New nonlinear stiffness actuator with predefined torque‒deflection profile

Abstract

A nonlinear stiffness actuator (NSA) could achieve high torque/force resolution in low stiffness range and high bandwidth in high stiffness range, both of which are beneficial for physical interaction between a robot and the environment. Currently, most of NSAs are complex and hardly used for engineering. In this paper, oriented to engineering applications, a new simple NSA was proposed, mainly including leaf springs and especially designed cams, which could perform a predefined relationship between torque and deflection. The new NSA has a compact structure, and it is lightweight, both of which are also beneficial for its practical application. An analytical methodology that maps the predefined relationship between torque and deflection to the profile of the cam was developed. The optimal parameters of the structure were given by analyzing the weight of the NSA and the mechanic characteristic of the leaf spring. Though sliding friction force is inevitable because no rollers were used in the cam-based mechanism, the sliding displacement between the cam and the leaf spring is very small, and consumption of sliding friction force is very low. Simulations of different torque‒deflection profiles were carried out to verify the accuracy and applicability of performing predefined torque‒deflection profiles. Three kinds of prototype experiments, including verification experiment of the predefined torque‒deflection profile, torque tracking experiment, and position tracking experiment under different loads, were conducted. The results prove the accuracy of performing the predefined torque‒deflection profile, the tracking performance, and the interactive performance of the new NSA.

Key words： compliant actuator; nonlinear stiffness actuator; nonlinear spring; predefined torque−deflection profile

Acknowledgements

This work was supported by the National Key R&D Program of China (Grant No. 2019YFB1312404) and the National Natural Science Foundation of China (Grant Nos. 51975401 and 51875393). There is no conflict of interest about our work with others.

References

1 Pratt G A , Williamson M M . Series elastic actuators. In: Proceedings of 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots. Pittsburgh: IEEE, 1995, 399–406

2 Van Ham R , Vanderborght B , Van Damme M , Verrelst B , Lefeber D . MACCEPA, the mechanically adjustable compliance and controllable equilibrium position actuator: design and implementation in a biped robot. Robotics and Autonomous Systems, 2007, 55(10): 761–768

3 Deboon B , Nokleby S , Delfa N L , Rossa C . Differentially-clutched series elastic actuator for robot-aided musculoskeletal rehabilitation. In: Proceedings of 2019 International Conference on Robotics and Automation (ICRA). Montreal: IEEE, 2019, 1507–1513

4 Pfeifer S , Pagel A , Riener R , Vallery H . Actuator with angle-dependent elasticity for biomimetic transfemoral prostheses. IEEE/ASME Transactions on Mechatronics, 2015, 20(3): 1384–1394

5 Aguirre-Ollinger G , Yu H Y . Lower-limb exoskeleton with variable-structure series elastic actuators: phase-synchronized force control for gait asymmetry correction. IEEE Transactions on Robotics, 2021, 37(3): 763–779

6 Van Ham R , Sugar T G , Vanderborght B , Hollander K W , Lefeber D . Compliant actuator designs. IEEE Robotics & Automation Magazine, 2009, 16(3): 81–94

7 Kong K , Bae J , Tomizuka M . A compact rotary series elastic actuator for human assistive systems. IEEE/ASME Transactions on Mechatronics, 2012, 17(2): 288–297

8 Paine N , Mehling J S , Holley J , Radford N A , Johnson J , Fok C L , Sentis L . Actuator control for the NASA-JSC Valkyrie humanoid robot: a decoupled dynamics approach for torque control of series elastic robots. Journal of Field Robotics, 2015, 32(3): 378–396

9 Zhang T , Huang H . Design and control of a series elastic actuator with clutch for hip exoskeleton for precise assistive magnitude and timing control and improved mechanical safety. IEEE/ASME Transactions on Mechatronics, 2019, 24(5): 2215–2226

10 Jung Y , Bae J . Torque control of a series elastic tendon-sheath actuation mechanism. IEEE/ASME Transactions on Mechatronics, 2020, 25(6): 2915–2926

11 Kwak J , Choi W , Lee C , Oh S . Gravity and impedance compensation of body weight support system driven by two series elastic actuators. IEEE/ASME Transactions on Mechatronics, 2021, 27(1): 190–201

12 Liu Y Y , Li Z J , Su H , Su C Y . Whole body control of an autonomous mobile manipulator using series elastic actuators. IEEE/ASME Transactions on Mechatronics, 2021, 26(2): 657–667

13 Pei Y N , Han T Y , Zallek C M , Liu T , Yang L J , Hsiao-Wecksler E T . Design and clinical validation of a robotic ankle-foot simulator with series elastic actuator for ankle clonus assessment training. IEEE Robotics and Automation Letters, 2021, 6(2): 3793–3800

14 Robinson D W . Design and analysis of series elasticity in closed-loop actuator force control. Dissertation for the Doctoral Degree. Cambridge: Massachusetts Institute of Technology, 2000, 18–19

15 Carpino G , Accoto D , Sergi F , Luigi Tagliamonte N L , Guglielmelli E . A novel compact torsional spring for series elastic actuators for assistive wearable robots. Journal of Mechanical Design, 2012, 134(12): 121002

16 Paine N , Oh S , Sentis L . Design and control considerations for high-performance series elastic actuators. IEEE/ASME Transactions on Mechatronics, 2014, 19(3): 1080–1091

17 Tsagarakis N G , Sardellitti I , Caldwell D G . A new variable stiffness actuator (CompAct-VSA): design and modelling. In: Proceedings of 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems. San Francisco: IEEE, 2011, 378–383

18 Wolf S , Eiberger O , Hirzinger G . The DLR FSJ: energy based design of a variable stiffness joint. In: Proceedings of 2011 IEEE International Conference on Robotics and Automation. Shanghai: IEEE, 2011, 5082–5089

19 Choi J , Hong S , Lee W , Kang S , Kim M . A robot joint with variable stiffness using leaf springs. IEEE Transactions on Robotics, 2011, 27(2): 229–238

20 Jafari A , Tsagarakis N G , Caldwell D G . A novel intrinsically energy efficient actuator with adjustable stiffness (AwAS). IEEE/ASME Transactions on Mechatronics, 2013, 18(1): 355–365

21 Liu Y W , Cui S P , Sun Y J . Mechanical design and analysis of a novel variable stiffness actuator with symmetrical pivot adjustment. Frontiers of Mechanical Engineering, 2021, 16(4): 711–725

22 Sun J T , Guo Z , Sun D Y , He S Y , Xiao X H . Design, modeling and control of a novel compact, energy-efficient, and rotational serial variable stiffness actuator (SVSA-II). Mechanism and Machine Theory, 2018, 130: 123–136

23 Wu J H , Wang Z R , Chen W , Wang Y Q , Liu Y H . Design and validation of a novel leaf spring-based variable stiffness joint with reconfigurability. IEEE/ASME Transactions on Mechatronics, 2020, 25(4): 2045–2053

24 Zhu Y H , Wu Q C , Chen B , Xu D W , Shao Z Y . Design and evaluation of a novel torque-controllable variable stiffness actuator with reconfigurability. IEEE/ASME Transactions on Mechatronics, 2021, 27(1): 292–303

25 Xu Y P , Guo K , Sun J , Li J F . Design, modeling and control of a reconfigurable variable stiffness actuator. Mechanical Systems and Signal Processing, 2021, 160: 107883

26 Sun Y X , Tang P , Dong D B , Zheng J , Chen X H , Bai L . Modeling and experimental evaluation of a pneumatic variable stiffness actuator. IEEE/ASME Transactions on Mechatronics, 2022, 27(5): 2462–2473

27 Mengacci R , Garabini M , Grioli G , Catalano M G , Bicchi A . Overcoming the torque/stiffness range tradeoff in antagonistic variable stiffness actuators. IEEE/ASME Transactions on Mechatronics, 2021, 26(6): 3186–3197

28 Li X , Zhu H Y , Lin W , Chen W J , Low K H . Structure-controlled variable stiffness robotic joint based on multiple rotary flexure hinges. IEEE Transactions on Industrial Electronics, 2021, 68(12): 12452–12461

29 Yang S K , Chen P , Wang D Q , Yu Y , Liu Y W . Design and analysis of a 2-DOF actuator with variable stiffness based on leaf springs. Journal of Bionic Engineering, 2022, 19: 1392–1404

30 Liu L , Misgeld B J E , Pomprapa A , Leonhardt S . A testable robust stability framework for the variable impedance control of 1-DOF exoskeleton with variable stiffness actuator. IEEE Transactions on Control Systems Technology, 2021, 29(6): 2728–2737

31 Koganezawa K, Watanabe Y, Shimizu N. Antagonistic muscle-like actuator and its application to multi-d.o.f. forearm prosthesis. Advanced Robotics, 1997, 12(7–8): 771–789

32 Hollander K W , Sugar T G , Herring D E . Adjustable robotic tendon using a ‘Jack Spring’/spl trade/. In: Proceedings of the 9th International Conference on Rehabilitation Robotics. Chicago: IEEE, 2005, 113–118

