Mechanical design and robust tracking control of a class of antagonistic variable stiffness actuators based on the equivalent nonlinear torsion springs

Abstract

The novel conceptual model of the antagonistic variable stiffness actuator based on the equivalent nonlinear torsion spring and the friction damper is demonstrated. For the dynamic model of the antagonistic variable stiffness actuator in the presence of parametric uncertainties, unknown bounded friction torques, unknown bounded external disturbance, and input saturation constraints, using the coordinate transformation, the state space model of the antagonistic variable stiffness actuator with composite disturbances and input saturation constraints is transformed into an extended integral chain–type pseudo-linear system with input saturation constraints. Subsequently, a combination of the linear extended state observer, sliding mode control, and adaptive input saturation compensation law is adopted for the design of the robust tracking controller that simultaneously regulates the position and stiffness of the antagonistic equivalent nonlinear torsion spring-based variable stiffness actuator. Under the proposed controller, the semi-global uniformly ultimately bounded stability of the closed-loop system has been proved via Lyapunov stability analysis. Simulation studies demonstrate the effectiveness and the robustness of the proposed robust adaptive tracking control method for the antagonistic variable stiffness actuator.

Keywords

Antagonistic variable stiffness actuator equivalent nonlinear torsion spring linear extended state observer sliding mode control input saturation compensation robust tracking control

Get full access to this article

View all access options for this article.

References

Vanderborght

Albu-Schaeffer

Bicchi

et al . Variable impedance actuators: a review. Rob Auton Syst 2013; 61: 1601–1614.

Jafari

Tsagarakis

Sardellitti

et al . A new actuator with adjustable stiffness based on a variable ratio lever mechanism. IEEE/ASME Trans Mechatr 2014; 19(1): 55–63.

Nam

Kim

Song

JB.

Compliant actuation of parallel-type variable stiffness actuator based on antagonistic actuation. J Mech Sci Technol 2010; 24(11): 2315–2321.

Schiavi

Grioli

Sen

et al . VSA-II: a novel prototype of variable stiffness actuator for safe and performing robots interacting with humans. In: 2008 IEEE international conference on robotics and automation, Pasadena, CA, 19–23 May 2008, pp.2171–2176. New York: IEEE.

Catalano

Grioli

Bonomo

et al . VSA-HD: from the enumeration analysis to the prototypical implementation. In: Proceedings of the 2010 IEEE/RSJ international conference on intelligent robots and systems, Taipei, Taiwan, 18–22 October 2010, pp.3676–3681. New York: IEEE.

Petit

Friedl

Höppner

et al . Analysis and synthesis of the bidirectional antagonistic variable stiffness mechanism. IEEE/ASME Trans Mechatr 2015; 20(2): 684–695.

Masahiko

Nobuyuki

Yuto

et al . Stiffness readout in musculo-skeletal humanoid robot by using rotary potentiometer. In: 2010 IEEE sensors conference, Piscataway, NJ, 1–4 November 2010, pp.2329–2333. New York: IEEE.

Migliore

Brown

Deweerth

SP.

Novel nonlinear elastic actuators for passively controlling robotic joint compliance. J Mech Des 2007; 129(4): 406–412.

Kilic

Yazicioglu

Kurtulus

DF.

Synthesis of a torsional spring mechanism with mechanically adjustable stiffness using wrapping cams. Mech Mach Theory 2012; 57: 27–39.

10.

Schmit

Okada

Design and realization of a non-circular cable spool to synthesize a nonlinear rotational spring. Adv Rob 2012; 26: 235–252.

11.

Palli

Berselli

Melchiorri

et al . Design of a variable stiffness actuator based on flexures. J Mech Rob 2011; 3: 034501.

12.

Sen

. Biologically inspired elastic transmission for stiffness variability in actuation: design and implementation. In: Proceedings of the 2011 IEEE international conference on robotics and biomimetics, Phuket, Thailand, 7–11 December 2011, pp.1973–1977. New York: IEEE.

13.

Koganezawa

Takami

Watanabe

. Antagonistic control of multi-DOF joint. In: Proceedings of the 2012 IEEE/RSJ international conference on intelligent robots and systems, Vilamoura, 7–12 October 2012, pp.2895–2900. New York: IEEE.

14.

Wang

Huang

. ADEA—active variable stiffness differential elastic actuator: design and application for safe robotics. In: Proceedings of the 2011 IEEE international conference on robotics and biomimetics, Phuket, Thailand, 7–11 December 2011, pp.2768–2773. New York: IEEE.

15.

Palli

Model and control of tendon actuated robots. PhD Thesis, Università degli Studi di Bologna, 2007.

16.

Palli

Melchiorri

Luca

A. On the feedback linearization of robots with variable joint stiffness. In: Proceedings of the 2008 IEEE international conference on robotics and automation, Pasadena, CA, 19–23 May 2008, pp.1753–1759. New York: IEEE.

17.

Luca

A Flacco

Bicchi

et al . Nonlinear decoupled motion-stiffness control and collision detection/reaction for the VSA-II variable stiffness device. In: Proceedings of the 2009 IEEE/RSJ international conference on intelligent robots and systems, St. Louis, MI, 11–15 October 2009, pp.5487–5494. New York: IEEE.

18.

Flacco

Modeling and control of robots with compliant actuation. PhD Thesis, Sapienza Università Di Roma, Roma, 2012.

19.

Petit

Daasch

Albu-Schäffer

Backstepping control of variable stiffness robots. IEEE Trans Control Syst Technol 2015; 23(6): 2195–2202.

20.

Zhakatayev

Rubagotti

Varol

et al . Closed-loop control of variable stiffness actuated robots via nonlinear model predictive control. IEEE Access 2015; 3: 235–248.

21.

Zhang

Huang

Robust adaptive control of antagonistic tendon-driven joint in the presence of parameter uncertainties and external disturbances. J Dyn Syst Meas Contr 2017; 139: 101003.

22.

Choi

Park

Lee

et al . Design of a robot joint with variable stiffness. In: 2008 IEEE international conference on robotics and automation, Pasadena, CA, 19–23 May 2008, pp.1760–1765. New York: IEEE.

23.

Palli

Melchiorri

. Robust control of robots with variable joint stiffness. In: International conference on advanced robotics, Munich, 22–26 June 2009, pp.1–6. New York: IEEE.

24.

Albu-Schäffer

Wolf

Eiberger

et al . Dynamic modelling and control of variable stiffness actuators. In: Proceedings of the 2010 IEEE international conference on robotics and automation, Anchorage, AK, 3–8 May 2010, pp.2155–2162. New York: IEEE.

25.

Sardellitti

Medrano-Cerda

Tsagarakis

et al . Gain scheduling control for a class of variable stiffness actuators based on lever mechanisms. IEEE Trans Robot 2013; 29(3): 791–798.

26.

Psomopoulou

Doulgeri

Rovithakis

et al . A simple controller for a variable stiffness joint with uncertain dynamics and prescribed performance guarantees. In: Proceedings of the 2012 IEEE/RSJ international conference on intelligent robots and systems. Vilamoura, 7–12 October 2012, pp.5071–5076. New York: IEEE.

27.

Psomopoulou

Theodorakopoulos

Doulgeri

et al . Prescribed performance tracking of a variable stiffness actuated robot. IEEE Trans Control Syst Technol 2015; 23(5): 1914–1926.

28.

Palli

Melchiorri

Output-based control of robots with variable stiffness actuation. J Robot 2011; 2011: 735407.

29.

Zhang

Yang

Adaptive neural network based variable stiffness control of uncertain robotic systems using disturbance observer. IEEE Trans Ind Electron 2017; 64(3): 2236–2245.

30.

Guo

Pan

Sun

et al . Adaptive neural network control of serial variable stiffness actuators. Complexity 2017; 2017: 5361246.

31.

Smith

Liu

et al . Disturbance observer based control with anti-windup applied to a small fixed wing UAV for disturbance rejection. J Intell Robot Syst 2017; 88: 329–346.

32.

Liu

Wang

et al . Disturbance observer-based antiwindup control for air-breathing hypersonic vehicles. IEEE Trans Ind Electron 2016; 63(5): 3038–3049.

33.

Chen

Yang

On relationship between time-domain and frequency-domain disturbance observers and its applications. J Dyn Syst Meas Contr 2016; 138: 091013.

34.

Chen

Yang

Guo

et al . Disturbance-observer-based control and related methods—an overview. IEEE Trans Ind Electron 2016; 63(2): 1083–1095.

35.

Liu

Fang

Feedback linearization and extended state observer-based control for rotor-AMBs system with mismatched uncertainties. IEEE Trans Ind Electron 2017; 64(2): 1313–1322.

36.

Yang

Chen

et al . Generalized extended state observer based control for systems with mismatched uncertainties. IEEE Trans Ind Electron 2012; 59(12): 4792–4802.

37.

Zhou

Zhu

Lei

et al . Observer-based dynamic surface control for high-performance aircraft subjected to unsteady aerodynamics and actuator saturation. Proc IMechE Part I: J Systems and Control Engineering 2017; 231(6): 481–494.

38.

Guo

Tian

Mechanical design and analysis of the novel 6-DOF variable stiffness robot arm based on antagonistic driven joints. J Intell Rob Syst 2016; 82: 207–235.

39.

Sarakoglou

Tsagarakis

Caldwell

. Development of a hybrid actuator with controllable mechanical damping. In: Proceedings of the 2014 IEEE international conference on robotics & automation (ICRA), Hong Kong, China, 31 May–7 June 2014, pp.1078–1083. New York: IEEE.

40.

Isidori

Nonlinear control systems: an introduction. 2nd ed. Berlin: Springer-Verlag; World Publishing Corporation, 1989, pp.145–226.

41.

Chen

Shi

Nan

et al . Adaptive neural dynamic surface sliding mode control for uncertain nonlinear systems with unknown input saturation. Int J Adv Rob Syst 2016; 13: 1–14.