0
Research Papers

A Controller Avoiding Dynamic Model Degeneracy of Parallel Robots During Singularity Crossing

[+] Author and Article Information
Damien Six

LS2N, UMR CNRS 6004,
Nantes 44321, France;
Ecole Centrale Nantes,
Nantes 44321, France
e-mail: Damien.Six@ls2n.fr

Sébastien Briot

LS2N, UMR CNRS 6004,
Nantes 44321, France
e-mail: Sebastien.Briot@ls2n.fr

Abdelhamid Chriette

LS2N, UMR CNRS 6004,
Nantes 44321, France;
Ecole Centrale Nantes,
Nantes 44321, France
e-mail: Abdelhamid.Chriette@ls2n.fr

Philippe Martinet

LS2N, UMR CNRS 6004,
Nantes 44321, France;
Ecole Centrale Nantes,
Nantes 44321, France
e-mail: Philippe.Martinet@ls2n.fr

1Corresponding author.

Manuscript received February 20, 2017; final manuscript received May 30, 2017; published online August 7, 2017. Assoc. Editor: Venkat Krovi.

J. Mechanisms Robotics 9(5), 051008 (Aug 07, 2017) (8 pages) Paper No: JMR-17-1046; doi: 10.1115/1.4037256 History: Received February 20, 2017; Revised May 30, 2017

Parallel robots present singular configurations that divide the operational workspace into several aspects. It was proven that type 2 and leg passive joint twist system (LPJTS) singularities can be crossed with a trajectory respecting a given dynamic criterion. However, the practical implementation of a controller able to track such trajectories is up to now limited to restrictive cases of type 2 singularities crossing. Analyzing the structure of the inverse dynamic model, this paper proposes a global solution allowing the tracking of trajectories respecting the general criterion for any singularity that leads to potential issues of dynamic model degeneracy. The tracking is operated in the robot joint space. Experimental results on a five-bar mechanism showed the controller ability to successfully cross type 2 singularities.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Merlet, J. , 2006, Parallel Robots, Springer, Dordrecht, The Netherlands.
Zlatanov, D. , Fenton, R. , and Benhabib, B. , 1994, “ Singularity Analysis of Mechanisms and Robots Via a Velocity-Equation Model of the Instantaneous Kinematics,” IEEE International Conference on Robotics and Automation (ICRA), San Diego, CA, May 8–13, pp. 986–991.
Zlatanov, D. , Bonev, I. A. , and Gosselin, C. M. , 2002, “ Constraint Singularities of Parallel Mechanisms,” IEEE International Conference on Robotics and Automation (ICRA), Washington, DC, May 11–15, pp. 496–502.
Conconi, M. , and Carricato, M. , 2009, “ A New Assessment of Singularities of Parallel Kinematic Chains,” IEEE Trans. Rob., 25(4), pp. 757–770. [CrossRef]
Briot, S. , Pagis, G. , Bouton, N. , and Martinet, P. , 2016, “ Degeneracy Conditions of the Dynamic Model of Parallel Robots,” Multibody Syst. Dyn., 37(4), pp. 371–412.
Gosselin, C. , and Angeles, J. , 1990, “ Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
Liu, X.-J. , Wang, J. , and Pritschow, G. , 2006, “ Kinematics, Singularity and Workspace of Planar 5R Symmetrical Parallel Mechanisms,” Mech. Mach. Theory, 41(2), pp. 145–169. [CrossRef]
Gogu, G. , 2004, “ Structural Synthesis of Fully-Isotropic Parallel Robots Via Theory of Linear Transformations and Evolutionary Morphology,” Eur. J. Mech. A/Solids, 23(6), pp. 1021–1039. [CrossRef]
Briot, S. , and Arakelian, V. , 2010, “ On the Dynamic Properties of Rigid-Link Flexible-Joint Parallel Manipulators in the Presence of Type 2 Singularities,” ASME J. Mech. Rob., 2(2), p. 021004. [CrossRef]
Nahon, M. A. , and Angeles, J. , 1989, “ Force Optimization in Redundantly-Actuated Closed Kinematic Chains,” IEEE International Conference on Robotics and Automation (ICRA), Scottsdale, AZ, May 14–19, pp. 951–956.
Kurtz, R. , and Hayward, V. , 1992, “ Multiple-Goal Kinematic Optimization of a Parallel Spherical Mechanism With Actuator Redundancy,” IEEE Trans. Rob. Autom., 8(5), pp. 644–651. [CrossRef]
Rakotomanga, N. , Chablat, D. , and Caro, S. , 2008, Kinetostatic Performance of a Planar Parallel Mechanism With Variable Actuation, Springer, Dordrecht, The Netherlands. [CrossRef]
Arakelian, V. , Briot, S. , and Glazunov, V. , 2008, “ Increase of Singularity-Free Zones in the Workspace of Parallel Manipulators Using Mechanisms of Variable Structure,” Mech. Mach. Theory, 43(9), pp. 1129–1140. [CrossRef]
Campos, L. , Bourbonnais, F. , Bonev, I. A. , and Bigras, P. , 2010, “ Development of a Five-Bar Parallel Robot With Large Workspace,” ASME Paper No. DETC2010-28962.
Zein, M. , Wenger, P. , and Chablat, D. , 2008, “ Non-Singular Assembly-Mode Changing Motions for 3-RPR Parallel Manipulators,” Mech. Mach. Theory, 43(4), pp. 480–490. [CrossRef]
Ider, S. K. , 2005, “ Inverse Dynamics of Parallel Manipulators in the Presence of Drive Singularities,” Mech. Mach. Theory, 40(1), pp. 33–44. [CrossRef]
Pagis, G. , Bouton, N. , Briot, S. , and Martinet, P. , 2015, “ Enlarging Parallel Robot Workspace Through Type-2 Singularity Crossing,” Control Eng. Pract., 39, pp. 1–11. [CrossRef]
Six, D. , Briot, S. , Chriette, A. , and Martinet, P. , 2016, “ A Controller for Avoiding Dynamic Model Degeneracy of Parallel Robots During Type 2 Singularity Crossing,” New Trends in Mechanism and Machine Science (Mechanisms and Machine Science), P. Wenger and P. Flores, eds., Springer, Cham, Switzerland, pp. 589–597. [CrossRef]
Khalil, W. , and Dombre, E. , 2002, Modeling, Identification and Control of Robots, Kogan Page Science, London.
Briot, S. , and Khalil, W. , 2015, Dynamics of Parallel Robots: From Rigid Bodies to Flexible Elements, Springer, Dordrecht, The Netherlands. [CrossRef]
Briot, S. , and Arakelian, V. , 2008, “ Optimal Force Generation in Parallel Manipulators for Passing Through the Singular Positions,” Int. J. Rob. Res., 27(8), pp. 967–983. [CrossRef]
Samson, C. , 1987, “ Robust Control of a Class of Non-Linear Systems and Applications to Robotics,” Int. J. Adapt. Control Signal Process., 1(1), pp. 49–68. [CrossRef]
Merlet, J. P. , 2004, “ Solving the Forward Kinematics of a Gough-Type Parallel Manipulator With Interval Analysis,” Int. J. Rob. Res., 23(3), pp. 221–235. [CrossRef]
Özgür, E. , Dahmouche, R. , Andreff, N. , and Martinet, P. , 2014, “ A Vision-Based Generic Dynamic Model of PKMs and Its Experimental Validation on the Quattro Parallel Robot,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Besacon, France, July 8–11, pp. 937–942.
Paccot, F. , Andreff, N. , and Martinet, P. , 2009, “ A Review on the Dynamic Control of Parallel Kinematic Machines: Theory and Experiments,” Int. J. Rob. Res., 28(3), pp. 395–416. [CrossRef]
Gautier, M. , Khalil, W. , and Restrepo, P. P. , 1995, “ Identification of the Dynamic Parameters of a Closed Loop Robot,” IEEE International Conference on Robotics and Automation (ICRA), Nagoya, Japan, May 21–27, pp. 3045–3050.
Renaud, P. , Vivas, A. , Andreff, N. , Poignet, P. , Martinet, P. , Pierrot, F. , and Company, O. , 2006, “ Kinematic and Dynamic Identification of Parallel Mechanisms,” Control Eng. Pract., 14(9), pp. 1099–1109. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Example of a five-bar mechanism in a type 2 singularity configuration. The vector x˙s represents the direction of the uncontrolled platform motion. f1 and f2 are the forces that can be generated through actuation on the platform. In this configuration, the resultant force that can be applied by the system on the platform is collinear to f1 and f2. Two actuators are used to generate an effort along one direction; an overconstraint is consequently generated in the mechanism.

Grahic Jump Location
Fig. 2

Computed-torque controller in joint space

Grahic Jump Location
Fig. 3

Five-bar mechanism and parametrization scheme

Grahic Jump Location
Fig. 4

Tracked trajectory in Cartesian space (to scale)

Grahic Jump Location
Fig. 5

Input torque applied, σ and σs values, and tracking error on a singularity crossing trajectory. σ = σs = 0 means that the robot is close to a singularity and the wrench projection in the controller is active.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In