Fractional Order Control of a Continuum Robot Arm

This paper studies the dynamic model of the continuum robots as a fractional order system. The viscoelastic Kelvin-Voigt model is applied and a fractional order system is proposed and discussed. The distributed model is transformed in a nonlinear fractional order system by a weighting technique of the state variables. A control law defined with respect to direct observable variable, with a physical meaning, is proposed. A fractional order observer is proposed. The frequential criterions that ensure the asymptotical stability of the global model“observer-system“ are discussed. Numerical simulations and experimental results confirm the quality of the proposed algorithms.

[1]  J. Bruce C. Davies,et al.  Continuum robots - a state of the art , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[2]  Gregory S. Chirikjian,et al.  An obstacle avoidance algorithm for hyper-redundant manipulators , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[3]  Ian D. Walker,et al.  A model-based sliding mode controller for extensible continuum robots , 2010 .

[4]  Hiromi Mochiyama,et al.  The shape Jacobian of a manipulator with hyper degrees of freedom , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[5]  Jing Xiao,et al.  Determining “grasping” configurations for a spatial continuum manipulator , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[6]  Mario Di Paola,et al.  Fractional differential equations and related exact mechanical models , 2013, Comput. Math. Appl..

[7]  Gregory S. Chirikjian,et al.  Equilibrium Conformations of Concentric-tube Continuum Robots , 2010, Int. J. Robotics Res..

[8]  Sara Dadras,et al.  A New Fractional Order Observer Design for Fractional Order Nonlinear Systems , 2011 .

[9]  Nirvana Popescu,et al.  A Spatial Weight Error Control for a Class of Hyper-Redundant Robots , 2013, IEEE Transactions on Robotics.

[10]  Nirvana Popescu,et al.  A decoupled sliding mode control for a continuum arm , 2015, Adv. Robotics.

[11]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .