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Bi-criteria minimization with MWVN–INAM type for motion planning and control of redundant robot manipulators

Published online by Cambridge University Press:  11 January 2018

Dongsheng Guo*
Affiliation:
College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
Kene Li
Affiliation:
School of Electrical and Information Engineering, Guangxi University of Science and Technology, Liuzhou 545006, China. E-mail: likene@163.com
Bolin Liao
Affiliation:
College of Information Science and Engineering, Jishou University, Jishou 416000, China. E-mail: mulinliao8184@163.com
*
*Corresponding author. E-mails: gdongsh@hqu.edu.cn, gdongsh2008@126.com

Summary

This study proposes and investigates a new type of bi-criteria minimization (BCM) for the motion planning and control of redundant robot manipulators to address the discontinuity problem in the infinity-norm acceleration minimization (INAM) scheme and to guarantee the final joint velocity of motion to be approximate to zero. This new type is based on the combination of minimum weighted velocity norm (MWVN) and INAM criteria, and thus is called the MWVN–INAM–BCM scheme. In formulating such a scheme, joint-angle, joint-velocity, and joint-acceleration limits are incorporated. The proposed MWVN–INAM–BCM scheme is reformulated as a quadratic programming problem solved at the joint-acceleration level. Simulation results based on the PUMA560 robot manipulator validate the efficacy and applicability of the proposed MWVN–INAM–BCM scheme in robotic redundancy resolution. In addition, the physical realizability of the proposed scheme is verified in practical application based on a six-link planar robot manipulator.

