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Ai W, Wu J, Long Y, Song K. A Rolling Light-Driven Pneumatic Soft Actuator Based on Liquid-Gas Phase Change. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2025; 37:e2418218. [PMID: 39924788 DOI: 10.1002/adma.202418218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2024] [Indexed: 02/11/2025]
Abstract
Light-driven wireless actuators provide obvious advantages for remote control. However, traditional double-layer actuators are restricted to the thin film deformation mode when undertaking complex tasks. Here, an actuator is proposed that employs thermal strain and local photothermal effects induced by low boiling point liquids to generate asymmetry along the fiber axis, thereby causing elastic deformation of the fiber. Under continuous irradiation, the sustained elastic deformation results in dynamic frustration within the fiber, creating torque around its axis. Based on this principle, the fiber actuator fabricated in this study enables rolling translation, while the ring actuator achieves simultaneous rolling and lifting motion for object manipulation. Continuous rolling under light eliminates the need for complex light manipulation. This new movement method offers an insight for various application scenarios.
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Affiliation(s)
- Wenfei Ai
- CAS Key Laboratory of Bio-inspired Materials and Interfaces Sciences, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, 100190, China
- School of Future Technology, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China
| | - Jiaxin Wu
- CAS Key Laboratory of Bio-inspired Materials and Interfaces Sciences, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, 100190, China
- School of Future Technology, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China
| | - Yue Long
- CAS Key Laboratory of Bio-inspired Materials and Interfaces Sciences, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, 100190, China
- Binzhou Institute of Technology, Weiqiao-UCAS Science and Technology Park, Binzhou City, Shandong Province, 256606, China
| | - Kai Song
- CAS Key Laboratory of Bio-inspired Materials and Interfaces Sciences, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, 100190, China
- School of Future Technology, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China
- Binzhou Institute of Technology, Weiqiao-UCAS Science and Technology Park, Binzhou City, Shandong Province, 256606, China
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Rana MT, Islam MS, Rahman A. Human-Centered Sensor Technologies for Soft Robotic Grippers: A Comprehensive Review. SENSORS (BASEL, SWITZERLAND) 2025; 25:1508. [PMID: 40096382 PMCID: PMC11902506 DOI: 10.3390/s25051508] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/22/2024] [Revised: 09/29/2024] [Accepted: 10/22/2024] [Indexed: 03/19/2025]
Abstract
The importance of bio-robotics has been increasing day by day. Researchers are trying to mimic nature in a more creative way so that the system can easily adapt to the complex nature and its environment. Hence, bio-robotic grippers play a role in the physical connection between the environment and the bio-robotics system. While handling the physical world using a bio-robotic gripper, complexity occurs in the feedback system, where the sensor plays a vital role. Therefore, a human-centered gripper sensor can have a good impact on the bio-robotics field. But categorical classification and the selection process are not very systematic. This review paper follows the PRISMA methodology to summarize the previous works on bio-robotic gripper sensors and their selection process. This paper discusses challenges in soft robotic systems, the importance of sensing systems in facilitating critical control mechanisms, along with their selection considerations. Furthermore, a classification of soft actuation based on grippers has been introduced. Moreover, some unique characteristics of soft robotic sensors are explored, namely compliance, flexibility, multifunctionality, sensor nature, surface properties, and material requirements. In addition, a categorization of sensors for soft robotic grippers in terms of modalities has been established, ranging from the tactile and force sensor to the slippage sensor. Various tactile sensors, ranging from piezoelectric sensing to optical sensing, are explored as they are of the utmost importance in soft grippers to effectively address the increasing requirements for intelligence and automation. Finally, taking everything into consideration, a flow diagram has been suggested for selecting sensors specific to soft robotic applications.
