Controlled Lagrangians and the Stabilization of
Mechanical Systems II: Potential Shaping
A.M. Bloch, D. E. Chang, N.E. Leonard, J.E. Marsden
IEEE Transactions on Automatic Control, Vol. 46, No.10, October
2001, p. 1556--1571.
We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves
complete state-space asymptotic stabilization of mechanical systems. The CL method deals with
symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for
state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic
shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends
the method of controlled Lagrangians to include a class of mechanical systems without symmetry such
as the inverted pendulum on a cart that travels along an incline.
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