Potential Shaping and the Method of Controlled Lagrangians
A.M. Bloch, N.E. Leonard, J.E. Marsden
Proc. of the 38th IEEE Conference on Decision and Control,
December 1999.
We extend the method of controlled Lagrangians
to include potential shaping for complete state-space
stabilization of mechanical systems. The method of
controlled Lagrangians deals with mechanical systems
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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