Configuration Controllability of Simple Mechanical Control Systems

Andrew D. Lewis and Richard M. Murray
SIAM Review, 41(3):555-574, 1999

[This paper is a revised and somewhat simplified version of a longer paper that appeared in SIAM J. Control and Optimization in 1998.  It was selected by the editorial board of the SIAM Review and rewritten slightly for a more general audience.]

In this paper we present a definition of "configuration controllability" for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this new version of controllability is also derived. This condition involves a new object which we call the symmetric product. Of particular interest is a definition of "equilibrium controllability" for which we are able to derive computable sufficient conditions. Examples illustrate the theory.

Review Paper (PDF, 12 pages, 657K)
Original Paper
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