An illustration of the assumptions and corollary. Link A (blue) represents robot links and link B (red) represents human limbs (thigh and shank). A spring–damper system connects the two, simulating a compliant human–robot interaction. is the load-side stiffness and is the load-side damping coefficient: a realistic pHRI model with human–robot connections on two links, joint misalignment, and a 6DOF spring–damper interface; a pHRI model in the sagittal plane only (Assumption 1) and with human–robot joint alignment (Assumption 2), resulting in a single-DOF spring–damper interface on both links; and the pHRI model used in this work, with two-point human–robot connection simplified to a single-point connection and an increase in the effective compliance to account for the effects of the missing connection point.
An illustration of the assumptions and corollary. Link A (blue) represents robot links and link B (red) represents human limbs (thigh and shank). A spring–damper system connects the two, simulating a compliant human–robot interaction. is the load-side stiffness and is the load-side damping coefficient: a realistic pHRI model with human–robot connections on two links, joint misalignment, and a 6DOF spring–damper interface; a pHRI model in the sagittal plane only (Assumption 1) and with human–robot joint alignment (Assumption 2), resulting in a single-DOF spring–damper interface on both links; and the pHRI model used in this work, with two-point human–robot connection simplified to a single-point connection and an increase in the effective compliance to account for the effects of the missing connection point.
Abstract
Series elastic actuators are increasingly adopted in wearable robots, due to superior sensing and actuating capabilities provided by the added internal compliance. However, when evaluating their performance in benchtop setups, the dynamics of the physical human–robot interface (i.e., external compliance) are usually overlooked despite it causing energy dissipation and delays in power transmission. This work closes the gap by emulating in a test bench the physical human–robot interaction dynamics and validating actuator performance against commonly used performance indices, including torque bandwidth, torque tracking, and transparency. The results show a significant impact of the interaction dynamics on the actuator performance. When interface dynamics is present, decreasing the actuator (internal) compliance has little to no effect on its bandwidth. When delivering a walking torque, decreasing internal (actuator) and external (interface) compliance has the same decreasing effect on the motor’s peak electrical power in the hip joint. Conversely, the motor peak electrical power decreases with an increase in internal (actuator) compliance but increases with an increase in external (interface) compliance in the knee joint. As such, this work demonstrates the importance of including interaction dynamics as a norm in designing and evaluating actuation units in wearable robots.
1 Introduction
Actuation units in wearable robots (WRs) and their physical connections (i.e., physical human–robot interface (pHRI)) to human limbs are the key hardware elements shaping the human–robot experience and the robots’ overall performance. Over the years, the focus has mainly been on developing safer, lighter, and more versatile actuation units, resulting in numerous designs [1]. For example, series elastic actuator (SEA) [2–4], a type of compliant actuation technology, has been around since the 1990s [5], finding many applications over the last 30 years in gait rehabilitation [6–8], prosthetic limb replacement [9–11], and more.
Many advantages of SEAs over competing actuation technologies stem from the mechanical compliance courtesy of a physical spring (i.e., internal compliance) in their design. The idea behind adding a spring is to add shock tolerance on the human and robot sides, delivering a more natural human–robot interaction, and allowing a range of actuation modalities (e.g., position and impedance control) [12,13]. By optimizing their design through, e.g., reducing peak motor power [14,15] or balancing torque bandwidth and resolution [16,17], SEAs opened up many new possibilities in shaping human–robot interaction and made the interaction safer for their human users.
However, SEAs don’t operate in isolation and physical human–robot interaction is not an ideally (i.e., infinitely rigidly) coupled system where SEAs’ benefits would come to the fore. Human soft tissue (external compliance) is a non-negotiable compliant element in human–robot interaction systems (which is referred to as load-side compliance in this work) that has largely been overlooked in designing actuation systems for WRs. The compliant soft tissue, combined with the human–robot kinematic incompatibility (robotic joints are often hinges while human joints are not) [18,19], have been shown to cause up to 55% power losses in force transmission [20], up to difference in human and exoskeleton joint angles [21,22], and a significant decrease in torque provided to the knee joint during assisted walking [18]. In other words, WRs underperform in real-world scenarios largely due to SEA designs that are optimized for unrealistic, ideal-case pHRIs.
A practical, safe, and effective way to explore the impacts of human soft tissue on the WRs’ actuator performance is by emulating its dynamics in traditional benchmarking setups and comparing it against typical performance indices, which include torque bandwidth, torque tracking, transparency [14–17]. This approach is largely missing as researchers generally opt for simple rigid setups that connect the actuator to a grounded output (infinitely rigid load)—-an ideal case scenario. A better representation of real-world conditions is needed in experimental validation to avoid poor design decisions becoming apparent only once the actual system is validated with human users [20–22].
In this paper, a comprehensive procedure for benchmarking SEAs with emulated load-side dynamics by means of a servo motor is presented. The actuator torque bandwidth, torque tracking, and transparency performance are measured for three levels of spring stiffness (internal compliance) and four levels of load-side stiffness (external compliance), including a rigid setup. Power and energy consumption of the SEA are also measured during torque tracking and transparency tests. The findings demonstrate that external compliance (i.e., emulated interaction stiffness) exerts a complex and non-negligible impact on the performance of the SEA. This underscores the importance of incorporating pHRI dynamics in actuator benchmarking protocols, as this will deliver a more authentic evaluation of actuator capabilities and better predict its real-life application performance.
2 Actuator Performance Indices
The study characterizes the actuator with three commonly used performance indices: torque bandwidth, torque tracking, and transparency. When reported together, these indices give a comprehensive understanding of the SEA characteristics. The following sections introduce the three indices and how these are measured in this study.
2.1 Torque Bandwidth.
Actuator torque bandwidth is the most commonly reported SEA performance indicator [23], defined as the input signal frequency beyond which the output is attenuated by more than 3 dB [24]. Traditionally, evaluations of the torque bandwidth of a rigid actuator are reported as a single number, but more recent studies propose multi-level torque bandwidth characterization [25,26] in recognition of the dynamics introduced by the physical spring (i.e., internal compliance). In this work, the former is referred to as conventional torque bandwidth (CTB). The multi-level characterization is extended in this paper by considering load-side (i.e., external) compliance, absent in the literature but essential for fully characterizing real-life SEA performance. To achieve this, the output is controlled by a load motor emulating movements of the actuated robot link (link A, Fig. 1(c)) while the human skeleton (link B) remains motionless. Load movement is governed by a spring–mass–damper dynamical system representation. A new performance index, called load-emulated torque bandwidth (LETB), is defined to characterize the multi-level bandwidth of the actuator when compliance in human tissues and pHRI are considered.

An illustration of the assumptions and corollary. Link A (blue) represents robot links and link B (red) represents human limbs (thigh and shank). A spring–damper system connects the two, simulating a compliant human–robot interaction. is the load-side stiffness and is the load-side damping coefficient: a realistic pHRI model with human–robot connections on two links, joint misalignment, and a 6DOF spring–damper interface; a pHRI model in the sagittal plane only (Assumption 1) and with human–robot joint alignment (Assumption 2), resulting in a single-DOF spring–damper interface on both links; and the pHRI model used in this work, with two-point human–robot connection simplified to a single-point connection and an increase in the effective compliance to account for the effects of the missing connection point.

An illustration of the assumptions and corollary. Link A (blue) represents robot links and link B (red) represents human limbs (thigh and shank). A spring–damper system connects the two, simulating a compliant human–robot interaction. is the load-side stiffness and is the load-side damping coefficient: a realistic pHRI model with human–robot connections on two links, joint misalignment, and a 6DOF spring–damper interface; a pHRI model in the sagittal plane only (Assumption 1) and with human–robot joint alignment (Assumption 2), resulting in a single-DOF spring–damper interface on both links; and the pHRI model used in this work, with two-point human–robot connection simplified to a single-point connection and an increase in the effective compliance to account for the effects of the missing connection point.
Torque bandwidth evaluation is done using a logarithmic chirp signal instead of the more commonly used linear chirp and multi-sine signals [27,28]. This enables increased accuracy in the estimation of the frequency response of the actuator across the entire frequency range, especially on the lower end of the range (e.g., around 1 Hz).
2.2 Torque Tracking.
Torque tracking is another commonly used performance index relevant to torque-assistive wearable robot applications. It measures how well the assistive devices are able to apply the required amount of physical assistance (in the form of torque/force) to the user. Typically, torque tracking performance is tested using sine wave [28,29] or biological torque [30] signals, with the actuator output shaft either fixed [28] or rigidly connected to a load [29]. However, the rigid connection assumption in these studies limits their translation to real-life SEA performance. To overcome this, the work presented herein includes load-side stiffness by emulating load-side compliance, called here dynamic configuration (see Fig. 3). In dynamic tests, the actuator output is connected to a load motor (Fig. 3(d)) emulating the motion of link B (Fig. 1(c)) that would otherwise be delivered by the exoskeleton during assistive activities. This is contrasted by static tests, where the actuator output is fixed to the test setup (Fig. 3(c)). In both cases, the actuator is commanded to track a torque reference derived from the human walking dataset [31], with differences coming from the load side. The emulated motion of the load motor changes depending on the load-side stiffness configuration.
2.3 Transparency.
The actuator transparency is defined as the ability to track zero torque in the presence of output motion [32]. The actuator is highly transparent if it can follow the reference output motion with minimum opposing torque. Despite its inherent ability to characterize the SEA sensitivity to the interaction torque (torque measurement resolution) and responsiveness to the output motion (output shaft position measurement resolution and control loop speed), this index is not frequently used in the literature. The most common way to measure transparency is by using the load motor to back-drive the actuator while its motor is either turned OFF (measuring reflected inertia and friction) or ON (measuring the controller performance) [14]. Other examples include back-driving using the natural pendulum motion [32] from an initial horizontal position.
These and other similar works in the literature are extended in this study by including dynamics on the output side. To achieve this, the load motor emulates the motion of the robot link with different load-side stiffness configurations while the actuator tracks a zero torque reference. This is repeated at different conditions, including several walking speeds. The metric used to quantify transparency is the root mean square (RMS) tracking error when following zero torque reference during back-driving motion.
3 Emulation of Compliant pHRI Modality
The main purpose of this study is to characterize the actuator performance considering different load-side stiffness values, which are missing in current benchmarks. Therefore, emulating the compliant pHRI behavior with the load motor is one core element of this study. In the literature, pHRI is most often approximated as a spring–damper–mass system of different complexity (i.e., with linear or nonlinear spring damper terms included) [33–35]. The same approach is taken herein to account for the setup limitations while still providing insights into the effects of compliant human–robot connection on the SEA performance (an experimental identification of the actual model is the topic of our ongoing work). A schematic of the model is given in Fig. 1(c), where link A represents the human limb and link B the robot link. The rest of the modeling method explanation takes human knee joint as an example with a single actuation point at the level of the shank.
The simplified pHRI emulation builds on three assumptions and one corollary outlined below, and is illustrated in Fig. 1:
Assumption 1: the relative displacement and interaction force only exist in the plane of actuation (i.e., the sagittal plane);
Assumption 2: the robotic and human joints are both hinge joints with aligned axes of rotation;
Assumption 3: the angular difference between link A and B is sufficiently small such that .
Corollary 1: It follows from Assumption 1 and Assumption 2 that the effects of a two-point compliant connection between the robotic and human limb for a 1DOF robot (e.g., at the shank and thigh levels for a knee exoskeleton) can be simplified to a single-point compliant connection (e.g., on the shank level only) with the compliance value increased (i.e., a less stiff setup).
The difference in the position between the two links (i.e., ) and the speed at which this occurs (i.e., ) is what characterizes the human–robot connection. Consequently, this is a behavior the load motor admittance controller needs to emulate. This behavior is realized in an iterative way by applying the backward-Euler discretization method at a sampling period (0.002 s in the controller). The allowed position difference defines the load motor reference position . Here is defined as zero or a biological joint angle (i.e., knee joint). In either case, the load motor only allows deviations around , with deviation amplitudes dependent on the spring-damper parameters.
The effects of the spring(-mass)-damper model on the actuator performance were tested in several configurations. Across all, the mass and damper values are fixed, while the spring stiffness varies with four values. The mass represents the wearable robot mass and is taken from Ref. [1] (see Table 1). The human soft tissue damping was fixed to 30 Ns/m, guided by estimates from Refs. [35,36], and the actuator instability issues that occurred during preliminary tests (30 Ns/m was the lowest value that didn’t lead to the actuator instability).
An overview of the human–robot interface model parameters used in testing
Load-side stiffness (N/m) | Damping | Inertia | Length | ||||
---|---|---|---|---|---|---|---|
Rigid | Compliant | (Ns/m) | () | (m) | |||
R | C1 | C2 | C3 | ||||
Hip | 4800 | 2400 | 1200 | 30 | 0.05 | 0.26 | |
Knee | 2400 | 1200 | 600 | 30 | 0.05 | 0.26 |
Load-side stiffness (N/m) | Damping | Inertia | Length | ||||
---|---|---|---|---|---|---|---|
Rigid | Compliant | (Ns/m) | () | (m) | |||
R | C1 | C2 | C3 | ||||
Hip | 4800 | 2400 | 1200 | 30 | 0.05 | 0.26 | |
Knee | 2400 | 1200 | 600 | 30 | 0.05 | 0.26 |
Note: The are the four load-side stiffness configurations, from rigid to the softest.
The literature provides limited guides on the spring coefficient in the direction of actuation (normal direction to the skin). In an experiment with three subjects, authors in Ref. [33] found stiffness values of 2400 and 4800 N/m for the shank and thigh limb segments, respectively. These values are taken as the starting point herein, with their dependency on experimental setups and various other factors in mind [21,35]. Following this, the values proposed in the literature are taken as the C1 compliance level just below the rigid level (see Table 1). The remaining two compliance levels are set to half and a quarter of the 2400 and 4800 N/m levels. This is because the overall stiffness of the pHRI system depends on two (or more) contact points between humans and robots, so it makes sense that a single-point contact assumption (Assumption 3) would be less stiff. Similarly, the exoskeleton structure and cuffs (with straps) themselves also introduce compliance in the system, further justifying the choice to test stiffness levels lower than the estimates found in the literature. The four stiffness values are chosen to compromise feasibility and the ability to capture the underlying trends (if any) in the stiffness. All the parameters are summarized in Table 1.
4 Experimental Setup
This section describes the mechatronics design of the actuator and its test bench, the implementation of multi-level controller of the actuator and the load motor, and the protocol of the benchmarking tests.
4.1 Actuator and Testbench Mechatronics Design.
In this section, we describe the mechatronics design of an SEA tailored for WR, specifically targeting high-functioning hemiparetic patients. We begin by outlining the actuator design requirements based on biomechanical parameters, followed by the selection of appropriate motor and gear ratios, which are validated through simulation. The mechanical details of the actuator, its corresponding test bench, and the electronic control system are presented.
4.1.1 Actuator Design Requirements.
A common approach to designing a WR actuator is to choose the activity of interest and the average user’s weight and use these to derive the actuator torque/speed requirements. In this work, an actuator is designed to deliver the biological joint (knee and hip) torque for a 70 kg person walking at 0.8 m/s. This walking speed is considered the lower boundary of the community ambulator category [37] and is typical of high-functioning hemiparetic patients [38], the target group of this SEA development. Translated into the motor requirements, this results in about 29 Nm torque and just over speed. To account for hard-to-model losses in transmission and heat dissipation, the component selection should allow higher torque and speed values. In addition, the nature of the target population’s physical recovery often leads to a change in torque-speed requirements, which introduces the capability to change the transmission ratio as needed as an additional design requirement.
