Examples of Planar Multilink Manipulators

  • Yunong Zhang
  • Zhijun Zhang


In Chaps.  2 and  3, we have theoretically demonstrated the effectiveness of such a physically constrained RMP scheme (and its solvers) on solving the joint-angle drift problem. In this chapter, a dual neural network (introduced in Chap.  4) and an LVI-based primal–dual neural network (introduced in Chap.  5) are presented for online repetitive motion planning (RMP) of redundant robot manipulators (with multilink planar manipulators as examples). As real-time QP solvers, the aforementioned two kinds of neural networks both have piecewise-linear dynamics and can globally exponentially converge to the optimal solution of strictly-convex quadratic programs. Furthermore, the neural-network-based physically constrained RMP scheme is simulated based on the multilink planar robot manipulators. Computer-simulation results substantiate the theoretical analysis and also show the effective remedy of the joint-angle drift problem of robot manipulators.


  1. 1.
    Zhang Y, Li X, Zhu H, Tan N (2009) Joint-angle-drift remedy of three-link planar robot arm performing different types of end-effector trajectories. In: Proceedings of IEEE international conference on intelligent computing and intelligent systems, pp 581–585 Google Scholar
  2. 2.
    Chen K, Zhang L, Zhang Y (2008) Cyclic motion generation of multi-link planar robot performing square end-effector trajectory analyzed via gradient-descent and Zhang et al’s neural-dynamic methods. In: Proceedings of the 2nd international symposium on systems and control in aerospace and astronautics, pp 1–6 Google Scholar
  3. 3.
    Zhang Y, Tan Z, Chen K, Yang Z, Lv X (2009) Repetitive motion of redundant robots planned by three kinds of recurrent neural networks and illustrated with a four-link planar manipulator’s straight-line example. Robot Auton Syst 57(6–7):645–651 CrossRefGoogle Scholar
  4. 4.
    Zhang Y, Tan Z, Yang Z, Lv X (2008) A dual neural network applied to joint angle drift-free resolution of five-link planar robot arm. In: Proceedings of IEEE international conference on information and automation, pp 1274–1279 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yunong Zhang
    • 1
  • Zhijun Zhang
    • 1
  1. 1.Sun Yat-sen UniversityGuangzhouPeople’s Republic of China

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