Trajectory Tracking Control in a Single Flexible-Link Robot using Finite Differences and Sliding Modes

In this article it is shown how the end effector position of a single flexible-link robot can be directly controlled by the angular position of its joint, so that, trajectory tracking in the end effector of the robot is possible by properly designing a reference trajectory for the joint angle. In order to ensure trajectory tracking of the angular position of the robot joint, a Sliding Modes Control (SMC) scheme is employed once the desired trajectory for the robot joint has been designed. SMC scheme is chosen because its known robust performance under dynamical disturbances and modeling inaccuracies. Then, the angular position of the robot joint plays the role of a virtual control input for the flexible dynamics of the link. Both, regulation and trajectory tracking of the end effector position are achieved by using the scheme devised in this work. The Finite Differences Method (FDM) is employed to simulate the closed loop performance of the flexible-link robot, because its dynamics are assumed to be governed by the undamped Partial Differential Equation (PDE) of the Euler-Bernoulli Beam (EBB).

[1]  Wayne J. Book,et al.  Modeling, design, and control of flexible manipulator arms: a tutorial review , 1990, 29th IEEE Conference on Decision and Control.

[2]  Fei-Yue Wang,et al.  Advanced Studies of Flexible Robotic Manipulators - Modeling, Design, Control and Applications , 2003, Series in Intelligent Control and Intelligent Automation.

[3]  Youngil Youm,et al.  Inverse kinematics of multilink flexible robots for high-speed applications , 2004 .

[4]  Motoji Yamamoto,et al.  On the trajectory planning of a planar elastic manipulator under gravity , 1999, IEEE Trans. Robotics Autom..

[5]  Giovanni Ulivi,et al.  Stable inversion control for flexible link manipulators , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[6]  Mrdjan J. Jankovic,et al.  Constructive Nonlinear Control , 2011 .

[7]  Bruno Siciliano,et al.  A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators , 1988, Int. J. Robotics Res..

[8]  Leonardo Lanari,et al.  Achieving minimum phase behavior in a one-link flexible arm , 1991 .

[9]  Rajnikant V. Patel,et al.  Flexible-Link Robot Manipulators: Control Techniques and Structural Design , 2000 .

[10]  심성한,et al.  Fundamentals of Vibrations , 2013 .

[11]  R. Olfati-Saber,et al.  Trajectory tracking for a flexible one-link robot using a nonlinear noncollocated output , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[12]  Marcelo H. Ang,et al.  Tip-trajectory tracking control of single-link flexible robots via output redefinition , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[13]  Motoji Yamamoto,et al.  A numerical method to minimize tracking error of multi-link elastic robot , 1998, Proceedings. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory, Practice and Applications (Cat. No.98CH36190).

[14]  M. Vidyasagar,et al.  Feedback linearizability of multi-link manipulations with one flexible link , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[15]  Abul K. M. Azad,et al.  Flexible Robot Manipulators: Modelling, simulation and control , 2017 .

[16]  K. Khorasani,et al.  Control of non-minimum phase singularly perturbed systems with application to flexible-link manipulators , 1996 .

[17]  G. Silva-Navarro,et al.  Cascade Control for a Rigid-Flexible Two-link Robot using Sliding Modes , 2011 .

[18]  Richard Haberman,et al.  Applied Partial Differential Equations with Fourier Series and Boundary Value Problems , 2012 .

[19]  R. Mattone,et al.  Control problems in underactuated manipulators , 2001, 2001 IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Proceedings (Cat. No.01TH8556).