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Affiliation(s)
- Md. Tasnim Rana
- Bangladesh Council of Scientific and Industrial Research (BCSIR), Dhaka 1205, Bangladesh
| | - Md. Shariful Islam
- Mechanical Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA;
| | - Azizur Rahman
- School of PCPM, Occupational Health and Safety/Ergonomics, City Campus, Royal Melbourne Institute of Technology, Melbourne, VIC 3000, Australia
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3
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Tasmim S, Baten A, Sivaperuman Kalairaj M, Wang S, Zimmern PE, Ware TH. Magnetoactive elastomer-based dynamic urethral support device for stress urinary incontinence. Acta Biomater 2025; 191:336-351. [PMID: 39581336 DOI: 10.1016/j.actbio.2024.11.039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2024] [Revised: 11/06/2024] [Accepted: 11/21/2024] [Indexed: 11/26/2024]
Abstract
Stress urinary incontinence (SUI) is the involuntary leakage of urine in response to increased intra-abdominal pressure during episodes of exertion. A common treatment method for SUI is sling implantation underneath the urethra to provide support. Most current sling procedures, however, cannot adjust urethral tension postoperatively. To address this limitation, we designed a soft magnetoactive elastomer (MAE) device capable of changing shape in response to moderate magnetic fields. To ensure shape change after fibrotic scar tissue encapsulation, MAE devices were embedded in agar gels with different stiffnesses, and their shape change was studied in response to up to 200 mT magnetic fields. A simple in vitro model of the lower urinary tract was designed to study device performance. Flow time was measured as a function of pressure in the simulated bladder as the model system leaked before and after activating sling with a hand-held magnet. MAE devices embedded in agar gel (100 kPa) in hammock-like configuration achieved 4.7% ± 1.1% change in height. Devices with silica-coated magnetic particles showed minimal loss in mass after two weeks in accelerated oxidative (2.36% ± 1.55%) and hydrolytic (0.58% ± 0.25%) conditions. Placing a sling under the model urethra provided urethral support; thus, increasing its resistance to flow. Normalized flow time significantly reduced from 1.56 ± 0.18 to 1.11 ± 0.16 when magnetic field was applied, indicating urethral support modulation at 60 cm-H2O. This dynamic sling, powered externally with physiologically safe magnetic fields, allowed for urethral support modulation in a model of the lower urinary tract. STATEMENT OF SIGNIFICANCE: Stress urinary incontinence (SUI) affects up to half the adult women during their lifetime, and slings are commonly used to treat severe cases. While sling implantation is minimally invasive and offers moderate to high cure rates, long-term sling complications, such as urine retention, remain a significant concern. Available adjustable SUI devices often require invasive surgeries, implantable electronics, and multiple mechanical components, increasing the overall invasiveness. Here, we report a proof of concept for using shape-morphing biomaterials to fabricate a dynamic device that can provide continence support and be triggered to change shape, enabling complete voiding. Such a dynamic device may prevent many complications associated with traditional slings and improve quality of life for women suffering from severe SUI.
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Affiliation(s)
- Seelay Tasmim
- Texas A&M University, Department of Biomedical Engineering, College Station, TX, United States
| | - Asha Baten
- Texas A&M University, Department of Biomedical Engineering, College Station, TX, United States
| | | | - Suitu Wang
- Texas A&M University, Department of Materials Science and Engineering, College Station, TX, United States
| | - Philippe E Zimmern
- The University of Texas Southwestern Medical Center, Department of Urology, Dallas, TX, United States
| | - Taylor H Ware
- Texas A&M University, Department of Biomedical Engineering, College Station, TX, United States; Texas A&M University, Department of Materials Science and Engineering, College Station, TX, United States.
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Cortez R, Sandoval-Chileño MA, Lozada-Castillo N, Luviano-Juárez A. Snake Robot with Motion Based on Shape Memory Alloy Spring-Shaped Actuators. Biomimetics (Basel) 2024; 9:180. [PMID: 38534865 PMCID: PMC10968179 DOI: 10.3390/biomimetics9030180] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2024] [Revised: 02/28/2024] [Accepted: 03/14/2024] [Indexed: 03/28/2024] Open
Abstract
This study presents the design and evaluation of a prototype snake-like robot that possesses an actuation system based on shape memory alloys (SMAs). The device is constructed based on a modular structure of links connected by two degrees of freedom links utilizing Cardan joints, where each degree of freedom is actuated by an agonist-antagonist mechanism using the SMA spring-shaped actuators to generate motion, which can be easily replaced once they reach a degradation point. The methodology for programming the spring shape into the SMA material is described in this work, as well as the instrumentation required for the monitoring and control of the actuators. A simplified design is presented to describe the way in which the motion is performed and the technical difficulties faced in manufacturing. Based on this information, the way in which the design is adapted to generate a feasible robotic system is described, and a mathematical model for the robot is developed to implement an independent joint controller. The feasibility of the implementation of the SMA actuators regarding the motion of the links is verified for the case of a joint, and the change in the shape of the snake robot is verified through the implementation of a set of tracking references based on a central pattern generator. The generated tracking results confirm the feasibility of the proposed mechanism in terms of performing snake gaits, as well as highlighting some of the drawbacks that should be considered in further studies.
