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Research Papers

Redundancy Resolution of Kinematically Redundant Parallel Manipulators Via Differential Dynamic Programing

[+] Author and Article Information
João Cavacanti Santos

Department of Mechanical Engineering,
School of Engineering of São Carlos,
University of São Paulo,
São Carlos 13566-590, SP, Brazil
e-mail: joao.cavalcanti.santos@usp.br

Maíra Martins da Silva

Professor
Department of Mechanical Engineering,
School of Engineering of São Carlos,
University of São Paulo,
São Carlos 13566-590, SP, Brazil
e-mail: mairams@sc.usp.br

1Corresponding author.

Manuscript received December 10, 2016; final manuscript received April 26, 2017; published online May 24, 2017. Assoc. Editor: Marc Gouttefarde.

J. Mechanisms Robotics 9(4), 041016 (May 24, 2017) (9 pages) Paper No: JMR-16-1372; doi: 10.1115/1.4036739 History: Received December 10, 2016; Revised April 26, 2017

Kinematic redundancy may be an efficient way to improve the performance of parallel manipulators. Nevertheless, the inverse kinematic problem of this kind of manipulator presents infinite solutions. The selection of a single kinematic configuration among a set of many possible ones is denoted as redundancy resolution. While several redundancy resolution strategies have been proposed for planning the motion of redundant serial manipulators, suitable proposals for parallel manipulators are seldom. Redundancy resolution can be treated as an optimization problem that can be solved locally or globally. Gradient projection methods have been successfully employed to solve it locally. For global strategies, these methods may be computationally demanding and mathematically complex. The main objective of this work is to exploit the use of differential dynamic programing (DDP) for decreasing the computational demand and mathematical complexity of a global optimization based on the gradient projection method for redundancy resolution. The outcome of the proposed method is the optimal inputs for the active joints for a given trajectory of the end-effector considering the input limitations and different cost functions. Using the proposed method, the performance of a redundant 3PRRR manipulator is investigated numerically and experimentally. The results demonstrate the capability and versatility of the strategy.

