Acrobot

20141218 MBD

Acrobot

Acrobot

Acrobot

Acrobot

Acrobot

Acrobot

Acrobot

Acrobot

Acrobot q2

q1

x

y

2nd Link (active)

1st Link (passive)

g

Swing-up problem

Acrobot

Acrobot

Acrobot

LQR

Nonlinear Control

Nonlinear Control

*etc

**etc

Acrobot

** Olfati-Saber, R. (2000). Control of underactuated mechanical systems with twodegrees of freedom and symmetry. In

Proceedings of the American controlconference. Chicago, USA (pp. 40924096)

* Spong, M. W. (1995). The swing up control problem for the acrobot. IEEE ControlSystems Magazine, 15(1), 4455

Acrobot

Acrobot

Acrobot

Hamilton-Jacobi

Riccati

Hamilton-Jacobi

Hamilton

Hamilton

*

*N. Sakamoto, A. J. van der Schaft: Analytical Ap- proximation Methods for the Stabilizing Solution of the Hamilton-Jacobi

Equation: IEEE Trans. Au- tomat Control, 53-10, 2335/2350 (2008)

Acrobot

Acrobot

Acrobot

2

Acrobot

Acrobot

Hamilton-Jacobi

Acrobot

Hamilton-Jacobi

Acrobot

Hamilton-Jacobi

Acrobot

m1,m2+10%

Acrobot

Hamilton-Jacobi

Hamilton-Jacobi

k=15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23