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Affiliation(s)
- Ricardo Cortez
- Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, Mexico City 07340, Mexico; (N.L.-C.); (A.L.-J.)
| | - Marco Antonio Sandoval-Chileño
- Unidad Profesional Interdisciplinaria de Energía y Movilidad, Instituto Politécnico Nacional, Mexico City 07738, Mexico;
| | - Norma Lozada-Castillo
- Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, Mexico City 07340, Mexico; (N.L.-C.); (A.L.-J.)
| | - Alberto Luviano-Juárez
- Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, Mexico City 07340, Mexico; (N.L.-C.); (A.L.-J.)
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Ai W, Hou K, Wu J, Long Y, Song K. Miniaturized and untethered McKibben muscles based on photothermal-induced gas-liquid transformation. Nat Commun 2024; 15:1329. [PMID: 38351311 PMCID: PMC10864313 DOI: 10.1038/s41467-024-45540-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2023] [Accepted: 01/24/2024] [Indexed: 02/16/2024] Open
Abstract
Pneumatic artificial muscles can move continuously under the power support of air pumps, and their flexibility also provides the possibility for applications in complex environments. However, in order to achieve operation in confined spaces, the miniaturization of artificial muscles becomes crucial. Since external attachment devices greatly hinder the miniaturization and use of artificial muscles, we propose a light-driven approach to get rid of these limitations. In this study, we report a miniaturized fiber-reinforced artificial muscle based on mold editing, capable of bending and axial elongation using gas-liquid conversion in visible light. The minimum volume of the artificial muscle prepared using this method was 15.7 mm3 (d = 2 mm, l = 5 mm), which was smaller than those of other fiber-reinforced pneumatic actuators. This research can promote the development of non-tethered pneumatic actuators for rescue and exploration, and create the possibility of miniaturization of actuators.
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Affiliation(s)
- Wenfei Ai
- Key Laboratory of Bio-inspired Materials and Interfacial Science, Technical Institute of Physics and Chemistry, CAS, Beijing, 100190, P. R. China
- School of Future Technology, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China
| | - Kai Hou
- Key Laboratory of Bio-inspired Materials and Interfacial Science, Technical Institute of Physics and Chemistry, CAS, Beijing, 100190, P. R. China
| | - Jiaxin Wu
- Key Laboratory of Bio-inspired Materials and Interfacial Science, Technical Institute of Physics and Chemistry, CAS, Beijing, 100190, P. R. China
- School of Future Technology, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China
| | - Yue Long
- Key Laboratory of Bio-inspired Materials and Interfacial Science, Technical Institute of Physics and Chemistry, CAS, Beijing, 100190, P. R. China.
- Binzhou Institute of Technology, Weiqiao-UCAS Science and Technology Park, Binzhou City, Shandong Province, 256606, China.
| | - Kai Song
- Key Laboratory of Bio-inspired Materials and Interfacial Science, Technical Institute of Physics and Chemistry, CAS, Beijing, 100190, P. R. China.
- School of Future Technology, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China.
- Binzhou Institute of Technology, Weiqiao-UCAS Science and Technology Park, Binzhou City, Shandong Province, 256606, China.
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Orban M, Guo K, Yang H, Hu X, Hassaan M, Elsamanty M. Soft pneumatic muscles for post-stroke lower limb ankle rehabilitation: leveraging the potential of soft robotics to optimize functional outcomes. Front Bioeng Biotechnol 2023; 11:1251879. [PMID: 37781541 PMCID: PMC10539589 DOI: 10.3389/fbioe.2023.1251879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Accepted: 08/31/2023] [Indexed: 10/03/2023] Open
Abstract
Introduction: A soft pneumatic muscle was developed to replicate intricate ankle motions essential for rehabilitation, with a specific focus on rotational movement along the x-axis, crucial for walking. The design incorporated precise geometrical parameters and air pressure regulation to enable controlled expansion and motion. Methods: The muscle's response was evaluated under pressure conditions ranging from 100-145 kPa. To optimize the muscle design, finite element simulation was employed to analyze its performance in terms of motion range, force generation, and energy efficiency. An experimental platform was created to assess the muscle's deformation, utilizing advanced techniques such as high-resolution imaging and deep-learning position estimation models for accurate measurements. The fabrication process involved silicone-based materials and 3D-printed molds, enabling precise control and customization of muscle expansion and contraction. Results: The experimental results demonstrated that, under a pressure of 145 kPa, the y-axis deformation (y-def) reached 165 mm, while the x-axis and z-axis deformations were significantly smaller at 0.056 mm and 0.0376 mm, respectively, highlighting the predominant elongation in the y-axis resulting from pressure actuation. The soft muscle model featured a single chamber constructed from silicone rubber, and the visually illustrated and detailed geometrical parameters played a critical role in its functionality, allowing systematic manipulation to meet specific application requirements. Discussion: The simulation and experimental results provided compelling evidence of the soft muscle design's adaptability, controllability, and effectiveness, thus establishing a solid foundation for further advancements in ankle rehabilitation and soft robotics. Incorporating this soft muscle into rehabilitation protocols holds significant promise for enhancing ankle mobility and overall ambulatory function, offering new opportunities to tailor rehabilitation interventions and improve motor function restoration.
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Affiliation(s)
- Mostafa Orban
- School of Biomedical Engineering (Suzhou), Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, China
- Suzhou Institute of Biomedical Engineering and Technology, Chinese Academy of Sciences, Suzhou, China
- Mechanical Department, Faculty of Engineering at Shoubra, Benha University, Cairo, Egypt
| | - Kai Guo
- School of Biomedical Engineering (Suzhou), Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, China
- Suzhou Institute of Biomedical Engineering and Technology, Chinese Academy of Sciences, Suzhou, China
| | - Hongbo Yang
- School of Biomedical Engineering (Suzhou), Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, China
- Suzhou Institute of Biomedical Engineering and Technology, Chinese Academy of Sciences, Suzhou, China
| | - Xuhui Hu
- Suzhou Institute of Biomedical Engineering and Technology, Chinese Academy of Sciences, Suzhou, China
| | - Mohamed Hassaan
- Mechanical Department, Faculty of Engineering at Shoubra, Benha University, Cairo, Egypt
| | - Mahmoud Elsamanty
- Mechanical Department, Faculty of Engineering at Shoubra, Benha University, Cairo, Egypt
- Mechatronics and Robotics Department, School of Innovative Design Engineering, Egypt-Japan University of Science and Technology, Alexandria, Egypt
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Bakeri H, Hasikin K, Abd Razak NA, Mohd Razman R, Khamis AA, Annuha M‘A, Tajuddin A, Reza D. Silicone Elastomeric-Based Materials of Soft Pneumatic Actuator for Lower-Limb Rehabilitation: Finite Element Modelling and Prototype Experimental Validation. APPLIED SCIENCES 2023; 13:2977. [DOI: 10.3390/app13052977] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
This study describes the basic design, material selection, fabrication, and evaluation of soft pneumatic actuators (SPA) for lower-limb rehabilitation compression therapy. SPAs can be a promising technology in proactive pressure delivery, with a wide range of dosages for treating venous-related diseases. However, the most effective design and material selection of SPAs for dynamic pressure delivery have not been fully explored. Therefore, a SPA chamber with two elastomeric layers was developed for this study, with single-side inflation. The 3D deformation profiles of the SPA chamber using three different elastomeric rubbers were analyzed using the finite element method (FEM). The best SPA-compliant behavior was displayed by food-grade silicone A10 Shore with a maximum deformation value of 25.34 mm. Next, the SPA chamber was fabricated using A10 Shore silicone and experimentally validated. During the simulation in FEM, the air pressure was applied on the inner wall of the chamber (i.e., the affected area). This is to ensure the applied pressure was evenly distributed in the inner wall while the outer wall of the chamber remained undeformed for all compression levels. During the inflation process, pressure will be applied to the SPA chamber, causing exerted pressure on the skin which is then measured for comparison. The simulation and experimental results show an excellent agreement of pressure transmission on the skin for the pressure range of 0–120 mmHg, as depicted in the Bland–Altman plots. The findings exhibited promising results in the development of the SPA chamber using low-cost and biocompatible food-grade silicone.
