Effective position–posture control strategy based on switching control for planar three-link underactuated mechanical system

ABSTRACT A planar three-link passive–active–active (PAA) underactuated mechanical system is a kind of nonlinear system with a passive first joint. The position–posture control objective for the planar PAA system is to move the end effector from an initial position to a target position with a specified posture. This paper presents a switch control strategy to solve the position–posture control problem. First, a Lyapunov function is constructed based on the system control objective. Then, a set of main controllers based on this Lyapunov function are designed. However, the main controllers may make the system stabilise at one of equilibrium points, which is not the system target position. To avoid the above phenomenon, when the system is about to stabilise at one non-target position, the main controllers are switched to a set of sub-controllers, which are designed according to another Lyapunov function constructed based on the control objective of the active links. When the sub-controllers are running, their design parameters are adjusted to try to keep the derivative of the first Lyapunov function being a non-positive function. Therefore, the switch control between the main controllers and the sub-controllers realises the position–posture control objective of the system. Finally, the simulation results demonstrate the effectiveness of the switch control strategy.

[1]  Haikun Wei,et al.  OPTIMAL CONTROL FOR SWITCHED DELAY SYSTEMS , 2014 .

[2]  Frédéric Plumet,et al.  Motion kinematics analysis of wheeled-legged rover over 3D surface with posture adaptation , 2010 .

[3]  Min Wu,et al.  Stable Control Strategy for Planar Three-Link Underactuated Mechanical System , 2016, IEEE/ASME Transactions on Mechatronics.

[4]  Mark W. Spong,et al.  The swing up control problem for the Acrobot , 1995 .

[5]  Giuseppe Oriolo,et al.  Motion planning and trajectory control of an underactuated three-link robot via dynamic feedback linearization , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[6]  Xin Xin,et al.  Analysis of the energy‐based swing‐up control of the Acrobot , 2007 .

[7]  Naoji Shiroma,et al.  Nonholonomic control of a three-DOF planar underactuated manipulator , 1998, IEEE Trans. Robotics Autom..

[8]  Bin Jiang,et al.  Adaptive control and constrained control allocation for overactuated ocean surface vessels , 2013, Int. J. Syst. Sci..

[9]  Weiming Xiang.  Necessary and Sufficient Condition for Stability of Switched Uncertain Linear Systems Under Dwell-Time Constraint , 2016, IEEE Transactions on Automatic Control.

[10]  S. Janardhanan,et al.  Configuration Control of Planar Underactuated Robotic Manipulator using Terminal Sliding Mode , 2016 .

[11]  Donghun Lee,et al.  Optimal design and workspace analysis of a mobile welding robot with a 3P3R serial manipulator , 2011, Robotics Auton. Syst..

[12]  W. Huo,et al.  Planar path following control for stratospheric airship , 2013 .

[13]  Arjan van der Schaft,et al.  Dynamics and control of a class of underactuated mechanical systems , 1999, IEEE Trans. Autom. Control..

[14]  Simon X. Yang,et al.  Comprehensive Unified Control Strategy for Underactuated Two-Link Manipulators , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Mahmut Reyhanoglu,et al.  Discontinuous feedback control of a 3 link planar PPR underactuated manipulator , 2001 .

[16]  Rogelio Lozano,et al.  Non-linear Control for Underactuated Mechanical Systems , 2001 .

[17]  Carlos Rodrigues Rocha,et al.  A comparison between the Denavit-Hartenberg and the screw-based methods used in kinematic modeling of robot manipulators , 2011 .

[18]  Mahmut Reyhanoglu,et al.  Controllability and point-to-point control of 3-DOF planar horizontal underactuated manipulators , 2005 .

[19]  Philippe Bidaud,et al.  Robust obstacle crossing of a wheel-legged mobile robot using minimax force distribution and self-reconfiguration , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[20]  Ligang Wu,et al.  State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties , 2015, Autom..

[21]  Yinglin Ke,et al.  Stiffness-oriented posture optimization in robotic machining applications , 2015 .

[22]  Md Atiqur Rahman Ahad,et al.  Inverse Kinematics solution for a 3DOF robotic structure using Denavit-Hartenberg Convention , 2014, 2014 International Conference on Informatics, Electronics & Vision (ICIEV).

[23]  M. Reyhanoglu,et al.  Discontinuous feedback control of a 3 link planar PPR underactuated manipulator , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[24]  Yuqiang Wu,et al.  Switching-based asymptotic stabilisation of underactuated ships with non-diagonal terms in their system matrices , 2015 .

[25]  Min Wu,et al.  Motion control of underactuated three-link gymnast robot based on combination of energy and posture , 2011 .

[26]  Alessandro De Luca,et al.  Stabilization of an underactuated planar 2R manipulator , 2000 .

[27]  Giuseppe Oriolo,et al.  Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.