4.1.2 Selection of Motor and Gear Ratios.
A widely used method in selecting a motor–gear combination is to match the peak (or nominal) torque found on the motor datasheet to the derived actuator design requirements [39,40]. However, care should be taken with this approach since the datasheet-specified peak motor torque is only achievable statically when no rotor dynamics or torque-velocity losses are considered [30]. A more accurate approach is to select actuator components by simulating activities of interest (e.g., walking) while using motor models considering more parameters. This reflects the dynamic and complex nature of the kind of assistance WRs’ actuators need to deliver and is supported by research showing that, e.g., including motor inertia in the model has a major effect on the outcomes of the SEA optimization, such as accounting for the major effect of the motor inertia in the outcomes of the SEA design optimization process [41].
The motor–gear–spring combination was selected by simulating the motor effort assuming perfect tracking during 0.8 m/s walking for hip and knee joints respectively, similar to Ref. [41], and selecting the best combination that minimized the motor electrical peak power while also satisfying other practical design requirements. Specifically, a two-stage optimization strategy was employed. In the first stage, we minimize the motor’s electrical peak power (objective function) using a 4QCEI model [42] over a practical range of three variables: spring stiffness , transmission ratio , and drive train inertia . This process results in a narrow range of sub-optimal variables around the optimal working point. In the second stage, we select specific gears and motors from an existing commercial database, ensuring the chosen components’ parameters fall within the identified range. For each combination of the selected motor and gear components, we compute the objective function using full motor model (FMM) [42]. We use a different model here as opposed to the first step due to its higher accuracy and lower penalty coming from its increased computational demands. A diagram illustrating the optimisation process is shown in Fig. 2. Incorporating real-world motors and gears as candidates for optimization in the second stage allows for more accurate simulation results by accounting for the specific electrical and mechanical parameters of each motor, particularly motor inertia, which is often overlooked. It is important to highlight that the technique used in this paper is just one approach to design. Other design methods can also be employed. The simulation results pointed toward an inner rotor motor—EC-i40 (Maxon, Sachseln, Switzerland) whose rotor inertia is 1.4% of a commonly used pancake motor (EC-flat90) in exoskeletons [39,40,43].

The two-stage actuator component selection methodology (M and G denote motor and gearbox, and denote spring stiffness, transmission ratio, and drive train inertia, respectively)
The actuator mechanical design is shown in Fig. 3(a). The brushless DC motor (EC-i 40 100W, 36V, Maxon Motor, Switzerland) has a maximum continuous torque of 0.207 Nm. An incremental encoder (Encoder 16 EASSY, 1024cpt, Maxon Motor, Switzerland) measures motor position and velocity. Motor output shaft and harmonic drive input shaft (LHD-17-100, Riff Precision Transmission, Shenzhen, China) connect via a 1:1.5 timing belt transmission ratio, combined with the 100:1 reduction ratio of the harmonic drive, yields a ratio of 150:1, resulting in a nominal output torque of 30 Nm and velocity of 244 deg/s (at 48 V nominal voltage). The harmonic drive output connects to a torsional spring outer ring, with five different values of thicknesses (2, 4, 6, 8, and 10 mm) resulting in a 100–500 Nm/rad stiffness range. The inner spring ring connects to the actuator output shaft. An incremental encoder (LM10, RLS, Komenda, Slovenia) on the output shaft provides a 13-bit resolution and minimum detectable spring deflection of , translating to a 0.077–0.384 Nm torque measurement resolution. The total weight of the actuator is approximately 1.4 kg.

Experiment setup: exploded view of the SEA and SEA spring, control architecture, test bench setup: fixed output, and test bench setup: dynamic output
4.1.3 Test Bench Mechanical Design.
The test bench was built as a cage with four 10 mm-thick aluminum alloy plates. Two configurations are available for output actuator shaft connection: fixed (Fig. 3(c)) and dynamic, controlled by a load motor (Fig. 3(d)). The load motor (RE65-250W, Maxon Motor, Switzerland) with a 25:1 GP81 Planetary gearbox (Maxon Motor, Switzerland), delivers 46.1 Nm torque at 15 A and 896.3 deg/s at 48 V. A dynamic torque sensor (TRS600-50Nm, FUTEK, Irvine, CA) connects the actuator and load motor (or fixed output) to measure interaction torque. The torque sensor shaft connects to the actuator and load motor shaft via two flexible couplings (SSCC50-18-19, Misumi) for potential misalignment adjustments. The bottom plate of the test bench is bolted to a wooden bench.
4.1.4 Electronics.
The test bench electronics consist of a motor driver, low-level and mid-level actuator controllers, and a high-level controller for overall system control. The integrated motor driver (ESCON, Maxon Motor, Switzerland) includes a driving circuit for the brushless direct current (BLDC) motor and a low-level controller. This low-level controller operates at 50 kHz and features a cascade design with outer velocity and inner current loops (field-oriented control (FOC)). Both motors utilize ESCON drivers with custom parameters. The mid-level controller manages motor velocity, while the high-level controller generates reference trajectories. Both are implemented in a MyRIO DAQ system (National Instruments, Austin, TX) operating at 500 Hz.
4.2 Controller Design.
The control architecture used in benchmarking consists of a three-layer structure: low, mid, and high-level control (Fig. 3(b)). The actuator and the load motor share the same low- and mid-level controller structure (implemented separately), and have their individual high-level controllers (indicated by SW1 in Fig. 3(b)).
4.2.1 Actuator High-Level Controller.
4.2.2 Load Motor High-Level Controller.
The load motor high-level controller is designed as an admittance controller to complement the impedance controller driving the actuator. In other words, while the actuator accepts movement (i.e., motor angle) as an input and produces effort (i.e., torque) at its output, the load motor accepts the effort (i.e., torque) at its input and yields the movement (i.e., motor angle). In practice, that translates to the load motor generating its reference movement based on the actuator driving (measured) torque and desired human movement trajectory (see Eq. (2)).
4.2.3 Mid- and Low-Level Controllers.
As Fig. 3(b) shows, the mid-level controller accepts a position signal ( or ) and converts it to a velocity signal at its output (). The velocity command consists of a desired motor velocity and a correction signal generated by feed-forward (FF) and feedback (FB) controllers. The signal in the feed-forward branch is multiplied by a gain, while the feedback loop corrects the error using a proportional-derivative controller. The outputs of the two branches are summed, passed through the motor velocity saturation block, and input to the low-level controller. The parameters of the mid-level controller are tuned by trial and error with the goal of achieving a highly responsive yet stable controller and are kept unchanged throughout all experiments.
The low-level controller is a cascaded controller with an outer velocity loop and an inner current loop (i.e., FOC). The velocity loop compares the desired and the measured motor speed (coming from the motor encoder) and sends a current correction signal () to the inner (current) loop. The inner loop measures the three-phase current of the motor and regulates the input voltage of the motor with the help of the power electronics. The low-level controller of both motors is implemented in the ESCON motor driver whose parameters are automatically tuned in the escon studio software by selecting the stiffest option setting.
4.3 Benchmarking Protocol.
As mentioned earlier, the main aim of this work is to investigate the effects of load-side stiffness on the performance of SEA with different spring stiffness. The experimental validation also includes conventional actuator benchmarking tests with rigid setup to provide a reference to benchmark against. Figure 4 visualizes all experimental conditions and performance indices measured per condition. The conditions can be categorized into actuator and load stiffness configuration and benchmarking test conditions, details of which are explained as in the following sections.

An overview of the tests carried out to characterize the actuator. The experimental conditions are labeled in green. Color-coded blocks in the table illustrate which benchmarking tests (corresponding to performance indices) are done under which stiffness configurations. The test conditions for each benchmarking test are further explained in the bottom section.

An overview of the tests carried out to characterize the actuator. The experimental conditions are labeled in green. Color-coded blocks in the table illustrate which benchmarking tests (corresponding to performance indices) are done under which stiffness configurations. The test conditions for each benchmarking test are further explained in the bottom section.
4.3.1 Actuator and Load Stiffness Configuration.
Actuator spring stiffness: three physical springs are used in benchmarking tests, ranging from compliant (No. 1, 132 Nm/rad) to semi-rigid (No. 2, 312 Nm/rad) to rigid (No. 3, 507 Nm/rad);
Load stiffness: four levels of load stiffness are used in benchmarking tests, from infinitely rigid (R) through to compliant (C3) with two levels (C1 and C2) in between; see Table 1 for the mass–spring–damper model values (notice that damping and mass remain constant while spring stiffness changes).
4.3.2 Benchmarking Test Condition.
Torque Bandwidth Test: The actuator is given a reference torque trajectory—a chirp signal with a frequency range of 0.1–50 Hz swept over 30 s with a peak amplitude of both 8 Nm and 16 Nm. For CTB tests, the actuator output shaft is grounded (Fig. 3(c)). For LETB tests, the bench configuration is dynamic (Fig. 3(d)), and the load motor emulates zero human limb movement with different load-side stiffness (refer to in Fig. 1(c) and Table 1).
Torque Tracking Test: In static torque tracking (STT) tests, bench configuration is fixed (Fig. 3(c)). The actuator is required to deliver separately four different reference torque trajectories of human walking with peak torque amplitude of 16 Nm—hip joint at slow (0.8 m/s) and normal (1.05 m/s) walking speeds, and knee joint at slow and normal walking speeds. The data of normal walking are obtained from the publicly available Winter dataset [31]. In dynamic torque tracking (DTT) tests, the bench configuration is set to dynamic (Fig. 3(d)). The actuator is required to deliver separately two different reference torque trajectories of human walking—hip joint at slow (0.8 m/s) walking speed, and knee joint at slow walking speed, with a peak torque amplitude of 16Nm. The load motor emulates the corresponding human joint movement with different load stiffness.
Transparency Test: Transparency test is done in the form of zero torque tracking (ZTT). The bench configuration is dynamic (Fig. 3(d)). The actuator is set to track a zero torque reference. The load motor emulates two reference joint angle trajectories of human walking (hip and knee joints at slow (0.8 m/s) walking speeds) with different load stiffness.
5 Results
In this section, we present the results of the benchmarking analysis in terms of the three performance indices, i.e., torque bandwidth, torque tracking in both static and dynamic conditions, and transparency. Additionally, we explore how different actuator-side and load-side stiffness impact motor power and energy consumption during simulated walking cycles at hip and knee joints.