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References

Luces, M. , Boyraz, P. , Mahmoodi, M. , Keramati, F. , Mills, J. K. , and Benhabib, B. , 2015, “ An Emulator-Based Prediction of Dynamic Stiffness for Redundant Parallel Kinematic Mechanisms,” ASME J. Mech. Rob., 8(2), p. 021021. [CrossRef]
Wu, J. , Wang, J. , and You, Z. , 2011, “ A Comparison Study on the Dynamics of Planar 3-DOF 4-RRR, 3-RRR and 2-RRR Parallel Manipulators,” Rob. Comput.-Integr. Manuf., 27(1), pp. 150–156. [CrossRef]
Fontes, J. V. , and da Silva, M. M. , 2016, “ On the Dynamic Performance of Parallel Kinematic Manipulators With Actuation and Kinematic Redundancies,” Mech. Mach. Theory, 103, pp. 148–166. [CrossRef]
Wu, J. , Zhang, B. , and Wang, L. , 2015, “ A Measure for Evaluation of Maximum Acceleration of Redundant and Nonredundant Parallel Manipulators,” ASME J. Mech. Rob., 8(2), p. 021001. [CrossRef]
Müller, A. , 2016, “ Local Kinematic Analysis of Closed-Loop Linkages Mobility, Singularities, and Shakiness,” ASME J. Mech. Rob., 8(4), p. 041013. [CrossRef]
Kotlarski, J. , Abdellatif, H. , Ortmaier, T. , and Heimann, B. , 2009, “ Enlarging the Useable Workspace of Planar Parallel Robots Using Mechanisms of Variable Geometry,” ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots (ReMAR), London, June 22–24, pp. 63–72.
Paccot, F. , Andref, N. , and Martinet, P. , 2009, “ Review on the Dynamic Control of Parallel Kinematic Machines: Theory and Experiments,” Int. J. Rob. Res., 28(3), pp. 395–416. [CrossRef]
Bourbonnais, F. , Bigras, P. , and Bonev, I. A. , 2015, “ Minimum-Time Trajectory Planning and Control of a Pick-and-Place Five-Bar Parallel Robot,” IEEE/ASME Trans. Mechatronics, 20(2), pp. 740–749. [CrossRef]
Lakhal, O. , Melingui, A. , and Merzouki, R. , 2016, “ Hybrid Approach for Modeling and Solving of Kinematics of a Compact Bionic Handling Assistant Manipulator,” IEEE/ASME Trans. Mechatronics, 21(3), pp. 1326–1335. [CrossRef]
da Silva, M. M. , de Oliveira, L. P. , Bruls, O. , Michelin, M. , Baradat, C. , Tempier, O. , Caigny, J. D. , Swevers, J. , Desmet, W. , and Brussel, H. V. , 2010, “ Integrating Structural and Input Design of a 2-DOF High-Speed Parallel Manipulator: A Flexible Model-Based Approach,” Mech. Mach. Theory, 45(11), pp. 1509–1519. [CrossRef]
Ahuactzin, J. M. , and Gupta, K. K. , 1999, “ The Kinematic Roadmap: A Motion Planning Based Global Approach for Inverse Kinematics of Redundant Robots,” IEEE Trans. Rob. Autom., 15(4), pp. 653–669. [CrossRef]
Cha, S.-H. , Lasky, T. A. , and Velinsky, S. A. , 2007, “ Singularity Avoidance for the 3-RRR Mechanism Using Kinematic Redundancy,” IEEE International Conference on Robotics and Automation (ICRA), Rome, Italy, Apr. 10–14, pp. 1195–1200.
Muller, A. , 2008, “ On the Terminology for Redundant Parallel Manipulators,” ASME Paper No. DETC2008-49112.
Ebrahimi, I. , Carretero, J. A. , and Boudreau, R. , 2006, “ Workspace Comparison of Kinematically Redundant Planar Parallel Manipulators,” Romansy 16, Vol. 487, Springer, Vienna, Austria, pp. 89–96.
Kotlarski, J. , Heimann, B. , and Ortmaier, T. , 2011, “ Experimental Validation of the Influence of Kinematic Redundancy on the Pose Accuracy of Parallel Kinematic Machines,” IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9–13, pp. 1923–1929.
Xie, F. , Liu, X.-J. , and Wang, J. , 2011, “ Performance Evaluation of Redundant Parallel Manipulators Assimilating Motion/Force Transmissibility,” Int. J. Adv. Rob. Syst., 8(5), pp. 113–124.
Ruiz, A. G. , Fontes, J. V. C. , and da Silva, M. M. , 2015, “ The Impact of Kinematic and Actuation Redundancy on the Energy Efficiency of Planar Parallel Kinematic Machines,” 17th International Symposium on Dynamic Problems of Mechanics, Natal, Brazil, Feb. 22–27, pp. 1–9.
Ukidve, C. S. , McInroy, J. E. , and Jafari, F. , 2008, “ Using Redundancy to Optimize Manipulability of Stewart Platforms,” IEEE/ASME Trans. Mechatronics, 13(4), pp. 475–479. [CrossRef]
Siciliano, B. , 1990, “ Kinematic Control of Redundant Robot Manipulators: A Tutorial,” J. Intell. Rob. Syst., 3(3), pp. 201–212. [CrossRef]
Shin, K. , and McKay, N. D. , 1986, “ A Dynamic Programming Approach to Trajectory Planning of Robotic Manipulators,” IEEE Trans. Autom. Control, 31(6), pp. 491–500. [CrossRef]
Nakamura, Y. , and Hanafusa, H. , 1987, “ Optimal Redundancy Control of Redundant Manipulators,” Int. J. Rob. Res., 6(1), pp. 32–42. [CrossRef]
Martin, D. P. , Baillieul, J. , and Hollerbach, J. M. , 1989, “ Resolution of Kinematic Redundancy Using Optimization Techniques,” IEEE Trans. Rob. Autom., 5(4), pp. 529–533. [CrossRef]
Deb, K. , Agrawal, S. , Pratap, A. , and Meyarivan, T. , 2002, “ A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: Nsga-II,” IEEE Trans. Evol. Comput., 6(2), pp. 182–197. [CrossRef]
Marcos, M. G. , Machado, J. A. T. , and Azevedo-Perdicoúlis, T.-P. , 2012, “ A Multi-Objective Approach for the Motion Planning of Redundant Manipulators,” Appl. Soft Comput., 12(2), pp. 589–599. [CrossRef]
Kim, H. , Miller, L. M. , Byl, N. , Abrams, G. , and Rosen, J. , 2012, “ Redundancy Resolution of the Human Arm and an Upper Limb Exoskeleton,” IEEE Trans. Biomed. Eng., 59(6), pp. 1770–1779. [CrossRef] [PubMed]
Minami, M. , Li, X. , Matsuno, T. , and Yanou, A. , 2016, “ Dynamic Reconfiguration Manipulability for Redundant Manipulators,” ASME J. Mech. Rob., 8(6), p. 061004. [CrossRef]
Kotlarski, J. , Thanh, T. D. , Heimann, B. , and Ortmaier, T. , 2010, “ Optimization Strategies for Additional Actuators of Kinematically Redundant Parallel Kinematic Machines,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 656–661.
Thanh, T. D. , Kotlarski, J. , Heimann, B. , and Ortmaier, T. , 2012, “ Dynamics Identification of Kinematically Redundant Parallel Robots Using the Direct Search Method,” Mech. Mach. Theory, 52, pp. 277–295. [CrossRef]
Boudreau, R. , and Nokleby, S. , 2012, “ Force Optimization of Kinematically-Redundant Planar Parallel Manipulators Following a Desired Trajectory,” Mech. Mach. Theory, 56, pp. 138–155. [CrossRef]
Bellman, R. , 2003, Dynamic Programming, Dover Publications, Mineola, NY.
Guigue, A. , Ahmadi, M. , Hayes, M. , Langlois, R. , and Tang, F. , 2007, “ A Dynamic Programming Approach to Redundancy Resolution With Multiple Criteria,” IEEE International Conference on Robotics and Automation (ICRA), Rome, Italy, Apr. 10–14, pp. 1375–1380.
Nakamura, Y. , and Hanafusa, H. , 1986, “ Inverse Kinematic Solutions With Singularity Robustness for Robot Manipulator Control,” ASME J. Dyn. Syst. Meas. Control, 108(3), pp. 163–171. [CrossRef]
Cahill, A. J. , James, M. R. , Kieffer, J. C. , and Williamson, D. , 1998, “ Remarks on the Application of Dynamic Programming to the Optimal Path Timing of Robot Manipulators,” Int. J. Robust Nonlinear Control, 8(6), pp. 463–482. [CrossRef]
Tassa, Y. , Mansard, N. , and Todorov, E. , 2014, “ Control-Limited Differential Dynamic Programming,” IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, China, May 31–June 7, pp. 1168–1175.
Rao, S. S. , 2009, Engineering Optimization: Theory and Practice, 4th ed., Wiley, Hoboken, NJ.
Patel, S. , and Sobh, T. , 2015, “ Manipulator Performance Measures—A Comprehensive Literature Survey,” J. Intell. Rob. Syst., 77(3), pp. 547–570. [CrossRef]

Figures

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Fig. 1

3PRRR: the kinematically redundant planar parallel manipulator built at São Carlos School of Engineering at University of São Paulo

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Fig. 2

Schematic representation of a 3PRRR

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Fig. 3

3RRR: (a) nonsingular configuration and (b) singular configuration, which mitigates mechanism rigidity

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Fig. 4

Illustration of persistent interchange between σ2 and σ3

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Fig. 5

The influence of c3 over H3

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Fig. 6

Pick-and-place task: reference poses

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Fig. 7

Numerical results: comparison between the reference and actual poses of the nonredundant manipulator's end-effector under torque disturbance (−0.05 N·m)

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Fig. 8

Experimental results: comparison between (a) the reference final pose and (b) the actual final pose of the nonredundant manipulator under no load disturbance

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Fig. 9

Numerical comparison between the reference and actual pose of the redundant manipulator's end-effector under torque disturbance (−1.30 N·m): (a) the end-effector's orientation and (b) the end-effector's translational positions

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Fig. 10

Experimental comparison between the reference and actual pose of the redundant manipulator's end-effector under no torque disturbance: (a) the end-effector's orientation and (b) the end-effector's translational positions

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Fig. 11

Active revolute joints' currents: (a) 3RRR and (b) 3PRRR

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