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16 pages, 6819 KiB  
Article
Evaluating Stacked Dielectric Elastomer Actuators as Soft Motor Units for Forming Artificial Muscles in Biomimetic Rehabilitation Robots
by Vahid Mohammadi, Sahel Mohammadi Ghalehney, Mohammad Tajdani, Samuel C. K. Lee and Ahad Behboodi
Actuators 2024, 13(10), 381; https://doi.org/10.3390/act13100381 - 29 Sep 2024
Viewed by 709
Abstract
The recent commercial availability of stacked dielectric elastomer actuators (SDEAs) has unlocked new opportunities for their application as “artificial skeletal muscles” in rehabilitation robots and powered exoskeletons. Composed of multiple layers of thin, elastic capacitors, these actuators present a lightweight, soft, and acoustically [...] Read more.
The recent commercial availability of stacked dielectric elastomer actuators (SDEAs) has unlocked new opportunities for their application as “artificial skeletal muscles” in rehabilitation robots and powered exoskeletons. Composed of multiple layers of thin, elastic capacitors, these actuators present a lightweight, soft, and acoustically noiseless alternative to traditional DC motor actuators commonly used in rehabilitation robotics, thereby enhancing the natural feel of such systems. Building on our previous research, this study aimed to evaluate the most recent version of commercial SDEAs to assess their potential for mechanizing rehabilitation robots. We quantified the stress and strain behavior and stiffness of these actuators in both single and 1 × 3 configurations (with three SDEAs connected in series). The actuators demonstrated the capability to generate up to 25 N of force and 115 KPa, a value surpassing human biceps, with a longitudinal strain measured at about 11%. The significant increase in force generation from 10 N in the previous version to 25 N and displacement from 3.3% to 11% substantially enhances the applicability of this actuator in rehabilitation robotics. SDEAs’ high force generation capability, combined with their strain and stress characteristics comparable to that of human biological muscles, make them ideal alternative actuators for biomimetic robots and applications where actuators must operate in the vicinity of the human body. Full article
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<p>(<b>A</b>) An elastic capacitor generates displacement through Maxwell pressure. Once the voltage is applied, the Maxwell pressure contracts the thickness of the elastic dielectric while its area expands, as demonstrated by the four arrows. (<b>B</b>) The stacked dielectric elastomer actuator (SDEA) configuration comprises multiple layers of elastic capacitors. (<b>C</b>) A typical SDEA may contain approximately 2500 capacitor layers.</p>
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<p>The reported mechanical property of CTsystems’ CT25.0-1515-71 (CT-SDEA).</p>
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<p>The control and data acquisition block diagram of the test rig is illustrated. NI MAX was used to control the HV amplifier that drove the actuators (SDEAs) and to read the force data via the NI 9237 module. Displacement data were directly recorded through the Micro-Epsilon software using a laser sensor.</p>
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<p>The figure illustrates an actuator under isometric conditions, with one fixed end at the bottom and the other end connected to a load cell. It is crucial for the actuator to remain vertical; therefore, we used a laser balance to ensure proper alignment and adjusted the actuator using two precision translation stages.</p>
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<p>The figure depicts isotonic conditions, which include: (<b>a</b>) fixing the actuator at the top end to the Z stage, hanging various loads from the bottom end, and measuring contraction using a displacement laser sensor; and (<b>b</b>) fixing a 1 × 3 configuration of SDEAs, hanging various loads from the bottom end, and measuring contraction using a displacement laser sensor.</p>
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<p>The figure depicts SDEAs under free-standing conditions, which include: (<b>a</b>) applying different voltages to an actuator fixed at the bottom and measuring contraction using a laser displacement sensor; and (<b>b</b>) applying different voltages to a 1 × 3 configuration of SDEAs and measuring contraction using the laser displacement sensor.</p>
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<p>The figure depicts an actuator under stiffness testing, (<b>a</b>) in a horizontal orientation and (<b>b</b>) in a vertical orientation. A Shimadzu universal testing machine applies a 1 mm displacement to the actuator at different voltages, and the feedback force is measured using the machine’s load cell.</p>
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<p>The graph shows the force and the stress that each of the 10 actuators can generate in isometric condition at voltages up to 1200 V.</p>
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<p>The graph shows seven separate experiments on one actuator at different voltages, up to 1200 V, using loads ranging from 100 g to 700 g.</p>
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<p>The graph shows the shortening of ten different actuators under a 200 g load and various voltages up to 1200 V.</p>
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<p>The graph shows the shortening of a 1 × 3 configuration of DEAs under different loads, ranging from 100 g to 700 g, and voltages up to 1200 V.</p>
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<p>The graph shows the shortening and the strain of ten different actuators under voltages up to 1200 V in a no-load condition.</p>
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<p>The graph shows the shortening of a 1 × 3 configuration of DEAs under voltages up to 1200 V in a no-load condition.</p>
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<p>The graph shows the stiffness of one actuator in the Y (vertical) and X (horizontal) directions under different voltages, ranging from 800 V to 1200 V.</p>
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<p>The measured mechanical property of SDEA-1550 at 800 V (the recommended voltage) and 1200 V (the recommended voltage for CT-SDEA) in comparison to our reported value for CT-SDEA [<a href="#B18-actuators-13-00381" class="html-bibr">18</a>]. The presented values are the mean values; the force and shortening values are presented as mean ± SD.</p>
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<p>The biomimetic AFO, which is powered by SDEA-based artificial muscles.</p>
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15 pages, 1261 KiB  
Article
Movement Intent Detection for Upper-Limb Rehabilitation Exoskeleton Based on Series Elastic Actuator as Force Sensor
by Yukio Rosales-Luengas, Daniel Centeno-Barreda, Sergio Salazar, Jonathan Flores and Rogelio Lozano
Actuators 2024, 13(8), 284; https://doi.org/10.3390/act13080284 - 27 Jul 2024
Viewed by 1264
Abstract
In this paper, serial elastic actuators (SEAs) in conjunction with an accelerometer are proposed as force sensors to detect the intention of movement, and the SEA is proposed as a gentle actuator of a patient’s upper-limb exoskeleton. A smooth trajectory is proposed to [...] Read more.
In this paper, serial elastic actuators (SEAs) in conjunction with an accelerometer are proposed as force sensors to detect the intention of movement, and the SEA is proposed as a gentle actuator of a patient’s upper-limb exoskeleton. A smooth trajectory is proposed to provide comfortable performance. There is an offset trajectory between the link and the motor, which increases safety by preventing sudden movements, and the offset is equivalent to the torsional elastic spring constant. The proposed control law is based on a backstepping approach tested in real-time experiments with robust results in a 2-DoF upper-limb rehabilitation exoskeleton. The experimental results showed a sensitivity of 100% and a positive predictive value of 97.5% for movement intention detection. Full article
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<p>Glenohumeral joint rehabilitation exoskeleton showing the two degrees of freedom that allow the flexion–extension and abduction–adduction movements.</p>
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<p>Configuration scheme of the serial elastic actuator used in the two joints of the exoskeleton.</p>
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<p>Schematic diagram of the exoskeleton’s shoulder with elastic joints.</p>
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<p>Movement intent signal diagram.</p>
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<p>Exoskeleton motion start algorithm flow chart.</p>
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<p>Example of exoskeleton motion start algorithm.</p>
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<p>Movement intent detection experimental tests.</p>
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<p>Trajectory tracking and control signal input for extension detection.</p>
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<p>Trajectory tracking and control signal input for abduction detection.</p>
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<p>Detail of trajectory tracking and control signal input for abduction exercise.</p>
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25 pages, 14564 KiB  
Article
Bidirectional Multi-Spectral Vibration Control: Insights from Automotive Engine Mounting Systems in Two-Dimensional Structures with a Damaged Vertical Active Element
by Dongwoo Hong, Hojoon Moon and Byeongil Kim
Actuators 2024, 13(5), 171; https://doi.org/10.3390/act13050171 - 1 May 2024
Viewed by 1237
Abstract
Active mounting systems have become more prevalent in recent years to effectively mitigate structure-induced vibration across the automobile chassis. This trend is particularly evident in engine mounts. Considerable research has been dedicated to this approach owing to its potential to enhance the quietness [...] Read more.
Active mounting systems have become more prevalent in recent years to effectively mitigate structure-induced vibration across the automobile chassis. This trend is particularly evident in engine mounts. Considerable research has been dedicated to this approach owing to its potential to enhance the quietness and travel comfort of automobiles. However, prior research has concentrated on a limited spectrum of specific vibrations and noise control or has been restricted to vertical vibration control. This article describes the modeling, analysis, and control of a source structure employing a multidirectional active mounting system designed to closely simulate the position and direction of an actual automobile engine mount. A piezoelectric stack actuator is connected in series to an elastic (rubber) mount to form an active mount. The calculation of the secondary force required for each active mount is achieved through the application of harmonic excitation forces. The control signal can also reduce vibrations caused by destructive interference with the input signal. Furthermore, horizontal oscillations can be mitigated by manipulating the parameters via dynamic interconnections of the source structure. We specifically examined the level of vibration reduction performance in the absence of a vertical active element operation and determined whether the control is feasible. Simulation outcomes demonstrate that this active mount, which operates in both the vertical and horizontal directions, effectively mitigates excitation vibrations. Furthermore, a simulation was conducted to mitigate the vibrations caused by complex signals (AM and FM signals) and noise. This was achieved by monitoring the system response using an adaptive filter NLMS algorithm. Adaptive filter simulations demonstrate that the control efficacy degrades in response to complex signals and noise, although the overall relaxation trend remains unchanged. Full article
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<p>(<b>a</b>) EV powertrain mounts; (<b>b</b>) EV mounting system.</p>
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<p>Application of active vibration control system in automotive mounts.</p>
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<p>Model of mounting system with defective vertical active path allowing multidirectional installation.</p>
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<p>Model of mounting system allowing multidirectional installation using mount coordinates.</p>
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<p>Dynamic movement of source via external force.</p>
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<p>Dynamic movement of receiver via external force.</p>
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<p>The configuration used in the experiment to determine the parameters.</p>
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<p>Response in steady state for harmonic excitation.</p>
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<p>Model schematic for simulation.</p>
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<p>Steady-state response controlled by Case 1.</p>
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<p>Steady state response controlled by Case 2.</p>
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<p>Steady state response controlled by Case 3.</p>
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<p>Steady state response controlled by Case 4.</p>
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<p>6-DOF NLMS control simulation schematic.</p>
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<p>Time domain comparison of NLMS control source in case of sine wave: (<b>a</b>) position 1; (<b>b</b>) position 2; and (<b>c</b>) position 3.</p>
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<p>Time domain comparison of NLMS control source in case of sine wave: (<b>a</b>) position 4 and (<b>b</b>) position 5.</p>
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<p>Multi-NLMS algorithm schematic diagram.</p>
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<p>Comparison of FRF of NLMS control in case of AM signal: (<b>a</b>) position 1; (<b>b</b>) position 2; and (<b>c</b>) position 3.</p>
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<p>Comparison of FRF of NLMS control in case of AM signal: (<b>a</b>) position 1; (<b>b</b>) position 2; and (<b>c</b>) position 3.</p>
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<p>Comparison of FRF of NLMS control in case of AM signal: (<b>a</b>) position 4 and (<b>b</b>) position 5.</p>
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<p>Comparison of FRF of NLMS control in case of FM signal: (<b>a</b>) position 1; (<b>b</b>) position 2; and (<b>c</b>) position 3.</p>
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<p>Comparison of FRF of NLMS control in case of FM signal: (<b>a</b>) position 4 and (<b>b</b>) position 5.</p>
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19 pages, 11459 KiB  
Article
Soft Sensory-Motor System Based on Ionic Solution for Robotic Applications
by Sender Rocha dos Santos and Eric Rohmer
Sensors 2024, 24(9), 2900; https://doi.org/10.3390/s24092900 - 1 May 2024
Viewed by 969
Abstract
Soft robots claim the architecture of actuators, sensors, and computation demands with their soft bodies by obtaining fast responses and adapting to the environment. Sensory-motor coordination is one of the main design principles utilized for soft robots because it allows the capability to [...] Read more.
Soft robots claim the architecture of actuators, sensors, and computation demands with their soft bodies by obtaining fast responses and adapting to the environment. Sensory-motor coordination is one of the main design principles utilized for soft robots because it allows the capability to sense and actuate mutually in the environment, thereby achieving rapid response performance. This work intends to study the response for a system that presents coupled actuation and sensing functions simultaneously and is integrated in an arbitrary elastic structure with ionic conduction elements, called as soft sensory-motor system based on ionic solution (SSMS-IS). This study provides a comparative analysis of the performance of SSMS-IS prototypes with three diverse designs: toroidal, semi-toroidal, and rectangular geometries, based on a series of performance experiments, such as sensitivity, drift, and durability. The design with the best performance was the rectangular SSMS-IS using silicon rubber RPRO20 for both internal and external pressures applied in the system. Moreover, this work explores the performance of a bioinspired soft robot using rectangular SSMS-IS elements integrated in its body. Further, it investigated the feasibility of the robot to adapt its morphology online for environment variability, responding to external stimuli from the environment with different levels of stiffness and damping. Full article
(This article belongs to the Section Electronic Sensors)
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<p>Diagram of the robot principle: the system designed can perceive the environment as a sensor and actuate in the environment as an actuator using an integrated soft body. The internal mechanical feedback from the body can be combined with external physical stimulation representing a redundancy of the sensory channels, improving the speed and simplifying the perception. The information processed by the perception module can go to the brain and activate the actuator part of the system, but it also can be processed in the sensory-motor coordination module without necessarily passing through the brain, speeding up the dynamic control of the robot.</p>
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<p>Diagram of the principle of functionality regarding soft sensory-motor system based on ionic solution. Three states of the SSMS-IS can be observed, i.e., (<b>A</b>) relaxed, when there is no air inlet in the system <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math> and the external pressure is null <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>; (<b>B</b>) compressed, when there is no air inlet in the system <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math> and there is an external pressure <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> </msub> <mo>≠</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math> in the system; and (<b>C</b>) inflated, when there is air inlet <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> <mo>≠</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math> in the system and the external pressure is null <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>. For each state, differences can be observed in the electric resistance measurement <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mi>x</mi> </msub> <mo stretchy="false">)</mo> </mrow> </semantics></math> for a determined voltage (V) based on the variation in the ionic solution area <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <msub> <mi>A</mi> <mi>x</mi> </msub> <mo stretchy="false">)</mo> </mrow> </semantics></math> and distance <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <mi>L</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> between the positive and negative cupper cable. The variation in the ionic solution area <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <msub> <mi>A</mi> <mi>x</mi> </msub> <mo stretchy="false">)</mo> </mrow> </semantics></math> is correlated with the variation in external pressure <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </semantics></math> and internal pressure <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) Internal components of soft sensory-motor system based on ionic solution: ionic solution, soft diaphragm, copper wire, air tube, and electrode. The internal view is based on the rectangular geometry but can be applied to any design of SSMS-IS. (<b>b</b>) Comparison of the size of the SSMS-IS rectangular design with a 1 cent coin.</p>
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<p>Bioinspired robot design based on the morphology of the isopod Armadilium Vulgare: it was formed by modules that represent the bioinspired segments and each segment of the soft robot should have a sensory motor based on the SSMS-IS to actuate in the environment when expanded and to sense when compressed. Also, it can execute the conglobation movement for self-protection using soft actuators in each segment.</p>
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<p>Details of the robot’s segment with two SSMS-IS elements integrated into an internal interface. Each segment is composed of two pumps to inflate the SSMS-IS, two servo motors to make the pumps made by syringes function, and a soft actuator responsible for generating the conglobation movement bioinspired from Armadillium Vulgare. The SSMS-IS elements are actuated by pumps embedded in the robot.</p>
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<p>Robot morphology adaptation. From <a href="#sensors-24-02900-t001" class="html-table">Table 1</a>, (<b>a</b>) State 1, when both SSMS-ISs in the soft robot shield are disabled; (<b>b</b>) State 2, when one SSMS-IS is enabled; (<b>c</b>) State 3, when one SSMS-IS is enabled; and (<b>d</b>) State 4, when both SSMS-ISs are enabled.</p>
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<p>Three SSMS-IS designs were investigated: toroidal, semi-toroidal, and rectangular geometries. They were fabricated using silicon rubber RPRO 20 (Reschimica<sup>®</sup>).</p>
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<p>Fabrication procedure for different SSMS-IS designs: (<b>a</b>) SSMS-IS manufacturing process for toroid geometry; (<b>b</b>) SSMS-IS manufacturing process for semi-toroid geometry; and (<b>c</b>) SSMS-IS manufacturing process for rectangular geometry.</p>
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<p>Design of the electrolyte volume for each mold: (<b>a</b>) toroidal electrolyte volume = 1272.35 mm<sup>3</sup>; (<b>b</b>) semi-toroidal electrolyte volume = 1276.74 mm<sup>3</sup>; and (<b>c</b>) rectangular electrolyte volume = 1270.67 mm<sup>3</sup>.</p>
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<p>Elastomer parts for each SSMS-IS design: (<b>a</b>) toroidal; (<b>b</b>) semi-toroidal; and (<b>c</b>) rectangular. The diaphragm’s thickness for each SSMS-IS was 1 mm to guarantee less resistance during mechanical expansion.</p>
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<p>(<b>a</b>) Circuit diagram regarding the acquisition data for the resistance variation in the SSMS-IS. (<b>b</b>) Setup of the tests composed of controllers, pump, resistance divider circuit, SSMS-IS, and battery.</p>
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<p>(<b>a</b>) Test setup for evaluating external pressure over different designs of SSMS-IS; (<b>b</b>) test setup for toroidal SSMS-IS; (<b>c</b>) test setup for semi-toroidal SSMS-IS; and (<b>d</b>) test setup for rectangular SSMS-IS.</p>
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<p>(<b>a</b>) Setup to test the response of both sensors simultaneously on the interface for external force input in the vertical direction as shown by the yellow arrow; (<b>b</b>) robot without external input force; and (<b>c</b>) vertical load pressing the shield in the vertical direction as shown by the yellow arrow in the picture, emulating an external input force over the robot.</p>
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<p>Robot module system configuration: one microcontroller; two SSMS-ISs; two servomotors; two air pumps connected with SSMS-IS; and a lithium-ion battery. The measurements performed by the microcontroller can be communicated with the PC.</p>
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<p>Resistance changes vs. pressure for toroidal geometry of the sensor: (<b>a</b>) sensitivity within the sensing range of external pressure of 0–79.08 mmHg and (<b>b</b>) drift in toroidal sensor for approximately 15 min.</p>
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<p>Resistance changes vs. pressure for semi-toroidal geometry of the sensor: (<b>a</b>) sensitivity within the sensing range of external pressure of 0–79.08 mmHg and (<b>b</b>) drift in semi-toroidal sensor for approximately 15 min.</p>
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<p>Resistance changes vs. pressure for the rectangular geometry of the sensor: (<b>a</b>) sensitivity within the sensing range of external pressure of 0–79.08 mmHg and (<b>b</b>) drift in rectangular sensor for approximately 15 min.</p>
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<p>Resistance changes vs. internal pressure for toroidal geometry of the sensor: (<b>a</b>) sensitivity within the sensing range of external pressure of 0–477.81 mmHg and (<b>b</b>) results of cyclic loading of the sensor for 3000 cycles of internal pressure at 224.61 mmHg.</p>
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<p>Resistance changes vs. internal pressure for semi-toroidal geometry of the sensor: (<b>a</b>) sensitivity within the sensing range of external pressure of 0–477.81 mmHg and (<b>b</b>) results of cyclic loading of the sensor for 3000 cycles of internal pressure at 224.61 mmHg.</p>
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<p>Resistance changes vs. internal pressure for rectangular geometry of the sensor: (<b>a</b>) sensitivity within the sensing range of external pressure of 0–477.81 mmHg and (<b>b</b>) results of cyclic loading of the sensor for 3000 cycles of internal pressure at 224.61 mmHg.</p>
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<p>Robot time response for two states over external pressure inputs. Initially, the robot was in a relaxed state, and after subjecting the robot to 3 levels of loads (1.8 N, 2.4 N, and 2.9 N), the levels of force due to the variation in the electric resistance of the SSMS-IS was detected. In the second moment of the test, the robot was in the actuated state, and after subjecting the robot to 3 levels of loads (1.8 N, 2.4 N, and 2.9 N), the levels of force due to the variation in the electric resistance of the SSMS-IS was detected, indicating that, even in the actuated state, the robot can sense differences in external forces using a unique device to actuate and to sense simultaneously.</p>
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<p>Boxplot for the soft robot response for each load applied in each performed state. For the relaxed state, each SSMS-IS in the robot could detect the external loads by the variation in the electric resistance. Also, when the value of the load was increased, the variation in the resistance proportionally increased. For the actuated state, each SSMS-IS in the robot could also detect the external loads by the variation in the electric resistance. When the value of the load was increased, the variation in the resistance also proportionally increased, indicating that in both states, relaxed and actuated, the robot can measure different external load values, and the variation in the internal resistance is proportional to the variation in the load.</p>
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<p>Mechanical deformation for each system design (toroidal, semi-toroidal, and rectangular) for each state of the system: relaxed, compressed, and inflated. The differences in the mechanical elasticity constraints for each SSMS-IS design can be noticed during the states of expansion and compression.</p>
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20 pages, 8485 KiB  
Article
Research on Compliance Control of Electro-Hydraulic Loading Experimental System
by Shuai Jiang, Haikuo Shen, Shaodan Zhi, Chao Cheng, Huimin Ren and Jiang Tong
Electronics 2024, 13(7), 1273; https://doi.org/10.3390/electronics13071273 - 29 Mar 2024
Cited by 1 | Viewed by 794
Abstract
This article discusses the challenges in preventing workpiece damage due to impacts in electro-hydraulic loading systems, especially in unknown environments. We propose an innovative compliance control strategy, synergizing a series elastic actuator with impedance control to significantly mitigate impact forces between the mechanism [...] Read more.
This article discusses the challenges in preventing workpiece damage due to impacts in electro-hydraulic loading systems, especially in unknown environments. We propose an innovative compliance control strategy, synergizing a series elastic actuator with impedance control to significantly mitigate impact forces between the mechanism and test workpieces. The controller consists of two loops: an internal loop and an outer loop. The internal loop integrates a position loop utilizing a radial basis function observer within a backstepping control framework, effectively countering the nonlinear dynamics of hydraulic actuators and ensuring precise trajectory tracking. The outer loop advances traditional impedance control by adaptively modifying the damping coefficient, resulting in a straightforward and easily implementable damping control law. For the unknown environment parameters, our system employs a parameter estimation law to estimate the unknown environmental stiffness and position parameters. The effectiveness of this strategy has been verified through comparative simulation with traditional impedance control, indicating that the proposed method can not only effectively reduce contact shock in unknown environments, improve response speed, and reduce overshoot, but also improve steady-state accuracy. We provided a feasible control scheme for similar systems to ensure precise and safe operation. Full article
(This article belongs to the Section Computer Science & Engineering)
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<p>The structure of the electro-hydraulic system.</p>
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<p>Loading motion of the contact process. (<b>a</b>) Initial state; (<b>b</b>) Free-space motion; (<b>c</b>) Contact state; (<b>d</b>) Loading motion.</p>
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<p>Tracking errors of sine wave simulation.</p>
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<p>Diagram of the proposed control algorithm.</p>
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<p>Simulation diagram of the electro-hydraulic load test system in Matlab.</p>
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<p>Constant force tracking results in the constant environment.</p>
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<p>Tracking performance of RBF state observer.</p>
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<p>Constant force tracking under changes in stiffness.</p>
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<p>Environmental stiffness estimation.</p>
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<p>Expected step loading force curve.</p>
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<p>Simulation results of step loading force tracking.</p>
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<p>Simulation results of sine loading force tracking.</p>
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23 pages, 9504 KiB  
Article
Actuators for Improving Robotic Arm Safety While Maintaining Performance: A Comparison Study
by Jiawei Xu and Gary M. Bone
Actuators 2024, 13(2), 69; https://doi.org/10.3390/act13020069 - 11 Feb 2024
Cited by 2 | Viewed by 2427
Abstract
Since robotic arms operating close to people are becoming increasingly common, there is a need to better understand how they can be made safe when unintended contact occurs, while still providing the required performance. Several actuators and methods for improving robot safety are [...] Read more.
Since robotic arms operating close to people are becoming increasingly common, there is a need to better understand how they can be made safe when unintended contact occurs, while still providing the required performance. Several actuators and methods for improving robot safety are studied and compared in this paper. A robotic arm moving its end effector horizontally and colliding with a person’s head is simulated. The use of a conventional electric actuator (CEA), series elastic actuator (SEA), pneumatic actuator (PA) and hybrid pneumatic electric actuator (HPEA) with model-based controllers are studied. The addition of a compliant covering to the arm and the use of collision detection and reaction strategies are also studied. The simulations include sensor noise and modeling error to improve their realism. A systematic method for tuning the controllers fairly is proposed. The motion control performance and safety of the robot are quantified using root mean square error (RMSE) between the desired and actual joint angle trajectories and maximum impact force (MIF), respectively. The results show that the RMSE values are similar when the CEA, SEA, and HPEA drive the robot’s first joint. Regarding safety, using the PA or HPEA with a compliant covering can reduce the MIF below the safety limit established by the International Organization for Standardization (ISO). To satisfy this ISO safety limit with the CEA and SEA, a collision detection and reaction strategy must be used in addition to the compliant covering. The influences of the compliant covering’s stiffness and the detection delay are also studied. Full article
(This article belongs to the Section Actuators for Robotics)
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<p>Structure of the system.</p>
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<p>Model of the robotic arm rotating about joint 1.</p>
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<p>Schematic of the CEA.</p>
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<p>Human head model for constrained impact.</p>
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<p>Human head and neck model for unconstrained impact.</p>
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<p>Structure of the torque control loop for the SEA.</p>
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<p>Motion control results for the robotic arm driven by the CEA: (<b>a</b>) desired and actual joint positions, (<b>b</b>) actuator torque, (<b>c</b>) joint position error, and (<b>d</b>) estimated and actual friction torques.</p>
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<p>Motion control results for the robotic arm driven by the SEA: (<b>a</b>) desired and actual joint positions, (<b>b</b>) actuator torque, (<b>c</b>) joint position error, and (<b>d</b>) Estimated and actual friction torques.</p>
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<p>Motion control results for the robotic arm driven by the PA: (<b>a</b>) desired and actual joint positions, (<b>b</b>) actuator torque, (<b>c</b>) joint position error, and (<b>d</b>) estimated and actual friction torques.</p>
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<p>Motion control results for the robotic arm driven by the HPEA: (<b>a</b>) Desired and actual joint positions, (<b>b</b>) actuator torque, (<b>c</b>) joint position error, and (<b>d</b>) estimated and actual friction torques.</p>
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<p>Impact force results for a constrained head impact when no compliant covering or collision reaction is used. The actuators used are: (<b>a</b>) CEA, (<b>b</b>) SEA, (<b>c</b>) PA, and (<b>d</b>) HPEA.</p>
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<p>Impact force results for an unconstrained head impact when no compliant covering or collision reaction is used. The actuators used are: (<b>a</b>) CEA, (<b>b</b>) SEA, (<b>c</b>) PA, and (<b>d</b>) HPEA.</p>
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<p>Impact force results for a constrained head impact when a compliant covering is added to the robot, with no collision reaction. The actuators used are: (<b>a</b>) CEA, (<b>b</b>) SEA, (<b>c</b>) PA, and (<b>d</b>) HPEA.</p>
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<p>Impact force results for an unconstrained head impact when a compliant covering is added to the robot, with no collision reaction. The actuators used are: (<b>a</b>) CEA, (<b>b</b>) SEA, (<b>c</b>) PA, and (<b>d</b>) HPEA.</p>
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<p>MIF vs. compliant covering stiffness when using no reaction (NR) to the collision, the TAO reaction strategy, and the WTA reaction strategy. All results are for a constrained head impact with the collision DRD set to 25 ms. The actuators used are: (<b>a</b>) CEA, (<b>b</b>) SEA, (<b>c</b>) PA, and (<b>d</b>) HPEA.</p>
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<p>MIF vs. compliant covering stiffness when using the WTA reaction strategy with DRD values of 5 ms, 25 ms, 50 ms, and 100 ms. All results are for a constrained head impact. The actuators used are: (<b>a</b>) CEA, (<b>b</b>) SEA, (<b>c</b>) PA, and (<b>d</b>) HPEA.</p>
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17 pages, 18726 KiB  
Article
Environment Aware Friction Observer with Applications to Force Control Benchmarking
by Eldison Dimo and Andrea Calanca
Actuators 2024, 13(2), 53; https://doi.org/10.3390/act13020053 - 31 Jan 2024
Viewed by 1496
Abstract
The benchmarking of force control algorithms has been significantly investigated in recent years. High-fidelity experimental benchmarking outcomes may require high-end electronics and mechanical systems not to compromise the algorithm’s evaluation. However, affordability may be highly desired to spread benchmarking tools within the research [...] Read more.