Type
Articles
Copyright
Copyright © Cambridge University Press 2018 

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References

1. Siciliano, B. and Khatib, O., Springer Handbook of Robotics (Springer-Verlag, Heidelberg, 2008).Google Scholar
2. Siciliano, B., Sciavicco, L., Villani, L. and Oriolo, G., Robotics: Modelling, Planning and Control (Springer-Verlag, London, 2009).Google Scholar
3. Zhang, Y. and Zhang, Z., Repetitive Motion Planning and Control of Redundant Robot Manipulators (Springer-Verlag, New York, 2013).Google Scholar
4. Jouybari, B. R., Osgouie, K. G. and Meghdari, A., “Optimization of kinematic redundancy and workspace analysis of a dual-arm cam-lock robot,” Robotica 34 (1), 2342 (2016).Google Scholar
5. Motahari, A., Zohoor, H. and Korayem, M. H., “A new motion planning method for discretely actuated hyper-redundant manipulators,” Robotica 35 (1), 101118 (2017).Google Scholar
6. Guo, D. and Zhang, Y., “Acceleration-level inequality-based MAN scheme for obstacle avoidance of redundant robot manipulators,” IEEE Trans. Ind. Electron. 61 (12), 69036914 (2014).Google Scholar
7. Guo, D. and Zhang, Y., “Simulation and experimental verification of weighted velocity and acceleration minimization for robotic redundancy resolution,” IEEE Trans. Autom. Sci. Eng. 11 (4), 12031217 (2014).CrossRefGoogle Scholar
8. Yu, L., Wang, Z., Yu, P., Wang, T., Song, H. and Du, Z., “A new kinematics method based on a dynamic visual window for a surgical robot,” Robotica 32 (4), 571589 (2014).Google Scholar
9. Liao, B. and Liu, W., “Pseudoinverse-type bi-criteria minimization scheme for redundancy resolution of robot manipulators,” Robotica 33 (10), 21002113 (2015).CrossRefGoogle Scholar
10. Shimizu, M., “Analytical inverse kinematics for 5-DOF humanoid manipulator under arbitrarily specified unconstrained orientation of end-effector,” Robotica 33 (4), 747767 (2015).Google Scholar
11. Nenchev, D., Okawa, R. and Sone, H., “Task-space dynamics and motion/force control of fixed-base manipulators under reaction null-space-based redundancy resolution,” Robotica 34 (12), 28602877 (2016).CrossRefGoogle Scholar
12. Isaksson, M., Gosselin, C. and Marlow, K., “An introduction to utilising the redundancy of a kinematically redundant parallel manipulator to operate a gripper,” Mech. Mach. Theory 101, 5059 (2016).Google Scholar
13. Qiu, B., Zhang, Y. and Yang, Z., “Revisit and compare Ma equivalence and Zhang equivalence of minimum velocity norm (MVN) type,” Adv. Robot. 30 (6), 416430 (2016).CrossRefGoogle Scholar
14. Guo, D. and Zhang, Y., “Li-function activated ZNN with finite-time convergence applied to redundant-manipulator kinematic control via time-varying Jacobian matrix pseudoinversion,” Appl. Soft Comput. 24, 158168 (2014).Google Scholar
15. Deo, A. S. and Walker, I. D., “Minimum effort inverse kinematics for redundant manipulators,” IEEE Trans. Robot. Autom. 13 (5), 767775 (1997).Google Scholar
16. Granvagne, I. A. and Walker, I. D., “On the structure of minimum effort solutions with application to kinematic redundancy resolution,” IEEE Trans. Robot. Autom. 16 (6), 855863 (2000).CrossRefGoogle Scholar
17. Zhang, Y., Guo, D., Li, J. and Li, K., “Unification and Comparison on Bi-Criteria Velocity, Acceleration and Torque Minimization Illustrated Via Three-Link Planar Robot Arm,” Proceedings of the Chinese Control Decision Conference (2011) pp. 3410–3415.Google Scholar
18. Guo, D., Zhai, K., Xiao, Z., Tan, H. and Zhang, Y., “Acceleration-Level Minimum Kinetic Energy (MKE) Scheme Derived Via Ma Equivalence for Motion Planning of Redundant Robot Manipulators,” Proceedings of the International Symposium on Computational Intelligence and Design (2014) pp. 26–30.Google Scholar
19. Tang, W. S. and Wang, J., “A recurrent neural network for minimum infinity-norm kinematic control of redundant manipulators with an improved problem formulation and reduced architecture complexity,” IEEE Trans. Syst., Man, Cybern., Part B 31 (1), 98105 (2001).CrossRefGoogle ScholarPubMed
20. Zhang, Y., Yin, J. and Cai, B., “Infinity-norm acceleration minimization of robotic redundant manipulators using the LVI-based primal-dual neural network,” Robot. Comput.-Integr. Manuf. 25 (2), 358365 (2009).Google Scholar
21. Zhang, Y., “Inverse-free computation for infinity-norm torque minimization of robot manipulators,” Mechatronics 16 (3–4), 177184 (2006).CrossRefGoogle Scholar
22. Guo, D. and Zhang, Y., “Different-level two-norm and infinity-norm minimization to remedy joint-torque instability/divergence for redundant robot manipulators,” Robot. Autonomous Syst. 60 (6), 874888 (2012).CrossRefGoogle Scholar
23. Lee, J., “A structured algorithm for minimum l -norm solutions and its application to a robot velocity workspace analysis,” Robotica 19 (3), 343352 (2001).Google Scholar
24. Latash, M. L., Control of Human Movement (Human Kinematics Publisher, Chicago, 1993).Google Scholar
