front/rear wire are presented along with the gait-analysis results. In the design criteria, we calculated the wire tension and wire speed required performances of SETA. In this graph, stair ascent and stair descent represent the calculated required performance parameters of the SETA. As mentioned previously, we only reflected 10% of the required knee joint moment. The SETA was confirmed to have been configured where the gait analysis results are present within the continuous duty zone with a sufficient margin. Here, the continuous duty zone is determined based on the speed–tension and continuous tension lines of the SETA. The speed–tension line is the relationship between speed ($v_T$) and tension ($F_T$) for the output wire of the SETA as defined in Equation (1). Here, $v_{0,T}$ is the no-load speed of the wire, reflecting gear reduction ($i_G$), pulley radius ($r_P$), motor speed constant ($k_n$), and motor supply voltage ($U_m$). $F_{H,T}$ is the stall force of the wire, reflecting pulley radius ($r_P$), motor torque constant ($k_m$), motor starting current ($I_A$), gear reduction ($i_G$), and gear efficiency (${\eta }_G$).

$$v_T=v_{0,T}-\frac{v_{0,T}}{F_{H,T}}\cdot F_T$$

(1)

where, $v_{0,T}=\frac{2\pi ·r_P·k_n·U_m}{60·i_G},F_{H,T}=\frac{k_m·I_A·i_G·{\eta }_G}{r_P}$.

In addition, the continuous tension line ($T_c)$ is the threshold of the wire tension at which the gear constituting the SETA can continuously operate, and can be estimated using Equation (2). Here, ${\tau }_{G_{max}}$ is the maximum continuous moment of the gear.

$$T_c=\frac{{\tau }_{G_{max}}}{r_P}$$

(2)

3.3. SETA Design

As shown in Figure 6, the SETA was designed using the selected motor, gear, and pulley. Figure 6a depicts the mechanism of the designed SETA module. The SETA module consists of a right drive unit for driving the right leg of an exosuit, a left drive unit for driving the left leg, and a unit assembly part. We used two drive units and a unit assembly part to modularize the SETA, thus reducing the weight and volume of the system. One drive unit has two SECs and delivers the generated tension to the front or rear wires depending on the driving direction of the motor. Each SEC is designed to slide 100 mm along the linear shaft. Figure 6b shows the detailed mechanism of SECs; they have input and output parts connected with four linear springs. SECs are designed such that linear springs are compressed by 5 mm during assembly, while the input and output parts are aligned at the point of balance of power generated by springs. The spring constant of each spring is 6.54 N/mm, while the spring constant of SECs of the four springs is 26.16 N/mm. SECs are designed with up to ±5 mm deformation by the HRI force, which is measured using an encoder. Figure 6c shows the SETA module and electric components fabricated for the exosuit. The weight of the fabricated SETA module including the lithium polymer battery (22.2 V, 10 Ah) is 4.9 kg.

3.4. SETA Control

The SETA requires force control for power assistance of a wearer using an exosuit. To control the SETA, this study implemented a position-based admittance controller in which the HRI force is required as an input. In general, an admittance controller is a cascade having inner motion and outer force loops [35].

Figure 7 shows the block diagram of an admittance controller for force control in the SETA. $F_d$ is the desired tension for power assisting an exosuit user and is set by the user. $F_{HRI}$ is the HRI force generated from the relative difference in motions between the human and exosuit, and is used as feedback in the controller. $F_{HRI}$ can be calculated using Equation (3). Here, $\Delta x_s$ is the deformation of SEC measured with an encoder, while $k_S$ is the spring constant of SEC determined during the design process, which is equal to 26.16 N/mm.

$$F_{HRI}=k_s·\Delta x_s$$

(3)

An admittance controller converts the force error into $x_d$ (desired position) to input in an inner position controller. The traditional PID controller is used as the position controller. The admittance of this controller is defined in Equation (4) in the Laplace domain.

$$I\left(s\right)=\frac{1}{m_v{s}^2+b_{v}s+k_v}$$

(4)

Here, $m_v$, $b_v,$ and $k_v$ represent virtual inertia, damping, and stiffness, respectively. An internal position controller compensates the dynamics and friction of an actuator; thus, an admittance controller enables an exosuit wearer to feel virtual inertia, damping, and stiffness [35]. We set the saturations of x_d to ensure the movement stops when hardware limitations of the SETA were reached. Accordingly, damage to exosuits and risk of users can be reduced by defining the system position and power limitation.

4. Results

4.1. Experimental Setup

The SETA was developed to control power and has output wires capable of generating tension of up to 100 N for utilizing a knee assistive exosuit. SEC deformation and force control experiments were conducted to evaluate whether the developed SETA can be applied to exosuits.