The benchmarking of force control algorithms has been significantly investigated in recent years. High-fidelity experimental benchmarking outcomes may require high-end electronics and mechanical systems not to compromise the algorithm’s evaluation. However, affordability may be highly desired to spread benchmarking tools within the research community. Mechanical inaccuracies due to affordability can lead to undesired friction effects which in this paper are tackled by exploiting a novel friction compensation technique based on an environment-aware friction observer (EA-FOB). Friction compensation capabilities of the proposed EA-FOB are assessed through simulation and experimental comparisons with a widely used static friction model: Coulomb friction combined with viscous friction. Moreover, a comprehensive stability comparison with state-of-the-art disturbance observers (DOBs) is conducted. Results show higher stability margins for the EA-FOB with respect to traditional DOBs. The research is carried on within the Forecast project, which aims to provide tools and metrics to benchmark force control algorithms relying on low-cost electronics and affordable hardware. Full article
(This article belongs to the Section Control Systems)
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<p>Two pictures of the Forecast testbed where (<b>a</b>) represents the configuration of a Series Elastic Actuator (SEA). (<b>b</b>) highlights each module and emphasizes the easy-to-configure idea. Also, a detailed CAD view of the leaf spring mechanism within the spring module can be observed. The red parts are fixed to the motor shaft while the gray parts are fixed to the virtual environment module.</p>
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<p>Three pictures representing issues due to friction effects in the Forecast testbed shown in <a href="#actuators-13-00053-f001" class="html-fig">Figure 1</a>. (<b>a</b>) shows simulated (red) and experimental (black) actuator torques during a <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>I</mi> </mrow> </semantics></math> velocity control, highlighting torque ripples due to friction. (<b>b</b>) shows that stick-slip effects affecting the testbed are extremely uncertain. (<b>c</b>) reports the outcome of three different friction identification procedures (each represented by a different color) highlighting different static friction magnitudes and different Stribeck curves.</p>
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<p>A figure showing three experimental step responses of a PD force controller with the same tuning. Friction effects lead to significantly different benchmarking outcomes.</p>
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<p>Block diagram representation of a series elastic actuator interacting with a generic environment <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>A block diagram of the considered DOB force control architecture, where <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>F</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> is a generic force controller, <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> represents the nominal model and <math display="inline"><semantics> <mrow> <mi>Q</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </semantics></math> is a low-pass filter used to both allow the nominal model inversion and to tune the frequency (<math display="inline"><semantics> <msub> <mi>w</mi> <mi>q</mi> </msub> </semantics></math>) up to which disturbances are rejected. The dynamics of <math display="inline"><semantics> <mrow> <mi>P</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </semantics></math> is expressed as (<a href="#FD2-actuators-13-00053" class="html-disp-formula">2</a>).</p>
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<p>Disk margins of the considered DOB solutions.</p>
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<p>Simulation results considering a SFM friction compensation and the proposed EA-FOB friction compensation.</p>
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<p>Torque profile of the spring module shown in <a href="#actuators-13-00053-f001" class="html-fig">Figure 1</a>b. The red line represents the spring torque profile, measured according to (<a href="#FD1-actuators-13-00053" class="html-disp-formula">1</a>). The black line represents the torque measured with the torque sensor (shown in <a href="#actuators-13-00053-f001" class="html-fig">Figure 1</a>) and drawn here as a ground truth.</p>
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<p>Extended SFM friction identification outcomes.</p>
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<p>Step responses considering the PD force controller without any friction compensation law. The red dashed line simulates how the system would perform under the control action of the PD in the absence of friction.</p>
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<p>Step responses considering the PD force control with an SFM compensation. The red dashed line simulates how the system would perform under the control action of the PD in the absence of friction.</p>
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<p>Step responses considering the PD force control with the proposed EA-FOB algorithm. The red dashed line simulates how the system would perform under the control action of the PD in the absence of friction.</p>
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<p>Torque tracking of the considered DOB architectures interacting with a soft and a stiff environment. Each experiment is carried out with the same <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>D</mi> </mrow> </semantics></math> force controller tuned as <span class="html-italic">P</span> = 5 and <span class="html-italic">D</span> = 0.1.</p>
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26 pages, 9753 KiB  
Article
Design and Research of Series Actuator Structure and Control System Based on Lower Limb Exoskeleton Rehabilitation Robot
by Chenglong Zhao, Zhen Liu, Liucun Zhu and Yuefei Wang
Actuators 2024, 13(1), 20; https://doi.org/10.3390/act13010020 - 5 Jan 2024
Cited by 3 | Viewed by 2217
Abstract
Lower limb exoskeleton rehabilitation robots have become an important direction for development in today’s society. These robots can provide support and power to assist patients in walking and movement. In order to achieve better interaction between humans and machines and achieve the goal [...] Read more.
Lower limb exoskeleton rehabilitation robots have become an important direction for development in today’s society. These robots can provide support and power to assist patients in walking and movement. In order to achieve better interaction between humans and machines and achieve the goal of flexible driving, this paper addresses the shortcomings of traditional elastic actuators and designs a series elastic–damping actuator (SEDA). The SEDA combines elastic and damping components in parallel, and the feasibility of the design and material selection is demonstrated through finite element static analysis. By modeling the dynamics of the SEDA, using the Bode plot and Nyquist plot, open-loop and closed-loop frequency domain comparisons and analyses were carried out, respectively, to verify the effect of damping coefficients on the stability of the system, and the stiffness coefficient ks = 25.48 N/mm was selected as the elastic element and the damping coefficient cs = 1 Ns/mm was selected as the damping element. A particle swarm optimization (PSO)-based algorithm was proposed to introduce the fuzzy controller into the PID control system, and five parameters, namely the the fuzzy controller’s fuzzy factor (ke, kec) and de-fuzzy factor (kp1, ki1, kd1), are taken as the object of the algorithm optimization to obtain the optimal fuzzy controller parameters of ke = 0.8, kec = 0.2, kp1 = 0.5, ki1 = 8, kd1 = −0.1. The joint torque output with and without external interference is simulated, and the simulation model is established in the MATLAB/Simulink environment The results show that when fuzzy PID control is used, the amount of overshooting in the system is 14.6%, and the regulation time is 0.66 s. This has the following advantages: small overshooting amount, short rise time, fast response speed, short regulation time, good stability performance, and strong anti-interference ability. The SEDA design structure and control method breaks through limitations of the traditional series elastic actuator (SEA) such as its lack of flexibility and stability, which is very helpful to improve the output effect of flexible joints. Full article
(This article belongs to the Special Issue Actuators and Robots for Biomedical Applications)
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<p>Three-dimensional model of lower limb exoskeleton rehabilitation robot.</p>
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<p>Trial fitting effect image.</p>
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<p>Joint motion parameters and GRF curves: (<b>a</b>) joint angle change; (<b>b</b>) joint output torque; (<b>c</b>) barefoot walking GRF curve.</p>
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<p>Joint angle limitation.</p>
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<p>Ankle joint structure.</p>
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<p>Overall structure of SEDA: 1—servo motor; 2—guiding shaft; 3—mold spring; 4—spring separator; 5—damper; 6—ball screw.</p>
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<p>Assembly diagram of SEDA before and after improvement: (<b>a</b>) original assembly diagram; (<b>b</b>) improved assembly diagram.</p>
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<p>Axial thrust model of SEDA.</p>
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<p>Finite element analysis of SEDA structure part I: (<b>a</b>) model diagram; (<b>b</b>) mesh diagram; (<b>c</b>) deformation diagram; (<b>d</b>) stress diagram.</p>
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<p>SEDA radial thrust model.</p>
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<p>SEDA structural finite element analysis II: (<b>a</b>) model diagram; (<b>b</b>) mesh diagram; (<b>c</b>) deformation diagram; (<b>d</b>) stress diagram.</p>
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<p>Schematic diagram of elastic actuator design.</p>
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<p>Schematic diagram of series elastic−damping actuator design.</p>
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<p>SEDA dynamic model based on force source control.</p>
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<p>Open-loop system bandwidth graph: (<b>a</b>) Nyquist diagram; (<b>b</b>) Bode diagram.</p>
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<p>Open-loop system output impedance plot: (<b>a</b>) Nyquist diagram; (<b>b</b>) Bode diagram.</p>
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<p>System shock resistance diagram: (<b>a</b>) system Bode diagram; (<b>b</b>) robot GRF curve.</p>
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<p>Bode diagram of open-loop system’s damping characteristics analysis: (<b>a</b>) output bandwidth Bode diagram; (<b>b</b>) output impedance Bode diagram; (<b>c</b>) shock absorption capability Bode diagram.</p>
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<p>Time-varying curves of output torque for different stiffness coefficients: (<b>a</b>) Simulink control system; (<b>b</b>) output torque variation curve.</p>
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<p>Time-varying curves of output torque for different stiffness coefficients: (<b>a</b>) Simulink control system; (<b>b</b>) output torque variation curve.</p>
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<p>Output torque variation curve for different damping coefficients: (<b>a</b>) Simulink control system; (<b>b</b>) output torque variation curve.</p>
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<p>Output torque variation curve for different damping coefficients: (<b>a</b>) Simulink control system; (<b>b</b>) output torque variation curve.</p>
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<p>Open-loop and closed-loop system stability comparison analysis: (<b>a</b>) output bandwidth Nyquist diagram comparison; (<b>b</b>) output bandwidth Bode diagram comparison; (<b>c</b>) output impedance Nyquist diagram comparison; (<b>d</b>) output impedance Bode diagram comparison.</p>
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<p>Output surface plots of <span class="html-italic">k<sub>p</sub></span>, <span class="html-italic">k<sub>i</sub></span>, <span class="html-italic">k<sub>d</sub></span> on their respective domains: (<b>a</b>) <span class="html-italic">k<sub>p</sub></span> output surface; (<b>b</b>) <span class="html-italic">k<sub>i</sub></span> output surface; (<b>c</b>) <span class="html-italic">k<sub>d</sub></span> output surface.</p>
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<p>Block diagram of PSO algorithm parameter optimization system.</p>
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<p>Simulink diagram of fuzzy PID control: (<b>a</b>) fuzzy PID controller subsystem diagram; (<b>b</b>) comparison diagram of 3 types of controllers.</p>
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<p>Simulink diagram of fuzzy PID control: (<b>a</b>) fuzzy PID controller subsystem diagram; (<b>b</b>) comparison diagram of 3 types of controllers.</p>
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<p>Simulink simulation results: (<b>a</b>) no disturbance; (<b>b</b>) with disturbance.</p>
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13 pages, 1205 KiB  
Article
Exploring the Just Noticeable Interaction Stiffness Differences of an Impedance-Controlled Series Elastic Actuator
by Rodrigo J. Velasco-Guillen, Felix Schofer, Adna Bliek and Philipp Beckerle
Actuators 2023, 12(10), 378; https://doi.org/10.3390/act12100378 - 5 Oct 2023
Cited by 3 | Viewed by 1516
Abstract
The integration of a passive elastic element in series between a motor and its load is popular in many human–robot interaction scenarios. By virtually imposing elastic behavior on the motor, an impedance control can act as a second stiffness to such an actuator. [...] Read more.
The integration of a passive elastic element in series between a motor and its load is popular in many human–robot interaction scenarios. By virtually imposing elastic behavior on the motor, an impedance control can act as a second stiffness to such an actuator. In this study, we investigated how participants perceived the different stiffness settings in a series elastic actuator by measuring the Just Noticeable Difference (JND) of the real stiffness of the elastic element and the virtual stiffness introduced by impedance control. We conducted a user study during which participants interacted with an impedance-controlled Series Elastic Actuator through a lever. During the user study, we varied the real stiffness of the elastic element and the virtual stiffness. We found that participants seem to perceive both the virtual stiffness and the real stiffness in the same way and in accordance to Weber’s law, which states that the stiffness JND is always equal to a fraction of the initial stiffness. Following these findings, we concluded that the impedance controller can implement an effective virtual stiffness with a behavior comparable to a real torsional spring. Therefore, a system combining real and virtual stiffness can simulate a single combined stiffness for a user interacting with it. Full article
(This article belongs to the Special Issue Actuation Solutions for Wearable Robots)
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<p>Picture of the VTS actuator with (1) DC motor with a gearbox (Actuation Unit 1), connected to the torsional rod via a coupling; (2) DC motor with gearbox (Actuation Unit 2), connected to torsional rod mechanism via a coupling; (3) Linear potentiometer measuring <math display="inline"><semantics> <msub> <mi>l</mi> <mi>s</mi> </msub> </semantics></math>; (4) Torsional rod with a mechanism to change its length <math display="inline"><semantics> <msub> <mi>l</mi> <mi>s</mi> </msub> </semantics></math>; (5) Torque sensor measuring <math display="inline"><semantics> <msub> <mi>τ</mi> <mi>s</mi> </msub> </semantics></math>; (6) Lever for user interaction.</p>
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<p>Mechanism to change effective length of the torsional rod. Actuation Unit 2 moves a counter bearing along the torsional rod that transmits the torque from the torsional rod to the lever, which is used for user interaction. Changing the position of the bearing thus changes the effective length <math display="inline"><semantics> <msub> <mi>l</mi> <mi>s</mi> </msub> </semantics></math> of the torsional rod.</p>
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<p>Structure of an impedance-controlled SEA with real stiffness <math display="inline"><semantics> <msub> <mi>k</mi> <mi>s</mi> </msub> </semantics></math>, load inertia <math display="inline"><semantics> <msub> <mi>J</mi> <mi>l</mi> </msub> </semantics></math>, and virtual impedance parameters: stiffness <math display="inline"><semantics> <msub> <mi>k</mi> <mi>d</mi> </msub> </semantics></math>, damping <math display="inline"><semantics> <msub> <mi>d</mi> <mi>d</mi> </msub> </semantics></math>, and inertia <math display="inline"><semantics> <msub> <mi>J</mi> <mrow> <mi>a</mi> <mo>,</mo> <mi>d</mi> </mrow> </msub> </semantics></math>. The system behaves as a two-mass torsional oscillator subject to the interaction torque <math display="inline"><semantics> <msub> <mi>τ</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> </semantics></math>.</p>
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<p>Interaction step responses. Deflection of <math display="inline"><semantics> <mrow> <mn>0.35</mn> <mi>rad</mi> </mrow> </semantics></math> from a fixed lever position. Setting A: <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>50</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <mn>150</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mrow> </semantics></math>; Setting B: <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>150</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <mn>50</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mrow> </semantics></math>. Tests show that the expected interaction behavior, i.e., <math display="inline"><semantics> <mrow> <msub> <mi>τ</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msub> <mover accent="true"> <mi>φ</mi> <mo>˜</mo> </mover> <mi>l</mi> </msub> </mrow> </semantics></math>, is obtained when implementing inertia shaping. Without it, unmodeled static friction components are noticeable and deform the interaction curve <math display="inline"><semantics> <msub> <mi>τ</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> </semantics></math> vs. <math display="inline"><semantics> <msub> <mover accent="true"> <mi>φ</mi> <mo>˜</mo> </mover> <mi>l</mi> </msub> </semantics></math>.</p>
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<p>Periodic interaction examples with setting A: <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>50</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <mn>150</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mrow> </semantics></math>. The periodic interaction signals are obtained by deflecting the position of the lever following a visual and auditory metronome. The plots show 15 cycles of measured torque and deflection measurements.</p>
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<p>Measured and theoretical Bode magnitude plot (<b>top</b>) and phase plot (<b>bottom</b>) of stiffness transfer function <math display="inline"><semantics> <mrow> <mi>K</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>τ</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mover accent="true"> <mi>φ</mi> <mo>˜</mo> </mover> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </semantics></math>. Setting A: <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>50</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <mn>150</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mrow> </semantics></math>, Setting B: <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>150</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <mn>50</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mrow> </semantics></math>. Natural frequencies of measured response match.</p>
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<p>VTS experimental setup. The actuator is fully covered by black plexiglass and a noise cancelling headset is used during experiments.</p>
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<p>Example run of one experiment. The varied stiffness is <math display="inline"><semantics> <msub> <mi>k</mi> <mi>d</mi> </msub> </semantics></math>, the initial value <math display="inline"><semantics> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> </semantics></math> is 50 <math display="inline"><semantics> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mi>1</mi> </mrow> </msup> </mrow> </semantics></math>. The value of <math display="inline"><semantics> <msub> <mi>k</mi> <mi>s</mi> </msub> </semantics></math> is 220 <math display="inline"><semantics> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mi>1</mi> </mrow> </msup> </mrow> </semantics></math> for all trials. Reversals are shown as filled red circles. The resulting JND is calculated using the average value of <math display="inline"><semantics> <msub> <mi>k</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> </msub> </semantics></math> of the last 10 trials.</p>
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<p>Boxplot of the obtained absolute JND (<b>left</b>) and normalized JND (<b>right</b>). Condition 1: Varied stiffness <math display="inline"><semantics> <msub> <mi>k</mi> <mi>s</mi> </msub> </semantics></math> (real), initial stiffness <math display="inline"><semantics> <mrow> <mn>100</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mi>1</mi> </mrow> </msup> </mrow> </mrow> </semantics></math>. Condition 2: Varied stiffness <math display="inline"><semantics> <msub> <mi>k</mi> <mi>s</mi> </msub> </semantics></math> (real), initial stiffness <math display="inline"><semantics> <mrow> <mn>50</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mi>1</mi> </mrow> </msup> </mrow> </mrow> </semantics></math>. Condition 3: Varied stiffness <math display="inline"><semantics> <msub> <mi>k</mi> <mi>d</mi> </msub> </semantics></math> (virtual), initial stiffness <math display="inline"><semantics> <mrow> <mn>100</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mi>1</mi> </mrow> </msup> </mrow> </mrow> </semantics></math>. Condition 4: Varied stiffness <math display="inline"><semantics> <msub> <mi>k</mi> <mi>d</mi> </msub> </semantics></math> (virtual), initial stiffness <math display="inline"><semantics> <mrow> <mn>50</mn> <mo> </mo> <mrow> <mi mathvariant="normal">N</mi> <mo> </mo> <mi mathvariant="normal">m</mi> <mo> </mo> <msup> <mi>rad</mi> <mrow> <mo>−</mo> <mi>1</mi> </mrow> </msup> </mrow> </mrow> </semantics></math>.</p>
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30 pages, 4051 KiB  
Article
Evaluation and Comparison of SEA Torque Controllers in a Unified Framework
by Wolfgang Rampeltshammer, Arvid Keemink, Menno Sytsma, Edwin van Asseldonk and Herman van der Kooij
Actuators 2023, 12(8), 303; https://doi.org/10.3390/act12080303 - 25 Jul 2023
Cited by 1 | Viewed by 1417
Abstract
Series elastic actuators (SEA) with their inherent compliance offer a safe torque source for robots that are interacting with various environments, including humans. These applications have high requirements for the SEA torque controllers, both in the torque response as well as interaction behavior [...] Read more.