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Affiliation(s)
- Hanisah Bakeri
- Department of Biomedical Engineering, Faculty of Engineering, Universiti Malaya, Kuala Lumpur 50603, Malaysia
- Medical Revolution Sdn. Bhd, 10 Boulevard, Petaling Jaya 47400, Malaysia
| | - Khairunnisa Hasikin
- Department of Biomedical Engineering, Faculty of Engineering, Universiti Malaya, Kuala Lumpur 50603, Malaysia
- Center of Intelligent Systems for Emerging Technology (CISET), Faculty of Engineering, Universiti Malaya, Kuala Lumpur 50603, Malaysia
| | - Nasrul Anuar Abd Razak
- Department of Biomedical Engineering, Faculty of Engineering, Universiti Malaya, Kuala Lumpur 50603, Malaysia
| | - Rizal Mohd Razman
- Faculty of Sports and Exercise Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia
| | - Abd Alghani Khamis
- Department of Mechanical Engineering, Faculty of Engineering, Universiti Malaya, Kuala Lumpur 50603, Malaysia
| | - Muhammad ‘Ammar Annuha
- Department of Biomedical Engineering, Faculty of Engineering, Universiti Malaya, Kuala Lumpur 50603, Malaysia
| | - Abbad Tajuddin
- Medical Revolution Sdn. Bhd, 10 Boulevard, Petaling Jaya 47400, Malaysia
| | - Darween Reza
- My Conceptual Robotics Sdn. Bhd (MyCRO), Kompleks Diamond, Bandar Baru Bangi 43650, Malaysia
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Guo M, Peng Y, Chen Z, Sheng N, Sun F. Smart Humidly Adaptive Yarns and Textiles from Twisted and Coiled Viscose Fiber Artificial Muscles. MATERIALS (BASEL, SWITZERLAND) 2022; 15:8312. [PMID: 36499808 PMCID: PMC9739715 DOI: 10.3390/ma15238312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/04/2022] [Revised: 11/10/2022] [Accepted: 11/18/2022] [Indexed: 06/17/2023]
Abstract
The self-adaptive nature of smart textiles to the ambient environment has made them an indispensable part of emerging wearable technologies. However, current advances generally suffer from complex material preparation, uncomfortable fitting feeling, possible toxicity, and high cost in fabrication, which hinder the real-world application of smart materials in textiles. Herein, humidity-response torsional and tensile yarn actuators from twisted and coiled structures are developed using commercially available, cost-effective, and biodegradable viscose fibers based on yarn-spinning and weaving technologies. The twisted yarn shows a reversible torsional stroke of 1400° cm-1 in 5 s when stimulated by water fog with a spraying speed of 0.05 g s-1; the coiled yarn exhibits a peak tensile stroke of 900% upon enhancing the relative humidity. Further, textile manufacturing allows for the scalable fabrication to create fabric artificial muscles with high-dimensional actuation deformations and human-touch comfort, which can boost the potential applications of the humidly adaptive yarns in smart textile and advanced textile materials.
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Affiliation(s)
- Mingrui Guo
- MOE Key Laboratory of Eco-Textiles, Jiangnan University, Wuxi 214122, China
| | - Yangyang Peng
- MOE Key Laboratory of Eco-Textiles, Jiangnan University, Wuxi 214122, China
- Laboratory of Soft Fibrous Materials, Jiangnan University, Wuxi 214122, China
| | - Zihan Chen
- College of Fashion Design, Jiaxing Nanhu University, Jiaxing 314001, China
| | - Nan Sheng
- MOE Key Laboratory of Eco-Textiles, Jiangnan University, Wuxi 214122, China
- Laboratory of Soft Fibrous Materials, Jiangnan University, Wuxi 214122, China
| | - Fengxin Sun
- MOE Key Laboratory of Eco-Textiles, Jiangnan University, Wuxi 214122, China
- Laboratory of Soft Fibrous Materials, Jiangnan University, Wuxi 214122, China
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Dynamics and Computed-Muscle-Force Control of a Planar Muscle-Driven Snake Robot. ACTUATORS 2022. [DOI: 10.3390/act11070194] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
This paper presents the dynamic formulation of an artificial-muscle-driven and computed-muscle–force control for the planar locomotion of a snake robot. The snake robot uses a series of antagonistic pneumatic artificial muscles, assembled at the joints, to generate the locomotion. Kinematics of the artificial-muscle-driven robot in the joint and Cartesian spaces was derived with respect to the muscles’ motion. The Lagrangian mechanics was employed for the formulation of the dynamic model of the robot and deriving the equations of motion. A model-based computed-muscle-force control was designed to track the desired paths/trajectories in Cartesian space. The feedback linearization method based on a change of coordinate was utilized to determine an equivalent linear (input-to-state) system. Then, a full state feedback control law was designed, which satisfies the stability and tracking problems. The performance of the dynamic model and the controller were successfully demonstrated in simulation studies for tracking a circle-shape path and a square-shape path with a constant linear velocity while generating the lateral undulation gait. The results indicate a low magnitude of tracking errors where the controlled muscle force are bounded to the actual pneumatic artificial muscle’s limitations.
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