Figure 8 displays the testbed designed for the experiments, which consists of the SETA module, main controller (NI cRIO-9053, NATIONAL INSTRUMENTS CORP., Austin, TX, USA), motion controller (Maxon EPOS4 Compact 50/5, Maxon motor, Alpnach, Switzerland), power supply (RSP-1600-24, MEAN WELL, Taipei, Taiwan), loadcell (DBCM-30, CASKOREA, Seongnam, Korea), loadcell amplifier (ST-AM100, CASSCALE KOREA, Seoul, Korea), pulley, and pulley pin. The front and rear wires of the SETA are linked with the testbed pulley, which are adjusted by tension adjusters to prevent the SETA linkages from loosening. We considered mechanical aspects for accurately measuring wire tension with a loadcell. The wire tension acts as a pressing force on the loadcell. We calibrated the loadcell prior to the experiments for accurate wire tension measurements. All experiments were repeated 10 times under the same conditions while using the pulley and pin to firmly fix the testbed.

4.2. SEC Deformation Experiments

The HRI force generates tension in the SETA wires, which causes the SECs of the SETA to deform. The SEC deformation experiments were conducted to verify the linearity between wire tension and SEC deformation. For the experiments, wire tension was gradually increased from 0 to 100 N to measure SEC deformation. The wire tension was measured with a loadcell of the testbed, while the SEC deformation was measured with an encoder attached to the SEC. Figure 9 shows the results of the SEC deformation experiments.

Figure 9a shows the results of measuring SEC deformation with respect to changes in wire tension. The calculated deformation is based on the spring constant of SEC (26.16 N/mm) while the measured deformation is from the SEC encoder. Figure 9b shows the mean and standard deviation of errors between calculated and measured deformations. The experimental results showed that the SEC deformation increased from 0 to 3.86 mm fairly linearly when the wire tension was increased from 0 to 100 N. In addition, the mean value and standard deviation of deformation error increased as the wire tension increased. However, the deformation error was less than ±0.1 mm, which is extremely small, when the wire tension was between 0 and 80 N, and did not exceed ±0.24 mm even when the wire tension was above 80 N.

4.3. Force Control Experiments

Exosuits require force control to provide power assistance for the wearer; therefore, the SETA must be verified with regards to its force control performance. Therefore, experiments were conducted to measure response and error when the ramp and step signals were inputted to the force controller of the SETA. The measured tension in this experiment is the HRI force calculated by measuring the SEC deformation.

Figure 10 presents the experimental results of measuring response and error when a ramp signal was inputted as the desired tension of the SETA to reach 100 N after 1.5 s. The SETA was controlled by estimating the desired tension using the developed force controller during which the control error did not exceed 2.5 N.

Figure 11 presents the experimental results of measuring control response and error when the step signal of 100 N was inputted. We verified that 100 N was reached after 0.05 s when a step signal of 100 N was inputted in the SETA as the desired tension, and the value was controlled to converge to 100 N after a slight vibration. The electromechanical time delay of human muscles is approximately 0.01–0.1 s [36], therefore, the force controller of the SETA is applicable to exosuits in terms of response speed. The measured vibration was generated due to mechanical characteristics of the springs constituting the SEC, and the discontinuous input such as step and impulse provided to a controller may pose risks to an exosuit wearer. Therefore, the force controller of the SETA must be applied with improvements on suppressing vibrations caused by discontinuous inputs.

5. Conclusions

This study proposed a tendon actuator applied with SEA technology to be used in an exosuit system for assisting power in the knee joint when walking up and down the stairs. Exosuits require force control for providing natural power assistance to users; therefore, the SETA was developed with force control by measuring the force generated from the HRI. A gait analysis was performed in this study for deducing the design requirements of the SETA. Further, the required performance parameters of the SETA, including wire tension, wire speed, and wire operating range were determined based on the analysis results. Furthermore, a new mechanical concept of the SETA applied using a linear spring was proposed to overcome the drawbacks of the conventional SETA applied with a torsion spring. The SETA can provide a certain amount of moment required when the human knee joint moves through front and rear wires; the HRI force generated during this process can be acquired by measuring the deformation in linear springs. We also implemented an admittance controller that uses the measured HRI force as feedback to control the tension in wires as the desired tension set by users.

A testbed was fabricated to verify the performance of the developed SETA, and SEC deformation experiments, as well as force control experiments, were performed. The experimental results showed that the SEC deformation increased from 0 to 3.86 mm when the wire tension increased from 0 to 100 N. The developed force controller had the maximum control error of up to 2.5 N for the ramp input. This controller demonstrated a slight vibration due to the mechanical properties of the springs constituting the SEC during the step input, but the value gradually converged to 100 N. In future research, the force controller of the SETA will be further improved to suppress the vibration caused by discontinuous input, which will ultimately improve the safety of exosuit systems.