Series elastic actuators (SEA) with their inherent compliance offer a safe torque source for robots that are interacting with various environments, including humans. These applications have high requirements for the SEA torque controllers, both in the torque response as well as interaction behavior with its environment. To differentiate state of the art torque controllers, this work introduces a unifying theoretical and experimental framework that compares controllers based on their torque transfer behavior, their apparent impedance behavior, and especially the passivity of the apparent impedance (i.e., their interaction stability) as well as their sensitivity to sensor noise. We compare classical SEA control approaches such as cascaded PID controllers and full state feedback controllers with advanced controllers using disturbance observers, acceleration feedback and adaptation rules. Simulations and experiments demonstrate the trade-off between stable interactions, high bandwidths and low noise levels. Based on these trade-offs, an application-specific controller can be designed and tuned, based on desired interaction with the respective environment. Full article
(This article belongs to the Section Actuators for Robotics)
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Figure 1

Figure 1
<p>Organization of this paper.</p>
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<p>Shown on the <b>left</b> is the physical representation of the SEA, with motor side damping <math display="inline"><semantics><msub><mi>b</mi><mi>m</mi></msub></semantics></math>, motor inertia <math display="inline"><semantics><msub><mi>j</mi><mi>m</mi></msub></semantics></math>, spring stiffness <span class="html-italic">k</span>, motor torque <math display="inline"><semantics><msub><mi>τ</mi><mi>m</mi></msub></semantics></math> and position <span class="html-italic">q</span>, as well as output position <math display="inline"><semantics><mi>θ</mi></semantics></math> and interaction torque <math display="inline"><semantics><msub><mi>τ</mi><mi>k</mi></msub></semantics></math>. Additionally, the transfer model of the presented SEA is shown on the <b>right</b>.</p>
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<p>Diagram for the FSFt controller. Controller includes a feedforward term as well as the state feedbacks of the interaction torque <math display="inline"><semantics><msub><mi>τ</mi><mi>k</mi></msub></semantics></math>.</p>
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<p>Diagram for the FSFm controller in its adapted form, including a feedforward term and state feedback of the motor velocity <math display="inline"><semantics><mover accent="true"><mi>q</mi><mo>˙</mo></mover></semantics></math>.</p>
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<p>Control diagram of the cascaded PID controller, with the inner velocity loop and its PI controller <math display="inline"><semantics><msubsup><mi>G</mi><mrow><mi>P</mi><mi>I</mi></mrow><mi>i</mi></msubsup></semantics></math>, and the outer torque loop and its PID controller <math display="inline"><semantics><msubsup><mi>G</mi><mrow><mi>P</mi><mi>I</mi><mi>D</mi></mrow><mi>o</mi></msubsup></semantics></math>.</p>
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<p>Control diagram of the PD controller with a feedforward term.</p>
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<p>MRAC control scheme including the adaptive control block, and adaptive gains <math display="inline"><semantics><mover accent="true"><mi>b</mi><mo stretchy="false">^</mo></mover></semantics></math> and <math display="inline"><semantics><mover accent="true"><mi>c</mi><mo stretchy="false">^</mo></mover></semantics></math>.</p>
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<p>Control scheme for a DOB, for an arbitrary controller <math display="inline"><semantics><msup><mi>C</mi><mi>i</mi></msup></semantics></math>.</p>
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<p>Control scheme for output acceleration feedback with an arbitrary controller <math display="inline"><semantics><msup><mi>C</mi><mi>i</mi></msup></semantics></math>. The noise for the acceleration signal <math display="inline"><semantics><mrow><msub><mi>η</mi><mover accent="true"><mi>θ</mi><mo>¨</mo></mover></msub><mo>=</mo><mi>s</mi><msub><mi>η</mi><mover accent="true"><mi>θ</mi><mo>˙</mo></mover></msub></mrow></semantics></math> is replaced in the diagram for clarity.</p>
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<p>Theoretical comparison of the torque tracking performance of the presented controllers. Controllers are tuned for a bandwidth <math display="inline"><semantics><mrow><msub><mi>ω</mi><mrow><mi>B</mi><mi>W</mi></mrow></msub><mo>=</mo><mn>30</mn><mspace width="3.33333pt"/><mi>Hz</mi></mrow></semantics></math> and similar resonance peaks. FSFt and FSFm have identical torque transfer. Additionally, ideal MRAC torque response is identical to FSFt.</p>
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<p>Theoretical comparison of the apparent impedance. On the <b>left side</b> the state-of-the-art controllers PD-DOB, FSFt, FSFm and Cascaded PID are compared. On the <b>right side</b>, both PD and FSFt controllers’ apparent impedance is improved with a DOB (dashed lines) and acceleration feedback (dotted lines). All gains are selected to achieve a marginally passive apparent impedance.</p>
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<p>Theoretical comparison of the noise spectral density for each controller. The panels in the <b>left column</b> show all controllers with pure torque feedback (FSFt, PD, MRAC, FSFt-DOB, PD-DOB). The <b>top panels</b> show the noise sensitivity for all presented torque controllers, with the <b>bottom panels</b> showing controllers with apparent impedance shaping methods. The noise spectral density demonstrates the effect of each noise source on the controlled interaction torque <math display="inline"><semantics><msub><mi>τ</mi><mi>k</mi></msub></semantics></math>.</p>
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<p>Setup of SEA for experimental evaluation. The <b>left side</b> depicts the setup and the <b>right side</b> depicts a schematic of the setup. The actuator is mounted to a heavy counterweight via a moveable axis to allow for test with high torques. The test setup can be used with endstops fixed in the hole of the actuator connection plate (<b>lower hole</b>), and with a locked output by mounting a bracket between the holes in the connection plate and the hole in the axle.</p>
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<p>Time series of the selected excitation frequencies <math display="inline"><semantics><mrow><mi>ω</mi><mo>∈</mo><mfenced separators="" open="{" close="}"><mn>0.1</mn><mo>,</mo><mn>0.3</mn><mo>,</mo><mn>0.7</mn></mfenced><mspace width="3.33333pt"/><mi>Hz</mi></mrow></semantics></math> of the apparent impedance identification experiment for the target bandwidth of 20 Hz. Each column has identically scaled axes, with the exception of the PD-AF and FSFm controllers, which exhibit higher torque responses. The data show that the target frequency and amplitude were reached consistently. It can also be seen that the excitation signal at low frequencies is more rectangular, compared to higher frequencies. Additionally, differences in apparent impedance magnitude can be observed from differences in the shape and magnitude of the joint torque.</p>
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<p>Torque tracking identification results for PD-DOB, FSFt, FSFm, Cascaded PID and MRAC controller. Identification was conducted over a set of frequencies, and each frequency resulted in a data point, as shown in the identified bode plots. Additionally, the target bandwidth is shown with the gray lines.</p>
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<p>Apparent impedance identification results for PD-DOB, FSFt, FSFm, Cascaded PID and MRAC controllers, as well as the improvement method FSFt-AF. Identification was conducted by manually exciting the output of the actuator. From the data points it can be seen that this was achieved consistently. The shown data confirms that apparent impedance can be lowered for target frequency ranges, and that the use of improvement methods causes additional phase lead in the closed loop system.</p>
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<p>Impact tests for all proposed controllers. Impact happens at the first jump of velocity. In between the first and second jump, the endstop is bending slightly, and rebound happens at time zero. Both jumps of velocity during impact are single sample measurement errors from the encoders. It is shown that all controllers are indeed passive (i.e., all velocities go back to zero at varying speeds) with only MRAC showing oscillations after impact.</p>
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12 pages, 3717 KiB  
Article
A Back-Drivable Rotational Force Actuator for Adaptive Grasping
by Xiaofeng Wu, Hongliang Hua, Che Zhao, Naiyu Shi and Zhiwei Wu
Actuators 2023, 12(7), 267; https://doi.org/10.3390/act12070267 - 29 Jun 2023
Cited by 2 | Viewed by 1383
Abstract
In this paper, a back-drivable and miniature rotary series elastic actuator (RSEA) is proposed for robotic adaptive grasping. A compact arc grooves design has been proposed to effectively reduce the dimension of the RSEA system. The elastic elements could be reliably embedded in [...] Read more.
