Control of constrained systems of controllability index two

Abstract

Many natural and man-made systems satisfy a strong controllability hypothesis which results from a natural partition of the state space into "position" and "velocity" coordinates. In particular, plane linkage systems used as biped locomotion models satisfy these conditions. Systems satisfying this hypothesis admit linear state-variable feedback, which can be used to position not only the poles of the system, but also (to a substantial extent) the corresponding eigenvectors. The resulting eigenstructures can be designed to stabilize and decouple systems in such a way that specified subspaces of the state-space are invariant under the dynamics of the closed loop system. Computations and simulations for several types of constrained motion arising in biped locomotion problems are presented.