Nonlinear dynamic analysis for elastic robotic arms

Abstract

The aim of the paper is to analyze the nonlinear dynamics of robotic arms with elastic links and joints. The main contribution of the paper is the comparative assessment of assumed modes and finite element methods as more convenient approaches for computing the nonlinear dynamic of robotic systems. Numerical simulations comprising both methods are carried out and results are discussed. Hence, advantages and disadvantages of each method are illustrated. Then, adding the joint flexibility to the system is dealt with and the obtained model is demonstrated. Finally, a brief description of the optimal motion generation is presented and the simulation is carried out to investigate the role of robot dynamic modeling in the control of robots.

Keywords

robotic arms / elastic link / elastic joint / nonlinear dynamics / optimal control

References

[1] Zhu G, Ge S S, Lee T H. Simulation studies of tip tracking control of a single-link flexible robot based on a lumped model. Robotica, 1999, 17(1): 71-78

[2] Kim J S, Uchiyama M. Vibration mechanism of constrained spatial flexible manipulators. JSME, Series C, 2003, 46(1): 123-128

[3] Green A, Sasiadek J Z. Dynamics and trajectory tracking control of a two-link robot manipulator. J. of Vib. and Cont, 2004, 10(10): 1415-1440

[4] Green A, Sasiadek J Z. Robot manipulator control for rigid and assumed mode flexible dynamics models, AIAA Guidance, Navigation, and Control Conference and Exhibit, 2003

[5] Subudhi B, Morris A S. Dynamic modelling, simulation and control of a manipulator with flexible links and joints. Robotics and Autonomous Systems, 2002, 41(4): 257-270

[6] Korayem M H, Rahimi Nohooji H. Trajectory optimization of flexible mobile manipulators using open-loop optimal control method. Springer-Verlag Berlin Heidelberg, LNAI, 2008, 5314(1): 54-63

[7] Usoro P B, Nadira R, Mahil S S. A finite element/Lagrange approach to modeling lightweight flexible manipulators. Journal of Dynamic Systems, Measurement, and Control, 1986, 108(3): 198-205

[8] Korayem M H, Haghpanahi M, Rahimi H N, Nikoobin A. Finite element method and optimal control theory for path planning of elastic manipulators, Springer-Verlag Berlin Heidelberg. New Advanced in Intelligent Decision Technology, SCI, 2009, 199: 107-116

[9] Zhang C X, Yu Y Q. Dynamic analysis of planar cooperative manipulators with link flexibility, ASME. Journal of Dynamic Systems, Measurement, and Control, 2004, 126: 442-448

[10] Mohamed Z, Tokhi M O. Command shaping techniques for vibration control of a flexible robot manipulator. Mechatronics, 2004, 14(1): 69-90

[11] Yue S, Tso S K, Xu W L. Maximum dynamic payload trajectory for flexible robot manipulators with kinematic redundancy. Mechanism and Machine Theory, 2001, 36(6): 785-800

[12] Korayem M H, Rahimi H N, Nikoobin A. Analysis of four wheeled flexible joint robotic arms with application on optimal motion design, Springer-Verlag Berlin Heidelberg, New Advan. in Intel. Decision Technology, 2009, 199: 117-126

[13] Chen W. Dynamic modeling of multi-link flexible robotic manipulators. Computers & Structures, 2001, 79(2): 183-195

[14] Fraser A R, Daniel R W. Perturbation techniques for flexible manipulators. Kluwer International Series in Engineering and Computer Science, 1991, 138

[15] Kirk D E. Optimal control theory, an introduction. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1970

[16] Koivo A J, Arnautovic S H. Dynamic optimum control of redundant manipulators. In: Proceedings of IEEE International Conference on Robotics and Automation, 1991, 466-471

[17] Mohri A, Furuno S, Iwamura M, Yamamoto M. Sub-optimal trajectory planning of mobile manipulator. In: Proceedings of IEEE International Conference on Robotics and Automation, 2001, 1271-1276

[18] Kelly A, Nagy B. Reactive nonholonomic trajectory generation via parametric optimal control. International Journal of Robotics Research, 2003, 22(8): 583-601

[19] Furuno S, Yamamoto M, Mohri A. Trajectory planning of mobile manipulator with stability considerations. In: Proceedings of IEEE International Conference on Robotics and Automation, 2003, 3403-3408

[20] Wilson D G, Robinett R D, Eisler G R. Discrete dynamic programming for optimized path planning of flexible robots. In: Proceedings of IEEE International Conference on lntelligent Robots and Systems, Japan, 2004

[21] Hull D G. Conversion of optimal control problems into parameter optimization problems. Journal of Guidance, Control, and Dynamics, 1997, 20(1): 57-60

[22] Wang L T, Ravani B. Dynamic load carrying capacity of mechanical manipulators- Part 2, J. of Dynamic Sys. Measurement and Control, 1988, 110: 53-61

[23] Wang C Y E, Timoszyk W K, Bobrow J E. Payload maximization for open chained manipulator: Finding motions for a Puma 762 robot. IEEE Transactions on Robotics and Automation, 2001, 17(2): 218-224

[24] Ge X S, Chen L Q. Optimal motion planning for nonholonomic systems using genetic algorithm with wavelet approximation. Applied Mathematics and Computation, 2006, 180(1): 76-85

[25] Haddad M, Chettibi T, Hanchi S, Lehtihet H E. Optimal motion planner of mobile manipulators in generalized point-to-point task. 9th IEEE International Workshop on Advanced Motion Control, 2006, 300-306

[26] Park K J. Flexible robot manipulator path design to reduce the endpoint residual vibration under torque constraints. Journal of Sound and Vibration, 2004, 275(3-5): 1051-1068

[27] Shiller Z, Dubowsky S. Robot path planning with obstacles, actuators, gripper and payload constraints. International Journal of Robotics Research, 1986, 8(6): 3-18

[28] Shiller Z. Time-energy optimal control of articulated systems with geometric path constraints. In: Proceedings of IEEE International Conference on Robotics and Automation, 1994, 4: 2680-2685

[29] Fotouhi R, Szyszkowski W. An algorithm for time-optimal control problems, Journal of Dynamic Systems, Measurement, and Control, Transactions of the ASME, 1998, 120(3): 414-418

[30] Agrawal O P, Xu Y.On the global optimum path planning for redundant space manipulators. IEEE T sys Man Cyb, 1994, 24(9): 1306-1316

[31] Bessonnet G, Chessé S. Optimal dynamics of actuated kinematic chains, Part 2: Problem statements and computational aspects. European Journal of Mechanics. A, Solids, 2005, 24(3): 472-490

[32] Bertolazzi E, Biral F, Da Lio M. Symbolic–numeric indirect method for solving optimal control problems for large multibody systems. Multibody System Dynamics, 2005, 13(2): 233-252

[33] Sentinella M R, Casalino L. Genetic algorithm and indirect method coupling for low-thrust trajectory optimization. 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, California, 2006

[34] Bryson A E, Ho Y. Applied optimal control: Optimization, estimation, and control, Ginn and company, 1969

[35] Shampine L F, Reichelt M W, Kierzenka J. Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c. Available at http://www.mathworks.com/bvp tutorial

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg