A switching inverse dynamics controller for parallel manipulators around drive singular configurations

Despite many advantages, parallel manipulators are known to possess drive singularities where the control of one or more degrees of freedom is lost. Around these singular configurations, the required actuator forces grow unbounded. Previous efforts in the literature put forward singularity-consistent trajectory planning and singularityrobust modification of the dynamic equations as a solution to this problem. However, this previous method is applicable only for the open-loop operation of the manipulator, whereas initial configuration errors, external disturbances, and modeling errors should necessarily be taken into account in a closed-loop sense in real-life applications. With this aim, a switching inverse dynamics controller is proposed in this study for the trajectory tracking control of parallel manipulators as they pass through drive singular configurations. Simulations of the application of the developed controller result in good tracking performance, even in the presence of modeling errors, while the actuator efforts remain bounded and continuous in the neighborhood of the singularity.

[1]  Ashraf Omran,et al.  A note on the inverse dynamic control of parallel manipulators , 2010 .

[2]  S. K. Ider Inverse dynamics of parallel manipulators in the presence of drive singularities , 2005 .

[3]  M. W. Spong,et al.  On the positive definiteness and uniform boundedness of the inertia matrix of robot manipulators , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[4]  Frank L. Lewis,et al.  Robot Manipulator Control: Theory and Practice , 2003 .

[5]  C. K. Jui,et al.  Path Tracking of Parallel Manipulators in the Presence of Force Singularity , 2005 .

[6]  Sébastien Briot,et al.  On the Dynamic Properties of Rigid-Link Flexible-Joint Parallel Manipulators in the Presence of Type 2 Singularities , 2010 .

[7]  J. G. Jalón,et al.  Multibody dynamics with redundant constraints and singular mass matrix: existence, uniqueness, and determination of solutions for accelerations and constraint forces , 2013 .

[8]  Shuang Cong,et al.  Nonlinear computed torque control for a high-speed planar parallel manipulator , 2009 .

[9]  Sébastien Briot,et al.  On the Dynamic Properties of Flexible Parallel Manipulators in the Presence of Type 2 Singularities , 2011 .

[10]  Jun Wu,et al.  Dynamic feed-forward control of a parallel kinematic machine , 2009 .

[11]  Clément Gosselin,et al.  Singularity analysis of closed-loop kinematic chains , 1990, IEEE Trans. Robotics Autom..

[12]  Ashitava Ghosal,et al.  Singularity and controllability analysis of parallel manipulators and closed-loop mechanisms , 2000 .

[13]  S. Kemal Ider Singularity robust inverse dynamics of planar 2-RPR parallel manipulators , 2004 .

[14]  M. Greenberg Advanced Engineering Mathematics , 1988 .

[15]  Firdaus E. Udwadia,et al.  Equations of motion for general constrained systems in Lagrangian mechanics , 2010 .

[16]  Sébastien Briot,et al.  Optimal Force Generation in Parallel Manipulators for Passing through the Singular Positions , 2008, Int. J. Robotics Res..

[17]  Sinan Kilicaslan,et al.  Tracking control of elastic joint parallel robots via state-dependent Riccati equation , 2015 .

[18]  Asier Zubizarreta,et al.  A procedure to evaluate Extended Computed Torque Control configurations in the Stewart-Gough platform , 2011, Robotics Auton. Syst..

[19]  S. Kemal Ider,et al.  Trajectory tracking control of parallel robots in the presence of joint drive flexibility , 2009 .