5.1 Torque Bandwidth.
The frequency response of spring No. 2 to a chirp (torque) signal of 16 Nm peak amplitude for all load-side configurations is shown in Fig. 5(a). The response is estimated using the matlab System Identification Toolbox The ideal case (16Nm-R) has a drop in magnitude, suggesting that it has linear characterization, which can be represented by a second-order linear time-invariant dynamic system (the response is very similar for springs No. 1 and No. 3).

Torque bandwidth: frequency response of the SEA spring No. 2 for the 16 Nm chirp signal excitation and actuator bandwidth across two torque levels, three SEA springs, and four pHRI compliance levels
The effect of load-side stiffness can be seen in the actuator cutoff frequency (frequency at which a decrease is measured in the amplitude response), which depends on the load-side stiffness levels. The more compliant the load (pHRI) is, the lower the actuator cutoff frequency. The major negative effect of load-side stiffness is seen to the right of about 12 Hz when the actuator response becomes unstable. This can be seen from the gain or phase margin (or both) becoming negative at the respective crossover frequency when the load is not rigid. When the load is rigid, both the gain and phase margins are positive at respective crossover frequencies, rendering the system stable.
A comparison of the actuator torque bandwidth across different spring stiffness, torque amplitudes, and load-side stiffness levels is given in Fig. 5(b). Overall, increasing the torque amplitude of a reference signal decreases the actuator bandwidth no matter the actuator spring or load stiffness. The relative drop, however, is smaller with a stiffer actuator spring. On the other hand, increasing the actuator stiffness only increases its bandwidth when the pHRI is set to be rigid. When compliance is considered on the output side, increasing the actuator stiffness has little to no effect on its bandwidth. Furthermore, increasing the compliance level on the output side decreases the actuator bandwidth for all spring conditions, albeit less so when the actuator is fitted with a stiffer spring.
5.2 Torque Tracking.
Static Torque Tracking. The actuator torque tracking performance during the static test (fixed output shaft, Fig. 3(c)) for a 16 Nm peak torque amplitude and all three actuator springs is shown in Fig. 6(a). The reference torque profiles are taken from the human walking datasets for the knee and hip at slow and normal walking speeds and scaled to 16 Nm peak amplitude [31]. Across all three springs, the highest RMS torque tracking error comes at about 1.25 Nm, and the highest peak tracking error at about 3.2 Nm. In both cases, the highest error was measured with the stiffest spring (No. 3) when delivering hip joint torque during normal walking. Spring No. 3 has a notably higher RMS tracking error across all four benchmarking testing conditions, reaching an error more than twice as large as the other two springs. Regarding the peak tracking error, there is an increase in error with an increase in spring stiffness across all four conditions. During all tests, the actuator hadn’t reached its torque or velocity limits.

Torque tracking and transparency: STT performance (all under rigid load stiffness), DTT performance and motor effort, ZTT performance and motor effort (DTT performance is grayed out to allow a direct comparison), and motor power and energy consumption in the DTT test, all data refer to slow walking (0.8 m/s), gait cycle starts at heel strike, shaded area represents stance phase

Torque tracking and transparency: STT performance (all under rigid load stiffness), DTT performance and motor effort, ZTT performance and motor effort (DTT performance is grayed out to allow a direct comparison), and motor power and energy consumption in the DTT test, all data refer to slow walking (0.8 m/s), gait cycle starts at heel strike, shaded area represents stance phase
Dynamic Torque Tracking. The actuator torque tracking performance during the dynamic tests (output shaft connected to a load motor, Fig. 3(d)) for a 16 Nm peak torque amplitude case, all three actuator springs, and all four load stiffness is shown in Fig. 6(b). Due to the limit of actuator capability, only two benchmarking test conditions are investigated, i.e., hip and knee during slow walking speed. In the hip joint case, the RMS torque tracking error (top row, left) remains less sensitive to actuator spring stiffness and load stiffness but does show increased variability for spring No. 2. The error remains largely in the same range in the case of the knee joint as well (top row, right), but is increasing with the increase in the actuator spring stiffness (up to in the worst case: going from spring No. 1 to spring No. 3 under load stiffness C1).
A much bigger effect of the actuator spring stiffness and load stiffness can be seen in the electrical power consumption (second row) and energy of the actuator motor (third row) in Fig. 6(b). In the hip joint, increasing stiffness at either side of the actuator output shaft—actuator spring stiffness or load stiffness has the same decreasing effect on the motor peak electrical power. The compliance at the load side only notably increases the motor peak electrical power when the actuator itself is stiff (No. 3). When the actuator is compliant (No. 1), changing the load-side stiffness affects the peak power less. The opposite is true at the knee joint. With the exception of one actuator stiffness configuration (actuator spring No. 3 and rigid load stiffness), the peak electrical power decreases with stiffer actuator spring but increases with stiffer load.
Regarding electrical motor energy, two trends can be noted in the case of the hip joint. When the actuator is compliant (spring No. 1; bottom row, left), adding compliance at the load-side is observed to increase the motor energy requirements. The opposite is true when the actuator is stiff (No. 3), as in this case load compliance has a positive effect on the required motor energy. A completely different trend can be seen at the knee joint (bottom row, right) regardless of the actuator stiffness level, albeit a trend somewhat similar to the hip and compliant actuator spring (No. 1). For all three actuator spring stiffnesses, the motor uses the least amount of energy when the load lies in the mid-range of the tested stiffness values, showing a clear minimum across the board for C2 and C3.
