Experimental real-time SDRE control of an underactuated robot

In this paper, State-Dependent Riccati Equation (SDRE) nonlinear control is used to regulate the Pendubot, a two-link underactuated robot developed at UIUC, at one of its unstable equilibrium positions. The plant is not fully feedback linearizable due to weakly nonminimum phase zero-dynamics. However, this does not present a problem for SDRE control. Presented results show that SDRE control outperforms LQR control even when the same design parameters are used. The real-time experiments are implemented using a specialized 60 MHz digital signal processor running customized code for SDRE control computation, which involves solving the Algebraic Riccati Equation online. For this highly nonlinear 4-state system, the implementation was successful at a sampling time sufficient for the particular electromechanical plant. To the authors' best knowledge, this is the first work in which SDRE control is implemented on a physical plant in realtime, where the SDRE control is repeatedly computed online.

[1]  C. Abdallah,et al.  Linear Quadratic Control: an introduction - Solutions manual , 1995 .

[2]  A. G. Alleyne,et al.  Globally stabilizing second order nonlinear systems by SDRE control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[3]  J. R. Cloutier,et al.  Nonlinear regulation and nonlinear H{sub {infinity}} control via the state-dependent Riccati equation technique: Part 3, examples , 1994 .

[4]  Mario Innocenti,et al.  Manipulator path control using SDRE , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[5]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[6]  Wei-Min Lu,et al.  Nonlinear optimal control: alternatives to Hamilton-Jacobi equation , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[7]  Jeff S. Shamma,et al.  Existence of SDRE stabilizing feedback , 2003, IEEE Trans. Autom. Control..

[8]  A. Alleyne,et al.  A stability result with application to nonlinear regulation: theory and experiments , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[9]  Ruth F. Curtain,et al.  Linear-quadratic control: An introduction , 1997, Autom..

[10]  Kelly D. Hammett,et al.  Controllability Issues in Nonlinear State-Dependent Riccati Equation Control , 1998 .

[11]  Mark W. Spong,et al.  Mechanical Design and Control of the Pendubot , 1995 .