In this paper, a back-drivable and miniature rotary series elastic actuator (RSEA) is proposed for robotic adaptive grasping. A compact arc grooves design has been proposed to effectively reduce the dimension of the RSEA system. The elastic elements could be reliably embedded in the arc grooves without any additional installation structures. The whole RSEA system is characterized as compact, miniature, and modular. The actuating force is controlled via a PI controller by tracking the deformation trajectory of the elastic elements. An underactuated finger mechanism has been adopted to investigate the effectiveness of the RSEA in robotic adaptive grasping. Results reveal that the underactuated finger mechanism could achieve adaptive grasping via the RSEA in a back-drive approach without the requirement of a fingertip force sensor. The RSEA could also exhibit an actuating compliance and a self-sensing characteristic. The actuating compliance characteristic helps in in guaranteeing the safety of human–robot interaction. The RSEA could estimate the external disturbance due to its self-sensing characteristic, which has the potential to replace the fingertip force sensor in grasping force perception applications. Full article
(This article belongs to the Special Issue Advancement in the Design and Control of Robotic Grippers)
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Figure 1
<p>3D CAD illustration of the RSEA system.</p>
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<p>Actuating principle of the RSEA. (<b>a</b>) Arc grooves design. (<b>b</b>) Principle of torque transfer. (<b>c</b>) Torque and spring deformation analysis.</p>
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<p>Experimental platform to measure the actuating force of the SEA system. (<b>a</b>) Unloading state. (<b>b</b>) Loading state.</p>
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<p>Model identification of <span class="html-italic">F<sub>o</sub></span> and <math display="inline"><semantics><mrow><msub><mi>θ</mi><mi>c</mi></msub></mrow></semantics></math>. (<b>a</b>) Fitting error <math display="inline"><semantics><mrow><msub><mrow><mrow><mo>‖</mo><mrow><msub><mi>E</mi><mi>F</mi></msub></mrow><mo>‖</mo></mrow></mrow><mn>2</mn></msub></mrow></semantics></math> and <math display="inline"><semantics><mrow><msub><mrow><mrow><mo>‖</mo><mrow><msub><mi>E</mi><mi>θ</mi></msub></mrow><mo>‖</mo></mrow></mrow><mn>2</mn></msub></mrow></semantics></math> with respect to different model order <math display="inline"><semantics><mi>n</mi></semantics></math>. (<b>b</b>) Comparison between <math display="inline"><semantics><mrow><msub><mover accent="true"><mi>F</mi><mo stretchy="false">˜</mo></mover><mi mathvariant="normal">o</mi></msub></mrow></semantics></math> and <math display="inline"><semantics><mrow><msub><mi>F</mi><mi mathvariant="normal">o</mi></msub></mrow></semantics></math>. (<b>c</b>) Comparison between <math display="inline"><semantics><mrow><msub><mover accent="true"><mi>θ</mi><mo stretchy="false">˜</mo></mover><mi>c</mi></msub></mrow></semantics></math> and <math display="inline"><semantics><mrow><msub><mi>θ</mi><mi>c</mi></msub></mrow></semantics></math>.</p>
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<p>Control responses of the RSEA with respect to different actuating force.</p>
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<p>O-type rubber ring loading experiment. (<b>a</b>) Original state. (<b>b</b>–<b>f</b>) Steady state of the rubber ring under different <span class="html-italic">t<sub>F</sub></span> ranges from −2 N to −6 N. (<b>g</b>) Self-sensed response of the actuating force under different <math display="inline"><semantics><mrow><msub><mi>t</mi><mi>F</mi></msub></mrow></semantics></math> ranges from −2 N to −6 N.</p>
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<p>Experimental setup for underactuated figure mechanism actuation.</p>
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<p>Adaptive grasping process of the underactuated finger mechanism. (<b>a</b>–<b>f</b>) Object grasping process. (<b>g</b>–<b>l</b>) Object releasing process.</p>
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<p>Object grasping state under different actuating force. (<b>a</b>) Actuating force = 5 N. (<b>b</b>) Actuating force = 10 N. (<b>c</b>) Self-sensed actuating force under different control target.</p>
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<p>Interaction with a human hand. (<b>a</b>–<b>h</b>) Motion sequences of the interaction. (<b>i</b>) Actuating force response.</p>
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21 pages, 5415 KiB  
Article
Design and Characterization of a Low-Cost and Efficient Torsional Spring for ES-RSEA
by Omar Sabah Al-Dahiree, Raja Ariffin Raja Ghazilla, Mohammad Osman Tokhi, Hwa Jen Yap and Mustabshirha Gul
Sensors 2023, 23(7), 3705; https://doi.org/10.3390/s23073705 - 3 Apr 2023
Cited by 2 | Viewed by 5162
Abstract
The design of torsional springs for series elastic actuators (SEAs) is challenging, especially when balancing good stiffness characteristics and efficient torque robustness. This study focuses on the design of a lightweight, low-cost, and compact torsional spring for use in the energy storage-rotary series [...] Read more.
The design of torsional springs for series elastic actuators (SEAs) is challenging, especially when balancing good stiffness characteristics and efficient torque robustness. This study focuses on the design of a lightweight, low-cost, and compact torsional spring for use in the energy storage-rotary series elastic actuator (ES-RSEA) of a lumbar support exoskeleton. The exoskeleton is used as an assistive device to prevent lower back injuries. The torsion spring was designed following design for manufacturability (DFM) principles, focusing on minimal space and weight. The design process involved determining the potential topology and optimizing the selected topology parameters through the finite element method (FEM) to reduce equivalent stress. The prototype was made using a waterjet cutting process with a low-cost material (AISI-4140-alloy) and tested using a custom-made test rig. The results showed that the torsion spring had a linear torque-displacement relationship with 99% linearity, and the deviation between FEM simulation and experimental measurements was less than 2%. The torsion spring has a maximum torque capacity of 45.7 Nm and a 440 Nm/rad stiffness. The proposed torsion spring is a promising option for lumbar support exoskeletons and similar applications requiring low stiffness, low weight-to-torque ratio, and cost-effectiveness. Full article
(This article belongs to the Collection Medical Applications of Sensor Systems and Devices)
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Figure 1
<p>Patterns of compliant elements for rotary series elastic actuators. (<b>a</b>) two identical custom torsion springs [<a href="#B16-sensors-23-03705" class="html-bibr">16</a>]. (<b>b</b>) compact torsion spring, adapted with permission from Ref. [<a href="#B17-sensors-23-03705" class="html-bibr">17</a>]. 2023 Copyright Omar Al-Dahiree. (<b>c</b>) customized torsion spring, adapted with permission from Ref. [<a href="#B18-sensors-23-03705" class="html-bibr">18</a>]. 2023 Copyright Omar Al-Dahiree. (<b>d</b>) torsion spring for Valkyrie’s series elastic actuator, adapted with permission from Ref. [<a href="#B19-sensors-23-03705" class="html-bibr">19</a>]. 2023 Copyright Omar Al-Dahiree. (<b>e</b>) torsional elastic module [<a href="#B22-sensors-23-03705" class="html-bibr">22</a>,<a href="#B23-sensors-23-03705" class="html-bibr">23</a>].</p>
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<p>ES-RSEA configuration.</p>
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<p>Cross-section of ES-RSEA.</p>
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<p>Flowchart of the spring design process.</p>
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<p>Elastic element module topologies considered: (<b>a</b>) Topology A; (<b>b</b>) Topology B; (<b>c</b>) Topology C; and (<b>d</b>) Topology D.</p>
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<p>Morphology of the chosen topology.</p>
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<p>Meshed module.</p>
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<p>Optimized module for torsion spring.</p>
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<p>FEM results: (<b>a</b>) Module deformation (mm); (<b>b</b>) Von Mises stress (MPa).</p>
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<p>Manufactured torsion spring.</p>
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<p>3D rendering of the testbed of the torsion spring: (<b>a</b>) Front view and (<b>b</b>) Back view.</p>
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<p>Characteristic of spring stiffness.</p>
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<p>Spring characteristics of compactness, weight, and torsion stiffness. (A) [<a href="#B15-sensors-23-03705" class="html-bibr">15</a>]. (B) [<a href="#B10-sensors-23-03705" class="html-bibr">10</a>]. (C) [<a href="#B16-sensors-23-03705" class="html-bibr">16</a>]. (D) [<a href="#B7-sensors-23-03705" class="html-bibr">7</a>]. (E) [<a href="#B17-sensors-23-03705" class="html-bibr">17</a>]. (F) [<a href="#B18-sensors-23-03705" class="html-bibr">18</a>]. (K) [<a href="#B25-sensors-23-03705" class="html-bibr">25</a>,<a href="#B26-sensors-23-03705" class="html-bibr">26</a>]. (L) [<a href="#B22-sensors-23-03705" class="html-bibr">22</a>,<a href="#B23-sensors-23-03705" class="html-bibr">23</a>].</p>
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<p>Spring characteristics of thickness, angular deflection, and weight-to-torque ratio. (A) [<a href="#B15-sensors-23-03705" class="html-bibr">15</a>]. (B) [<a href="#B10-sensors-23-03705" class="html-bibr">10</a>]. (C) [<a href="#B16-sensors-23-03705" class="html-bibr">16</a>]. (D) [<a href="#B7-sensors-23-03705" class="html-bibr">7</a>]. (E) [<a href="#B17-sensors-23-03705" class="html-bibr">17</a>]. (F) [<a href="#B18-sensors-23-03705" class="html-bibr">18</a>]. (K) [<a href="#B25-sensors-23-03705" class="html-bibr">25</a>,<a href="#B26-sensors-23-03705" class="html-bibr">26</a>]. (L) [<a href="#B22-sensors-23-03705" class="html-bibr">22</a>,<a href="#B23-sensors-23-03705" class="html-bibr">23</a>].</p>
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<p>Materials cost estimation for torsion springs. (A) [<a href="#B15-sensors-23-03705" class="html-bibr">15</a>]. (B) [<a href="#B10-sensors-23-03705" class="html-bibr">10</a>]. (C) [<a href="#B16-sensors-23-03705" class="html-bibr">16</a>]. (D) [<a href="#B7-sensors-23-03705" class="html-bibr">7</a>]. (E) [<a href="#B17-sensors-23-03705" class="html-bibr">17</a>]. (F) [<a href="#B18-sensors-23-03705" class="html-bibr">18</a>]. (K) [<a href="#B25-sensors-23-03705" class="html-bibr">25</a>]. (L) [<a href="#B22-sensors-23-03705" class="html-bibr">22</a>].</p>
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18 pages, 5930 KiB  
Communication
Negative-Stiffness Structure Vibration-Isolation Design and Impedance Control for a Lower Limb Exoskeleton Robot
by Yaohui Sun, Jiangping Hu and Rui Huang
Actuators 2023, 12(4), 147; https://doi.org/10.3390/act12040147 - 30 Mar 2023
Cited by 7 | Viewed by 2426
Abstract
The series elastic actuator (SEA) is generally used as the torque source of the exoskeleton robot for human–robot interaction (HRI). In this paper, an impedance control method for lower limb exoskeleton robots driven by SEA is presented. First, considering the low-frequency vibrations generated [...] Read more.