5.3 Transparency.
The actuator performance in tracking the zero-torque reference (i.e., transparency) for the same stiffness configurations and benchmarking test conditions as in dynamic torque tracking is given in Fig. 6(c). There are no noticeable trends in RMS torque tracking error across the two joints under changing compliance conditions, albeit slightly higher errors are present in the knee joint. The reason is the actuator motor velocity saturation, which is reached for the knee but not for the hip joint. In other words, compliance (actuator or load) does not play a major role in the actuator transparency when operating within its velocity limits. A comparison to the RMS torque tracking error in the DTT case (grayed out in Fig. 6(c)) shows a smaller error across all conditions when in the transparency mode, albeit less so in the knee joint case.
When it comes to the actuator motor demands, no clear trends exist in the peak electrical power in the hip joint, operating well under the actuator velocity limits. On the other hand, the electrical motor energy per gait cycle is the lowest when the actuator and load stiffness are opposite: stiff actuator—compliant pHRI, and compliant actuator—stiff pHRI. Different trends can be seen at the knee joint, whose peak motor power reduces with decreasing load stiffness, irrespective of the actuator stiffness levels (with the exception of No. 3-R combination, as seen by comparing to the grayed out values). Electrical motor energy remains in the same range across all three actuator springs but tends to be the lowest in the mid-range of load stiffness, a behavior seen in delivering the torque in dynamic torque tracking tests (compared to the corresponding grayed-out values).
5.4 Case Study: Motor Power and Energy in Time Domain.
The actuator torque tracking performance across conditions can be understood by its behavior per gait cycle. Figures 6(d)–(g) show the actuator power and energy consumption during slow walking at the hip and knee joints for two actuator springs (No. 1 and No. 3) and two load stiffness levels (R and C3 at the hip, R and C1 at the knee). At the hip (top row), an increase in peak motor power when the load is made more compliant (from R to C3) comes from a spike in power observed at the time of heel strike, regardless of the actuator stiffness level (see also Fig. 6(b), middle row, left). The actuator stiffness plays a role in energy consumption, though, as demonstrated by very different (No. 1, top left) and almost equal (No. 3, top right) energy demands during the stance phase (0–1.2 s) when comparing R and C3. A rigid (R) load is always more energetically demanding during the swing phase. At the knee joint, the motor consumes the least amount of energy when pHRI compliance falls within the mid-range of the tested values. As observed in Figs. 6(f) and 6(g), the softer load (C1) exhibits a higher power peak and hence energy consumption after the heel strike, while the rigid load (R) consumes more energy during the swing phase.
6 Discussion
The presented study investigated the influence of a combined internal (i.e., series elastic actuator) and external (i.e., physical human–robot interface) compliance on the actuator performance in a benchtop environment emulating real-life pHRI for a wearable robot. Our results demonstrate for the first time the complex interplay between the actuator and interface compliance levels and the importance of considering the latter when designing and benchmarking actuators for WRs. Our results suggest that the design of WR actuation systems should extend beyond traditional approaches, which typically focus on application-specific human biomechanics as design requirements and actuation models in simulations to optimize the final design and components. It is essential to also include physical interface dynamics and validate the performance of the overall actuation-interface system through experimental setups.
Torque Bandwidth: Torque bandwidth tests showed that the actuator torque bandwidth increases with higher actuator spring stiffness but decreases with higher reference torque amplitude (Fig. 5(b)). This finding was previously reported in the literature [14,26,44], but was limited to unrealistic scenarios when no load-side compliance is considered in the transmission chain (i.e., infinitely rigid human–robot interface). When interface dynamics (external compliance) are considered, as is the case in this work, the benefits to the actuator torque bandwidth from increasing its spring stiffness are mostly canceled out, with the biggest drop in performance in the case of the stiffest actuator configuration (No. 3). This happens despite the C1 load stiffness being more than twice as stiff as the No. 3 actuator spring (; ). Similarly, the lower the load stiffness, the lower the actuator torque bandwidth. Seeing as no ideal pHRI connection (the R load stiffness configuration) exists outside the lab, the results clearly demonstrate that there is little benefit to the actuator bandwidth when increasing its internal (spring) stiffness in real-life applications.
Torque Tracking: When the actuator operates within its velocity/torque/power limits, the torque tracking error in delivering biological joint torque (in both knee and hip joints) increases with the actuator stiffness. Granted, this is more pronounced in static (Fig. 6(a)) than dynamic (Fig. 6(b)) tests, which is in line with results presented in Refs. [14,26]. Both of these studies have demonstrated that task dynamics can benefit the actuator performance and should be the cornerstone in benchmarking the real-life performance of the actuator. However, neither showed the results to hold beyond an ideal load configuration as both studies assumed infinitely rigid human–robot connection.
The work presented herein is the first to extend this notion by providing evidence that even dynamic tests can be misleading if the physical human–robot interaction is not emulated and considered. This is clear by looking at Fig. 6(c), which shows the actuator power and energy consumption under different testing conditions. In the hip joint and for a given load-side stiffness, higher actuator stiffness decreases the peak motor power, especially when the load is infinitely rigid. This is the opposite effect of the bandwidth case, where load-side compliance canceled the effects of increasing actuator stiffness. Interestingly, higher load-side compliance levels increase the actuator energy consumption only when the actuator itself is more compliant. When the actuator is stiff, higher load-side compliance decreases the actuator energy consumption, owing mainly to a decreased energy consumption during the stance phase (Figs. 6(d) and 6(e)).
The knee joint, with its unique torque/velocity demands during walking [31], puts the actuator-pHRI transmission chain through a completely different pace. Different from the hip joint, increasing the actuator spring stiffness increases peak motor power while adding compliance at the load-side counteracts this by decreasing the peak power requirements. In terms of electrical motor energy consumption, the actuator seems to benefit the most when its internal stiffness is increasing and the load-side compliance level stays in the middle (of the tested values). These results show for the first time that the effects of load-side stiffness (inevitable in real-life applications) on the actuator power and energy consumption depend on the activity, actuator and load stiffness levels. Consequently, researchers should approach the selection of the actuator spring stiffness using a more balanced approach [14,16,17] that includes interface dynamics as done in this work rather than pursuing a single objective [23], as is often the case.
The role different activities play in the interplay of the actuator and load compliances can be seen in Figs. 6(d)–6(g). In the hip joint, a dominant motor power peak occurs during the early stance phase, notably increasing the motor energy consumption and more so when the load is less stiff. This changes during the swing phase, when a more stiff load configuration is beneficial from the energy point of view. Conversely, the highest motor peak power in the knee joint predominantly occurs in the swing phase, albeit this is dependent on the actuator stiffness values (similar to Ref. [14]). The effects on the energy consumption of load-side compliance are similar across the knee and hip joints, with a higher load compliance more beneficial during the stance and lower load compliance during the swing phases of gait. These results demonstrate the complex interplay between the actuator and load compliance, re-iterating the importance of both specifying the target activity (common in the literature) and using the relevant pHRI model (novelty presented herein) when designing actuators by optimizing their energy consumption, as is often the case [15,41,45].
Transparency: The ability of the actuator to deliver no torque while following human movement (i.e., transparency), an important feature in WRs, is contrasted to the dynamic tracking performance in Fig. 6(c). When the actuator is working within its velocity and torque limits, the load-side stiffness levels have some to no effects on the RMS torque tracking error. As the figure shows, similar trends can be observed across the two tests, albeit with lower error amplitudes compared to dynamic torque tracking of the same joint angle profile. The same cannot be said about the effects of the actuator stiffness levels, whose increase leads to higher tracking errors, especially in the knee joint. This agrees with the observation that the transparency of the actuator correlates with its torque tracking performance [46], where higher transparency relates to lower impedance and thus a more accurate and precise tracking of a desired trajectory.
Overall, zero-torque tracking requires lower power and energy from the motor in the case of the hip joint and equal or higher power and energy in the case of the knee joint. A considerable reduction in the motor peak power at the hip joint compared to DTT is independent of actuator and load stiffness levels, remaining steady across all actuator-load stiffness combinations (with the exception of No. 1-R configuration). A similar trend can be observed in the case of motor energy demands, albeit a relative decrease in energy is much smaller than the one in power Fig. 6(c), middle and bottom row, left column).
Conversely, the motor peak power at the knee joint remains largely unchanged compared to DTT tests, indicating two things. First, high velocity demands (of the knee joint movement) on a DC motor can have as big an impact as reference output torque, demonstrating once again the importance of considering the motor inertia [41] and the reflected output inertia in the design of a (compliant) actuator. Second, highly dynamic tasks can work both against and for the actuator, adding to or benefiting its power and energy consumption, as previously demonstrated in the ankle joint [26]. Interestingly, higher energy demands during zero-torque tracking compared to DTT and unchanged peak motor power suggest the actuator is better at utilizing assistive torque than inertia-induced torque in improving its energy efficiency (noted, this is likely a function of the transmission ratio). Finally, the actuator and load stiffness levels only play a minor role in the motor power and energy demands, more so in the case of the peak motor power.
Limitations: Emulating physical human-robot interaction in experimental benchtop setups presents many challenges due to the inevitable joint misalignment [19] and multiple DOF interaction dynamics [33,47]. Furthermore, it remains difficult to measure real-life interaction stiffness and damping coefficients, which makes the information on their respective relevant ranges very limited. Consequently, our work builds on three assumptions commonly used in the field to emulate simplified yet realistic real-world human-robot interactions [1,48,49]. Similarly, the damping coefficient is kept constant and the range of stiffness extracted from a study with few conditions, both of which limit the scope of our work and require caution when interpreting results. Also worth noting is the reduced range of the tested SEA stiffness compared to the literature (500 Nm/rad versus 800 Nm/rad) due to the limited encoder resolution.
7 Conclusion
This study demonstrates the complex interaction between the actuator spring and load (i.e., pHRI) stiffness on the performance of the SEA. The proposed testing benchtop environment emulated realistic scenarios by including different realizations of the load-side stiffness. The results show that changing activity profiles and, for the first time, levels of pHRI compliance have significant and complex effects on the SEA performance, underlining the importance of including external compliance for realistic actuator benchmarking. In our future research, we plan to extend these findings to multi-degrees-of-freedom lower limb orthoses with the aim of improving the design and performance of the actuation units of wearable robots.
Conflict of Interest
There are no conflicts of interest.
Data Availability Statement
The authors attest that all data for this study are included in the paper.