33 Hutter M , David C D , Siegwart R . Design of an articulated robotic leg with nonlinear series elastic actuation. In: Tosun O, Akin H L, Tokhi M O, Virk G S, eds. Mobile Robotics: Solutions and Challenges. New Jersey: World Scientific, 2009, 645–652

34 Thorson I , Caldwell D . A nonlinear series elastic actuator for highly dynamic motions. In: Proceedings of 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems. San Francisco: IEEE, 2011, 390–394

35 Chen W H , Zhou L B , Wang J H , Zhao Z , Chen W J , Bai S P . A Maxwell-slip based hysteresis model for nonlinear stiffness compliant actuators. IEEE Transactions on Industrial Electronics, 2021, 69(11): 11510–11520

36 Rodríguez A G , Chacón J M , Donoso A , González Rodríguez A G . Design of an adjustable-stiffness spring: mathematical modeling and simulation, fabrication and experimental validation. Mechanism and Machine Theory, 2011, 46(12): 1970–1979

37 Li B K , Hao G B . Nonlinear behaviour design using the kinematic singularity of a general type of double-slider four-bar linkage. Mechanism and Machine Theory, 2018, 129: 106–130

38 Liu Y W , Wang D Q , Yang S K , Liu J G , Hao G B . Design and experimental study of a passive power-source-free stiffness-self-adjustable mechanism. Frontiers of Mechanical Engineering, 2021, 16(1): 32–45

39 Li Z Y , Bai S P , Chen W H , Zhang J B . Nonlinear stiffness analysis of spring-loaded inverted slider crank mechanisms with a unified model. Journal of Mechanisms and Robotics, 2020, 12(3): 031011

40 Migliore S A , Brown E A , DeWeerth S P . Biologically inspired joint stiffness control. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation. Barcelona: IEEE, 2005, 4508–4513

41 Shao Y X , Zhang W X , Su Y J , Ding X L . Design and optimisation of load-adaptive actuator with variable stiffness for compact ankle exoskeleton. Mechanism and Machine Theory, 2021, 161: 104323

42 Hao G B . A framework of designing compliant mechanisms with nonlinear stiffness characteristics. Microsystem Technologies, 2018, 24(4): 1795–1802

43 Palli G , Berselli G , Melchiorri C , Vassura G . Design of a variable stiffness actuator based on flexures. Journal of Mechanisms and Robotics, 2011, 3(3): 034501

44 Radaelli G , Herder J L . Shape optimization and sensitivity of compliant beams for prescribed load-displacement response. Mechanical Sciences, 2016, 7(2): 219–232

45 Schepelmann A , Geberth K A , Geyer H . Compact nonlinear springs with user defined torque-deflection profiles for series elastic actuators. In: Proceedings of 2014 IEEE International Conference on Robotics and Automation (ICRA). Hong Kong: IEEE, 2014, 3411–3416

46 Kuo P H , Deshpande A D . A novel joint design for robotic hands with humanlike nonlinear compliance. Journal of Mechanisms and Robotics, 2016, 8(2): 021004

47 Bi S S , Qiao T , Zhao H Z , Yu J J . Stiffness analysis of two compliant pivots used in series elastic actuators. Transactions of the Canadian Society for Mechanical Engineering, 2012, 36(3): 315–328

48 Kuo P H , Deshpande A D . Muscle-tendon units provide limited contributions to the passive stiffness of the index finger metacarpophalangeal joint. Journal of Biomechanics, 2012, 45(15): 2531–2538

49 Lan S B , Song Z B . Design of a new nonlinear stiffness compliant actuator and its error compensation method. Journal of Robotics, 2016, 2016: 7326905

50 Zhao Y R , Song Z B , Ma T Y , Dai J S . Optimisation of stiffness to achieve increased bandwidth and torque resolution in nonlinear stiffness actuators. IEEE Transactions on Industrial Electronics, 2020, 67(4): 2925–2935

51 Song Z B , Lan S B , Dai J S . A new mechanical design method of compliant actuators with non-linear stiffness with predefined deflection-torque profiles. Mechanism and Machine Theory, 2019, 133: 164–178

52 Hu X Q , Song Z B , Ma T Y . Novel design method for nonlinear stiffness actuator with user-defined deflection-torque profiles. Mechanism and Machine Theory, 2020, 146: 103712

53 Qi K K , Song Z B , Dai J S . Safe physical human-robot interaction: a quasi whole-body sensing method based on novel laser-ranging sensor ring pairs. Robotics and Computer-Integrated Manufacturing, 2022, 75: 102280