Stabilization of systems with one degree of underactuation with energy shaping, a geometric approach

Details Stabilization of systems with one degree of underactuation with energy shaping, a geometric approach Stabilization of systems with one degree of underactuation with energy shaping, a geometric approach

2010-02-10

arxiv.org/abs/1002.2135v1

Mathematics

Optimization and Control

Scientific paper

A geometric formulation for stabilization of systems with one degree of underactuation which fully solves the energy shaping problem for these system is given. The results show that any linearly controllable simple mechanical system with one degree of underactuation is stabilizable by energy shaping, possibly via a closed-loop metric which is not necessarily positive-definite. An example of a system with one degree of underactuation is provided for which the stabilization by energy shaping method is not achievable using a positive-definite closed-loop metric.

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