25. Iqbal, K. and Pai, Y. C., “Predicted region of stability for balance recovery: Motion at the knee joint can improve termination of forward movement,” J. Biomechanics 33 (12), 16191627 (2000).CrossRefGoogle ScholarPubMed
26. O'Neil, K. A., “Divergence of linear acceleration-based redundancy resolution schemes,” IEEE Trans. Robot. Autom. 18 (4), 625631 (2002).CrossRefGoogle Scholar
27. Zhang, Y., Wang, J. and Xu, Y., “A dual neural network for bi-criteria kinematic control of redundant manipulators,” IEEE Trans. Robot. Autom. 18 (6), 923931 (2002).CrossRefGoogle Scholar
28. Zhang, Y., Cai, B., Zhang, L. and Li, K., “Bi-criteria velocity minimization of robot manipulators using a linear variational inequalities-based primal-dual neural network and PUMA560 example,” Adv. Robot. 22, 14791496 (2008).Google Scholar
29. Zhang, Y. and Yin, J., “Bi-Criteria Acceleration Minimization of Redundant Robot Manipulator Using New Problem Formulation and LVI-Based Primal-Dual Neural Network,” Proceedings of the Sixth International Conference on Machine Learning and Cybernetics (2007) pp. 19–22.Google Scholar
30. Zhang, Y., Tan, N. and Lai, C., “Bi-Criteria Torque Minimization of Redundant Robot Arms with Schemes, Models and Methods Compared,” Proceedings of the IEEE International Conference on Robotics and Biomedicaal (2009) pp. 2397–2402.Google Scholar
31. Guo, D. and Zhang, Y., “Zhang neural network for online solution of time-varying linear matrix inequality aided with an equality conversion,” IEEE Trans. Neural Netw. Learn. Syst. 25 (2), 370382 (2014).Google Scholar
32. Zhang, Y. and Guo, D., Zhang Functions and Various Models (Springer-Verlag, Heidelberg, 2015.)CrossRefGoogle Scholar
33. Xiao, L., “A new design formula exploited for accelerating Zhang neural network and its application to time-varying matrix inversion,” Theo. Computer Sci. 647, 5058 (2016).Google Scholar
34. Zhang, Y., Li, W., Guo, D., Zhang, Z. and Fu, S., “Feedback-Type MWVN Scheme and its Acceleration-Level Equivalent Scheme Proved by Zhang Dynamics,” Proceedings of the International Conference on Control Engineering and Communication Technology (2012) pp. 180–183.Google Scholar
35. Zhang, Y., Guo, D. and Ma, S., “Different-level simultaneous minimization of joint-velocity and joint-torque for redundant robot manipulators,” J. Intell. Robot. Syst. 72 (3–4), 301323 (2013).CrossRefGoogle Scholar
36. Bazarra, M. S., Sherali, H. D. and Shetty, C. M., Nonlinear Programming – Theory and Algorithms (Wiley, New York, 1993).Google Scholar
37. He, B., “Solving a class of linear projection equation,” Numer. Math. 68 (1), 7180 (1994).Google Scholar
38. He, B., “A new method for a class of linear variational inequalities,” Math. Program. 66 (2), 137144 (1994).Google Scholar
39. Cheng, F. T., Chen, T. H. and Sun, Y. Y., “Resolving manipulator redundancy under inequality constraints,” IEEE Trans. Robot. Autom. 10 (1), 6571 (1994).Google Scholar
40. Cheng, F. T., Sheu, R. J. and Chen, T. H., “The improved compact QP method for resolving manipulator redundancy,” IEEE Trans. Syst., Man, Cybern. 25 (11), 15211530 (1995).Google Scholar
41. Park, K. C., Chang, P. H. and Kim, S. H., “The Enhanced Compact QP Method for Redundant Manipulators Using Practical Inequality Constraints,” Proceeddings of the IEEE International Conference on Robotics and Automation (1998) pp. 107–114.Google Scholar
42. Chen, D. and Zhang, Y., “Minimum jerk norm scheme applied to obstacle avoidance of redundant robot arm with jerk bounded and feedback control,” IET Control Theory Appl. 10, 18961903 (2016).Google Scholar
43. Zhang, Z., Beck, A. and Magnenat-Thalmann, N., “Human-like behavior generation based on head-arms model for robot tracking external targets and body parts,” IEEE Trans. Cybern. 45 (8), 13901400 (2015).Google Scholar
44. Xiao, L. and Zhang, Y., “Dynamic design, numerical solution and effective verification of acceleration-level obstacle avoidance scheme for robot manipulators,” Int. J. Syst. Sci. 47, 932945 (2016).Google Scholar
45. Guo, D. and Li, K., “Acceleration-Level Obstacle-Avoidance Scheme for Motion Planning of Redundant Robot Manipulators,” Proceedings of the IEEE International Conference on Robotics and Biomimetics (2016) pp. 1313–1318.Google Scholar
46. Ferreau, H. J., Bock, H. G. and Diehl, M., “An online active set strategy to overcome the limitations of explicit MPC,” Int. J. Robust Nonlin. Control 18 (8), 816830 (2008).Google Scholar
47. Ferreau, H. J., Kirches, C., Potschka, A., Bock, H. G. and Diehl, M., “qpOASES: A parametric active-set algorithm for quadratic programming,” Math. Prog. Comp. 6 (4), 327363 (2014).Google Scholar
48. Frasch, J., Vukov, M., Ferreau, H. J. and Diehl, M., “A New Quadratic Programming Strategy for Efficient Sparsity Exploitation in SQP-Based Nonlinear MPC and MHE,” Proceedings of the 19th IFAC World Congress (2014) pp. 2945–2950.Google Scholar
49. Kouzoupis, D., Zanelli, A., Peyrl, H. and Ferreau, H. J., “Towards Proper Assessment of QP Algorithms for Embedded Model Predictive Control,” Proceedings of the European Control Conference (2015) pp. 2609–2616.Google Scholar