The series elastic actuator (SEA) is generally used as the torque source of the exoskeleton robot for human–robot interaction (HRI). In this paper, an impedance control method for lower limb exoskeleton robots driven by SEA is presented. First, considering the low-frequency vibrations generated by the lower limb exoskeleton robot during walking, the displacement generated by the robot is regarded as an external disturbance to the SEA motor. An SEA structure with negative stiffness structure (NSS) is designed to achieve vibration isolation in the low-frequency excitation region. Second, the dynamics model of the SEA-driven exoskeleton robot system is proposed, and the impedance control strategy is integrated into the proposed system. In addition, the numerical responses of the vibration-isolation system in both time and frequency domains are given, and the designed NSS is designed to achieve vibration isolation. The amplitude-frequency responses of the system are obtained. The harmonic balance (HB) method is used to give the analytical solution of the designed negative-stiffness isolation system, and the effects of different characteristic parameters on the isolation system are analyzed. Moreover, the stability of the SEA-driven exoskeleton impedance control system is demonstrated using the Lyapunov method. Finally, numerical simulations are carried out in order to show the effectiveness of the control method. Full article
(This article belongs to the Special Issue Nonlinear Active Vibration Control)
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<p>A simplified technical drawing of the NSS and exoskeleton designs.</p>
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<p>Overview of the mechanical structure schematic of SEA: (<b>a</b>) Diagram of SEA structure with NSS. (<b>b</b>) Diagram of the placement of the elastic element.</p>
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<p>Overview of the model structure schematics: (<b>a</b>) Diagram of vibration isolation structure with negative stiffness. (<b>b</b>) Schematic diagram of HRI with vibration-isolation structure.</p>
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<p>Dimensionless force-deflection characteristics for various configuration parameters: (<b>a</b>) for various <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>1</mn> </msub> </semantics></math>, (<b>b</b>) for various <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>2</mn> </msub> </semantics></math>.</p>
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<p>Dynamic stiffnesscurves with linear stiffness for the various values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p>Time and frequency amplitude response curves: (<b>a</b>) frequency and amplitude response curve, (<b>b</b>) time and amplitude response curve.</p>
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<p>Amplitude and frequency response curve for various (<b>a</b>) <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>2</mn> </msub> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </semantics></math>.</p>
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<p>Schematic diagram of the dynamics of the SEA-driven robot.</p>
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<p>Schematic diagram of impedance control.</p>
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<p>The position and velocity trajectory of the robot.</p>
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<p>The position and velocity trajectory of the SEA actuator.</p>
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<p>The interaction force of the human–robot.</p>
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<p>The position and velocity trajectory of the robot.</p>
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<p>The position and velocity trajectory of the SEA actuator.</p>
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<p>The position and velocity trajectory of the robot.</p>
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<p>The position and velocity trajectory of the SEA actuator.</p>
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<p>The position and velocity trajectory of the robot.</p>
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<p>The position and velocity trajectory of the SEA actuator.</p>
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21 pages, 2146 KiB  
Article
Forced Servoing of a Series Elastic Actuator Based on Link-Side Acceleration Measurement
by Zhuo Wang, Shenghong Liu, Bo Huang, Haowu Luo and Feiyan Min
Actuators 2023, 12(3), 126; https://doi.org/10.3390/act12030126 - 15 Mar 2023
Cited by 1 | Viewed by 2127
Abstract
Joint stiffness of an elastic-joint robot can be changed according to joint stiffness requirements. A series elastic actuator (SEA) can reduce the contact stiffness between the body and the environment or human, which can further ensure interactive operation in a human–machine-compatible environment. However, [...] Read more.
Joint stiffness of an elastic-joint robot can be changed according to joint stiffness requirements. A series elastic actuator (SEA) can reduce the contact stiffness between the body and the environment or human, which can further ensure interactive operation in a human–machine-compatible environment. However, the introduction of the SEA improves the complexity of the robot dynamics model. In this paper, we propose a control schema based on link-side acceleration measurement to eliminate the overshoot and vibration in the transient process of force control. An extended Kalman filter (EKF) algorithm that fuses photoelectric encoders and accelerometers is first presented based on the link-side acceleration measurement. Following this, based on the external torque estimation, the vibration reduction control algorithm is designed. The simulation model is built, and the algorithm design and simulation of position control and force control are carried out and finally tested on the real robot platform. The effectiveness of the control algorithm is proved. The experimental results show that the dynamic response of the external force estimation is about 2 ms faster than that of the force sensor, and the error between the estimated external torque and the real external torque is within ±0.16 N·m. Full article
(This article belongs to the Special Issue Intelligent Control of Flexible Manipulator Systems and Robotics)
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<p>Schematic of an elastic-joint robot driven by an SEA.</p>
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<p>Flexible robot dynamic model.</p>
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<p>Spring stiffness fitting results.</p>
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<p>Comparison of external torque estimation methods.</p>
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<p>Accelerometer calibration schematic.</p>
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<p>Schematic diagram of the nonlinear relationship between accelerometer output and angular acceleration.</p>
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<p>Extend Kalman filter algorithm.</p>
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<p>Motor-side model applied to disturbance observer.</p>
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<p>Resonance proportional torque control structure diagram.</p>
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<p>Non-linear disturbance compensation on the link side.</p>
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<p>Structural diagram of resonance proportional force control with disturbance compensation.</p>
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<p>The flexible robot system experimental setup.</p>
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<p>The system controller scheme.</p>
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<p>Model validation results. (<b>a</b>) Trajectory; (<b>b</b>) Comparison of model output torque and actual torque (link side); (<b>c</b>) Comparison of model output torque and actual torque (motor side).</p>
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<p>The link state in different stages of system motion.</p>
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<p>The result of external torque estimation.</p>
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<p>The result of external torque estimation during physical interaction.</p>
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<p>The output results of the physical system based on the resonance proportional force control.</p>
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23 pages, 3419 KiB  
Article
Rapid Robust Control of a Marine-Vehicle Manipulator with Series Elastic Actuators Based on Variable Power Log Reaching Law
by Yufei Guo, Shengyue Xu, Hao Chen, Hao Zheng, Zhiqiang Hao and Zhigang Wang
J. Mar. Sci. Eng. 2023, 11(3), 474; https://doi.org/10.3390/jmse11030474 - 22 Feb 2023
Cited by 1 | Viewed by 1403
Abstract
Marine-vehicle manipulators, which represent a kind of mechanical systems installed on marine surface or underwater vehicles, are mostly suffering from the problem of waves (or ocean currents)-caused base oscillations. The oscillations have a significant impact on system stability. Numerous control strategies have been [...] Read more.
Marine-vehicle manipulators, which represent a kind of mechanical systems installed on marine surface or underwater vehicles, are mostly suffering from the problem of waves (or ocean currents)-caused base oscillations. The oscillations have a significant impact on system stability. Numerous control strategies have been investigated, but the majority of them are concentrated on the control’s robust performance. This study focuses on an innovative marine-vehicle manipulator (ammunition transfer manipulator on warships) with novel compliant actuators (series elastic actuators), for which the control performance of convergence speed and flexible-vibration suppression should also be considered. To address these issues, this paper proposes a unique hybrid control based on the singular perturbation method, by which the control problem is decomposed into two time scales. In the slow time-scale, it is given a rapid trajectory tracking controller that integrates the computed torque method and the terminal sliding mode control law with a novel reaching law (variable power log reaching law). For the fast time-scale control, a derivative-type controller is used to achieve the suppression of the flexible vibrations. To demonstrate the effectiveness of the proposed control method, theoretical proofs and numerical simulations are both presented. According to our knowledge, this study presents the first control strategy for rapid robust control of marine-vehicle manipulators that are subject to base-oscillation-caused disturbance and compliant-actuator-induced flexible vibrations. Full article
(This article belongs to the Section Ocean Engineering)
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<p>The ammunition transfer manipulator mounted on an oscillating marine-vehicle.</p>
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<p>Virtual prototype of the novel ammunition transfer manipulator with SEAs. (<b>a</b>) is the SEA for the rotating part, (<b>b</b>) is the SEA for the lifiting part, and (<b>c</b>) is the manipulator subject to three base oscillations.</p>
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<p>Simplified model of the ammunition transfer manipulator with base oscillations.</p>
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<p>Sliding mode variable in the phase plane.</p>
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<p>Time response of the sliding mode variable.</p>
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<p>The loop of the proposed control strategy.</p>
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<p>Three base oscillations.</p>
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<p>Position of lifting part (Group 1).</p>
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<p>Angle of rotating part (Group 1).</p>
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<p>Velocity of lifting part (Group 1).</p>
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<p>Angular velocity of rotating part (Group 1).</p>
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<p>Position of lifting part (Group 2).</p>
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<p>Angle of rotating part (Group 2).</p>
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<p>Velocity of lifting part (Group 2).</p>
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<p>Angular velocity of rotating part (Group 2).</p>
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<p>Position of lifting part (Group 3).</p>
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<p>Angle of rotating part (Group 3).</p>
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<p>Velocity of lifting part (Group 3).</p>
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<p>Angular velocity of rotating part (Group 3).</p>
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<p>Velocity error of lifting part (Group 3).</p>
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<p>Angular velocity error of rotating part (Group 3).</p>
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<p>Position of lifting part (Group 4).</p>
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<p>Angle of rotating part (Group 4).</p>
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<p>Velocity of lifting part (Group 4).</p>
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<p>Angular velocity of rotating part (Group 4).</p>
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