Optimal control of 2-link underactuated robot manipulator

Robot manipulators are nonlinear multi-link system, having higher disturbances and uncertainties. Thus, the controlling of robot manipulator is matter of concern. In this paper for deriving the dynamics of robot manipulator Euler Lagrange (EL) method is used. This paper proposes a nonlinear optimal control approach of 2-link robot manipulator. At first stage linearization of robot manipulator is performed at its operating point using Taylor series expansion. For optimal control, Linear Quadratic Regulator (LQR) is designed after linearization of nonlinear dynamics of 2-link robot. This uses the feed forward gain to control the robot manipulator and to achieve desired position and velocity. This proposed paper shows that Linear Quadratic Regulator (LQR) controlled robot manipulator is locally stable.

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

[2]  Mohd Isa,et al.  DC Motor Controller Using Linear Quadratic Regulator (LQR) Algorithm Implementation on PIC , 2008 .

[3]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[4]  Guilherme V. Raffo,et al.  An H-infinity nonlinear control approach for multi-DOF robotic manipulators , 2016 .

[5]  Raktim Bhattacharya,et al.  Linear quadratic regulation of systems with stochastic parameter uncertainties , 2009, Autom..

[6]  Hartmut Logemann,et al.  Multivariable feedback design : J. M. Maciejowski , 1991, Autom..

[7]  M. Spong,et al.  Robot Modeling and Control , 2005 .

[8]  Z. M. Doina.  LQG/LQR optimal control for flexible joint manipulator , 2012, 2012 International Conference and Exposition on Electrical and Power Engineering.

[9]  Michael J. Wozny,et al.  Computer Aided Multivariable Control System Design Package , 1982, 1982 American Control Conference.

[10]  M. de Mathelin,et al.  Robust control of robot manipulators: A survey , 1999 .

[11]  Linear Quadratic Regulator Lqr State Feedback Design , 2021 .

[12]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[13]  M. A. Townsend,et al.  A Practical Solution to the Deterministic Nonhomogeneous LQR Problem , 1996 .

[14]  Frank L. Lewis,et al.  Robot Manipulator Control: Theory and Practice , 2003 .

[15]  Eshita Rastogi,et al.  Comparative performance analysis of PD/PID computed torque control, filtered error approximation based control and NN control for a robot manipulator , 2015, 2015 IEEE UP Section Conference on Electrical Computer and Electronics (UPCON).

[16]  R. Banavar,et al.  Sub time-optimal swing up of the acrobot , 2001, 2001 European Control Conference (ECC).

[17]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[18]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .